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NEW MANUAL

OF

LOGARITHMS.

NEW MANUAL

OF

LOGARITHMS

TO

SEVEN PLACES OF DECIMALS

EDITED

BY

DR. B R U H N S

DIRECTOR OF THE OBSERVATORY AND PROFESSOR OF ASTRONOMY AT LEIPZIG.

SECOND STEREOTYPE EDJTION

OF T

UNIVERSITY

01

BERNHARD TAUCHNITZ LEIPZIG 1878.

t;

IS 73

Astron. Dopt.

r e f a c e.

Kohler's Handbook of Logarithms , which has hitherto been published by Tauchnitz, and which will still be continued to be published by them, has always found a very favourable reception from the public both on account of its arrangement and its exactness. However Bremikerls^Edition of Y6^^ seven figure logarithms extended and improved well known and frequently used, and Schron's logarithmic tables are preferable for many elaborate astronomical calculations. Bremiker gives in the trigonometrical Tables the logarithms of the Sine and Tangent for the first 5 degrees to every second and the logarithms of the Sine, Tangent, Cotangent, Cosinus from o° to 45° (and therewith it is self-evident of the whole quadrant) for every 10 seconds; whilst Schron has added to the last an extensive Inter polation Table.

The publishers did not wish to be behindhand with their Hand book of logarithms and when they became aware that I was willing to undertake the necessary labour of preparing one — they determined to pre serve Kohler's in its present form as it is obviously well adapted for many purposes — and desired me to prepare an entirely new Manual, which I now lay before the reader and of which this is the principal arrangement. The logarithms of the numbers from I to 108000 as they are in Kohler have been reduced to the extent of from i to 100000 since the addition of the logarithms of the numbers from 100000 to 108000 does not appear to offer a sufficient advantage.

The logarithms of the first 6 degrees of the trigonometrical functions, Sine, Cosine, Tangent and Cotangent have been given to every second, with the addition of the differences and where the space would allow of it, of the proportional parts.

Such an arrangement has been desired in many quarters and will save the calculator much labour and waste of time spent in interpolation. This table makes an essential distinction between this and other logarithmic tables

VI Preface.

and as far as I know it is exceeded by none in completeness and facility of use.

The remaining 39 degrees of the trigonometrical functions are given to every 10 seconds, whilst in Kohler from the 9th degree they are only given to every minute.

As with these 3 Tables the work already consists of 38 sheets, we have omitted the Addition and Subtraction logarithms (Gauss's) which have been lately many times published. And we have also omitted the gonio- metrical and trigonometrical formulae contained in Kohler, as well as the other tables which though useful are not so frequently wanted; so that the present work with the exception of some few small additional Tables consists merely of the logarithms of numbers and of the trigonometrical logarithms.

The arrangement of the Tables is on a plan easily understood, not overladen with directions, printed with a clear distinct type and of undoubted correctness.

The final arrangement of the Tables is the result of much corre spondence with many eminent calculators and much thought has been bestowed upon it.

With regard to Table I., the first column which in Kohler contains the degrees and minutes contained in the adjacent number considered as seconds, is omitted and in its place, similar to what has been done by Bremiker and Schron, under the logarithms is a small table by which it is easily possible to change seconds into minutes and degrees.

In general we have adopted the form of Bremiker's table and just as he and Schron have expressed the logarithms of J~L, -—-^ under the notation S and T we have done the same, but we have placed these at the bottom of the Table and not as Kohler at the top. Further Bremiker is again also followed in this respect, that the successive numbers are given from o to 50 and from 50 to 100 (thus repeating the logarithms of the Numbers at the top and bottom of each page) instead of from o to 49 and from 50 to 99 as they stand in Kohler and Schron.

In order to find the numbers more readily, every tenth number is enclosed with horizontal lines as Bremiker has done, and a space left be tween the logarithms of every three numbers. The proportional parts are as in other tables; yet arranged again as in Bremiker, since they seem to me to be thus more readily found.

In the arrangement of the 2nd table, we have entered for the first 10 minutes (from o to 9 minutes) only the logarithms of the Sine, Cosine, Tangent, Cotangent together with the differences for every second for each single minute on one page.

In order to find the number required, more readily, in these 10 minutes we have seperated by a horizontal line every 5 seconds; so that the eye may

Preface. vn

more readily keep the line which it has taken, thus preventing uncertainty, and making the differences also, more readily distinguished. Proportional parts can only be given in these first i o minutes at large intervals of differ ences — but these are taken successively smaller and smaller. Whenever there was space among the logarithms the multiples of smaller intervals have been added.

As after 10 minutes the differences of the logarithms of Sine, Tangent and Cotangent proceeding by seconds, consisted of four figures only, it was possible to bring two minutes on to every page , if the first two decimals of each of the logarithms could be placed over, at the decades of the seconds. In the single columns for the logarithms of the Sine, Tangent and Cotangent from o° 1 i' as far as i° 20' only the five last decimals and for the Cosine only the four last decimals have been inserted, since this has been found quite sufficient. The differences are given completely for every second to the Logarithms of the Sine, Tangent and Cotangent whilst this was not necessary for the logarithms of the Cosine. From o° 10' to i° 20' no pro portional parts could be given, for otherwise the page would have been much too broad and every calculator must therefore supply these for himself when wanted. In Bremiker's table of the first 5° for every second, no proportional parts nor differences are given, while in Schron these logarithms themselves are entirely omitted.

After i° 20' the differences of the logarithms to every second consist only of three figures, and it was possible to separate 3 decimals instead of two, at every decade, by which means so much space was gained, that in the middle, at each minute, the seconds from o to 60 and from 60 to o could be repeated; yet all the proportional parts could not be given but only at intervals of 3, then of 2 and lastly of one unit.

As in the logarithms of numbers a stroke over the first figure of the decimals denotes, that the last decimal of the number standing at the pre ceding decade must be increased by a unit, while in the case where it must be diminished by a unit a small star * is inserted.

Table III. From 6° up to 45° the trigonometrical functions are given for every 10 seconds, and the arrangement is as in Bremiker and Schron, except as to the succession of the particular functions. The repetition of the first 6 degrees in intervals of 10 seconds appears to be superfluous here — Bremiker has repeated his first 5 degrees — because in tables II. and III. all the functions are given and their succession is not changed.

The succession Sine, Cosine, Tangent, Cotangent is here advisedly chosen rather than the bad order Sine, Tangent, Cotangent and Cosine used by some recently, because the calculator solves most questions by the aid of the first form and, indeed, the logarithms of the Sine and Cosine here stand ing close together, are frequently wanted at the same time.

The symmetry which in the succession Sine, Tangent, Cotangent, Co sine from above from left to right, below from right to left occurring as it

VHI Preface.

does in all the old Tables we have given up. If we consider ourselves as passing on the course of a line, and we take only two functions, then we have the symmetry for these two existing; so that appears to me to be no disadvantage.

Since we frequently require only 6 decimals and are using tables with 7 places, if a 5 stand in the last place, it is doubtful whether this has been increased; in the whole of the three tables when this has been the case a mark is placed over the 7th decimal. In calculations therefore with six decimals when 5" occurs it is simply omitted. Hence for example the loga rithm to seven places of the number 83601 = 4,9222115 and the logarithm to six places of this number is 4,922211, whilst the 7 figure logarithm of the number 91752 = 4,9626155 the six figure logarithm of this number is, since the last 5 has no mark over it = 4,962616. The mark with all the last figures as introduced by Schron does not appear to me advantageous since after repeated experience on my own part and on that of other cal culators, these marks seldom come into use and the eye is fatigued by their number.

The opinion of many calculators has been obtained on the form of the type of the Tables. More than three fourths of them find the thick Egyptian type used by Kohler and Schron to be more irksome than the old English type used by Bremiker and others. Although perhaps the beauty of the printing is increased, if the figures, stand all in one line, as the Egyptian, yet the eye distinguishes single figures more readily, and an interchange of one for another is less to be feared, if they are as in the old English type partly above the line and partly below. The 3 and the 8 for example are dis tinguished by this means, since the 3 falls below considerably, but not the 8 ; 7 and i are readily distinguished and likewise 6 and 9. The type of the figure here used is admirable for its size, the figures of Bremiker's table admirable as they are, exciting many complaints on account of their small- ness. The size of the book is not much larger than Bremiker's, notwith standing the magnitude of the figures and the printers have made every exertion to use distinct and also beautiful type.

The magnitudes log -^~- = S, log -^- = T which are at the foot of the logarithms of the numbers in table I. , and go from i o to I o seconds are given for the sake of accuracy to 8 decimals in order to obtain greater certainty in the last decimal in the Interpolations. They run from o" to 2° 46' 40 " and have a particular value for the determination of a small angle, since we can therewith reckon exactly the arcs to the trigonometrical functions of small angles even to the 3rd, 4th and 5th decimal of a second.

In the proportional parts we have generally given also the first decimal, so that in the Interpolation we may be certain to some tenths of the last decimal.

On page 186 we have given the multiple of the modulus of the natural system of logarithms, in order to convert Briggs logarithms into

Preface. IX

natural and the converse. On page 608 the arcs of the circle are expressed in parts of the radius; on page 609 the conversion of the degrees of the circle into time, hours, minutes and seconds and lastly on page 610 some Constants and the relations of the most frequently used measures of length to the metre are given.

The logarithms to the numbers to 7 places have been taken directly from Vega's "Thesaurus logarithmorum " to ten places and partly where the three last figures were 495 and 505, partly from 498 to 502 out of the loga rithms of prime numbers from i to 1 200 as they are printed in Callet's table, calculated anew and compared with the excellent tables of Kohler, Bremiker and Schron. No difference in the last place has been found from any of the known tables.

The Table II. containing the logarithms of the trigonometrical func tions sine, cosine, tangent, cotangent, have been obtained for every second in the following way ; by Dr. Low the logarithms of the sine and tangent in intervals partly of 320, partly of 256 seconds were calculated to 15 decimals and for the first four degrees for every 40 seconds, for the 5th and 6th degrees for every 32 seconds and interpolated to this number of decimal places, then again interpolated for every second to fewer decimals and finally reduced to 7 decimals. The logarithms of the cosine have been interpolated with 14 decimals for every second for all 6 degrees. For the sixth degree the loga rithms were taken of the sine for every second to 14 decimals and of the cosine for every second to 14 decimals, and from these were derived the logarithms of the tangents and cotangent, and then the whole reduced to 7 decimal places.

For the first 2 degrees an immediate comparison may be made, since they are contained to 10 decimals in Vega's "Thesaurus logarithmorum"; for the logarithms of the sine and tangent of the first 5 degrees can be compared with Bremiker's 7 figure table and lastly for all functions a com parison may be made with Taylor's. Where any difference was found the last decimal was directly calculated; in Bremiker's Edition of Vega's table to 7 places (51st ed.) we found in log tan o° 9' 59" only one error in the last decimal, whilst in Vega's Thesaurus and in Taylor (I had not Bagay* at my command) frequently differences of i and 2 units occurred in the last place.

The Table III. contains the logarithms of the trigonometrical functions for every 10 seconds taken from the Thesaurus of Vega and very carefully compared with other tables and eventually recalculated.

The examination of the logarithms has been made with the greatest precision and anxiety. They were first read by the printer: the second examination which consisted in reading them with Schron's and Bremiker's tables was made by Dr. Low and M. Leppig, the third examination by

* Bagay is to every Second of the Quadrant to 7 places, but there are no differences or proportional parts whatever.

X Preface.

Qu. Miiller and Richter, both examinations were superintended by myself, and I particularly examined the headings, the first decimals of the Sine, Cosine, Tangent and Cotangent, the differences, the accuracy of the pro portional parts, &c. A fourth examination was made by myself and Leppig with Vega's "Thesaurus logarithmorum" and Taylor's "Tables of loga rithms &c.", London 1792. A fifth examination was finally made throughout by M. Heineman. All the errors were most carefully corrected by the Printer. The fourth and fifth corrections were read from the stereotype plates and there were found only 2 errors in the logarithms of the numbers, in the logarithms of the trigonometrical functions only 1 5 , whence we may estimate the care with which the three first corrections had been made.

The publishers have omitted no trouble or cost, and hope that these tables will meet with a correspondingly favourable reception from the scien tific world.

Leipzig, August 1869.

Dr. C. Bruhns.

Introduction.

The following Theorems are indispensable for the use of logarithms.

They are:

log (A X B) = log A -f log B

log £ = log A — log B

log Am = m log A

log fk = ± log A,

or at full length: the logarithm of a product is equal to the sum of the logarithms of the factors; the logarithm of a quotient is equal to the differ ence of the logarithms of the Dividend and of the Divisor, the logarithm of a power is equal to the product of the exponent into the logarithm of the basis, and the logarithm of the mth root of a number is equal to the loga rithm of the basis divided by the exponent m of the root.

§.2.

The logarithms given in these Tables are Briggs's logarithms whose basis, as is well known is 10. Therefore we have o = log of the number i — i = log of the fraction -~-= 0,1

i= „ „ 10 —2= „ „ -^-=0,01

2 = » it IOO — 3 = „ „

3 = ff ff I00° — 4 — » it

&c. &c.

The remaining rational numbers that are not powers of 10 have ir rational logarithms, thus since 7241 <|QO t^ie ^°£ °^ 724I is eQU3^ to 3 H~ an irrational fraction 0,8597985 . . . ., the log of 0,07 <J°~I is equal to — 2 -\- the irrational fraction 0,8450980.

The common or Briggs's logarithm of a number consists therefore in general of two parts; of a whole number called the characteristic and of a fractional part called the mantissa. The last are given in the Tables; for the characteristic belonging to every number we have the following rule derived from the table given above.

The characteristic of a power of 10 greater than one is equal to the number of the figures less one; the characteristic of a proper fraction is negative and if we convert it into a decimal fraction is equal to the number of noughts which precede the significant figures. The mantissae according to what is said above are always positive and agree with the characteristic or are contrary to it according as the characteristic is positive or negative.

Since we frequently want logarithms that are not immediately given in the Tables, that must be found by Interpolation the following Theorem

XII Introduction.

must be assumed: for a small interval, the difference of the arguments is pro portional to the difference of the function ; in the present case a logarithm.

§• 3- Table I.

Pages 2 to 5 inclusive contain the logarithms of the first Chiliad. The numbers are in the column N and the logarithms belonging to them will be found in the column headed Log, that is the mantissae or decimal part of the logarithm.

Pages 6 to 185 contain the logarithms of the numbers from 1000 to 100000.

Page 1 86 contains the multiples of M and of ~- for the conversion of Briggs's logarithms into natural logarithms and conversely.

At the foot of the Table we find the values of log -^~- and log -^~ for the discovery of the logarithms of small angles and conversely. If we wish to use 6 places only we must increase the 6th figure by a unit when the last figure is 5, 6, 7, 8 or 9, but not so when the last (7th) figure is o, i, 2, 3, 4 or 5 that is 5 with a mark over.

§•4- Problem. To find the logarithm belonging to a given number.

The numbers up to 10000 are found from pages 2 to 185 in the columns with N written above them and in the next column o the logarithm belonging to them. If however the number consists of five figures (in which one or more noughts may precede or follow, for these noughts affect only the characteristic of the logarithm and not the mantissae), we seek the first four figures in the column N and then precede in this line to the right hand until we come to that column which has the fifth figure at the head. The four figures standing there make with the three separated in the column o, standing in the same line, the mantissa of the logarithm of the number required. Should there be no separated figures in this line of column o, the three figures standing next above must be taken, except in the case, where the first of the 4 figures has a mark above it, in which case we must take the next three below. The characteristic must be appended according to the rule given in §. 2.

For example it is required to find the logarithm of 14459. Find the first four figures 1445 on page 14 in the column marked N and seek on a horizontal line proceeding to the right the column over which stands the fifth figure of the number, namely 9. We find in this column 1383 and with the three separated figures 160 standing in the column marked o we have the mantissa 1601383 and annexing the characteristic the logarithm of the number 14459 is 4,1601383.

§•5.

If the number of which we seek the logarithm contain more than five figures but fewer than eight (for the 8th figure of the logarithm required from the table will be uncertain) then the excess must be interpolated by the rule given above.

Let it be required to find the logarithm of the number 219467,83.

Introduction. XIII

In table I. at page 29 is found

for the number 21946 the mantissa 3413554 21947 „ „ 3413752

consequently the difference I in the number corresponds to the difference 198 in the logarithm and to the remaining figures 783 of the number which we must consider as 0,783 belongs, according to the formula

i : 198 = 0,783 : x; x = 155,

155 is the difference of the logarithm, which difference is to be added to the smallest mantissa, so that the mantissa is

3413554 + 155 = 3413709 and with the addition of the characteristic the logarithm of the given number

is 5,34i3709-

The calculation may be facilitated by the proportional parts P. P. given at the side of the logarithm, wherein are contained the particular decimal of each difference. With the help of these the calculation stands in the follow ing form:

For the difference 198 we find at page 29 for 7 (0,7) 138,6 I „ 8 (0,08) 15,8 i sum =155, i» 3 (0,003) 0,6 J which number as before must be added to the smallest logarithm.

The whole interpolation may after a little practice be easily and certainly performed without writing down a single figure.

As another example we will find the logarithm to the number 59,487321.

We have for the number 59487 the mantissa 7744221 59488 „ 7744294

and therefore the difference 73. To this difference the P. P. are

to 3 (0,3) 21,9 „ 2 (0,02) 1,46 „ i (0,00 1 ) 0,07

sum = 23

which 23 must be added to the smallest logarithm and taking care to annex the proper characteristic the log is 1,7744244 for the number 59,487321.

§.6.

If the logarithm to a fraction is required, we may proceed in two ways, either subtract the logarithm of the denominator from the logarithm of the numerator or convert the fraction into a decimal and find the loga rithm to it in the manner pointed out above.

For example let it be required to find the logarithm of the fraction -^-4 We have the logarithm of 45 = 1,6532125 the logarithm of 532 = 2,7259116 therefore the logarithm of -^- = 0,9273009 — 2' t for which is commonly written 8,9273009 — 10.

But now since -~ = 0,084586466, we seek on page 155 the logarithm of 84586466 and again find after attending to the characteristic 0,9273009 — 2 or 8,9273009 — 10.

XIV Introduction.

§• 7- Problem. To find the number belonging to a logarithm.

Seek the first three figures of the mantissa among those separated in the o column, the four following figures in the columns marked i to 9 and take the number which will have five places of figures out of the table. If the given logarithm is not contained directly in the table we must have recourse to interpolation. The proportional parts P. P. are for this purpose. For example let it be required to find the number belonging to the logarithm 5,3413709- We find on page 29 the next smallest mantissa 34I3554 a* *ne number 21946, the next greatest mantissa 3413752 at the number 21947. The difference of the two logarithms is 198, the difference between the nearest and the given mantissa is 155 and we have the pro portion

i : x = 198 : 155, x =-^= 0,783

therefore the number 21946,783, but because the characteristic is 5 belonging to the logarithm 5,3413709 the number is 219467,83.

If we use the small tables of proportional parts the calculation will be as follows — the given logarithm 5,3413709

to the number 21946 on page 29 belongs 3413554

difference 155

With P. P. 198 belongs to 7 (0,7) 138,6

16,4

to 8 (0,08) 15,84

56

to 3 (0,003) 59

consequently the number 219460 + 7,83 = 219467,83.

Second Example. Required the number belonging to the logarithm 9,1890460 — 10. On page 16

the mantissa 1890409 belongs to the number 15454 the mantissa 1890690 belongs to the number 15455.

The difference between the greatest and least mantissa is 281, and between the given mantissa and the smallest 51, therefore

to 51

P. P. 281 for i (0,1) 28,1

22,9

for 8 (0,08) 22,48 42

for i (0,00 1 ) 281

consequently the number is 15454181 or with the addition of the char acteristic 0,15454181.

§.8.

If we wish to extract a root or raise a number to a given power, we have then according to the formula given in §. I. to multiply or divide the logarithm of the basis, by the exponent which, if the exponent is a whole number, may be easily done. It is seldom however that this is the case, so

Introduction. XV

that it is easier to take the logarithm of the number from the logarithm of the basis and to add or subtract the result from the logarithm of the exponent, then to find again the logarithm of the number, again to consider this number as a logarithm and once more to obtain the corresponding number. If for instance it is required to find the value of 4, 753 2 2-»8 We have

log to 4,7532 = 0,6769861, and this multiplied by 2,48 gives 1,678925528 to which belongs the number 47,74474. We can however proceed thus

log 0,6769861 = 9,8305798 — 10

log 2,48 = 0,3944517 _

0,2250315

to which belongs the number 1,6789259 and this considered as a logarithm corresponds to the number 47,74478 and this errs only in the last decimal which cannot be entirely avoided from that found in the other way.

As another example let it be required to find the 4,75th root of 300 then we have the log of 300 = 2,4771213 which divided by 4,75 gives 0,5214992 to which belongs the number 3,322762. We can however proceed thus

log 2,4771213 = 0,3939473

log 4,75 = 0,6766936

~ I0

to which the number 0,5214993 belongs, and this regarded as a logarithm corresponds to the number 3,322762 which agrees sufficiently well with the preceding. In the extraction of roots however it may under some cir cumstances be more convenient actually to set down the negative logarithm.

§.9-

In order with the help of the magnitudes S and T placed at the foot of Table I. to find the logarithms of the sines and tangents of small arcs and the converse ; we make use of the following formulae

log sine = log arc" -f- S

log tangent = log arc" -f- T

log arc" = log sine — S

log arc" = log tangent — T

that is, in words, the logarithm of the sine or tangent the logarithm of an arc (arcus") expressed in seconds plus S or T and inversely the logarithm of the arc in seconds is equal to the logarithm of the sine or of the tangent minus S or T.

§. 10.

Problem. It is required to find the logarithm of the sine and of the tangent of the arc of if 56",76

17' 56",76 = io76",76 gives log io76",76 = 3,0321189 According to page 7 after the required %

interpolation io76",76 S = 4,6855729

T = 4,6855788

therefore log sin = 7,7176918

log tang = 7,7176977

XVI Introduction.

Problem. It is required to find the arcs belonging to log sin 7,4897320 and log tang 8,0079482.

In Table II. we see that on page 198 and page 210 to the log sine of the arcs between o° 10' 37" and o° 10' 38" and to the log tang of the arcs between o° 35' o" and o° 35' i" belong the values of S and T on pages 4 and 28 namely S = 4,6855742 and T = 4,6855899. These subtracted from the above given logarithms give log arc = 2,8041578 and 3,3223583 to which belong the numbers (p. 113 and 28)

637^,0269 = 10' 37^,0269 and 2100^672 = 35' o",6j2.

It is self evident that we can with the magnitudes S and T find also the cosine and cotangent of angles which are between 87° 40' and 90°.

§• ii.

Table II.

contains the logarithms of the trigonometrical functions Sine, Cosine, Tan gent, Cotangent to 7 decimals to every second for the first and last 6 degrees of the quadrant, all with differences and for the most part also with proportional parts. From page 188 to 197 a minute is on every page and from page 198 to page 372 two minutes are on every page.

From o° to 6° the degrees and minutes stand at the top of the page, the seconds in the vertical column on the left, from 84° to 90° the degrees and minutes are at the bottom of the page and the seconds belonging to them in the vertical columns on the right. From page 198 to 232 the characteristic and the two first decimals of the functions (which are named on the top of the page) namely Sine, Tangent, Cotangent and from page 233 to 372 the three first decimals, are separated and placed above with the tenths of the seconds, so that in the vertical column are contained first the five last and afterwards the three last decimals of the logarithms of these functions. From page 198 to 372 the characteristic and the three first decimals of the logarithm of the Cosine are separated also.

The sign — placed on the first place of the division means that the above separated decimals of the logarithms must be increased by a unit, and the sign * that the separated decimals must be diminished by a unit when they are combined with the other decimals to take out a logarithm.

The differences of the logarithms standing in the division marked above Sine are in the division to the right and they are not here required for the Cosine; for the tangent and cotangent since they have a common difference they stand in the division between the two functions, marked above with the letters d. c. It may as well also be here mentioned that the Sine and Cosine for the whole quadrant, the tangents between o° and 45° the cotangents between 45° and 90° are proper fractions and the char acteristics of these functions have all been increased by 10 in order that the characteristic — 10 may be omitted from these functions.

§• I*--

Problem. It is required to find the logarithm of the functions sin, cos, tan

and cotan, for a given acute angle.

If the given arc is found in the Table II. then the function required is taken directly out of the corresponding column. But if this is not the case

Introduction. XVTI

we must interpolate and in doing this care must be taken whether the successive values of the function form an increasing or decreasing series, because on this it will depend, whether the quantity obtained by inter polation is to be added or subtracted from the given magnitude.

Example: It is required to find the logarithms of the sin, cos, tan and cotan of the acute angle 4° 16' 23",73. We have from page 321

log sin 4° 16' 23" = 8,8722132, d. = 2 82 increasing and with the P. P. for 7 (0,7) 197,4

» 3 (Q,03) 8,5

therefore log sin 4° 1 6' 23^,73 — 8,8722338

Further we have from page 321

log cos 4° 16' 23" — 9,9987911 log cos 4° 1 6' 24" = 9,9987909

whence we obtain without difficulty for the 0^,73 the difference i, decreasing consequently we get for log cos 4° 16' 2 3", 73 = 9,9987910. Again we have from page 321

log tan 4° 16' 23" — 8,8734221, d. c. — 284 log cotan 4° 16' 23" — 1,1265779. With the P. P. of the difference 284 we obtain for 7 (0,7) 198,8

" 3 (Q,Q3) 8,5

207

which added to the log tan and subtracted from the log cotan gives for the log tan = 8,8734428 and log cotan = 1,1265572.

§- 13.

Problem. // is required to find the angle belonging to a given trigonometrical

logarithm.

Seek the logarithm in the division which is marked either above or at the bottom with the function to which the logarithm belongs. If the given logarithm is exactly found, then we have the angle immediately and it ends with a whole number of seconds. If the logarithm is not found exactly then we take the next smallest or the next largest according as the logarithm of the arc is increasing or diminishing, and interpolate for the difference between the given logarithm and that found, with the difference given in the table for a second, for the required fraction of a second.

Example: It is required to find the arc or angle v belonging to the given log tan v = 8,7852346.

We find on page 297 the next smallest logarithm since the logarithm is increasing with the arc

log tan 8,7852057 at 3° 29' 23" and d. c. = 347; we have given log tan 8,7852346 difference = 289, whence from the proportion

347 : 289 = i" : x we obtain x = o",83.

XVIII Introduction.

With the assistance of the proportional parts we have for

289 with 347 P. P. 8 (0,8) 277,6

, u,4

3 (0,03) 10,4

again therefore 0^,83 as before and the required angle v is = 3° 29' 23",83. Second Example: It is required to find the angle v of which the given log cos v is = 8,4932917.

On page 246 we find the next greater logarithm of the cosine, because the logarithm diminishes when the arc increases

log cos 8,4933102 at 88° 12' 56" and d. — 676, we have given log cos 8,40,32017

^ — - — : — The P. P. belonging to 676 are omitted from want of

difference = 185 space, we take therefore 675 and add to the given

2 (O 2) I 3S 2 P. P. the proportional parts of the difference i, that

* ' ' every one can easily form in his head and add but

49 »* which we may perform by means of the table given

7(0,07) 47,3 in§'15'

therefore v — 88° 12' 56//,27.

It is self evident that we might have taken the next smallest logarithm that belongs to the cos 88° 12' 57". Then we should have obtained o",73 as the fraction of the second that must be subtracted from 88° 12' 57" which leads to the same result.

§• 14-

Since on account of the want of space the proportional parts are

nitted belonging to the trigonometrical functions of o° 10' as far as i° 20'

3 /e have to seek by interpolation (as in the proportion given in the first

example of the former §.) the fraction of the second required. It may also

be remarked, that from the same cause, want of space, all the differences of

the proportional parts could not be given, in such a case therefore we must

take the nearest P. P. and form the excess mentally or with the help of the

following table, either of which may be easily done.

If we v/ish to calculate with only 6 decimal places, just as with the logarithms of numbers with 6 decimals, whenever the seventh figure is o, i, 2 , 3 , 4 or 5" the sixth figure is not changed ; but it must be increased by unity when the seventh decimal is 5, 6, 7, 8 or 9. The differences and the proportional parts given in the 7 figure tables can be directly used, taking notice, that the decimal point must be moved from the seventh to the sixth place, or that the tenths of the seventh place are units of the sixth place.

§• IS-

Table III.

contains from page 374 to 507 the logarithms of the four trigonometrical functions of the remaining 78 degrees of the quadrant namely from 6° o' to 83° 60' for every tenth second. The arrangement is similar to that in Table II. only that the degrees from 6 to 44 run from above and from 45 degrees to 83 from below; only the minutes and every tenth second for the first portion of the degrees (6 . . 44) stand in two divisions to the left and for the last portion (45 . . 83) in two divisions to the right.

Introduction.

XIX

Proportional parts are not given for all differences, they are omitted for the differences of the logarithms of the Cosines from 6° to 9° and are given for the differences of the logarithms of the Sine , Tangent and Cotan gent in the first instance at intervals of 10 units and further on at 5, 4, 3, 2 and lastly one unit.

If now the porportional parts of the required difference are not given, but only that of the nearest difference, then we may either increase this mentally or make use of the small table printed on a separate page of the following form.

Table for the interpolation of the P. P.

Complement of the difference.
	1 1 2	3	4	5	Q	7	8	9
I	O.I	O.2	0.3	0.4	0-5	0.6	0.7	0.8	0.9
2	O.2	0.4	0.6	0.8	I.O	1.2	1.4	1.6	1.8
3	0-3	0.6	0.9	1.2	i -5	1.8	2.1	2.4	2.7
4	0.4	0.8	1.2	1.6	2.0	2.4	2.8	3-2	3-6
5	0.5	I.O	L-S	2.0	2-5	3-0	3o	4.0	4-5
6	0.6	1.2	1.8	2.4	3-o	3-6	4.2	4.8	5-4
7	0.7	1.4	2.1	2.8	3-5	4.2	4-9	S-6	6-3
8	0.8	1.6	2.4	3-2	4.0	4.8	5.6	6.4	7.2
9	0.9	1.8	2.7	3-6	4-5	5-4	6-3	7.2	8.1

What was said at the conclusion of §. n. with regard to Table II., applies also with respect to Table III., namely, with regard to the augmenta tion and increase of the characteristic of the logarithms of the sine and cosir » of the tangents from o° to 45° and the cotangents from 45° to 90°.

§. 1 6.

The use of Table III. is quite similar to that of Table II. only it is o be taken notice, that the numbers standing in the difference column are i )t the differences for i" as in Table II. but are for 10". Some examples will facilitate the use of the Table.

Example: It is required to find the logarithm of sin, cos, tan and cotan for the acute angle 9° 10' 45",45. We have from page 393

log sin 9° 10' 40" = 9,2027561, d. = 1303 increasing. The difference 1303 multiplied by 0,545 (for 5",45) gives 710 and this added to the above gives

log sin 9° 10' 45",45 — 9,2028271.

If we would make use of the P. P. given on page 393 we do not find the difference 1303 but only 1300, we make use of this and then again reckon for the 3 as follows:

P. P. for 5" (0,5) 650

0,4 (0,04) 52,0 0,05 (0,005) 6,5

708,5.

separate tablet for the difference 3 we have

for 0,5 1,5 ,, 0,045 o*1 so

Then from the above

sum is 7IQ again

as before. — We might have used the difference 1310 and then we should have had to have subtracted the small quantities belonging to 7.

XX Introduction.

In order to find the log cos

log cos 9° io7 40" = 9,9944044, d. = 34 decreasing, and 34 x 0,545 (for 5^,45) = — 18,53 therefore

log cos 9° 10' 45",45 = 9,9944025-

The small table of differences for 34 cannot be inserted from want of space. Again log tan 9° io7 40" — 9,2083517, d. — 1337 increasing. The nearest difference given is 1340

P. P. for 5" (0,5) 670 „ 0,4 (0,04) 53,6 „ 0,05 (0,005) 6,7 Since the difference is 3 units too great we

have to subtract 3x0, 545 — 1,6

729

therefore log tan 9° io7 45",45 = 9,2084246.

Lastly the log cotan 9° io7 40" = 0,7916483, d. = 1337 decreasing and 1337x0,545 =

therefore log cotan 9° io' 45^,45 = 0,7915754.

Second Example: It is required to find the log cotan and log sin of 56° i' g",6g.

We have on page 541 log cotan 56° i' o" = 9,8287149, d. = 45 4 decreasing. P. P. for 9" (0,9) — 408,6

„ 0,6 (0,06) — 27,2

„ 0,09 (0,009) — 4»i

therefore log cotan 56° i; g"fog = 9,8286709. For log sin 56° i' o" = 9,9186594, d. = 142 increasing.

.P.P. for 9" (o,9) 127,8

-i . » 0,6 (0,06) 8,5

„ 0,09 (0,009) _ 1,3 therefore log sin 56° i7 g",6g = 9,9186732.

It would have been easier in this example to have made use of interpolation, if we had taken 56° i7 9/7,69 = 56° I7 io77 — o/7,3i and have found the logarithm of 56° i7 io77 and interpolated for o",3i. The calculation would have stood as follows:

log cotan 56° i7 io77 = 9,8286695, d. — 454 decreasing. P.P. for — o/7,3 (0,03) 13,6

„ — 0,01 (0,00 1 ) _ 0,5 log cotan 56° i7 g",6g = 9,8286709. And we have

log sin 56° i7 io77 = 9,9186736, d. = 242 increasing. P. P. for — o77,3 (0,03) — 4,3

„ — 0,01 (0,001) — 0,1

log sin 56° i7 9^,69 = 9,9186732.

§• 17-

If we would find the acute angle belonging to a given log sin, cos, tan, cotan; then we proceed also as in Table II. We seek in the Table III. the ney* emailer or the next larger logarithm— the first when the logarithms of the sine or tangent are given and the last if the cosine or cotangent.

Introduction. XXI

We form between these given logarithms and that taken out of the table a difference which we shall call z/. We now take out of the table the difference d standing between the next smallest and next largest logarithm, and calcu late the proportion

d : z/ = 10" : x

and so find x, which added to the angle we have obtained from the table gives the required angle.

For the solution of the proportion we may also make use of the small tables of differences and their proportional parts, but as all the differences are not tabulated we must augment the proportional parts which is easily done from the table in §. 15.

Example: We have given log tan v = 0,4137916 and we seek the angle v belonging to it.

On page 464 we have the next smaller logarithm

log tan 68° 54' 30" = 0,4137495, d. — 627 the given log = 0,4137916

z/ = 421

therefore 627 : 421 = 10" : x and x = 6", 71 and the required angle v is 68° 54' 3 6", 7 1.

With the P. P. we have, as the difference of 627 is entered

421

P. P. for 6" (0,6) 376,2

44,8 „ 0,7 (0,07) 43,89

„ 0,01 (0,00 1 ) 63

and we get again 6",7i.

Second Example: It is required to find the angle v belonging to log co- tan v = 0,6067049.

On page 421 we find the next largest logarithm

log cotan 13° 53' 30" = 0,6067396, d. = 903 given logarithm = 0,6067049

A = 347

therefore 903 : 347 = 10" : x and x = 3", 84 and the required angle v is 13° 53' 33",84.

There is no difference table for 903 the nearest are 905 and 900. We may use either. If we take the first, then since 903 = 905 — 2

^ = 347

P. P. for 3" (0,3) with d = 905 271,5 1 ,,3 „ d = — 2 -0,6 JJ

76,1

P. P. for o",8 (0,08) with d = 905 72,4 | ,,o,8 „ d = — 2 — 16]

3,86

P. P. for o",04 (0,004) with d = 905 3*620 1 „ 0,04 „ d = — 2 — 8 J

and thus we again get 3^,84 just as above.

XXII

Introduction.

A well practised calculator will perform this completation of the P. P. for the most part mentally, nor is it necessary to enter all the decimals places which is here done to offer a complete example.

It has been already said in §. 16. that it is often more advantageous when we seek the angle belonging to some given log sin, log cos, log tan, log cotan not from the next smallest and greatest logarithm in the Table but contrariwise from the next greatest and next smallest so that seconds and fractions of seconds may be taken negatively.

§. 18.

The Tables II. and III. contain the logarithms of the trigonometrical functions of the first quadrant (if we limit ourselves to the four quadrants) in which all the functions are to be taken positively. In the 2nd quadrant the sine alone is positive cos, tan and cotan are negative; in the 3rd quadrant sine and cosine are negative and tan and cotangent positive; in the 4th qua drant cosine alone is positive and sin, tan, and cotangent negative.

If an arc or angle is given greater than* 90° subtract 90° from the given angle as often as possible. If we have subtracted two right angles or 1 80° then we may obtain the function which is left directly in the tables taking notice however of their signs, but if we have subtracted I or 3 right angles that is 90° or 270° then -we must seek the complement of the angle, therefore instead of the sine the cosine, instead of the tangent the cotangent or inversely taking notice likewise of the sign of the function.

We may easily fix these rules in the memory and also the signs which are used by help of the following Table

Angle	Sine	Cosine	Tangent	Cotangent
X	+ sin x	+ cosx	+ tan x	-f- cotan x
90° + x	+ COSX	— sin x	— cotan x	— tan x
i8o° + x	— sin x	— cosx	H-tanx	+ cotan x
270° -f x	— cos x	+ sin x	— cotan x	— tan x

Conversely if we seek the arc or angle belonging to a function, we find, limiting ourselves to four quadrants, that 4 angles belong to every single value when the sign is left out of sight, but if the sign is given, then there are only 2 angles belonging to each value. We must therefore to prevent ambiguity, fix the quadrant in which the angle lies, or the sign as well as the function must be given, but even then the two functions cannot be both tangents nor both cotangents. In most cases the logarithms of two numbers are given for the determination of an angle that are proportional to the sine and cosine; for instance log asinA and log acosA and by subtraction we find log tan A. The quadrant in which the angle A lies is pointed out as well by the sign of the tangent and that of the sine or cosine.

§• J9-

The tables of the trigonometrical functions may be also used for the calculation of exponential magnitudes as well those with real exponents, on

r tne ? . - ter than 360° suLtract 360° as often as it may be necessary until

an arc is left which is less than 360°.

, Introduction. XXIII

which the so-called hyperbolic functions depend, as also those with imaginary exponents comprising the complex units. If we put

,»-* = tan — qp or p x = log tan — qp

where /* = — 0,4342945, then we obtain

sin gj = x 4- -x * cos ^ = * *. 4- ^"x ' ^n qp = —

and for imaginary arcs sin

In ix = — - — , tan ix — i cos <r , cos I'OT = —r-

fon JY> " c-ir\

where in order that it may be expressed in degrees

y is = 57,2957795 •*• For example if we have given x = o, 75 , then

IM* = — 0,3257209 = 9,6742791 — 10 = log tan ~ qp

-f-g> = 25° I7'4",i3, qr ^ 50° 34' 8",26 and therewith

log • • = log Sin5o03'4,8,,)26 = log cos 0,75 «• = 0,121 .326

^>,75_tf-o,73 j I

log - - - =I°g tan 50° 3V 8^,26 = = log 7 sm o'75 ' = 9.QI5O393

log ^ = log cos 50° 34' 8",26 — log y tan 0,75 i = 9,8028757.

If there were appended to the trigonometrical tables which contain the log sin, cos, tan and cotan an additional column, giving the log tan of the semi-angle, then we could get the logarithms of the hyperbolic functions without the necessity of seeking out the angle. The logarithm of the Tan gents facilitates also the solution of the quadratic and cubic equations which it is well known may be performed by the trigonometrical tables, as is shown in every treatise on the theory of equations.

Moreover if we should have to reckon many hyperbolic functions, then we should do better to calculate some tables from which the angle q> with the argument x may be taken and conversely with the argument qp we may take out x.

§• 20.

In conclusion we may enumerate that the Tables on page 186 for the conversion of natural logarithms into common logarithms and the inverse, that on page 608 of parts of the arc in terms of the radius on page 609 for the conversion of degrees of arc into time , hours , minutes and seconds , as well as that on page 610 of constants and the comparison of the various foot lengths of the principal continental states with the metre are so easily used that it is not necessary here to offer any further explanation or example.

Conten ts.

Preface

Introduction .............

I. Table of Briggs's or common Logarithms of the natural numbers from I to looooo and the auxiliary trigonometrical functions S and T for the calculation of the Logarithms of Sines, Tangents and Cotangents of the Angles from o to 10000 seconds, &c. &c. ..........

II. Table of the trigonometrical functions from o° to 6° and 84° to 90° for every

second 187

III. Logarithms of the trigonometrical functions from 6° o' to 84° o' for every ten

seconds 373

TABLE

OF

BRIGGSS OR COMMON LOGARITHMS

OF THE NATURAL NUMBERS

FROM 1 TO 100000

AND THE

AUXILIARY TRIGONOMETRICAL FUNCTIONS S AND T

FOR THE CALCULATION OF THE

LOGARITHMS

OF SINES, TANGENTS AND COTANGENTS OF THE ANGLES FROM 0 TO 10000 SECONDS &C. &C. '

0 — 250

N.	Log.	N.	Log.	N.	Log.	N.	Log.	N.	Log.
0 I 2 3 4 6 8 9 10 n 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50	— cc	50 51 52 53 54 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 11 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100	698 9700	100 101 102 103 104 105 106 107 1 08 109 110 III 112 114 116 117 118 119 120 121 122 I23 124 125 126 127 128 129 130 131 132 133 134 135 136 138 139 140 141 142 143 144 145 146 147 148 149 150	000 0000	150 151 152 '55 156 157 158 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 176 177 178 ISO 181 182 183 184 185 186 187 188 189 190 191 192 193 194 '95 196 197 198 199 200	1760913	200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250	301 0300
000 0000 301 0300 477 1213 602 0600 698 9700 7781513 845 0980 903 0900 954 2425	707 5702 7160033 724 2759 7323938 740 3627 748 1880 755 8749 763 4280 770 8520	0043214 008 6002 0128372 0170333 021 1893 025 3059 029 3838 033 4238 037 4265	1789769 181 8436 1846914 187 5207 I9033I7 193 1246 195 8997 1986571 201 3971	303 1961 30535H 307 4960 309 6302 3ii 7539 313 8672 3159703 3*80633 320 1463
000 0000	7781513	041 3927	204 1200	3222193
041 3927 079 1812 1139434 146 1280 1760913 2O4 1200 230 4489 2552725 2787536	785 3298 7923917 799 3405 806 1800 8129134 819 5439 826 0748 832 5089 838 8491	045 3230 0492180 053 0784 056 9049 060 6978 0644580 068 1859 071 8820 075 5470	2068259 2095150 212 1876 2148438 2174839 22O I08l 2227165 225 3093 227 8867	324 2825 3263359 328 3796 3304138 332 4385 3344538 336 4597 338 4565 340 4441
301 0300	845 0980	079 1812	2304489	342 4227
3222193 342 4227 361 7278 3802112 397 9400 4H9733 431 3638 4471580 462 3980	851 2583 8573325 863 3229 869 2317 8750613 8808136 886 4907 892 0946 897 6271	0827854 0863598 0899051 0934217 096 9100 1003705 103 8037 1072100 no 5897	2329961 235 5284 238 0461 240 5492 243 0380 2455127 247 9733 25* 4200 2528530	344 3923 3463530 348 3049 350 2480 3521825 354 1084 3560259 3579348 3598355
4771213	903 0900	H39434	2552/25	361 7278
491 3617 505 1500 5185139 53i 4789 544 0680 5563025 5682017 5797836 591 0646	9084850 9I38I39 9190781 924 2793 9294189 934 4985 9395193 944 4827 949 3900	1172713 1205739 1238516 127 1048 1303338 133 5389 1367206 1398791 143 0148	257 6786 2600714 2624511 2648178 2671717 269 5129 271 8416 274 1578 2764618	3636120 365 4880 3673559 3692159 371 0679 372 9120 374 7483 376 5770 3783979
602 0600	9542425	146 1280	2787536	3802112
6127839 623 2493 633 4685 643 4527 6532125 662 7578 672 0979 681 2412 690 1961	9590414 963 7878 9684829 973 1279 977 7236 9822712 9867717 991 2261 995 6352	1492191 1522883 i55336o 1583625 161 3680 1643529 I673I73 1702617 1/31863	281 0334 283 3012 285 5573 2878017 290 0346 292 2561 294 4662 296 6652 2988531	3820170 3838154 385 6063 3873898 389 1661 390 9351 392 6970 3944517 396 1993
698 9700	000 0000	1760913	301 0300	397 9400
IN.	. Log-	N.	Log.	N.	Log.	N.	Log.	N.	. Log.
o"= o°o/ o" S. =4.685 5748 7 T. =4.685 5748 7 50 = o o 50 5748 6 5748 8 100 = o i 40 5748 5 5749 o 150 = o 2 30 5748 3 5749 4 200 = 0 3 20 5748 0 5750 0

250 — 500

X. LO.CT.	X. Log.	X. Log.	X. Log.	X.	Log.
250 251 252 253 254 1 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 2/4 2/5 276 277 278 2/9 280 281 282 283 284 285 . 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300	397 9400	300 301 302 303 304 305 306 307 308 309 310 311 312 313 3H 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350	r7/I2I3	350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 3/6 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400	544 0680	400 401 402 403 404 405 406 407 408 409 410 4ii 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450	602 0600	450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500	6532125
399 6737 401 4005 403 1205 404 8337 406 5402 408 2400 4099331 411 6197 4132998	4/8 5665 480 0069 481 4426 482 8736 4842998 4857214 4871384 488 5507 4899585	545 3071 5465427 547 7747 549 0033 5502284 55i 4500 552 6682 553 8830 555 0944	603 1444 604 2261 605 3050 6063814 6074550 608 5260 609 5944 610 6602 611 7233	6541765 655 1384 6560982 6570559 6580114 6589648 659 9162 660 8655- 661 8127
4149733	491 3617	5563025	612 7839	6627578
4166405 4183013 4199557 421 6039 423 2459 4248816 4265113 428 1348 429 7523	492 7604 4941546 495 5443 496 9296 4983106 499 6871 501 0593 5024271 503 7907	557 5072 5587086 559 9066 561 1014 562 2929 563 4811 564 6661 565 8478 5670264	6138418 6148972 6159501 6170003 618 0481 6190933 620 1361 621 1763 622 2140	663 7009 664 6420 665 5810 666 5180 6674530 6683859 6693169 670 2459 671 1728
43i 3638	505 1500	568 2017	623 2493	672 0979
432 9693 434 5689 436 1626 437 7506 4393327 440 9091 442 4798 444 0448 445 6042	506 5050 50/8559 509 2025 5J05450 5118834 5132176 5H5478 5158738 5I7I959	5693739 5705429 571 7088 5728716 5740313 575 1878 57634H 5774918 578 6392	624 2821 6253125 626 3404 627 3659 6283889 629 4096 6304279 631 4438 6324573	673 0209 673 9420 6748611 675 7783 676 6936 677 6070 6785184 6794279 6803355
447 I58°	5185139	579 7836	633 4685	681 2412
448 7063 450 2491 451 7864 4533183 454 8449 456 3660 4578819 459 3925 460 8978	5198280 521 1381 522 4442 523 7461 525 0448 5263393 527 6299 5289167 5301997	5809250 5820634 583 1988 5843312 585 4607 586 5873 5877110 5888317 589 9496	634 4773 635 4837 636 4879 6374S97 638 4893 639 4865- 640 4814 641 4741 642 4645	682 1451 683 0470 683 9471 684 8454 6857417 686 6363 687 5290 6884198 689 3089
462 3980	53i 4789	591 0646	643 4527	690 1961 j
463 8930 465 3829 466 8676 468 3473 469 8220 4712917 472 7564 4742163 4756712	5327544 5340261 535 2941 5365584 5378191 5390761 540 329" 54i 5792 5428254	592 1768 593 2861 594 3926 595 4962 596 597i 597 6952 598 7905 5998831 600 9729	6444386 645 4223 646 4037 647 3830 648 3600 649 3349 650 3075 651 2780 16522463	691 0815 691 9651 692 8469 693 7269 694 6052 6954817 6963564 697 2293 698 1005
477 1213	544 0680	.602 0600	16532125	698 9700
X. ! - Log.	N. - Log.	N. Log.	X. Log.	X. Log.
250"= o°4'io" S. =4.685 5747 6 T. =4.685 5750 8 300 = o 5 o 5747 i 5751 7 350 = o 5 50 5746 6 5752 8 400 = o 6 40 5745 9 5754 i 450 = o 7 30 5745 2 5755 6

500 — 750

N.	Log.	N.	Log.	N.	Log.	N.	Log.	N.	Log.
500	698 9700	550	7403627	600	778I5I3	650	8129134	700	845 0980
501 502 503 504 505 506 507 508 509	699 8377 700 7037 701 5680 702 4305 703 2914 704 1505 705 0080 705 8637 7067178	55i 552 553 554 555 556 557 558 559	741 1516 741 9391 7427251 743 5098 744 2930 745 0748 745 8552 746 6342 7474118	60 1 6O2 603 604 605 606 607 608 609	778 874? 779 596S 7803173 781 0369 78i 7554 782 4726 783 1887 783 9036 7846173	651 652 653 654 655 656 657 658 659	813 5810 8142476 8149132 815 5777 8162413 8169038 8175654 818 2259 8188854	701 702 703 704 705 706 707 708 709	845 7180 8463371 846 9553 847 5727 848 1891 848 8047 8494194 8500333 850 6462
510	707 5702	560	748 1880	610	7853298	660	8195439	710	851 2583
511 512 5^3 5H 515 516 5^7 518 519	708 4209 709 2700 7101174 7109631 711 8072 7126497 713 4905 7143298 715 1674	561 562 563 564 565 566 567 568 569	748 9629 749 7363 750 5084 751 2791 7520484 752 8164 7535831 754 3483 755 1123	611 612 613 614 6i5 616 617 618 619	7860412 7867514 787 4605 788 1684 7888751 789 5807 790 2852 790 988^ 791 6906	661 662 663 664 665 666 667 668 669	820 2015" 8208580 8215135 822 1681 8228216 823 4742 824 1258 824 7765- 825 4261	711 712 7J3 714 715 716 717 718 719	851 8696 8524800 853 0895 853 6982 8543060 8549130 8555192 856 1244 856 7289
520	7160033	570	755 8749	620	7923917	670	826 0748	720	857332^
521 522 523 524 525 526 527 528 529	7168377 7176705 7185017 719 33*3 7201593 7209857 721 8106 722 6339 723 4557	57i 572 573 574 575 576 577 578 579	7566361 7573960 758 1546 7589119 759 6678 760 4225 761 1758 761 9278 762 6786	621 622 623 624 625 626 627 628 629	7930916 793 7904 794 4880 795 1846 795 8800 796 5743 797 2675 797 9596 798 6506	671 672 673 674 675 676 677 678 679	8267225 827 3693 8280151 828 6599 8293038 829 9467 830 5887 831 2297 831 8698	721 722 723 724 725 726 727 728 729	8579353 8585372 859 1383 8597386 8603380 8609366 861 5344 862 1314 862 7275
530	724 2759	580	763 4280	630	799 3405	680	832 5089	730	863 3229
531 532 533 534 535 536 537 538 539	725 0945 7259116 726 7272 7275413 7283538 729 1648 729 9743 7307823 731 5888	581 582 583 584 585 586 587 588 589	764 1761 764 9230 765 6686 7664128 7671559 767 8976 7686381 769 3773 770H53	63i 632 633 634 635 636 637 638 639	800 0294 800 7171 80 1 4037 802 0893 802 7737 803 4571 804 1394 804 8207 805 5009	681 682 683 684 685 686 687 688 689	833 H71 833 7844 834 4207 8350561 835 6906 8363241 8369567 837 5884 8382192	73 1 732 733 734 735 736 737 738 739	8639174 864 5111 865 1040 865 £961 * -2873 866 8778 8' - 467? 860 056^ 868 6444
540	7323938	590	7708520	640	806 1800	690	838 8491	740	869 2317
54i 542 543 544 545 546 547 548 549	733 1973 733 9993 734 7998 735 5989 7363965 7371926 737 9873 738 7806 739 5723	59i 592 593 594 595 596 597 598 599	77i 587S 7723217 773 0547 773 7864 7745170 775 2463 775 9743 7767012 7774268	64i 642 643 644 645 646 647 648 649	806 8580 807 5350 808 2110 808 8859 809 5597 8102325 8109043 8H5750 812 2447	691 692 693 694 695 696 697 698 699	839 478o 840 1 06 1 840 7332 841 359J 841 9848 842 6092 843 2328 843 8554 844 4772	741 742 743 744 745 746 747 748 749	8(39 8182 870 4039 870 9888 871 5729 8721563 872 7388 873 3206 873 9016 8744818
550	7403627	600	778i5i3	650	812 9134	700	845 0980	750	8750613
N.	Log.	N.	Log.	N.	Log.	N.	Log.	N.	Log.
	5oc 55C 6oc 65C 7oc	"= 0° = 0 = 0 I = 0 I = O I	8' 20" £ 9 10 0 0 o 50 i 40	. = 4.6*	}5 5744 4 5743 5 5742 5 574i 5 5740 3	rp	4-685 575 575 576< 576 576	7 2 ) o 3 9 3 o 5 3	•

750 — 1000

X. | Log.	X. | Log.	X.	Log.	N. | Log.	X.	Log.
750 75i 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 .780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797' 798 799 800	8750613	800 801 802 803 804 805 806 807 808 809 810 811 812 8i3 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 84i 842 843 844 845 846 847 848 849 850	903 0900	850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 8/2 873 874 8/5 876 877 878 8/9 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900	9294189	900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939- 940 941 942 943 944 945 946 947 948 949 950	954 2425	950 95i 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 9/8 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000	977 7236
875 6399 8762178 8/6 7950 8773713 877 9470 878 5218 879 0959 879 6692 8802418	903 6325 9041744 9Q471 55 905 2560 905 7959 9063350 906 8735 9074114 907 9485	929 9296 9304396 930 9490 93i 4579 931 9661 932 4738 932 9808 933 48/3 933 9932	9547248 955 2065 9556878 956 1684 956 6486 957 1282 957 6073 9580858 958 5639	978 1805 978 6369 9790929 979 5484 9800034 9804579 9809119 98i 3655 981 8186
8808136	908 4850	934 4985	9590414	982 2712
881 3847 881 9550 882 5245 883 0934 8836614 8842288 884 7954 885 3612 885 9263	909 0209 909 5560 9100905 910 6244 911 1576 911 6902 912 2221 9127533 9132839	935 0032 935 50/3 9360108 9365137 9370161 93751/9 9380191 9385197 9390198	9595184 959 9948 960 4708 960 9462 961 4211 961 895^ 962 3693 962 8427 9633155	9827234 983 i/5i 983 6263 984 0770 984 5273 9849771 985 4265 985 8754 9863238
886 4907	9I38I39	9395193	963 /8/8	9867717
8870544 8876173 888 179^ 8887410 8893017 8898617 890 4210 890 9796 891 5375	9H3432 9148718 9153998 9159272 9164539 9169800 9I75055 9180303 9185545	9400182 9405165 941 0142 9415114 9420081 942 5041 942 9996 943 4945 943 9889	964 2596 964 7309 965 2017 965 6720 966 1417 966 6110 967 0797 967 5480 9680157	9872192 987 6663 988 1128 988 5590 989 0046 989 4498 989 8946 9903389 990 7827
892 0946	9190781	944 4827	9684829	991 2261
8926510 893 2068 893 7618 8943161 894 8697 895 4225 895 9747 896 5262 897 0770	919 6010 9201233 920 6450 921 1661 921 6865 922 2063 922 7253- 923 2440 923 7620	944 9759 945 4686 945 9607 946 4523 946 9433 947 4337 947 9236 9484130 948 9018	968 9497 9694159 9698816 9/o 3469 970 8116 971 2758 971 7396 9722028 9726656	991 6690 992 1115" 9925535 9929951 993 4362 993 8769 9943172 994 7569 995 1963
8976271	924 2/93	949 3900	973 12/9	995 6352
898 1765 898 7252 899 2732 899 8205 900 3671 9009131 901 4583 902 0029 902 5468	924 7960 9253121 925 8276 926 3424 9268567 927 3704 927 8834 9283959 928 9077	949 87/7 9503649 9508515 951 3375 951 8230 952 3080 952 7924 953 2/63 953 7597	9735896 974 0509 9745H7 974 9720 97543*8 9758911 9/6 3500 976 8083 9772662	996 0737 9965117 996 9492 997 3864 9978231 998 2593 9986952 999 1305 9995655
903 0900	9294189	954 2425	9777236	OOO OOOO
X. Log.	X. Log.	X. i Leg.	X. ! Log.	X.	Log.
750"= oci2'3o" $.=4.685 5739 i T. =4.685 5767 8 800 = o 13 20 5737 8 577° 4 850 = o 14 10 5736 4 5773 3 900 = o 15 o 5734 9 57/6 2 950 = o 15 50 5733 3 5779 4

1000 — 1050

N.	o I i	2 3	4	5	6	7	8	9	P. P.
1000 01 02 03 04 05 06 07 08 09 1010 II 12 13 14 15 16 17 18 19 1020 21 22 23 24 26 27 28 29 1030 31 32 33 34 35 36 37 38 39 1040 41 42 43 44 45 46 47 48 49 1050	000 0000	0434	0869	1303	r737	2171	260^	3039	3473	3907	i 2 3 4 S 6 7 8 9 i 2 3 4 i 7 8 9 i 2 3 4 5 6 7 8 9 i 2 3 4 5 6 9 i 2 3 4	435 43.5 87.0 130.5 *74.o 217.5 261.0 304.5 348.0 391-5 432 43-2 86.4 129.6 172.8 216.0 259.2 302.4 345-6 388.8 429 42.9 85.8 128.7 171.6 214.5 257-4 300.3 343-2 386.1 426 42.6 85.2 127.8 170.4 213.0 255-6 298.2 340.8 383.4 423 42.3 84.6 126.9 169.2	434 43-4 86.8 130.2 173-6 217.0 260.4 303.8 347-2 390.6 431 43.1 86.2 129.3 172.4 215.5 258.6 301.7 344-8 387.9 428 42.8 85.6 128.4 171.2 214.0 256.8 299.6 342.4 385-2 425 42.5 85.0 127.5 170.0 212.5 255.0 297.5 340.0 382.5 422 42.2 84.4 126.6 168.8	433 43.3 86.6 129.9 173.2 216.5 259.8 303.1 346.4 389.7 430 43.0 86.0 129.0 172.0 215.0 258.0 301.0 344-0 387-0 427 42.7 85.4 128.1 170.8 213.5 256.2 298.9 341.6 384.3- 424 42.4 84.8 127.2 169.6 212. 0 254.4 296.8 339-2 381.6 421 42.1 84.2 126.3 168.4
4341 8677 ooi 3009 7337 002 1661 5980 003 029^ 4605 8912	477^ 9111 3442 7770 2093 6411 0726 5036 9342	5208 9544 3875 8202 252^ 6843 1157 5467 9772	5642 9977 4308 863? 2957 7275 1588 5898 0203	6076 0411 4741 9067 3389 7706 2019 6328 0633	6510 0844 5174 9499 3821 8138 2451 6759 1063	6943 1277 5607 9932 4253 8569 2882 7190 H93	7377 1710 6039 0364 468^ 9001 3313 7620 1924	7810 2143 6472 0796 5116 9432 3744 8051 2354	8244 2576 690^ T228 5548 9863 4174 8481 2784
004 3214	3%4	4074	4504	4933	5363	5793	6223	6652	7082
7512 005 1805 6094 006 0380 4660 8937 007 3210 7478 008 1742	7941 2234 6523 0808 5088 936^ 3637 7904 2168	8371 2663 6952 1236 55i6 9792 4064 8331 2594	8800 3092 7380 1664 5944 0219 4490 8757 3020	9229 352i 7809 2092 6372 0647 4917 9184 3446	9659 3950 8238 2521 6799 1074 5344 9610 3872	0088 4379 8666 2949 7227 1501 5771 0037 4298	0517 4808 9094 3377 7651 1928 6198 0463 4724	0947 5237 9523 38o^ 8082 2355 6624 0889 5150	T376 5666 9951 4233 8510 2782 7051 1316 5576
6002	6427	6853	7279	7704	8130	8556	8981	9407	9832
009 0257 4509 8756 oio 3000 7239 on 1474 5704 9931 0124154	0683 4934 9181 3424 7662 1897 6127 0354 4576	1108 5359 9605 3848 8086 2320 6550 0776 4998	1533 5784 0030 4272 8510 2743 6973 1198 5420	1959 6208 0454 4696 8933 3166 739'6 162 1 5842	2384 6633 0878 5120 9357 3590 7818 2043 6264	2809 7058 T303 5544 9780 4013 8241 2465 6685	3234 7483 1727 5967 0204 .4436 8664 2887 7107	3659 7907 2151 6391 0627 4859 9086 33io 7529	4084 8332 2575 6815- 1050 5282 9509 3732 795i
8372	8794(9215	9637	0059	0480	0901	T323	T744	2165
0132587 6797 014 1003 5205 9403 0153598 7788 016 1974 6i55	3008 7218 1424 5625 9823 4017 8206 2392 6573	3429 7639 1844 6045 0243 4436 8625 2810 6991	3850 8059 2264 6465 0662 485^ 9044 3229 7409	4271 8480 268^ 6885 1082 5274 9462 3647 7827.	4692 8901 3ioS 730^ 1501 5693 9881 4065 824^	5H3 932i 3525 772^ 1920 6112 0300 4483 8663	5534 9742 3945 8144 2~340 6531 0718 4901 9080	5955 0162 4365 8564 2759 6950 Ti37 53*9 9498	6376 5583 4785 8984 5178 7369 T555 5737 9916
6 7 8 9 i 2 3 4 5 6 7 8 9 i 2 3 4 S 6 7 8 9	253.8 296.1 338.4 380.7 420 42.0 84.0 126.0 168.0 210.0 252.0 294.0 336.0 378.o 417 41.7 83.4 125.1 166.8 208.5 250.2 291.9 333-6 375-3	253-2 295.4 337-6 379-8 419 41.9 83.8 !25-7 167.6 209.5 251.4 293.3 335-2 377-1 416 41.6 83.2 124.8 166.4 208.0 249.6 291.2 332.8 374-4	252.6 294.7 336.8 378.9 418 41.8 83.6 125.4 167.2 209.0 250.8 292.6 334.4 376.2 415 41.5 83.0 124.5 166.0 207.5 249.0 290.5 332.0 373-5
0170333	0751	1168	1586	2003	2421	2838	3256	3673	4090
4507 8677 018 2843 700^ 019 1163 5317 9467 020 3613 7751	4924 9094 3259 7421 1578 5732 9882 4027 8169	5342 9511 3676 7837 1994 6147 0296 4442 8583	5759 9927 4092 8253 2410 6562 0711 4856 8997	6176 0344 4508 8669 282^ 6977 Ti26 5270 9411	6593 0761 492S 9084 3240 7392 T54Q 5684 9824	7010 Ti77 534i 9500 3656 7807 T95S 6099 0238	7427 T594 5757 9916 4071 8222 2369 6513 0652	7844 2010 6173 3332 4486 8637 2784 6927 To66	8260 2427 6589 0747 4902 9052 3198 734i T479
021 1893	2307	2720	3134	3547	396i	4374	4787	5201	56l4
U- N<	0	1	o	3	4	5	6	1	8	9	P. P.
10000"= 2°46'4o" 1000"= o°i6'4O" S. = 4-685 5731 7 T. = 4.685 5782 7 10100 = 2 48 20 1010 = o 16 50 5731 3 5783 4 I020O = 2 50 0 1020 = 0 17 0 573! O 5784 I 10300 = 2 51 40 1030 = o 17 10 5730 6 5784 8 10400 = 2 53 20 1040 = o 17 20 5730 3 5785 5

1050 — 1100

N.	0 1 2 i 3 i 4	5 6 7 | 8	9	P. P.
1050	0211893 2307:2720 3134 3547	3961	4374	4787	5201	5614
51	6027	6440	6854	7267	7680	8093	8506	8919	9332	9745	i	414 41.4	413 41 3	412 41 2
52	0220157	057°	0983	1396	1808	2221	2634	3046	3459	3871	2	82.8	82.6	82;4
53	4284	4696	5109	5521	5933	6345	6758	7170	7582	7994	3 4	124.2 165.6	123.9 165.2	123.6 164.8
54	8406	8818	9230	9642	0054	0466	0878	1289	1701	2113	5	207.0	206.5	206.0
55	023 2523-	2936	3348	3759	4171	4582	4994	5405	.5817	6228	6 240.4 7 280 £	247.8 280 i	247.2 288.4
56	6639	7050	7462	7873	8284	8695	9106	9517	9928	0339	' y- 8 33L2	*uy. j. 330.4	329.6
											Q 372 6	OTT i	370 8
57	0240750	1161	1572	1982	2393	2804	3214	3625	4036	4446	y j/^*^ j/ -•/	o/u»°
58	4857	5267	5678	6088	6498	6909	7319	7729	8i39	8549		411	410	409
59	8960	9370	9780	0190	0600	TOIO	1419	1829	2239	2649	i 2	41.1 82.2	41.0 82.0	40.9- 81.8
1060	025 3059	3468	3878	4288	4697	510"	55J6	5926	6335	6744	3 4	123.3 164.4	123.0 164.0	I22.7 163,6
61	7154	7563	7972	8382	8791	9200	9609	0018	0427	0836	5	205.=	205.0	204.5
62	026 1245	1654	2063	2472	2881	3289	3698	4107	4515	4924	61240.01240.0:245.4 7 287.7 '287.0 '286.3
63	5333	5741	6150	6558	6967	7375	7783	8192	8600	9008	8j32§.8 328.0 327.2
64	9416	9824	0233	0641	T049	T457	T86J	2273	2680	3088	9 369.9'369.o 368.1
65	027 3496	3904	4312	4719	5127	5535	5942	6350	6757	7i65		408 i 407	406
66	7572	7979	8387	8794	9201	9609	0016	0423	0830	T237	i 2	40.8 81.6	40.7 81.4	40.6 81.2
67	028 1644	2051	2458	2865	3272	3679	4086	4492	4899	5306	3	122.4	122. 1	121. 8
68	5713	6119	6526	6932	7339	7745	8152	8558	8964	9371	4 I	163.2 2O.1 O	162.8	162.4
69	9777	0183	0590	0996	1402	T8o8	2214	2620	3026	3432	6	•^^-t.0 244.8	2O3.5 *-»-'o>N-' 244.2 243.6
1070	0293838	4244	4649	5055	546i	5867	6272(6678	7084 | 7489	7 8	285.6 326.4	284.9 284.2 325.6h24.8
71	7895	8300	8706	9111	95l6	9922	0327	0732	"38	T543	9	367.2	366.31365.4
72	030 1948	2353	2758	3163	3568	3973	4378	4783	5188	5592		405	404	403
73	5997	6402	6807	7211	7616	8020	8425	8830	9234	9638	i 2	40.5 81.0	40.4 80.8	40.3 80.6
74	031 0043	0447	0851	1256	1660	2064	2468	2872	3277	3681	3	121.5	121. 2	120.9
75	4085	4489	4893	5296	5700	6104	6508	6912	7315	7719	4 -	IO2.O 2O2 ^	161.6	161.2
76	8123	8526	8930	9333	9737	0140	0544	0947	T35Q	T754	5 6	243.0	242.4	201.5 241.8
77	0322157	2560	2963	3367	3770	4173	4576	4979	5382	5785	7 8	283.5 282.8 324.0 323.2	282.1 322.4
78	6188 6590	6993	7396	7799	8201	8604	9007	9409	9812	9 364.5 363.6	362.7
79	033 0214 0617 1019	1422	1824	2226	2629	3031	343313835		402 1 401	400
1080	4238] 4640 | 5042	5444	5846	6248	6650	7052	7453 7855	i	40.2] 40.1 Rn l\ fl^ o	40.0 80 o
81	8257	8659	9060	9462	9864	0265 0667	To68	T47o|T87i	3 120.6 120.3	120.0
82 83	034 2273 6285	2674 6686	3075 7087	3477 7487	3878 7888	4279 1 4680 8289 i 8690	5081 9091	5482 5884 9491:9892	4 5 6	loo.e 160.4 2OI.O 2OO.5 241.2 240.6	160.0 200.0 240.0
84	0350293	0693	1094	1495	1895	V 2296 1 2696	3096	3497 3897	7 8	281.4 280.7 280.0 321.6,320.8 320.0
85	4297	4698	5098	5498	5898	6298 1 6698	7098	7498 j 7898	0 361.81360.9 360.0
86	8298	8698	9098	9498	9898	0297 0697	1097	1496 1896	i 399 1 398	397
87	0362295	2695	3094	3494(3893	4293	4692	5091 5491 5890		39-9	39.8	39.7
88	6289	6688	7087	748617885	8284	8683	9082 j 9481	9880	2	79.8	79.6 79.4
89	037 0279	0678	1076	H75 11874	2272	2671	3070 j 3468	3867	4 159.6	119,4 II9.* 159.2 158.8
1090	4265	4663 1 5062	546015858	6257	6655	7053 i 7451 : 7849	51199.5 199.0.198.5 6,239.4 238.8 238.2
91	824818646 9044	9442 9839	0237	0635	T033	1431 1829	7)279.3 278.6 8 319.2 318.4	277.9 317.6
92	0382226	2624	3022	3419 3817	4214	4612	5009	5407 5804	9 359.11358.2	357.3
93	6202	6599	6996	7393 I 779i	8188	8585	8982	9379 9776	(3961395	394
94	0390173	0570	0967	1364	1761	2158	2554	2951	3348	3745	i	39-6	39-5	39-4
95	4141	4538	4934	533i	5727	6124	6520 6917	7313	7709	2	n8°8	79.o	78.8
96	8106	8502	8898	9294	9690	0086	0482 j 0878	1274	1670	3 4	158^	118.5 158.0	157-6
97 98	040 2066 6023	2462 6419	2858 6814	3254 7210]	3650 7605	4045 8001	4441 i 4837 8396 8791	5232 5628 9187 9582	5 6 7	198.0 237.6 277.2	197.51197.° 237.0236.4 276.5 275.8
99	9977	0372	0767	1162 1557	"195212347 2742	3137 3532	8316.8 9 356.4	316.0315.2 T^.(;h'U.6
1100	0413927 4322 14716 5111 5506	5900)6295 669017084 7479
X.	0 1 2 ! 3 ' 4	5 6 7 8 I 9	P. P.
10500"= 2°55' o" 1050"= o°i7'3o	S. =4.685 5729 9 T. =4.685 5786 2
10600 = 2 56 40 1060 = 0 17 40 5729 6 5786 9
10-00 = 2 58 20 10-0 = 0 17 50 5729 2 5787 6
10800 = 300 1080 = o 18 o 5728 8 5788 4
10900 = 3 i 40 1090 = o 18 10 5/28 5 5789 i

1100 — 1150

N.	0 1 1	2	3	4	5	6	7	8	9	P. P.
1100 01 02 03 04 05 06 07 08 09 1110 II 12 13 14 II 17 18 19 1120 21 22 23 24 25 26 27 28 29 1130 31 32 33 34 35 36 37 38 39 1140 41 42 43 44 45 46 47 48 49	041 3927	4322	4716	Sin	5506	5900	6295 | 6690	7084	7479	i 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 •9 i 2 3 4 5 6 7 8 9 i 2 3 4 5 6 8 9 i	395 39-5 79.° 118.5 138.0 X97.5 237.o 276.5 316.0 355. 5 392 39.2	394 39.4 78.8 "8.2 *57.6 197.0 236.4 275.8 315.2 354.6 391 39.i	393 39.3 78.6 "7-9 IS7.2 196.5 235.8 275.1 314.4 353-7 390 39.o
7873 042 1816 5755 9691 043 3623 755i 044 1476 5398 9315	8268 2210 6149 0084 4016 7944 1869 5790 9/07	8662 2604 6543 0477 4409 8337 2261 6181 0099	9056 2998 6936 0871 4802 8729 2653 6573 0490	945i 3392 7330 1264 5I9J 9122 3045 6965 0882	9845 3786 7723 T657 5587 95H 3437 7357 1273	0239 4180 8117 2050 5980 9907 3829 7749 1664	0633 4574 8510 244.4 6373 0299 4222 8140 2056	T028 4968 8904 2837 6766 0692 4614 8532 2447	1422 536i 9297 3230 7159 1084 5006 8924 2839
0453230(3621	4012	4403	4795	5186	5577	5968	6359	6750	117.6 156.8 196.0 235.2 274.4 313.6 352.8 389 38.9 77.8 "6.7 155.6 194.5 233.4 272.3 3H.2 350.1 386 38.6 77-2 "5.8 154.4 i93.0 231.6 270 2 308.8 347.4 383 38.3 76.6 "4-9 153.2 i9r-5 229.8 268.1 306.4 344.7 380 38.0 76.0 114.0 152.0 190.0 228.0 266.0 304.0 342.o i 2 3 4 5 6 7 8 9	"7-3 156.4 195.5 234.6 273.7 312.8 35L9 388 38.8 77.6 "6.4 155.2 194.0 232.8 271.6 3io.4 349-2 385 38.5 77-0 "5-5 IS4.° 192.5 231.0 269.5 308.0 346.5 382 38.2 76.4 "4.6 152.8 191.0 229.2 267.4 305.6 343.8 379 37.9 75.8 "3.7 irfi.6 189.5 227.4 265.3 303.2 34LI 377 37.7 75.4 "3.1 150.8 188.5 226.2 263.9 301.6 339.3	117.0 156.0 i95.o 234.o 273.o 312.0 35i.o 387 38.7 77.4 116.1 154.8 193.5 232.2 270.9 309.6 348.3 384 38.4 76.8 "5-2 153.6 192.0 230.4 268.8 307.2 345.6 381 38.1 76.2 "4.3 152.4 190.5 228.6 266.7 304.8 342.9 378 37.3 75.6 "3.4 151.2 189.0 226.8 264.6 . 302.4 340.2
7141 046 1048 4952 8852 047 2749 6642 048 0532 4418 8301	753i H38 5342 9242 3138 7031 0921 4806 8689	7922 1829 5732 9632 3528 7420 1309 5195 9077	8313 2219 6122 0021 3917 7809 1698 5583 9465	8704 2610 6512 0411 4306 8198 2087 5972 9853	9095 3000 6902 0801 4696 8587 2475 6360 0241	9485 339i 7292 Tigo 5085 8976 2864 6748 0629	9876 378i 7682 1580 5474 9365 3253 7136 1017	0267 4171 8072 1970 5864 9754 3641 752? T403"	0657 456i 8462 2359 6253 3i43 4030 7913 1792
049 2180	2568	2956	3343	3731	4119	4506	4894	5281	5669
6056 9929 0503798 7663 051 1525 5381 9239 0523091 6939	6444 0316 4184 8049 1911 5770 9624 3476 7324	6831 0703 4571 8436 2297 6i55 0010 3861 7709	7218 Togo 4958 8822 2683 6541 0*395 4246 8093	7606 T477 5344 9208 3069 6926 0780 4631 8478	7993 1863 5731 9591 3455 7312 Ti66 5016 8862	8380 2250 6117 998i 3841 7697 T55I 5400 9247	8767 2637 6504 0367 4227 8083 1936 5785 9631	9154 3024 6890 0753 4612 8468 2321 6170 0016	9541 34ii 7277 TI39 4998 8854 2706 655? 0400
053 0784	1169	1553	1937	2321	2706	3090	3474	T O - O 355°	4242
4626 8464 054 2299 6131 9959 055 3783 760^ 056 1423 5237	5010 8848 2682 6514 0341 4166 7987 1804 5619	5394 9232 3066 6896 0724 4548 8369 2186 6000	5778 9615 3449 7279 Tio6 4930 8750 2567 6381	6162 9999 3832 7662 T489 5312 9132 2949 6762	6546 0382 4215 8045 1871 5694 95H 3330 7H3	6929 0766 4598 8428 2254 6077 9896 3712 7524	73 1 3 1149 4981 8811 2636 6459 0278 4093 7905	7697 T532 536^ 9193 3019 6841 0659 447b 8287	8081 1916 5748 9576 3401 7223 "1041 4856 8668	3 4 5 6 7 8 9 i 2 3 4 1 7 8 9
9049	9429 9810	0191	0572	0953	T334	1714	2095	2476
0572856 6661 058 0462 4260 805^ 059 1846 5634 9419 0603200	3237 7041 0842 4640 8434 2225 6013 9797 3578	3618 7422 1222 5019 88I3 2604 6391 0175 3956	3998 7802 1602 5399 9193 2983 6770 0554 4334	4379 8182 1982 5778 9572 3362 7148 0932 4712	4759 8562 2362 6158 995 1 3741 7527 1310 5090	5HO 8942 2741 6537 0330 4119 7905 T688 5468	5520 9322 3121 6917 0709 4498 8284 2066 5845!	5900 9702 3501 7296 To88' 4877 8662 5444 6223	6281 0082 3881 7676 T467 5256 9041 2822 6601
1150	6978	7356	7734	Sin	8489	8866 9244	9621	9999	0376
N.	0	1	2 3	4	5	6	7	8 1 9	P. P.
11000"= 3° 3' 20" 1100"= o°i8'2o" S. =4.685 5728 i T. =4.685 5789 8 moo = 350 mo = o 18 30 5727 7 5790 6 1 1200 = 3 6 40 1 120 = o 18 40 5727 3 5791 4 11300 = 3 8 20 1130 = o 18 50 5726 9 5792 i 11400 = 3 10 o 1140 = o 19 o 5726 6 5792 9

1150 — 1200

N.	0 12 3 4	5 6 ! 7 8 9	P. P.
1150 51 S2 53 54 55 56 57 58 59 1160 61 62 63 64 65 66 67 68 69 1170	060697817356:7734	8111 8489	8866	9244	9621	9999	0376	i •2 3 4 S 6 8 9 i 3 4 | a g i 2 3 4 5 6 S 9 i 2 3 4 5 6 7 S 9 I 2 3 4 S 6 7 8 9 i 2 3 S 6 S 9	378 37.8 75.6 H3.4 151.2 189.0 226.8 264.6 302.4 340.2 375 37.5 75.Q 112.5 150.0 187.5 225.0 262.5 300.0 337-5 372 37.2 74.4 in. 6 148.8 186.0 223.2 260.4 297.6 334-8 369 36.9 73-8 110.7 147.6 184.5 221.4 258.3 295.2 332.1 366 36.6 73.2 109.8 146.4 183.0 219.6 256.2 292.8 329.4 363 36.3 72.6 108.9 145.2 181.5 217.8 254.1 290.4 326.7	377 37.7 75.4 113.1 150.8 188.5 226.2 263.9 301.6 339-3 374 37.4 74.8 112. 2 149.6 187.0 224.4 261.8 299.2 336.6 371 37-1 74.2 in. 3 148.4 185.5 222.6 259.7 296.8 333-9 368 36.8 73.6 no. 4 H7.2 184.0 220.8 257-6 294.4 331.2 365 36.5 73.0 109.5 146.0 182.5 219.0 255.5 292.0 328.5 362 36.2 72.4 108.6 144.8 181.0 217.2 253.4 289.6 325.8	376 37.6 75.2 1 12.8 150.4 188.0 225.6 263.2 300.8 338.4 373 37.3 74.6 111.9 149.2 186.5 223.8 261.1 298.4 335-7 370 37.o 74.o III.O 148.0 185.0 222.0 259.0 296.0 333-0 367 36.7 73.4 no i 146.8 1830 220.2 256.9 293.6 330.3 364 36.4 72.8 109.2 145.6 182.0 218.4 254.8 291.2 327.6 361 36.1 72.2 108.3 144.4 180.5 216.6 252.7 288.8 324.9
061 0753 452? 8293 062 2058 5820 9578 063 3334 7086 0640834	1131 4902 8670 2434 6196 9954 3709 7461 1209	1508 5279 9046 28ll 6572 0330 4084 7836 1584	1885 5656 9423 3187 6948 °7°5 4460 8211 1958	2262 6032 9799 3563 7324 To8i 483^ 8585 2333	2639 6409 0176 3939 7699 H56 5210 8960 2708	3017 6786 0552 43i6 8075 T832 5585 9335 3082	3394 7163 0929 4692 8451 2207 5960 9710 3457	3771 7540 1305 5068 8827 2583 6335 008^ 3831	4148 7916 1682 5444 9203 2958 6711 0460 4205
4580	4954 1 5329	5703	6077	6451	6826	7200	7574	7948
8322 065 2061 5797 9530 0663259 6986 067 0709 4428 8i45	8696 2435 6171 9903 3632 7358 1081 4800 8517	9070 2809 6544 S276 400^ 7730 H53 5172 8888	9444 3182 6917 0649 4377 8103 182^ 5544 9259	9818 3556 7291 T022 4750 8475 2197 5915 9631	0~I92 3930 7664 T39S 5123 8847 2569 6287 OOO2	0566 4303 8037 1768 5495 9220 2941 6659 0374	0940 4677 8410 2141 5868 9592 3313 7030 0/43	T3H 5050 8784 2514 6241 9964 368^ 7402 Tn6	T688 5424 9157 2886 6613 0336 4057 7774 1487
068 1859	2230	2601	2972	3343	37H |4085| 4456	4827	5198
7i 72 73 74 75 76 77 78 79	5569 9276 069 2980 6681 070 0379 40/3 7/61 071 H53 5138	5940 9647 3350 705i 0748 4442 8i34 1822 5506	6311 0017 3721 7421 1118 4812 8503 2190 58/S	6681 0388 4091 7791 1487 5181 8871 2559 6243	7052 0758 4461 8160 1857 5550 9240 2927 6611	7423 1129 4831 8530 2226 5919 9609 3296 6979	7794 1499 5201 8900 2596 6288 9978 3664 7348	8164 1869 5571 9270 2965 6658 0347 4033 7716	853? 2240 5941 9639 3335 7027 0715 4401 8084	8906 2610 6311 0009 3704 7396 1084 4770 8452
1180	8820	9188	9556	9924	0292	0660 T028	T396	T/63	2i3V
81 82 83 84 85 86 8/ 88 89	072 2499 617^ 9847 0733517 7184 074 0847 4507 8164 075 1819	2867 6542 0213- 3884 755° 1213 4873 8530 2184	3234 6910 0582 4251 7916 1579 5239 8895 2549	3602 7277 0949 4617 8283 1945 5605 9261 2914	3970 7644 1316 4984 8649 2311 5970 9626 3279	4337 Son T683 535i 9016 2677 6336 9992 3644	4701 8379 2050 5717 9382 3043 6702 0357 4010	5072 8746 2416 6084 9748 3409 7068 0723 437^	5440 9H3 2783 6450 0114 3775 7433 To88 4740	5807 9480 3*50 6817 0481 4141 7799 H53 5105
1190	54/0	i- Q-»~ D°03	6199	6564 6929	7294	7659! 8024 8388	8/53
91 92 93 94 95 96 97 98 99 1200	9118 076 2763 6404 0770043 3679 7312 078 0942 4568. 8192	9482 3127 6768 040/ 4042 7675 1304 4931 8554	9847 3491 7*32 0771 4406 8038 1667 5293 8916	02 1 1 3855 7496 H34 4769 8401 2030 5656 9278	o.S/6 4220 7860 1498 5133 8764 2393 6018 9640	0940 4584 8224 1862 5496 9127 2/55 6380 Qoo3	130^ 4948' 8588 2225 5859 9490 3118 6743 0365	1669 5312 8952 2589 6222 9853 348o 7105 0727	2034 5676 93i6 2952 6585 0216 3843 7467 1089	2398 6040 9680 33i6 6949 0579 4206 7830 "1451
079 1812	2174	2536 2898 3260	3622	3983 4345 4707	5068
N.	0 1234.	5 6 7 8,9	P. P.
11500"= 3°ii'4o" 1150"= o°i9'ro" S. =4.685 5726 2 T. =4.685 5793 7 11600 = 3 13 20 1160 = o 19 20 5725 8 5794 5 11700 = 3 15 o 1170 = o 19 30 5725 4 5795 2 11800 = 3 16 40 1180 = o 19 40 5725 ° 5796 ° 11900 = 3 18 20 1190 = o 19 50 5724 6 5796 9

1200 — 1250

N.	0 | 1	234	567	8 | 9	P. P.
1200	079 1812	2174	2536 2898	3260	3622	3983	4345	4707	5068
OI 02	5430 9045	5792 9406	6i53 9767	0128	6876 0490	7238 0851	7599 T2I2	7961 T573	8322	18683 2295		362 36.2	361 ,5 T	360
03	080 2656	3017	3378	3739	4100	4461	4822	5183	5543	5904	2	72.4	o^.1 72.2	72.0
04	626^	6626	6986	7347	7707	8068	8429	8789	9150	95io	3 4	108.6 144,8	108.3 144.4	108.0 144.0
05	9870	0231	0591	0952	T3I2	1672	2O32	2393	2753	3113	5	181.0	180.5	180.0
06	081 3473	3833	4193	4553	4913	5273	5633	5993	6353	6713	6 7	217.2 253.4	216.6 252.7	216.0, 252.0
07	7073	7432	7792	8152	8512	8871	9231	9591	9950	0310	8 Q	289.6 •>•>? 8	288.8	288.0
08	082 0669	1029	1388	1748	2107	2467	2826	3185	3541	3904	y j~j»v o*-*t»y IO^T-^
09	4263	4622	4981	534i	5700	6059	6418	6777	7136	749^
1210	7854	8213	857i	8930	9289	9648	0007	0365	0724	1083		359	358 ic 8	357
ii	083 1441	1800	2159	2517	2876	3234	3593	3951	4309	4668	2	35-S 7i.8	35-° 71.6	35-7 7L4
12	5026	538?	5743	6101	6459	6817	7176	7534	7892	8250	3	107.7	107.4	107.1
13	8608	8966	9324	9682	0040	0398	0756	1114	1471	1829	4 5	*43«^ 179.5	r43.2 179.0	i78"s
H	0842187	254^	2902	3260	3618	3975	4333	4690	5048	5405	6 7	215.4 251.3	214.8 250.6	214.2 249.9
15	5763	6120	6478	6831	7192	7550	7907	8264	8621	8979	8	287.2	286.4	285.6
16	9336	9693	0050	0407	0764	TI2I	T478	T835	2192	2549	9	323.1	322.2	321.3
17	085 2906	3263	3619	3976	4333	4690	5046	5403	5760	6116
18	6473	6829	7186	7542	7899	8255	8612	8968	9324	9681		356	355	354
19	086 0037	0393	0750	1106	1462	1818	2174	2530	2886	3242	i	35.6 7T O	35-5	35.4 70 8
1220	3598	3954	43io	4666	5022	5378	5734	6089	6445	6801	3	*•** 106.8	71.0 106.5	106.2
21	7157	7512	7868	8224	8579	893?"	9290	9646	0001	3357	4 S	142.4 178.0	177.5	177.0
22 23	0870712 426J	1067 4620	1423 497S	1778 5330	2133 5681	2489 6040	2844 6395	3199 6750	3554 7104	3909 7459	6	213.6 249.2 284.8	213.0 248.5 284.0	212.4 247.8 283.2
24	7814	8169	8524	8878	9233	9588	9943	0297	0652	Too6	9	320.4	319.5	318.6
25	088 1361	1715	2070	2424	2779	3133	3488	3842	4196	4550
26	4901	5259	5613	5967	6321	6676	7030	7384	7738	8092		353	352	351
27 28	8446 089 1984	8800 2337	9153 2691	9507 304'	9861 3398	0215 3752	3569 4105	0923 4459	7276 4812	1630 5165	i 2 3	35.3 70.6 I05-9	35.2 7°.4 105.6	35. ! 70.2 I05-3
29	5519	5872	6226	6579	6932	7285	7639	7992	8345	8698	4	141.2	140.8	140.4 T*7C C
1230	9051	9404	9757	OIIO	0463	0816	1169	1522	T875	2228	5 6	17^.5 2II.8	211. 2	17o«5 210.6
•71	090 2^81	•7n*2 7	•2-?8fi	•5 f\^ n			A f\r\n	co/i n	r* A r\^	C7Cf	7 3	247.*	24O.4	2o^'g
J A 32	6107	•^766 6460	^zoo 6812	3°39 7164	3991 75*7	4344 7869	4097 8222	ou^y 8574	:»'tu-i 8926	D/ 3D 9279	9	317.7	316.8	315.9
33	9631	9983	5335	0687	1039	1392	1744	2096	2448	2800
34	0913152	3504	3855	4207	4559	490	5263	5614	5966	6318		350	349	348
35	6670	7021	7373	7724	8076	8427	8779	9130	9482	9833	i	35.0	34.9	34.8
36	0920183"	0536	0887	1239	1590	1941	2292	2644	2991	3346	2 3	70.0 105.0	69.8 104.7	69.6 104.4
37	3697	4048	4399	4750	5101	5452	5803	6154	6505	6856	4	140.0	139.6	139.2
38	7206	7557	7908	8259	8609	8960	93H	9661	0012	S363	5 6	210.0	*74«5 209.4	208.8
39	0930713	1064	1414	1764	2IIJ	2465	2816	3166	3516	3867	7 g	245.0	244.3	243.6 278 4
1240	4217	4567	4917	5267	56l8	5968	6318	6668	7018	7368	9	315.0	279*2 314.1	*i/°.T1 313.2
41	7718	8068	8418	8768	9117	9467	9817	0167	5517	0866
42	094 1216	1566	1915	226^	2614	2964	3313	3663	4012	4362		347
43	47 1 1	5061	5410	5759	6109	6458	6807	7156	7506	7851	i	34.7
- 44	8204	8553	8902	9251	9600	9949	0298	0647	0996	T345	2 3	69.4 104.1
45	095 1694	2042	2391	2740	3089	3437	3786	4131	4483	4832	4	138.8
46	5180	5529	5877	6226	6574	6923	7271	7620	7968	8316	5 6	173.5 208.2
47 48	8665 0962146	9013 2494	936i 2842	9709 3190	0057 3538	0406	0754 4233	TI02 4581	T45Q 4929	1798 5277	7 8 9	242.9 277.6 312.3
49	5624	5972	6320	6667	7015	7363	7710	8058	8405	8753
1250	9100	9448	9791	0142	0490	0837	1184	T53I	T879	2226
N.	0	1	234	5	6	rj	8	9	P. P.
12000"= 3°20' 0" 1200"= 0°20' o" S.	= 4.685 5724 2 T. =4.685 5797 7
12100 = 3 21 40 1210 = o 20 10 " 5723 8 5798 5
12200 = 3 23 20 1220 = o 2o 20 5723 3 5799 3
12300 = 3 25 o 1230 = o 20 30 5722 9 5800 i
12400 = 3 26 40 1240 = o 20 40 5722 5 5801 o

10

1250 — 1300

X.	0	1 -2 314	5 <3 ; 7 8 j 9		1	. P.
1250	096 9100; 9448 9795 0142 0490	0837 1184! 1531 T879 2226
5* 53	097 2573 6043	2920 6390 9857	3267 6737 0204	3614 3962 7084 7431 0550 0897	4309 4656 7777 8124 1243 1590	5003 8471 T936	5349 ! 5696 881719164 2283 2629	i 2	348 | 347 34.8 34.7 69.6 69.4	346 34.6 69.2
54	098 2975	3322	3668	4014 4360	4707 5053	5399	5745 6091	4	104.4	104.1 138.8	103.8 138.4
55 56	6437 9896	6783 0242	7129 j 7475 7821 0588 0934 1279	8167 1625-	8513 T97I	8859 2316	9203 9551 2662 3007	5 174.0 I73o!l73.° 6 208.8 2o8.2J207,6 7 243.61242.9 242.2
57 58	099 3353 6806	3698 7152	4044 4389 4735 7497 7842 8187	5080 5425 8532! 8877	5771 9222	6116 9567	6461 9912	8 g	278.4	277.6 276.8
59	1000257	0602	0947	129211637	198212327	2671 3016 3361
1260	3705	4050	439?	4739 ' 5084	5429 i 5773 |6n8 6462	6806		345	3441343 3 A A.I *» j -»
6i	7151	7495	7840	8184:8528	8873	9217	9561	9905 0249	2	69.0	OT'4 68.8	JtO 68.6
62 63	101 0594 4034	0938 4377	1282 4721	1626 1970 5063 5409	23H 5752	2658 6096	3002 6440	3346 6784	3690 7127	3 4 5	103.5 103.2 138.01137.6 I72.5JI?2.0	102.9 137.2 I7L5
64	7471	7814	8158	8501 8843	9188	9532 9875	0219 0562	6 7	207.0 24L5	240.8	240.1
65	IO2 0905	1249	1592	193512278	2621	2965	3308	3651	3994	8	276.0	275.2	274.4
66	4337	4680	5023	5366(5709	6052		6738	7081	7423	9 310.51309.6:308.7
67 68	7766 103 1193	8109 1535	8452 1877	8794J9I37 2220! 2562	9480 2905-	9822 3247	0165" 3589	0507 3932	0850 4274		342	341	340
69	4616	4958 5301	5643 1 598?	6327	6669	7011	7353	7695	i 2	34.2	34.i 68.2	34.o 68.0
1270	8037	8379	8721	9063 940^	9747	0089 | 0430	0772	TII4	3	102.6 136 £	102.3	102.0
/i	104 1456	1797	2139	2480	2822	3164	3505 3847	4188	4530	5	171.0	136.4 170.5	170.0
72	4871	5213	5554	5895	6237	6578	6919	7260	7602	7943	0	205.2	204.6 n-S ~	204.0
73	8284	8625	8966	9307	9648	9989	0331	0671	TOI2	T353	7 *-3y-t •'O"./ 8 273.6 272.8	272.0
74	105 1694	2035	2376	2717	3058	3398	3739	4080	4421	4761	9,307.8(306.9	306.0
75	5102	5442	5783	6124	6464	6805	7H5	7486	7826	8166
76	8507	8847	9187	9528	9868	0208	0548	0889	1229	T569		339	3381337
77	106 1909	2249	2589	2929	3269	3609	3949	4289	4629	4969	i	33.9 £.- Q	33.8	33.7
78	5309	5648	5988	6*28	6668	7°°7	7^47	7687	8026	8366		O7.O	7-
79	8705	9041	9385 9724 0063	0403 0742	To82	T42I	T76o	4	135.6 169.5	i35.2ii34.8 160,0 T^9 *•
1280	107 2IOO	2439 2778	3H7 3457	3796	4I3b	4474 4813	5152	6	203.4	202.8 236 6	2O2. 2
81	5491	5830)6169	6508 I 6847	7186	752?	7864 | 8203	8541	8	237.3 271.2	2/0.4	235.9 269.6
82	8880	9219 9558	9896(0235	0574	0912	1251 1590	T928	91305.I	304.2	303.3
83	I08226/	2605	2944	3282	3620	3959	4297	4635	4974	5312
84	5650	5988	6327	6665-	7003	7341	7679	8017	89ft JD5	8693		336	335	334
85	9031	9369	9707	0045	0383	0721	TQ59	T396	T734	2072	i	33.6	33.5	33.4
86	I0924IO	2747	3085	3423		4098	4435	4773		5448	2 3	67.2 100.8	67.0 100.5	66.8 IOO.2
87	5785	6123	6460	6798	7135	7472	7810	8147	8484	8821	4	134.4 -/CO «	i34.o	133.6 ,£.— —
88	9159	9496	9833	0170	0507	0844	Tl8l	T5i8	T855	2192	5 AUO.U j.wy.3 xu/.vj 6 2OI.6;2OI.O,'2OO.4
89	II02529	2866	3203	3540	38/7	4213	4550	4887	5224	5560	7 Q	235.2 234.5 233.8 o^9 «!,-,£C ^ nt,- r.
1290	5897	6234! 6570	6907	7244	758o	7917	8253	8590	8926	91302.4 301.5 300.6
91	9262	9599	9935	0272	0608	0944	T28o	T6i7	^953	2289
92	III 2625	2961	3297	3633	3969	4306	4642	4977	5313	5649			333
93	5985	6321	6657	6993	7329	7664	8000	8336	8671	9007		I	33-3
94	9343	9678	0014	03 ^f	0685	T02I	T356 1691	2027	2362		2 3	66.6 99.9
95	112 2698	3333	3368 3704	4039	4374	4709	5045	538o 5715		4	133.2
96	6050	6385	6720	7°55 7390	7725 8060	8395	8730 9065		5 6	166.* 199.8
97	9400	9735	0069	0404 0739	To/4 1408	1743	2078	2412		7
98	U32747	3081 3416	375i 4085	4420	4754	5088	5423	5757		9	299.7
99	6092 6426 6760	7094 j 7429	7763 8097 8431	8765 9099
1300	9434 19768 0102 0436 0770	TI04 7437 T77I	2105 2439
N.	0 1 ' : 2 " 3 4	5 6 7	8 9		P	. P.
12500"= 3C28' 20" 1250"= o°20' 50" S. =4.685 5722 i T. = 4.68.5 5801	8
12600 = 3 30 o 1260 = o 21 ~o 5721 7	5802	7
12700 = 3 31 40 1270 = 0 21 10 5/21 2	5803	5
12800 = 3 33 20 1280 = o 21 20 5720 8	5804	4
'00 = 3 35 o 1200 = o 21 3., 57-0 4	5*05	3

n

1300 — 1350

N.	0	1	2 | 3	4	5	6	7	8	9	P. P.
1300 OI 02 03 04 05 06 07 08 09 1310 ii 12 13 14 15 16 J7 18 19 1320 21 22 23 24 25 26 2/ 28 29 1330 31 32 33 34 35 36 37 38 39 1340 41 42 43 44 45 46 47 48 49 1350	1139434	9768	0102	0436	0770	1104	T437	T77I	2105	2439	i 2 3 4 5 6 9 i 2 3	334 33.4 66.8 100.2 133.6 107.0 200.4 233.8 267.2 300.6 332 33.2 66.4 99-6	333 33.3 66.6 99>9 133.2 166.5 199.8 233.1 266.4 299.7 331 33.1 66.2 99-3
1142773 6110 9444 1152776 6105 9432 116 2756 6077 9396	3107 6443 9777 3109 6438 9764 3088 6409 9728	3441 6777 OIII 3442 6771 0097 3420 6741 0060	3774 7110 0444 377S 7103 0429 3753 7073 -0392	4108 7444 0777 4108 7436 0762 408^ 7405 0723	4442 7777 TIIO 4441 7769 1094 4417 7737 1055	4775 8111 1444 4774 8101 1427 4749 8069 T387	5109 8444 T777 5107 8434 T759 5081 8401 1718	5443 8777 2110 5439 8767 2091 5413 8733 2050	5776 9111 2443 5772 9099 2424 5745 9065 2381
1172713	3044	3376	3707	4039	4370	4702	5033	5364	5696
6027 9338 118 2647 5954 9258 H92559 5858 9154 1202448	6358 9669 2978 6284 9588 2889 6187 9484 2777	6689 0000 3309 6615 9918 3219 6517 9813 3106	7021 033i 3639 6945 0248 3549 6847 oi43 3436	7352 0662 3970 7276 0578 3879 7177 0472 3765	7683 0993 430i 7606 0909 4209 7506 0801 4094	8014 1324 4631 7936 1239 4539 7836 TI3I 4423	8345 T65I 4962 8267 T569 4868 8165 1460 4752	8676 1986 5293 8597 T899 5198 8495 T789 5081	9007 2316 5623 8927 2229 5528 882^ 2119 54io	5 6 7 8 9 i 2 3 4 5 6 { 9 i 2 3 4 6 7 8 Q I 2 3 4 5 6 7 8 9 i 2 3 4 5 6 7 8 9 i 2 4 5 6 7 8 9	166.0 199.2 232.4 265.6 298.8 330 33.o 66.0 99.o 132.0 165,0 198.0 231.0 264.0 297.0 328 32.8 65.6 98.^ 131.2 164.0 196.8 229.6 262.4 295.2 326 32.6 65.2 97.8 I3°.4 163.0 195.6 228.2 260.8 293.4 324 3*2.4 64.8 97.2 I29;6 162.0 J94.4 226.8 259.2 291.6 322 32.2 64.4 96.6 128.8 161.0 193.2 225.4 257.6 289.8	165^5 198.6 23L7 264.8 297.9 329 32.9 65.8 98.7 131.6 164.5 197.4 230.3 263.2 296.1 327 32.7 65.4 98.1 130.8 163.5 196.2 228.9 261.6 294.3 325 32.5
5739	6068	6397	6726	7°55	7384	7713	8042	8371	8699
9028 1212315 5598 8880 1222159 5435 8709 123 1981 5250	9357 2643 5927 9208 2487 5763 9036 2308 5577	9686 2972 625? 9536 2814 6090 9364 2635 5903	0014 3300 6583 9864 3142 6418 9691 2962 6230	0343 3628 6911 0192 3470 6745 0018 3289 6557	0672 3957 7239 0520 3797 7073 0345 3616 6883	TOGO 4285 7568 0848 4125 7400 0672 3942 7210	1329 4614 7896 1175 4453 7727 TOOO 4269 7537	T657 4942 8224 T503 4780 8051 1327 4596 7863	1986 5270 8552 1831 5108 8382 T654 4923 8190
8516	8843	9169	9496	9822	0149	0475	0802	TI28	1454
124 1781 5042 8301 1251558 4813 8063- 126 1314 456i 7806	2107 5368 8627 1884 5138 8390 i639 4886 8130	2433 5694 8953 2209 5463 8715 1964 5210 8454	2759 6020 9279 253S 5788 9040 2288 5531 8779	3086 6346 960^ 2860 6114 9361 2613 5859 9103	34i2 6672 9930 3186 6439 9690 2938 6184 9427	3738 6998 0256 35ii 6764 ooi^ 3263 6508 9751	4064 7324 0582 3837 7089 0339 3587 6833 0076	4390 7650 0907 4162 7414 0664 3912 7157 5400	4716 7976 T233 4487 7739 0989 4237 7481 0724	97.5 130.0 162.5 i95.o 227.5 260.0 292.5 323 32.3 64.6 96.9 129.2 161.5 193.8 226.1 258.4 290.7 321 32.1 64.2 96.3 128.4 160.5 192.6 224.7 256.8 288.9
127 1048	1372	1696	2020	2344	2668	2992	33i6	3640	3964
4288 7525 1280760 3993 7223 1290451 3676 6899 1300119	4612 7849 1083 43i6 7546 0773 3998 7221 0441	4935 8172 1407 4639 7869 1096 4321 7543 0763	5259 8496 1730 4962 8191 1418 4643 7865 1085	5583 8819 2053 5285 85H 1741 4965 8187 1407	5907 9H3 2377 =5608 8837 2064 5288 8510 1729	6230 9466 2700 5931 9160 2386 5610 8832 2051	6554 9790 3023, 6254 9483 2709 5932 9154 2372	6878 0113 3346 6577 9805 3031 6255 9476 2694	7202 0437 3670 6900 0128 3354 6577 9798 3016
3338	3659	398i | 4303	4624	4946 15267	5589	5911 6232
N.	0	1	2 3	4	5 G	1 8	9	P. P.
13000"= 3°36'4o" 1300"= o°2i/40// S. = 4.685 5719 9 T. =4.685 5806 2 13100 = 3 38 20 1310 = o 21 50 5719 5 5807 i 13200 = 3 40 o 1320 — o 22 o 5719 o 5808 o 13300 = 3 41 40 1330 = o 22 10 5718 6 5808 9 13400 = 3 43 2£ 1340 = o 22 20 5718 I 5809 8

1350 — 1400

X.	0 1234	5 ! G 7 i 8 0	P. P.
1350 5i 52 53 54 55 56 57 58 59 1360 6i 62 63 64 65 66 6? 68 69 1370 71 72 73 74 75 76 77 78 79 1380 81 82 83 84 85 86 87 88 89 1390 91 92 93 94 95 96 97 98 99 1400	i303338|3659 398i 4303 4624	4946 5267 5589	59ii	6232	j 3 4 5 6 ! i 2 3 4 7 8 9 ; 2 « ej 6 7 8 Q I 2 3 4 5 6 7 8 9 3 4 5 6 I 9 i 2 3 4 5 6 7 9	8221 32.2 64.4 96.6 128.8 161.0 193.2 225.4; 257.6 289.8 320 32.0 64.0 96.0 128.0 160.0 192.0 224.0 256.0 288.0 318 31.8 63.6 95.4 127.2 159.° 190.8 222.6 254.4 286.2 316 31.6 63.2 94.8 126.4 158.0 189.6 221.2 252.8 284.4 314 31.4 62.8 94.2 125.6 157.0 188.4 219.8 251.2 282.6 312 31.2 62.4 93-6 124.8 156.0 187.2 218.4 249.6 280.8 31 i 3 2 6 3 9. 4 12 5 15 6 18 7 21' 824; 91275	321 32.1 64.2 96.3 128.4 160.5 192.6 224.7 256.8 288.9 319 31.9 63.8 95-7 127.6 159.5 191-4 223.3 255.2 287.1 317 31.7 63.4 95.i 126.8 158.5 190.2 221.9 253.6- 285.3 315 3L5 63.0 94-5 126.0 157.5 189.0 220.5 252.O 283.5 313 3L3 62.6 93.9 X25.2 156.5 187.8 219.1 250.4 281.7 311 31.1 62.2 93.3 124.4 155.5 186.6 217.7 248.8 279.9 LO c.o J.O J.o f.° ;.° 5.o ".o S.o ).°
6553 9767 131 2978 6187 9393 1322597 5798 8998 I332I95	6875 0088 3299 6507 9713 2917 6119 9317 2514	7196 0409 3620 6828 0034 3237 6439 9637 2834	7518 0730 394i 7H9 0354 3558 6758 9957 3153	7839 1052 4262 7469 0-675 3878 7078 (5277 3473	8161 T373 4583 7790 0995 4198 7398 0596 3792	8482 1694 4903 8111 1316 45i8 7718 0916 4112	8803 201^ 5224 8431 T636 4838 8038 T236 4431	9124 2336 5545 8752 T956 5158 8358 T555 4750	9446 2657 5866 9072 2277 5478 8678 T875 5°7°
5389	5708	6028	6347 6666	6985	730^	7624	7943 | 8262
8581 1341771 4959 8144 135 1327 4507 7685 1360861 4034	8900 2090 5277 8462 1641 4821 8003 1178 4352	9219 2409 5596 8780 1963 5H3 8320 1496 4669	9538 2728 59H 9099 2281 546i 8638 1813 4986	9857 3046 6233 9417 2599 5779 8956 2131 5303	0176 3365 6551 9735 2917 6096 9273 2448 5620	0495 3684 6870 0054 3235 6414 9591 2765 5937	08I4 4003 7188 5372 3553 6732 9908 3083 6255	"33 4321 75°7 0690 3871 7050 0226 3400 6572	1452 4640 7825 Too8 4189 7367 0543 3717 6889
7206	7523	7840	8i57	8473	8790	9107	9424 | 9741	0058
1370375 3541 6705 9867 1383027 6184 9339 1392492 5643	0691 3858 7022 0183 3343. 6500 965F 2807 5958	1008 41/4 7338 0499 3659 68l6 9070 3122 6272	132! 4491 7654 0815 3974 7i3i 0285 3438 6587	1641 4807 7970 TI3I 4290 7447 0601 3753 6902	1958 5124 8287 T447 4606 7762 0916 4068 7217	2275 5440 8603 T763 4922 8078 1231 4383 7532	2591 5756 8919 2079 5237 8393 T547 4698 7847	2908 6073 9235 2"395 5553 8709 T862 5013 8161	322J 6389 9551 2711 5869 9024 2177 5328 8476
8791	9106 9420 Q/35	0050	0364 0679! 0993 1308	T622
1401937 5080 8222 141 1361 4498 7632 1420765" 3893 7022	2251 5391 8536 16/5 4811 7946 1078 4208 7335	2566 5709 8850 1988 5121 8259 1391 4520 7648	2880 6023 9164 2302 5438 8572 1704 4833 7960	3191 6337 9478 2616 5752 8885 2017 5H6 8273	3509 6651 9792 2930 6065 9199 2330 5459 8586	3823 6966 0106 3243 6379 9512 2643 5772 8898	4138 7280 0419 3557 6692 9825 2956 6084 9211	4452 7594 0733 3871 7006 0138 3269 6397 9523	4766 7908 1047 4184 7319 0451 3582 6710 9836
1430148	0460	0/73| 1085	1398	1710	2022	233J	2647	2959
32/1 6392 95ii 1442628 5742 8854 145 1964 5072 8177	3584 6704 9823 2939 6053 9165 2271 5382 8488	3896 70l6 oi 31 3251 636^ 9476 2586 5693 8798	4208 7328 0446 3562 6676 9787 2897 6004 9108	4520 7640 3758 3874 6987 0098 3207 63H 9419	4832 7952 1070 4185 7298 0409 3518 6625 9729	5H4 8264 T38i 4497 7610 0720 3829 6935 0039	5456 8576 T693 4808 7921 1031 4140 7246 0350	5768 8888 200^ 5H9 8232 ^342 4450 7556 0660	6080 9199 2316 5431 8543 T653 4761 7867 0970
146 I280| 1591 1901 |22II	2521	2831 3141	3451	376i	4071
N.	0 ' 1	213 4	516 7 8 9	P. P.
13500"= 3°45' o" 1350"= oc22'3o" S. = 4.685 5717 7 '^.=4.685 5810 7 13600 = 3 46 40 1360 = 0 22 40 5717 2 13700 = 3 48 20 1370 = o 22 50 57l6 7 58i2 5 13800 = 3 50 o 1380 = o 23 o 57i6 3 58i3 5 I390- = 3 5i 40 1390 = o 23 10 57*5 8 5814 4

1400 — 1450

N.	0	1 2	3	4	5	6	1	8	9	P. I1.
1400 01 02 03 04 05 06 07 08 09 1410 ii 12 13 . 14 15 16 17 18 19 1420 21 22 23 24 25 26 27 28 29 1430 31 32 33 34 35 36 37 38 39 1440 41 42. 43 44 45 46 47 48 49 1450	146 1280	i59i	1901	2211 2521	2831	3Hi	345i	376i	4071	i 2 3 4 i 7 8 9 i 2 3 4 i 7 8 9 i 2 3 4 5 6 7 8 9 i 2 3 4 S 6 7 8 Q I 2 3 4 5 6 7 8 9 i 2 3 4 5 6 7 8 9	311 31. i 62.2 93.3 124.4 155.5 186.6 217.7 248.8 279-9 309 30.9 61.8 92.7 123.6 154.5 185.4 216.3 247.2 278.1 3of 30.7 61.4 92.1 122.8 IS3-5 184.2 214.9 245.6 276.3 305 30.5 DI.O 91.5 I22.O 152.5 183.0 213.5 244.0 274.5 303 30.3 60,6 90.9 121. 2 I5I.5 181.8 212. 1 242.4 272.7 301 3°.i 60.2 90.3 1 20. 4 iSo.S 180.6 210.7 240.8 270.9 21 I 2( 2 5< 3 8c 4 lie 5 14$ 6 i7( 7 20C 823C 926c	310 31.0 62.0 93.o 124.0 iSS.o 186.0 217.0 248.0 279.0 308 30.8 61.6 92.4 123.2 154.0 184.8 215.6 246.4 277.2 '306 30.6 61.2 91.8 122.4 153.0 183.6 214.2 244.8 275.4 304 3°.4 60.8 91.2 121. 6 152.0 182.4 212.8 243.2 273.6 302 30.2 6o.4 90.6 i2o;8 151.0 181.2 211. 4 241.6 271.8 300 30.0 60.0 90.0 120.0 150.0 180.0 210.0 240.0 270.0 >9 >.9 >.8 1-7 >.« ).5 ).4 ).3 ).^ ).i
438i 7480 H70577 36/1 6763 9853 148 2941 6027 9110	4691 7790 0886 398o 7072 0162 3250 633? 9418	5001 8100 1196 4290 738i 0471 3558 6643 9726	5311 8409 1505 4599 7690 0780 3867 6952 003?	5621 8719 1815 4908- 7999 1089 4175 7260 0343	5931 9029 2124 5217 8308 1397 4484 7569 0651	6241 9338 2434 5527 8617 1706 4793 7877 0959	655i 9648 2743 5836 8926 201? 5101 8185 T267	6861 9958 3052 614? 9235 2324 54io 8493 T575	7170 0267 3362 6454 9544 2632 57i8 8802 1883
149 2191	2499	2807	3H5	3423	3731	4039	4347	4655	4962
5270 8347 150 1422 4494 7564 151 0633 3699 6762 9824	5578 865? 1729 4801 7871 0939 400^ 7069 0130	5886 8962 2036 5108 8178 1246 43ii 7375 0436	6i93 9270 2344 5415 8485 1553 4618 7681 0742	6501 9577 2651 5722 8792 1859 4924 7987 1048	6809 9885 2958 6030 9099 2166 5231 8293 T354	7116 0192 3265 6337 9406 2472 5537 8600 T66o	7424 0499 3573 6644 9712 2779 5843 8906 1966	7732 0807 3880 6951 0019 3085 6150 9212 2272	8039 1114 4187 7257 0326 3392 6456 95i8 2578
^1522883	3189	3495	3801	4107	4412	4718	5024	5329	5635
5941 8996 1532049 5100 8149 I54H95 4240 7282 1550322	6246 9301 2354 540? 8453 1500 4544 7586 0626	6552 9607 2659 57io 8758 1804 4848 7890 0930	6858 9912 2964 6015 9063 2109 5153 8i94 1234	7163 0217 3270 6320 9368 2413 5457 8498 1538	7469 0523 3571 662^ 9672 2718 576i 8802 1842	7774 0828 3880 6929 9977 3022 6065 9106 2145	8080 TI33 4i8? 7234 0281 3327 6370 9410 2449	8385 T439 4490 7539 0586 3631 6674 97H 2753	8691 1744 4791 7844 0891 3935 6978 0018 3057
336o	3664	3968	4271	4575	4879	5182 8217 1249 4280 7308 0334 3359 6381 9401 2418	5486	5789	6093
6396 943Q 1562462 5492 8519 1 57 1 544 4568 7589 1580608	6700 9733 276? 5794 8822 1847 4870 7891 0910	7003 0037 3068 6097 9124 2149 5172 8193 1212	7307 0340 3371 6400 9427 2452 5474 8495 1513	7610 0643 3674 6703 9729 2754 5776 8797 1815	79i4 0946 3977 7006 0032 3056 6079 9099 2117	8520 T553 4583 7611 0637 3661 6683 9702 2720	8824 1856 4886 7914 0939 3963 6985 0004 3022	9127 2159 5189 8216 1242 4265 7287 0306 3323
3625	3927	4228	4530	4831	5133	5434	5736	6037	6338
6640 9653 159 2663 5672 8678 1 60 1683 4685 7686 161 0684	6941 9954 2964 5973 8979 1983 4985 7986 0984	7243 525? 3265 6273 9280 2284 5286 8285 1283	7544 0556 3566 6574 9580 2584 5586 8585 1583	7845 0857 3867 6875 9881 2884 5886 8885 1883	8146 1158 4168 7175 0181 3184 6186 9i85 2182	8448 H59 4469 7476 0481 3481 6486 948? 2482	8749 1760 4770 7777 0782 378? 6786 978? 2781	9050 2061 5070 8077 T082 4085 7086 0084 3081	935i 2362 5371 8378 T383 4385 7386 0384 338o
3680	3980 4279	4578	4878	5177	5477	5776	6075	637S
.	0	1	2	3	4	5	6	7	8	9	P. P.
14000"= 3- 53' 20" 1400"= o°23/2o// S. = 4.685 5715 3 T. =4.685 5815 4 14100 = 3 55 o 1410 = o 23 30 5714 8 5816 3 14200 — 3 56 40 1420 = o 23 40 5714 4 5817 3 14300 = 3 58 20 1430 = o 23 50 5713 9 5818 2 14400 = 400 1440 = o 24 o 5713 4 5819 2

14

1450 — 1500

N.	0	123	4	5 6	7	8 9	P. P.
1450 51 52 53 54 55 56 57 58 59	161 3680	3980	4279 4578	4878	5177	5477	5776	6075 637J		300 30.0 60.0 90.0 120.0 I5O.O 180.0 210.0 240.0 270.0 298 29.8 59.6 89.4 119.2 149.0 178.8 208.6 238.4 268.2 296 =9.6 59-2 ss.s 118.4 148.0 177.6 207,2 236.8 266.4 294 29-4 58.8 88.2 117.6 I47.° 176.4 205.8 m 292 29.2 58.4 87.6 116.8 146.0 175.= 204.4 233.6: 262.8! 290 29.0 58.0 87.0 116.0 145.° 174.° 203.0 232.0 261.0	299 29.9 59.8 89.7 119.6 *49.5 179.4 209.3 239.2 269.1 297 *9-7 59.4 89.1 118.8 I4«.5 178.2 * 207.9 ' 237.6 267.3 i 29$ 2^o If 118.0 147.5- 17740 206.5 2T,6f 265 1? ! 293V sti 87.9 117.2 146.5 175.8. 205.1 234.4; 263.7 291 29.1 58.2 87.3 116.4 !43.5 174.6 203.7 232.8 261.9 289 28.9 57.8 86.7 115.6 144.5 173-4 202.5 231.2 jOO.I
6674 9666 1622656 5644 8630 163 1614 4596 7575 1640553	6973 9965 2955 5943 8928 1912 4894 7873 0851	7273 0264 3254 6241 9227 2210 5192 8171 1148	75/2 0563 3553 6540 9525 2508 5490 8469 1446	7871 0862 3852 6839 9824 2807 5788 8767 !/43	8170 Ti6i 4150 7137 0122 3I03- 6086 9064 2041	8470 1460 4449 7436 0420 3403 6384 9362 2339	8769 T759 4748 7734 0719 3701 6682 9660 2636	9068 2058 5047 8033 1017 3999 6979 9958 2934	9367 2357 5345 8331 T3i5 4297 7277 0255 3231	i 2 3 4 5 6 7 8 9
1460	3529	3826	4123	4421	4718	5016	5313	5610	5908	6205"	i 2 3 4 5 6 I 9 2 3 4 5 6 9 , \ 9 i 2 3 4 5 6 I 9 i 2 3 4 5 6 7 S 9
61 62 63 64 65 66 67 68 69	6502 9474 165 2443 54ii 83/6 166 1340 430i 7261 167 0218	6799 9771 2740 5707 8673 1636 4597 7556 05i4	7097 0068 3037 6004 8969 IQ22	7394 036! 3334 6301 9265 2228	7691 0662 3631 6597 9562 2^21	7988 0959 3927 6894 9858 2821	8285 T256 4224 7190 oi 5 1 3H7 6077 9035 1991	8582 T553 4521 7487 0451 3413 6373 933i 2287	8880 1850 4817 7783 0747 3709 6669 9627 2582	9177 2146 5H4 8080 TQ43 4005 696^ 9922 2878
4893 7852 0809	5189 8148 IIOJ	5485 8444 1400	5781 S740 1696
1470	3173	3469 I 3764	4060	435T	4650	4946	5241	5536	5831
71 72 73 74 75 /6 77 78 79	6127 9078 168 2027 4975 7920 169 0864 38oj 6744 9682	6422 9373 2322 5269 8215 1158 4099 7038 9975	6717 9668 2617 5564 8509 1452 4393 7332 0269	7012 9963 2912 5859 8803 1746 4687 7626 0563	7308 0258 3207 6i53 9098 2040 498i 7920 0856	7603 0553 3501 6448 9392 2335 5273 8213 1150	7898 0848 3796 6742 9686 2629 5569 8507 T443	8i93 "43 4091 7037 9981 2923 5863 8801 T737	8488 T438 4386 7331 0275 3217 6i57 9094 2030	8783 T733 4680 7626 0569 3511 6450 9388 2324
1480	1702617	2911	3204	3497	3791	4084	4377	4671	4964	5-57
81 82 83 84 85 86 87 88 89	555i 8482 171 1412 4339 726^ 1720188 3110 6029 8947	5844 8775 1704 4632 7557 0480 3402 6321 9239	6i37 9068 1997 4924 7849 0773 3694 6613 9530	6430 936i 2290 5217 8142 1065" 3986 6905 9822	6723 9654 2583 5509 8434 1357 4278 7197 0113	7017 9947 2876 5802 8727 1649 457° 7488 0405	73io 0240 3168 6095 9019 1941 4862 7780 0697	7603 0533 346i 6387 93ii 2233 5154 8072 0988	7896 0826 3754 6680 9604 2526 5446 8364 T28o	8189 TlIO 4046 6972 9896 28l8 5737 8655 T57i
1490	173 1863	2154	2446	2737 3°2S	3320 3611	3903	4194	4485
91 92 93 94 95 96 97 98 99 1500	4776 7688 i/4 0598 3506 6412 93i6 1752218 5118 8016	5068 7979 0889 3797 6702 9606 2508 5408 8306	5359 8270 1180 4087 6993 9897 2798 5698 8596	5650 8561 H7I 4378 7283 0187 3088 5988 8885	594i 8852 1761 4669 7574 0477 13378 6278 J9I75	6233 9143 2052 4959 7864 0767 3668 6567 9465	6524 9434 2343 5250 815^ T057 3958 68v 9754	68iJ 9725 2634 5540 8441 T348 4248 7147 0044	7106 0016 292^ 5831 8735 1638 4538 7437 0333	7397 0307 3215 6121 9026 1928 4828 7727 0625
176 0913	I2O2 1492 I78l|2O7I	2360 ! 2649	2939	^228	35i8
x	0 1234	5678	9	P. R
1-4500"= 4°i'40" 1450"- 0^24' 10" S. =4-685 5712 9 T. =4-«>«!> sjjtzo -j 14600 = 4 3 20 1460 = o 24 20 5712 4 . 2g~n ~ 14700 = 450 1470 = o 24 30 ?g23 > 14800 = 4 6 40 1480 = o 24 40 ^82^ 2 . » - 4 8 20 1490 — o 24 50 57 i^ 9 — -

1500 — 1550

N.	0	1	2	3	4	5	6	7	8	9	P P.
1500	1760913	1202	1492	1781	2071	2360	2649	2939 3228	35i8
OI	3807	4096	4386	4675	4964	5253	5543	5832	6121	6410
02	6699	6988	7278	7567	7856	8145"	8434	8723	9012	9301		zyu	as»y
03	9590	9879	0168	0457	o"745	T034	T323	T6i2	1901	2190	i 2	29.0	28.9 57.8
04	1772478	2767	3056	3345	3633	3922	4211	4499	4788	5076	3 4	87!o 116.0	86.7