^: L. P. SHIDY USEFUL TABLES FROM BOWDITCH'S PRACTICAL NAVIGATOR A. NEW EDITION, WITH ADDITIONAL TABLES. BUREAU OF NAVIGATION, NAVY DEPARTMENT; WASHINGTON: GOVERNMENT PRINTING OFFICE 1874. v ' ' NOTE. A new edition of the Useful Tables from Bowditch's Navigator having been called for, they have been reprinted, together with Tables VII, IX, XXXII, and XXXIII, not included its the former editions. They are all printed from the original stereotype plates of the Tables to which, the suc- ceeding explanations apply. Corrections have been made in the plates for several discovered errors in the Tables, BUREAU OF NAVIGATION, January 28, 1868. FN MEMORIAM PREFACE The following explanations relative to the Tables included in this col- lection are taken from the Preface by the late Dr. Bowditch to tfce revised edition (of 1837) of the Practical Navigator: Tables I and II were calculated by the natural sines taken from the fourth edition of Sherwin's Logarithms, which were previously examined, by differences ; when the proof-sheets of the first edition were examined, the numbers were again calculated by the natural sines in the second edition of Button's Logarithms; and if any difference was found, the numbers were calculated a third time by Taylor's Logarithms. Table III contains the meridional parts for every degree and minute of the quadrant, calculated by the following rule, viz : M = T x 0.0007915704468, in which T is the log. tangent less radius of half the latitude, increased by 45, taken to seven places of figures, reckoned as integers; and M is the meridional parts of that latitude in miles. Table VII contains the amplitudes of the sun for various latitudes and decimations, calculated by Taylor's Logarithms, by this rule: Log. sec. lat. + log. sine declination - 10.0000000 = log. sine amplitude. Table IX contains the time of the sun's rising and setting, calculated by Taylor's Logarithms, by this rale: Log. cos. hour = log. tang, declin. -f- log tang, latitude - 10.0000000. Table X contains the distances at which any object is visible at sen, calculated by the rule given in 195 of Yince's Astronomy, in which the terrestrial refraction is noticed. This circumstance was neglected by Robertson, Moore, and others, and, of course, their tables are erroneous. The rule given by Mr. Vince, expressed in logarithms, is this: 0-12155 + half log. of height in feet = log. of distance in statute miles. In reducing the rule to logarithms, the radius of the earth was called 20911790 feet, which agrees nearly with the mean value given ID 1 Lande's Astronomy. Table X A contains the parallax in altitude of a planet. Table XII contains the refraction of the heavenly bodies, calculated bv Dr. Bradley's rule, supposing the refraction to be as the tangent ( the apparent zenith distance of the object, decreased by three times IV PREFACE. refraction, the horizontal refraction being supposed equal to 38'. The rule, expressed in logarithms, is this : Log. tang. (app. zen. dist. 3. refraction) 8.243834 = log. of ref. in sec. Tlie numbers calculated by this rule agree nearly with those published in Table I of Maskleyne's Requisite Tables. Table XIII contains the dip of the horizon for various heights, calcu- lated by the rule in 197 of Vince's Astronomy, in which the terrestrial refraction is allowed for. All numbers of this table differ a little from those published by Dr. Maskleyne, who had made a different allowance for that refraction. The rule given by Mr. Yince, expressed in loga- rithms, is, 1.7712711 -{- half the log. of the height in feet = log. dip in seconds. Table XIV contains the sun's parallax in altitude, calculated by mul- tiplying the natural sine of the apparent zenith distance by the sun ? s horizontal parallax 8f". The numbers in this table agree with those published by Dr. Maskleyne. Table XV contains the Augmentation of the moon's semi-diameter = 15".626 X sine })'s altitude. This table agrees nearly with that published by Maskleyne. Table XVI contains the dip for various distances and heights, calcu- lated by this rule : D = |d + 0.56514 X h d , in which D represents the dip in miles or minutes, d the v distance of the land in sea miles, and h the height of the eye of the observer in feet. Table XXII, for turning time into degrees, is the same as in other works of this kind. Table XXII contains the proportional logarithms for three hours. The numbers of this table may be found by subtracting the logarithm of the time in seconds from the log. of 10800", or, which is the same thing, by the following rule : Prop, log. T = 4. 0334738 log. of T in seconds, neglecting the three right-hand figures of the remainder. Table XXIV was compared with Sherwin's and Mutton's tables, and a few errors corrected. Table XXV contains the log. sines, log. tangents, etc., corresponding to points and quarter points of the compass. This was compared with Sherwin's, Hutton's c and Taylor's Logarithms. Plate XXVI, containing the common logarithms of munbers, was com- pared with Sherwin's, Hutton's, and Taylor's Logarithms. Table XXV11 contains the common log. sines, tangents, secants, etc. This was compared with Sherwin's, Hutton's, and Taylor's tables. Two PREFACE. V jiddilional columns are given in tins table, which are very coupon Unit in imding the time from an altitude of the sun ; also, three columns of pro- portional parts for seconds of space ; and a small table at the bottom of each page for finding the proportional parts for seconds of time. The degrees are marked to 180, which saves the trouble of subtracting the given angle from 180 when it exceeds 90. Table XXXII contains the variation of the altitude of any heavenly body, for one minute of time from noon, for various degrees of latitude and declination. The following method was used in constructing the table : A and B were calculated for each degree of declination by these formulas : Log. A = log. 1". 08349 + 2 log. cos. declination 20.00000, Log. H =log. A -f log. tang, decimation 10.00000; and then the correction of the table corresponding to the zenith distance Z (= lat. -f dec.) was found by this formula: OB A X cotang. Z 13. To facilitate the computation of these numbers, a table of the products of A by the whole numbers from 1 to 9 was calculated. Table XXXIII contains the squares of the minutes and parts of a minute of time corresponding to every second from Os. to 12m. 59s. This require: 1 , no explanation. Table LI. To change mean solar time into sidereal time. Table LII. To change sidereal time into mean solar time. Table on page 76 of the text contains the corrections in minutes, to be added to the Middle Latitude to obtain the correct Middle Latitude. REMAKES OF PROFESSOR PEIROE. By the admirable contrivance of logarithms, the name of their in- ventor was raised high in the list of the benefactors of his race and the promoters of science. All the numerical calculations in the higher departments of theoretical and practical mathematics are performed by their aid, and the success of the computer principally depends upon the skill and precision with which he uses his logarithmic tables. It is worthy of inquiry, then, whether instruction in their use should not be more common in the schools ; they ought to be studied both as the most remarkable instrument for facilitating calculations, and as a useful means of forming the mind to habits of accuracy. Discretion should be exer- cised in the choice of the tables, for, if ill-constructed and inaccurate, they will certainly lead to awkward and slovenly forms of calculation. They should be well-proportioned in their parts; and, if of small extent, they should not be carried beyond five places of decimals. It is a great mistake to carry the small tables to six or seven places of decimals; without any valuable increase of accuracy, they are thus rendered clumsy and inconvenient. Tables of seven places should be proportionally ex- tensive, as the large ones of Taylor; while those of six places are of little value for they are not delicate enough for the higher orders of calculation, and are not needed for inferior operations ; but, on the con- trary, the disproportionate labor of using them destroys that brevity of computation which is the sole recommendation of logarithms. None of the smaller tables can be compared in accuracy with those of Dr. Bow- ditch; for, besides the repeated and rigid examinations to which they have been subjected by the author and his sons, they have been so long- in common use that 110 important error can have escaped detection. Dr. Bowditch's singular practical tact is also exhibited in their skilful ar- rangement, of which they are models deserving careful study. Feeling the want of such a set of tables for popular use, 1 have urged upon their proprietors the expediency of publishing the following selection from them, which will, I hope, be regarded as judiciously made. This may not be thought an improper occasion to press upon teachers the inexpediency of forcing the youthful intellect to a premature com- prehension of abstruse mathematical reasoning, at the expense of failing to impart' familiarity with the forms of calculation, and readiness and VIII REMARKS OF PROFESSOR PEIRCE. accuracy in the use of .figures, at the flexible age when the seeds of habit most readily germinate. Teach the lad how to obtain results, and you inspire him wii;h the surest stimulus to investigate and apprehend the nature of the process. Imbue him with the spirit of accuracy, and you give him a taste for definite and precise thought, which is the solid foundation of true science, and one of the best antidotes to the laxity of reasoning and vagueness of research with which the atmosphere of the times is infected. BENJAMIN PEIRCE, Perkins Professor of Astronomy and Mafhematite, Harvard University. CAMBRIDGE, 1849. TABLE I. "r^P Difference of Latitude and Departure for Point. N.JE. , N.iW. S.|E. s.i\V. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Disl. Lat. Dep. I oi .0 00.0 61 60.9 o3 i. 121 !20. 9 o5. 9 181 180.8 08.9 24 1 240 . 7 u .8 2 02 .0 00. I 62 61 .9 o3.o 22 12.. 9 06.0 82 181.8 08.9 42 2-1 I -7 1 1 .9 3 4 6 o3 ,o 04.0 o5.o on . o oo. i 00.2 r '0 . 2 oo.3 63 64 65 66 62 , o 63. 9 64.9 65.9 o3li 03. a 03.2 23 24 25 26 122.9 123. 9 124.8 125.8 06,0 06. i 06.1 06.2 83 84 85 86 182,8 i83.8 184.8 i85.8 (19 o 09.0 09.1 09.1 43 44 45 46 I .\ i . 1 243 7 244-7 245.7 M 9 12.0 12.0 12. 1 8 07.0 08.0 oo.3 00.4 07 68 66.9 67.9 o3.3 o3.3 2,8 126.8 127.8 06.2 o6.3 87 88 186.8 187.8 09.2 09.2 47 48 246.7 247.7 12. I 12.2 9 09.0 00.4 69 68.9 o3.4 2 9 128.8 o6.3 89 188.8 09.3 4912.48.7 12.2 10 10. oo.5 70 69.9 o3.4 3o i 129.8 06.4 90 189.8 09.3 5o 249-7 12.3 n r i .0 oo . 5 71 70.9 o3.5 i3i i3o.8 06.4 191 190.8 09.4 25l 250.7 12.3 12 12.0 00.6 72 71.9 o3.5 32 i3i.8 o6.5 92 191 .8 09.4 52 25l .7 12.4 i3 i3 .0 00.6 73 72-9 o3.6 33 i32.8 o6.5 9 3 192.8 09.5 53 252.7 12.4 i4 [4.o 00.7 74 7 3. 9 o3.6 34 1 33.8 06.6 94 193.8 09.5 54 253. 7 12.5 i5 i5.o 00.7 75 74-9 o3. 7 35 1 34 .8 06.6 95 194.8 09.6 55 254.7 12.5 16 16.0 00.8 76 75-9 o3. 7 36 1 35.8 06.7 96 195.8 09.6 56 255. 7 12.6 i - 17.0 00.8 77 76.9 o3.8 37 i36.8 06.7 97 196.8 09.7 5y 2.56.7 12.6 18 18.0 00.9 78 77-9 o3.8 38 i3 7 .8 06.8 98 .97.8 09.7 58 25 7 . 7 12.7 '9 19.0 00.9 79 78.9 03.9 3 9 1 38.8 06.8 99 198.8 09.8 59 258. 7 12.7 20 20. o 01 .0 80 79-9 03.9 4o 139.8 06.9 200 199.8 09.8 60 25 9 . 7 12.8 21 21 .O 01 .0 81 80.9 04.0 i4i i4o.8 06. 9 201 200 . 8 09.9 261 260 . 7 12.8 2.2 22 .0 01 . I 82 81 .9 o4-o 42 i4i.8 07.0 02 2.01 .8 09.9 62 261 .7 12.9 23 23.0 01 . I 83 82.9 04. i 43 i4a.8 07.0 o3 202.8 IO.O 63 262.7 12.9 24 24.0 OI .2 84 83. 9 04.1 44 i43.8 07.1 o4 2o3.8 10. 64 263. 7 i3.o 25 25.0 OI .2 85 84.9 04.2 45 i44.8 07.1 o5 204.8 10. I 65 264.7 i3.o 26 26.0 oi.3 86 85. 9 04.2 46 i45.8 07.2 06 2o5.8 10. I 66 265. 7 i3. i ?7 1*7.0 oi.3 87 86.9 o4.3 4 7 146.8 07.2 07 206.8 10-2 67 266.7 i3. i 28 i28-0 01 .4 88 87.9 o4.3 48 147.8 07.3 08 207.7 10.2 68 267.7 i3.a 2 9 2.9.0 01.4 89 88.9 c4-4 49 i48.8 o 7 .3 09 208.7 io.3 69 268.7 13.2 3o 3o.o 01 .5 9 89-9 o4-4 5o 1 4 9 . 8 07.4 10 209.7 io.3 70 ?6 9 . 7 13.2 3i 3 1 .0 oi.5 9' 90.9 o4 . 5 i5i ID0.8 07.4 21 I 210.7 10.4 271 270.7 i3.3 32 J32.0 oi .6 92 91 .9 o4.5 52 i5i.8 o 7 .5 12 211 .7 10.4 72 271.7 .-3.3 33 33.o oi .6 93 92.9 o4.6 53 i52.8 07.5 13 212.7 io.5 73 272.7 i3.4 34 34.0 oi .7 94 93.9 04.6 54 i53.8 07.6 i4 ii3-7 io.5 74 7.73.7 .3.4 35 ?5.o 01 .7 95 94.9 o4-7 55 1 54. 8 07.6 1 5 214.7 io.5 75 274.7 .3.5 36 36. o oi .8 96 95.9 04.7 56 i55.8 07.7 1 6 2i5. 7 10.6 76 275.7 1 3 5 3 7 37.0 oi .8 97 96.9 04.8 5 7 .i56.8 07.7 17 216.7 10.6 77 2. 7 6. 7 i3.6 38 38.o oi .9 98 97-9 04.8 58 i5 7 .8 07.8 18 217.7 10.7 78 277-7 i3.6 39 39.0 oi .9 99 98.9 04.9 5 9 1 58.8 07.8 ' '9 218.7 10.7 79 278.7 i3.7 4o 4o . o 02. .0 IOO 99.9 04.9 60 159.8 07.9 20 219.7 10.8 80 >79-7 i3. 7 4i 4 1 .0 02 .0 IOI 100.9 o5.o 161 160.8 07.9 221 220.7 10.8 2.8 I 380.7 i3.8 42. 41.9 05. I 02 IOI .9 o5.o 62 161.8 07.9 22 221.7 10.9 82 281. 7 i3.8 43 42.9 02. I o3 102.9 o5.i 63 162.8 08.0 23 222.7 10.9 83 282.7 ,3. 9 44 43.9 02. . 2 o4 i o3 . 9 o5.i 64 1 63.8 08.0 24 223.7 I 1 .0 84 2.83.7 i3. 9 45 46 44.9 45.9 02 .2 02.3 o5 06 1 04 . 9 K)5.Q 05.2 o5.a 65 66 1 64. 8 i65.8 08. i 08. i 25 26 224. 7 225 .7 II .0 1 1 . 1 85 86 284.7 285.7 14.0 47 46.0 02.3 07 106.9 o5.3 6 7 166.8 08.2 27 226.7 II . I 87 786.7 14.1 48 47-9 O2 .4 08 107.9 o5.3 68 167.8 08.2 28 227.7 I I .2 88 287.7 14.1 4 9 5o 48. 9 49.9 02.4 02.5 09 10 108.9 I OQ . 9 o5.3 o5.4 69 70 ,68.8 .6 9 .8 o8.3 o8.3 3o 228.7 229.7 11.2 ii. 3 89 9 1-89.7 14.2 14.2 "5 1 5o. 9 02.5 1 1 1 I 10-9 o5.4 I 7 I 170.8 08.4 23l 23o.7 ii. 3 291 ,90.6 i4-3 59 51.9 02.6 12 III-9 o5.5 72 171.8 08.4 32 a3i.7 ii. 4 92 s> 9 i .6 i4-3 53 54 55 56 57 58 59 60 52.9 54*9 55. 9 56. 9 57-9 |58. 9 59.9 02.6 02.6 02 .7 02.8 02.8 02.9 02 .9 i3 i4 i5 16 17 18 '9 20 1 1 3 . 9 114.9 1 16.9 1 17.9 118.9 119.9 o5.5 o5.6 o5.6 o5. 7 o5.7 o5.8 o5.8 o5. 9 73 7 r 76 77 78 E 172.8 173.8 174.8 i 7 5.8 1 76 . 8 177.8 178.8 179.8 o8.5 o8.5 08.6 38.6 08.7 08.7 08.8 08.8 33 34 35 36 3-7 38 3 9 4o 232.7 233.7 234.7 235.7 236.7 237-7 238.7 239.7 ii. 4 n. 5 ii. 5 11.6 n.6 n. 7 11,7 11.8 97 98 99 3oo '.'.92 . 6 293.6 294.6 2 9 5.6 296.6 297.6 298.6 .4.4 i4-4 i4-5 i4.5 i4.6 Jill. Dist. Pop. Lat. Hist. Dep. Lat. Dist. Pop. LJII. Dist. Oep. Lat. Dist. Pop- laL E. 4N. E..iS. W JN. W..JS. [for /:j romlfr. rages] TABLE 1. Difference of Latitude and Departure for Point. N.JE. JN.iW. S.^E. S.W. Dist. Lat. Dep. Dist. Lat. Dep. Disl. Lat Dep. Dist. Lat. Dep. Dist.j Lat. Dep. I 01 .O OO.I 61 60.7 06.0 121 120.4 11.9 181 180. l l-7 241 239.8 23.6 2 02.0 OO.2 62 61.7 06. i 22 121 .4 12. 82 i8x. 17.8 42 240 . 8 23-7 3 o3.o oo.3 63 62.7 06.2 23 122.4 12. I 83 182. 17.9 43 241.8 23.8 4 o4.o 00.4 64 63. 7 o6.3 24 123.4 12.2 84 i83. 18.0 44 242.8 23.9 5 06.0 oo.5 65 64-7 o6.4 25 124.4 12.3 85 184. 18.1 45 240.8 24.0 6 06.0 00.6 66 65.7 o6.5 26 125.4 12.4 86 1 85. 18.2 46 244.8 24.1 7 07.0 00.7 67 66.7 06.6 27 126.4 12.4 87 1 86. i8.3 47 245.8 24.2 8 08.0 00.8 68 67.7 06.7 28 127.4 12.5 88 18-. 18.4 48 246.8 24.3 9 09.0 00.9 69 68.7 06.8 2 9 128.4 12.6 89 1 88. i8.5 4 9 247.8 24-4 10 10. or .0 70 6 9 /7_ 06.9 3o 129.4 12.7 9 189. 18.6 5o 248.8 24.6 ii 10.9 OI I 7i 70.7 07.0 i3i i3o.4 12.8 191 190. l8~T 25l T4o~8~ 24.6 12 11.9 01 .2 72 71.7 07.1 32 i3i.4 12.9 92 191. 18.8 62 260 8 24.7 i3 12.9 oi.3 73 72.6 07.2 33 i32.4 i3.o 93 192 18.9 53 261.8 24.8 M 1-3:9 01 .4 74 7 3.6 7 .3 34 i33.4 i3.i 94 193. 19.0 54 262.8 24.9 i5 14.9 oi.5 75 74-6 07.4 35 i34.3 13.2 95 i94. 19.1 55 253.8 26.0 16 15.9 01 .6 76 7 5.6 07.4 36 i35.3 i3.3 96 19?: 19.2 56 254.8 26.1 i? 16.9 01.7 77 76.6 07.5 37 i36.3 i3.4 97 196. i 9 .3 67 266.8 25.2 18 17.9 01.8 78 77.6 07.6 38 i3 7 .3 i3.5 98 197.0 19.4 58 266.8 25.3 19 18.9 01 .9 79 78.6 07.7 39 i38.3 i3.6 99 198.0 19.6 59 267.8 26.4 20 19.9 02 .0 80. 79.6 07.8 4o i3 9 .3 i3. 7 200 199.0 19.6 60 268.7 25.5 21 20.9 02 . 1 81 80.6 07.9 i4i i4o.3 i3.8 201 200. o 19.7 261 269.7 26.6 22 21 .9 O2 .2 82 81.6 08.0 42 i4i.3 i3. 9 02 201 .0 19.8 62 260.7 25. 7 23 22.9 02.3 83 82.6 08. i 43 142.3 14.0 03 202.0 J 9-9 63 261 .7 26.8 24 23.9 02.4 84 83.6 08.2 44 i43.3 14.1 o4 203.0 20.0 64 262.7 26.9 25 24-9 02.5 85 84.6 o8.3 45 i44.3 14.2 o5 204.0 20.1 65 263.7 26.0 26 26.9 02.5 86 85.6 o8.4 46 i45.3 i4.3 06 206 . o 20.2 66 264.7 26.1 27 26.9 02. .6 87 86.6 o8.5 47 i46.3 i4.4 07 206.0 20.3 67 266.7 26.2 28 27.9 02.7 88 87.6 08.6 48 i47.3 i4.5 08 207 . o 20.4 68 266.7 26.3 2 9 28.9 02.8 89 88.6 08.7 4 9 i48.3 14.6 09 208 . o ic 5 69 267.7 26.4 3o 29.9 02.9 _92. 89.6 08.8 5o i49.3 14.7 IO 209.0 20.6 TO 268.7 26.6 3i 3o. 9 o3.o 9 1 90.6 08.9 i5i i5oTT i4-8 211 210.0 20.7 271 269.7 26.6 32 3i.8 o3.i 92 91 .6 09.0 52 i5i.3 14.9 12 211 .O 20.8 7 2 270. 7 26.7 33.32.8 03.2 93 92.6 09.1 53 i5a.3 16.0 i3 2 12 . 20.9 73 271.7 26.8 34 33.8 o3.3 94 9 3.5 09.2 54 i53.3 i5.i i4 2l3.O 21 .0 74 272.7 26.9 35 34.8 o3.4 9 5 94.5 09.3 55 i54.3 15.2 i5 214.0 21 . 1 75 273.7 27.0 36 35.8 o3.5 96 95.5 09.4 56 i55.2 i5.3 16 2t5.0 21.2 76 274-7 27.1 37 36.8 o3.6 97 96.5 09.5 57 i56.2 i5.4 17 216.0 21.3 77 276.7 27.2 38 3 7 .8 o3. 7 98 97-5 09.6 58 167.2 i5.5 18 217.0 21.4 78 276.7 27.2 3 9 38.8 o3.8 99 98.5 09.7* 5 9 i58.2 i5.6 1 9 217.9 21.5 79 277.7 27.3 4o 3 9 .8 03.9 100 99-5 09 . 8 60 If. 9 .2 i5. 7 20 218.9 21.6 80 278.7 27-4 4i 4o.8 04.0 1 01 loo.S 09.9 161 160.2 i5.8 221 219.9 21.7 281 27 9 .6 27.5 42 4i.8 04.1 02 101 .5 10. 62 161 .2 16.9 22 220.9 21.8 82 280.6 27.6 43 42.8 04.2 o3 102 .5 10. I 63 162.2 16.0 23 221.9 21.9 83 281.6 27.7 44 43.8 o4.3 04 io3.5 10.2 64 i63.2 16.1 24 222.9 22.0 84 282.6 27.8 45 44.8 c>4-4 o5 io4.5 io.3 65 164.2 16.2 25 223.9 22.1 85 283.6 27-9 46 45.8 04.5 06 io5.5 10.4 66 166.2 i6.3 26 224.9 22.2 86 284.6 28.0 4? 46.8 04.6 07 io6.5 io.5 67 166.2 16.4 27 226.9 22.2 87 286.6 28.1 48 47-8 04.7 08 107.5 10.6 68 167.2 i6.5 28 226.9 22.3 88 286.6 28.2 49 48.8 04.8 09 io8.5 10.7 69 168.2 16.6 29 227.91 22 -4 89 287.6 28.3 5o 4<;.8 04.9 IO 1 09 . 5 10.8 70 169.2 16.7 3o 228.9 22.5 9 288. 6 : 28. 4 5T 5". 8 o5.o II I i io.5 10.9 171 170.2 16.8 23l 229.9 22.6 291 28 9 .6 28.6 62 5, .7 o5. i 12 ni.5 1 I .0 72 171.2 16.9 32 23o.9 22.7 92 290.6 ?8.6 ! 53 52. 7 05.2 i3 112. 5 ii . i 73 172.2 17.0 33 a3i.9 22.8 9 3 2 9 1 .6 28.7 54 53 7 o5.3 i4 u3.5 II .2 74 173.2 17.1 34 -^2.9 22.9 94 292.6 28.*: 55 5/i 7 o5.4 i5 n4.4 ii. 3 75 174.2 17.2 35 233.9 23. D 9 5 2 9 3.6 28.9 56 55 7 o5.5 16 u5.4 ii. 4 76 176.2 i 7 .3 36 234.9 23.1 96 294.6 29.0 57 56 7Jo5.6 17 116.4 ii. 5 77 176.1 i 7 .3 37 235.9 23.2 97 296.6 29.1 58 57 7 o5.7 18 117-4 ii. 6 78 177.1 17-4 38 2.36. 9 23 3 98 296.6 29.2 59 58 7 o5.8 *9 ,18.4 n .7 79 178.1 I 7 .5 3 9 2 3 7 .8 ?3.4 99 297.6 29.3 60 i5 9 . 7 06.9 20 119.4 ii. 8 80 179.1 17.6 4o 238.8 23.5 3oo 298.6 29.4 Di-t. D - 92.6 9 3.o 9 3.3 38 35.8 12.8 98 33.o 58 i48.8 53.2 18 2o5.3 73.4 78 261 .7 93.7 3 9 Jo. 7 i3. i 99 9 3.2 33.4 59 149.7 53.6 19 206.2 73.8 79 262 .7 9 4-o 4o 37.7 ,3.5 IOO 9 4.2 33.7 60 i5o.6 53. 9 20 207.1 74n 80 263.6 9 4-3 4i 38.6 .3.8 .01 9 5.i 34.o 16, i5i.6 54.2 221 208.1 -4-5 281 264.6 94-7 42 3 9 . b ,4.1 02 96.0 34-4 62 i5 2 .5 54.6 22 209.0 74-8 82 265.5 9 5.o 43 4o.5 ,4.5 o3 97.0 34-7 63 i53.5 54-9 23 2 IO.O -5.i 83 2.66 . 5 95.3 44 4i -4 14.8 o4 97-9 35.o 64 i54.4 55.2 24 2,0.9 7 5.5 84 267.4 9 5. 7 45 42.4 1 5 . * o5 98.9 35.4 65 ,55.4 55.6 25 21 , .8 75.8 85 268.3 9 6.o 46 43.3 i5.5 06 99.8 35.7 66 i56.3 55. Q 26 2,2.8 76.1 86 269.3 96.4 47 44.3 1 5. 8 07 100.7 36.o 67 ,5 7 .2 56.3 27 2,3.7 7 6.5 87 270.2 96.7 48 45.2 16.2 08 ,01 .7 56.4 68 .58.2 56.6 28 2l4-7 76.8 88 27. .2 9 7- 49 i 46 . i .6.5 09 1 02 .6 36. 7 69 159.1 56. 9 29 2.5.6 77-1 89 272.1 97-4 5o 47.1 16.8 10 io3.6 3 7 .I 70 160.1 5 7 .3 3o 2,6.6 77-5 9 273.0 97-7 5i 48.o 1-7.2 1 1 io4.5 3 7 .4 171 61 .0 5 7 .6 23l 2,7.5 77-8 2 9 I 274.0 98.0 52 49.0 I 7 .5 12 io5.5 3 7 .7 72 161 . 9 57-9 32 218.4 78.2 9 2 274.9 98.4 53 49.9 I 7 .9 i3 106.4 38.i 73 62. 9 58.3 33 2,9.4 -8.5 93 275.0 98-7 54 18.2 i4 107. 3 38.4 74 63.8 58.6 34 220. 3 78.8 94 2 7 6.8 99.0 55 5i.8 i8.5 i5 io8.3 38.7 75 64.8 5 9 .o 35 221.3 7 9 .2 95 277-8 99-4 56 52.7 18.9 16 109.2 3 9 .i 76 65. 7 5 9 .3 36 222.2 7 9 -5 96 278 7 99-7 5- 53.7 19.2 17 II0.2 3o.4 77 66.7 5 9 .6 3 7 223.1 79-8 97 279 6 OO.l 58 54-6 r 9 .5 18 III .1 3 9 .8 78 67.6 60.0 38 224.1 80.2 98 280 6 00.4 59 55.6 i 9 . 9 19 I I 2.0 4o.i 79 68.5 6o.3 39 225.0 8o.5 99 28) 5 00.7 60 56.5 2O. 2 20 u3.o 4o.4 80 69.5 60.6 4o 226.O Bo. 9 oo a8a.5 01. 1 D st.j Dep. 1 Lat. isl. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. K*t. Dep. Lat. E.N.K.|E. E.S.E.JE. W.N.W..4W. W.S.W.jW. [For \\ Points. Page 8] TABLE I Difference of Latitude and Departure for 2 Points. N.N.E. N.N.W. S.S.E. S.S.W. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. 1 .at. Dep. i 00.9 00.4 61 56.4 23.3 12.1 in. 8 46.3 181 167.2 69.3 24 1 222. 7 92.2 2 01.8 00.8 62 5 7 -3 23. 7 22 112.7 46.7 82 168.1 69.6 42 223.6 92.6 3 02.8 01 .1 63 58.2 24.1 23 n3.6 47-1 83 169.1 70.0 43 224.5 93.0 4 o3. 7 oi.5 64 5 9 .J 24.5 24 114.6 4 7 -5 84 170.0 70.4 44 >25.4 93.4 5 04.6 01 .9 65 60. i 24.9 25 ii5.5 47-8 85 170.9 70.8 45 226.4 9 3.8 6 o5.5 02.3 66 61 .0 25.3 26 116.4 48.2 86 171.8 71.2 46 227.3 o4-i 7 o6.5 02.7 67 61 .9 25.6 2 7 n 7 .3 48.6 87 172.8 71.6 47 228.2 94-5 8 07.4 o3.i 68 62.8 26.0 28 ii8.3 49.0 88 173.7 71.9 48 229. 1 94.9 9 o8.3 o3.4 69 63. 7 26.4 2 9 119.2 49.4 89 174-6 72.3 49 2.30.O 95.3 10 09.2 o3.8 70 64-7 26.8 3o 1 20. i 49.7 90 175.5 72.7 5o 23l .0 9 5 -7 1 1 IO. 2 04.2 7i 65.6 27.2 i3i 121 .0 5o.i 191 176.5 7 3.i 21 23l .9 96.1 j ^ 1 I . I 04.6 72 66.5 27.6 32 122.0 5o.5 92 177-4 7 3.5 52 232.8 96.4 i3 12 .O o5.o 73 67.4 27.9 33 122.9 60.9 93 178.3 73.9 53 233.7 96.8 14 12.9 o5.4 74 68.4 28.3 34 123.8 5i.3 94 179.2 74.2 54 234.7 97.2 i5 i3.o o5. 7 75 69.3 28.7 35 1 24 . 7 5i. 7 95 180.2 74-6 55 235.6 97 .6 16 14.8 06. i 76 70.2 29.1 36 125.6 52.0 96 181.1 7 5.o 56 236.5 98.0 i? l5.T o6.5 77 11 .1 29.5 3 7 126.6 5 2 .4 97 182.0 7 5.4 5 7 2 3 7 .4 9 8,3 18 16.6 06.9 78 72.1 29.8 38 127.5 52.8 98 182.9 75.8 58 238.4 9 8. 7 W 17.6 o 7 .3 79 7 3.o 30.2 3 9 128.4 53.2 99 183.9 7 6.2 5 9 s3 9 .3 99.1 2O i8.5 07.7 80 73. 9 3o.6 4o 129.3 53.6 200 184.8 76.5 60 240 . 2 g9.5 21 19.4 08.0 61 74-8 3i.o Mi i3o.3 54-0 201 185.7 76.9 261 24l .1 99-9 22 20.3 08.4 82 7 5.8 3i.4 42 l3l.2 54.3 02 186.6 77-3 62 2.42 . I ioo.3 23 21 .2 08.8 83 76.7 3i.8 43 I32.I 54.7 03 187.5 77-7 63 243.0 100.6 24 22 .2 09.2 84 77.6 32.1 44 1 33.o 55.i o4 i88.5 78.1 64 243. 9 I 01 25 23.1 09.6 85 7 8.5 32.5 45 1 34.0 55.5 OD 189.4 78.5 65 244.8 101 4 26 24.0 09.9 86 79-5 32. 9 46 1 34.Q 55. 9 06 190.3 78.8 66 245.8 1 01. 8 27 24.9 10.3 87 8o.4 33.3 47 i35.8 56.3 07 191 .2 79-2 67 246. 7 102.2 28 25. 9 10.7 88 8i.3 33.7 48 1 36.7 56.6 08 192.2 79.6 68 247-6 102.6 2 9 26.8 1 1 . i 89 82.2 34.i 49 1 37:7 5 7 .o 09 i 9 3.i 80.0 69 248.5 102.9 3c 27.7 n. 5 9 83.i 34-4 5o 1 38.6 5 7 -4 IO 194.0 80.4 70 249.4 io3.3 3i 28.6 11.9 91 84.1 34.8 ibi i3 9 .5l5 7 .8 21 I 194.9 8o. 7 271 25o.4 K)3 - 32 29,6 12.2 92 85.o 35.2 52 i4o.4 58.2 12 i 9 5. 9 81.1 72 2 5i.3 K>4 1 33 3o.5 12.6 93 85.9 35.6 53 i4i.4 58.6 i3 196.8 8i.5 73 252.2 io4 5 34 3i.4 i3.o 94 86.8 36.o 54 142.3 58. 9 M 197.7 8i. 9 74 253.1 104.9 o^ %*N^ 3^.3 i3.4 95 87.8 36.4 55 M3.2 5o.3 i5 198.6 82.3 75 254.1 105.2 36 33.3 i3.8 96 88.7 36.7 56 i44-i 5 9 -7 16 199.0 82.7 76 255.0 io5.6 37 34.2 14.2 97 89.6 3 7 .i 57 i45.o 60. i 17 200.5 83.o 77 255.0 1 06.0 38 35.i i4.5 98 90.5 3 7 .5 58 i46.o 6o.5 18 201 .4 83.4 78 256.8 106.4 39 36.o i4-9 99 9 i.5 37-9 5 9 146.9 60.8 19 202.3 83.8 79 2.57.8 106.8 4o 3 7 .o i5.3 100 92.4 38.3 60 147-8 6.1. a 20 203.3 84.2 80 2.58.7 107.2 4i 37-9 i5. 7 101 9 3.3 38. 7 161 148-7 61.6 221 204.2 84.6 281 2.5 9 .6 107.5 42 38.8 16.1 02 94.2 39.0 62 149.7 62.0 22 205. I 85.o 82 260 . 5 107.9 43 39-7 i6.5 o3 95.2 39.4 63 i5o.6 62.4 23 206.0 85.3 83 261.5 u,8 '3 44 40.7 16.8 o4 96.1 3 9 .8 64 i5i.5 62.8 24 206.9 85. 7 84 262.4 108.7 45 4i .6 17.2 o5 97.0 40.2 65 i52.4 63.i 25 207.9 86.1 85 263.3 IOQ.1 46 42.5 17.6 06 97.9 4o.6 66 i53.4 63.5 26 208.8 86.5 86 264 . 2 109.4 47 43.4 18.0 07 98.9 40.9 67 i54.3 63. o 27 209.7 86.9 8 7 365.2 109.8 48 44.3 18.4 08 99- 8 4i.3 68 i55.2 64.3 28 2IO.6 8-^.3 88 266.1 I 10.2 49 45.3 18.8 09 100.7 4i-7 6 9 i56.i 64-7 2 9 21 I .6 8 7 .6 8 9 | 26-7.0 1 10.6 5o 46.2 19.1 10 101 .6 42.1 70 167.1 65.. 3o 212.5 88.0 9 2.67.9 I I 1 .0 5i 47.1 IQ.5 II I 102.6 42.5 171 i5b.o 65.4 23l ai3.4 88.4 291 268.8 1 1 1. 4 52 48.0 19.9 12 io3.5 42.9 72 1 58.0 65.8 32 2i4.3 88.8 92 269.8 111.7 53 49.0 20.3 i3 104.4 43.2 73 i5 9 .8 66.2 33 215.3 89.2 93 2.70.7 1 12.1 54 49.9 20.7 i4 io5.3 43.6 74 160.8 66.6 34 2ID.2 89.5 94 271 .6 I 12.5 55 5o.8 21 .O i5 106.2 44-0 75 161 .7 67.0 35 217.1 80.9 9 5 272.5 1 12.9 56 5i. 7 21.4 ;6 107.2 44-4 76 162.6 67-4 36 218.0 9 o.3 96 2 7 3.5 ii3.3 5 7 52. 7 21.8 17 108.1 44.8 77 i63.5 67-7 3 7 219.0 9-7 97 274.4 u3. 7 58 53.6 22.2 18 109.0 45.2 78 i64.5 68.1 38 219.9 91.1 98 2 7 5.3 1 1 4 '-> 5 9 54.5 22.6 19 109.9 45.5 79 i65.4 68.5 39 220.8 91 is 99 2 7 6.2 11 4 -4 Go| 55.4 23.0 20 110.9 45-9 80 i66.3 68.9 4o 221 .7 91.8 3oo 277.2 ii 4-8 DiSt.. I)C|>. Lat. Dist. Dop. 1 Lat. Dist. Dep. Lat. Dist. Dcp. Lat. Dist. Dep. Lat. E.iN.E. E.S.E. W N.W. W.S.W. [For (5 Points. TABLE J. [Page 9 Difference of Latitude and Departure for 2 Points. N.N.E.iE. N.N.W.4W. S.S.E.^E. S.S.W.^W. Dist. Lat. Dep. Disi. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. I Dep. i 00.9 00.4 61 55.1 26.1 121 109.4 5. .7 101 r63.6 77.4 241 21-7.9 icS.o 2 3 . 4 5 6 01 .8 02 .7 o3.6 o4.5 o5.4 o6.3 00.9 01 .3 01.7 02. I 02 .6 o3 o 62 63 64 65 66 67 56.o 5 7 .o 57.9 58.8 5 9 -7 60.6 26.5 26.9 2 7 .4 27.8 28.2 28.6 22 23 24 25 26 27 no. 3 III .2 I 12 . I i i3.o 114.8 52.2 52.6 53.o 53.4 53. 9 54.3 82 83 84 85 86 87 i64.5 i65.4 i66.3 167.2 168.1 169.0 77.8 78.2 78.7 79.1 79.5 80.0 42 43 44 45 46 47 218.8 220.6 221.5 222.4 223.3 io3.5 103.9 io4.3 104.8 I05.2 io5.6 8 07.2 o3.4 68 6i.5 29.1 28 u5. 7 54. 7 88 169.9 80.4 48 224.2 1 06.0 9 08. i o3.8 b 9 62.4 29.5 29 116.6 55.2 89 170.9 80.8 225.1 i o6.5 10 09.0 o4-3 70 63.3 29.9 3o ii 7 .5 55.6 90 171.8 81.2 5o 226.O 106.9 1 1 09.9 04.7 71 64.2 3o.<| i3i 118.4 56.o 191 172. 7 81.7 25l 226. 9 io 7 .3 1.3 10.8 o5.i 72 65.i 3o.8 32 u 9 .3 56.4 92 173.6 82.1 5?. 22 7 .8 107.7 i3 ii. 8 o5.6 73 66.0 3l.2 33 120.2 56.9 Q 3 174.5 82.5 53 228.7 108.2 i4 12.7 06.0 74 66.9 3i.6 3^4 121 . I 5 7 .3 94 175.4 82.9 54 229.6 1 08 .6 i5 1 3. 6 06.4 75 67.8 32.1 35 122.0 57-7 95 176.3 83.4 55 9 In 5 109.0 16 i4.5 06.8 76 68.7 32.5 36 122. 58.i Q6 177.2 83.8 56 23i.4 109.5 17 i5.4 o 7 .3 77 69.6 32. 9 3 7 123.8 58.6 97 178.1 84.2 57 232.3 109.9 18 i6.3 07.7 78 70.5 33.3 38 124.8 59.0 98 1-79.0 84-7 58 233.2 i io.3 19 17.2 08. i 79 71-4 33.8 3 9 125.7 5 9 .4 99 '79-9 85.i 59 234.1 I IO. 7 20 18. i j 08.6 80 7 2.3 34.2 4o 126.6 5 9 . 9 200 180.8 85.5 60 235.0 1 1 1.3 21 19.0 09.0 81 7 3.2 34.6 i4i 127,5 6o.3 201 181.7 85. 9 261 235. 9 1 1 1.6 22 19.9 09.4 8-j 74-1 3D. I 42 128.4 60.7 O2 182.6 86.4 6a 2.36.8 112.0 23 20.8 09.8 83 7 5.o 35.5 43 129.3 61.1 o3 1 83 .'5 86.8 63 23 7 . 7 II2.4 24 21 .7 io.3 84 75-9 35. 9 44 i3o.2 61.6 o4 184.4 87.2 64 238.7 1 12.9 25 22.6 10.7 85 76.8 36.3 45 i3i . i 62.0 o5 i85.3 87.6 65 23 9 .6 n3.3 26 2 3.5 ii . i 86 77-7 36.8 46 l32.0 62.4 06 186.2 88.1 66 24o.5 u3. 7 27 24.4 ii. 5 87 7 8.6 3 7 .2 47 132.9 62.9 07 187.1 88.5 67 24i-4 I 1 4. 2 28 2 5.3 12.0 88 79.6 3 7 -6 48 i33.8 63.3 08 188.0 88.9 68 242.3 ti4.6 29 26.2 12.4 89 8o.5 38.i 49 1 34. 7 63.7 09 188.9 8 9 .4 69 243.2 1 1 5.o 3o 27.1 12.8 90 81.4 38.5 5o i35.6 64.i 10 189.8 8 9 .8 70 244.1 ii 5.4 3 1 28.0 i3.3 9 1 82.3 38.9 i5i 1 36.5 64.6 211 190.7 9 0.2 271 245.0 i i5.o 32 28.9 i3. 7 92 83.2 3 9 .3 52 i3 7 .4 65.o 12 191.6 9 o.6 72 245.9 u6.3 33 29.8 93 84.1 3 9 .8 53 1 38,3 65.4 i3 192.5 91.1 73 246.8 I 1 6. 7 34 30.7 .4.5 Q4 85.o 40.2 54 139.2 65.8 i4 i 9 3.5 9i.5 74 247-7 117.2 35 3i.6 1 5.o Q5 85.9 4o.6 55 i4o.i 66.3 i5 194.4 91.9 75 248.6 I 17.6 36 32.5 i5.4 86.8 4 1 .0 56 i4i -o 66.7 16 195.3 92.4 76 24 9 .5 118.0 3 7 33.4 i5.8 97 87- 7 4i.5 5 7 i4i. 9 67.1 17 196.2 92.8 77 2.5o.4 118.4 38 34.4 16.2 Q8 88.6 4i-9 58 142.8 6 7 .6 18 197.1 93.2 78 s5i .3 118.9 3o 35.3 16.7 99 89.5 423 59 i43.7 68.0 19 198.0 93.6 79 252.2 1 19.3 4o 36.2 17.1 IOO 90.4 42.8 60 1 44.6 68.4 20 198.9 9 4.i 80 253.1 1 19.7 4i 3 7 .i i7.5 101 9 i.3 43.2 161 i45.5 68.8 221 199-8 94-5 281 254.0 1 20. i 4 a 38.o 18.0 02 92.2 43.6 62 146.4 69.3 22 200.7 94.9 82 254. 9 120.6 43 38.9 18.4 o3 44-0 63 i4 7 -4 69-7 23 2OI .6 9 5.3 83 255.8 121.0 44 18.8 o4 94.0 44-5 64 i48.3 70.1 24 2O2.5 9 5.8 84 256. 7 I 2 1. 4 45 46 40.7 4i .6 19.2 19.7 o5 06 94.9 95.8 44-9 45.3 65 66 149.2 i5o.i 7 o.5 71.0 25 26 2o3.4 2o4.3 96.2 96.6 85 86 25 7 .6 258.5 I2I-9 122.3 47 48 42.5 43.4 20. i 20.5 07 08 9 6. 7 97-6 45.7 46.2 6 7 68 i5i .0 l5i.O 7 i.4 7 i.8 27 28 205 . 2 206. 1 97.1 97 .5 87 88 2 5 9 .4 260.3 [22.7 12.3.. 44.3 21 .O 09 9 8.5 46.6 69 i52.8 72.3 29 207.0 97-9 89 261.3 12.3.6 5o 45.2 21.4 10 99.4 47.0 70 1 53.7 72-7 3o 207.9 9 8.3 9 262 . 2 1 24.0 5i 46.i 21.8 in 100.3 47-5 i 7 i 1 54- 6 7 3.i 23 I 208.8 98.8 291 ?,63 . i 124-4 52 53 47-0 47 22.2 22 .7 12 1 3 101 .2 102.2 47-9 48.3 72 73 i55.5 1 56.4 7 3.5 7 4.o 32 33 209.7 2IO.6 99.2 99.6 93 264.0 264.9 124.8 125.3 54 48.8 23.1 i4 103.1 48.7 74 1 5 7 .3 74-4 M 211. 5 100.0 9 4 265.8 I2D.7 55 56 58 49.7 5o.6 5i.5 52 4 2.3.5 23. 9 24-4 24 8 1 5 16 17 18 104.0 104.9 io5.fi io6. 7 4 9 .2 49.6 5o.o 5o.5 75 76 77 78 1 58.3 159.1 160.0 160.9 74-8 75.3 75-7 76.1 35 36 3 7 38 212.4 ai3.3 2l4-2 215.1 i co. 5 100.9 toi.3 101.8 $ 266 . 7 26-7.6 268 . 5 269.4 I 20. 1 1266 I2 7 I 27 4 53 3 54.2 25.2 2.5. 7 20 io 7 .6 io8.5 50.9 5i.3 79 80 idi.8 162.7 7 6.5 77.0 3 9 4o ai6.i 217.0 102.2 102.6 99 3oo 270.3 2 7 I .2 I2 7 .8 i?8.3 Dist. Den. | Lat. Dist. Dep. 1 Lat. Dist Dep. 1 Lat. Dist. Dep. Lat. Disi. Den. Lai. NEbvE.?E. S.E.byE.|E. N.W.byW.ifW. S.W.byW.JW. (For V> Points. Page 10] TABLE I. Difference of Latitude and Departure for 2 Points. N.N.E.E. N.N.W^W. S.S.E.^E. S.S.W.JW. Dist. Lat. Deo. Dist. Lat. Dep. Dist. Lat. Dep. Dist Lat. Dep. Dist. La. Dep. I oo . 9 oo.5 61 53.8 28.8 121 106.7 5 7 .o 181 159.6 85.3 241 212.5 ii3.6 2 01.8 00.9 62 54 7 29.2 22 1 07 . 6 5 7 .5 82 i6o.5 85.8 42 2134 u4.i 3 02.6 01 .4 63 55.b 29.7 23 io8.5 58.o 83 161.4 86.3 43 214 3 u4.5 4 o3.5 01 .9 64 56.4 3o.2 24 109.4 58.5 84 162.3 86.7 44 215.2 i i5.o 5 04.4 02 .4 65 5 7 .3 3o.6 25 I 10.2 58.9 85 i63.2 8 7 .2 45 216 i 1 1 5.5 6 o5.3 02.8 66 58.2 3i.i 26 II I .1 5 9 -4 86 164.0 87.7 46 2 1 7 . 1 16.0 7 06.2 o3.3 67 5 9 .i 3i.6 2 7 [ 12. 59.9 87 164.9 88.2 4 7 217.8 116.4 8 07.1 o3.8 68 60.0 32.1 28 112.9 6o.3 88 i65.8 88.6 48 218.7 16.9 9 07.9 04.2 69 60.9 32.5 2 9 n3.8 60.8 89 166.7 89.1 49 219.6 17-4 10 08.8 04.7 70 6,. 7 33.o 3o 114.6 6r.3 9 167.6 89.6 5o 220.5 57.8 1 1 09.7 05.2 ?i 62.6 33.5 i3i ii5.5 61.8 191 i68.4 90.0 25l 221 .4 i8.3 12 10.6 o5. 7 72 63.5 33. 9 32 116.4 62.2 92 169.3 90.5 52 222.2 18.8 i3 1 1 .5 06. i ?3 64 ..4 34-4 33 n 7 .3 62. 7 9 3 170.2 91.0 53 223.1 i 9 .3 i4 12.3 06.6 74 65.3 34.9 34 118.2 63.2 94 171.1 91.5 54 224.0 119.7 i5 l3.2 07.1 75 66.1 35.4 35 1 19. 1 63.6 95 172.0 91.9 55 22.4.9 120.2 16 14.1 o 7 .5 76 67.0 35.8 36 119.9 64.1 96 I72. 9 92.4 56 225.8 I20. 7 i? 1 5.0 08.0 77 6 7 : 9 36.3 3 7 120.8 64.6 97 173.7 92.9 5 7 226. 7 121. 1 18 i5,o o8.5 78 68.8 36.8 38 121.7 65.i 98 174-6 93.3 58 22 7 .5 121. 6 X 9 16.8 09.0 79 69.7 3 7 .2 3 9 122.6 65.5 99 i 7 5.5 93.8 59 228.4 I 22. 1 20 .7.6 09.4 80 70.6 3 7 . 7 4o 123.5 66. o 200 176.4 94-3 60 229.3 122.6 21 i8.5 09.9 81 71-4 38.2 i4i 124.4 66.5 201 177.3 94-8 261 230.2 123.0 22 19.4 10.4 82 72.3 38. 7 42 125.2 66.9 02 178.1 9 5.2 62 231.1 123.5 23 20.3 10.8 83 7 3.2 3 9 .i 43 126.1 t7.4 03 I 79 .0 95.7 63 23l .9 124.0 24 21 .2 n. 3 84 74.i 3 9 .6 44 127.0 67-9 04 179-9 96.2 64 232.8 124.4 25 22.0 ri.8 85 7 5.o 4o.i 45 127.9 68.4 o5 180.8 96.6 65 233.7 124.9 26 22.9 12.3 86 7 5.8 4o.5 46 128.8 68.8 06 181.7 97.1 66 234.6 12.5.4 27 23.8 I2. 7 87 76.7 4 i.o 47 120.6 69.3 07 182.6 97-6 67 235.5 i s5.o 23 24-7 l3.2 88 77-6 4i.5 48 i3o.5 69.8 08 i83.4 98.1 68 236.4 ,26.3 29 25.6 .3. 7 89 7 8.5 42.0 49 i3i.4 70.2 09 i84.3 98.5 69 23 7 .2 126.8 3o 26.5 14.1 90 79-4 42.4 5o i3a.3 70-7 10 i85.2 99.0 70 2.38 . i 127.3 3i a 7 .3 14.6 9> 8o.3 42.9 i5i i33.2 7 1.2 211 186.1 99-5 271 2.39.0 127.7 32 28.2 i5.i 92 81.1 43.4 52 1 34. 1 71-7 12 187.0 99-9 7 3 239.9 12.8.2 33 29.1 i5.6 9 3 82.0 43.8 53 i34.Q 72.1 13 187.8 io(9.4 73 240.8 128.7 34 3o.o 16.0 94 82.9 44-3 54 i35.8 72.6 14 188.7 100.9 74 241.6 129.2 35 3o.9 i6.5 9 5 83.8 44-8 55 i36. 7 7 3.i i5 189.6 101.4 75 242.5 129.6 36 3i. 7 17.0 96 84-7 45.3 56 i3 7 .6 7 3.5 16 190.5 101.8 76 243.4 i3o.i 37 3>..G : 7 .4 97 85.5 45. 7 57 i38.5 7 4-o 17 191 .4 102.3 77 244.3 1 36.6 38 33.5 17.9 98 86.4 46.2 58 139.3 74-5 18 192.3 102.8 78 245.2 1 3 1 .0 3 9 34.4 18.4 99 8 7 .3 46. 7 5 9 1 40 . 2 7 5.o ] 9 193.1 IO3.2 79 246.1 i3i.5 4o 35.3 18.9 100 88.2 47-1 60 i4i . i 75-4 20 194.0 io3. 7 80 246.9 1 32.0 4i 36.2 i 9 .3 101 89.1 4 7 -6 ~i6T 142 .0 75-9 22.1 194.9 104.2 281 24-7.8 1 32. 5 42 3 7 .o 19.8 02 90.0 48.1 62 142.9 76.4 22 195.8 i4-7 82 248. 7 I 3 2 .9 43 37-9 20.3 o3 90.8 48.6 63 i43.8 76.8 23 196.7 io5.i 83 249.6 1 33.4 44 38.8 20.7 o4 91.7 49.0 64 i44.6 77-3 24 197.6 io5.6 84 25o.5 133.9 45 3 9 -7 21 .2 o5 92.6 49-5 65 i45.5 77-8 25 198.4 1 06. i 85 2 5i.3 1 34.3 46 4o.6 21.7 06 9 3.5 5o.o 66 i46.4 7 8.3 26 199.3 i o6.5 86 252.2 1 I 34.8 47 4i.5 22.2 07 94-4 5o.4 67 i47-3 78-7 27 2OO . 2 I0 7 .0 87 253.1 1 35.3 48 42.3 22.6 08 9 5.2 5o. 9 68 i48.2 79.2 28 201 .1 io 7 .5 88 254.o i35. 49 43.2 23.1 09 96.1 5i.4 69 149.0 79-7 29 202.0 10-7.9 89 2.54.9 i36.2 5o 44.i 23.6 10 97.0 5i. 9 7 i49-9 80. i 3o 202.8 108.4 9 255.8 1 36- 5i 45 o 24.0 in 97-9 52.3 171 i5o.8 80.6 23l 203. 7 108.9 291 256.6 l3 7 -2 52 45 o 24.5 12 98.8 52.8 72 i5i. 7 81.1 32 204.6 109.4 92 2 5 7 .5 i3 7 .6 53 46. 7 25.0 i3 99-7 53.3 73 i52.6 81.6 33 2o5 . 5 109.8 93 258.4 1 38.i 54 47-6 25.5 r4 100.5 53. 7 74 i53.5 82.0 34 206.4 i io.3 94 2.59.3 1 38. 6 55 48.5 2.5.9 i5 101 .4 54.2 75 i54.3 82.5 35 207.3 1 10.8 95 260.2 139.1 56 49.4 26.4 16 1 02 .3 54. 7 76 i55.2 83.o 36 208.1 I I 1.2 96 26.1 .0 139.5 57 5o.3 26.9 17 103.2 55.2 77 i56.i 83.4 3 7 2.09.0 III.7 97 261 .9 i4o.-j 58 5i.a 2 7 J 18 io4- 1 55.6 78 i5 7 .o 83. 9 38 209.9 I 12.2 98 262.8 i4o 5 5 9 52.0 2 7 .8 1 9 104.9 56.i 79 157.9 84.4 3 9 210.8 rra.7 99 263.7 1409 60 5 2 . 9 28.3 20 io5.8 56.6 80 1 58 . 7 84.9 4o 211 .7 u3.i 3oo 264.6 r4i-4 bist Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat Dist.j Dep. Lat. Dist. Dep. Lat. N.E.byE.A>E. S.E.byE.^E. N.W.byW.^W. S.W.byW.^W. [For o Points. TABLE I. [Page u Difference of Latitude and Departure for 2| Points. N.N.E4E. N.N.W.fW. S.S.E.JE. S.S.W.|W. Oist.l Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. ' Dep. Dist.I Lat. [ Dep. I 00.9 oo.5 61 52.3 3i.4 121 io3.8 62.2 181 i55.2 Q3.1 24 1 206.7 123.9 2 3 4 01 .7 02.6 o3.4 o4.3 01 .0 oi.5 02.1 02.6 62 63 64 65 53.2 54.o 54-9 55.8 31.9 3 2 .4 32. 9 33.4 22 23 24 25 104.6 u.5.5 106.4 107.2 62.7 63.2 63. 7 64-3 82 83 84 85 i56.i 157.0 i57.8 i58. 7 93.6 94-1 946 95.1 42 43 44 45 20 7 .6 208.4 209.3 2 1 . I i 124-4 124.9 125.4 * ?6 o 6 7 8 o5.i 06.0 06.9 o3.i o3.6 04. i bb 67 68 56.6 5 7 .5 58.3 33. 9 34-4 35.o 26 27 28 108.1 108.9 109.8 64.8 65.3 65.8 86 87 88 i5 9 .5 160.4 i6i.3 956 96,1 967 46 47 ! 48] 21 1 .0 21 I .9 2 1 Z . 7 126.5 127.0 127.5 9 07.7 o4.6 69 5 9 .2 3b.5 2 9 110.6 66.3 89 162. i 97.2 49 ai3.6 128.0 IO 08.6 o5.i 70 60.0 3b.o 3o in. 5 66.8 90 i63.o 97-7 5o 2i4.4 128.5 1 1 09.4 o5. 7 7i 60.9 36.5 i3i 112.4 6 7 .3 191 i63.8 98.2 25 1 2i5.3 1 29.0 12 io.3 06.2 72 61.8 3 7 .o 32 II3.2 67.9 92 164.7 98-7 52 216. i 129.6 i3 I I .2 06.7 73 62.6 3 7 .5 33 n4,i 68.4 93 i65.5 992 53 217.0 i3o.i i A 12 .O 07.2 74 63.5 38.o 34 114.9 68.9 94 166.4 997 54 217.9 i3o.6 i5 12.9 07.7 75 64.3 38.6 35 u5.8 69.4 95 i6 7 .3 too 3 55 2l8.7 i3i.i 16 l3. 7 08.2 76 65.2 3 9 .i 36 116.7 69.9 96 168.1 100.8 56 219.6 i3i.6 T 7 t4-6 08.7 77 66.0 3 9 .6 37 u 7 .5 70.4 97 169.0 101. 3 5 7 220.4 I32.I 18 ID. 4 09.3 ?8 66.9 4o-i 38 118.4 70.9 9 169.8 101. 8 58 221.3 i3^.6 19 r6.3 09.8 79 67.8 4o.6 \ 1 19.2 71.5 99 170.7 IO2.3 5 9 222.2 1 33. 2 20 17.2 To.3 80 68.6 4i.i 4c< I 20. I 72.0 200 i7i.5 102.8 60 223.0 i33.7 21 18.0 10.8 81 69.5 4i.6 i4i I2O-9 72.5 201 172.4 io3.3 261 223-9 1 34.2 22 18.9 u. 3 82 70.3 42.2 42 121. 8 7 3.0 O2 i 7 3.3 io38 62 224-7 1 34-7 23 19.7 n. 8 83 71.2 42.7 43 122.7 7 3.5 o3 i74.i io44 63 225.6 i35.2 24 20.6 12.3 84 72.0 43.2 44 123.5 74-0 o4 175.0 104.9 64 226.4 i35. 7 25 21. 4 12.9 85 72.9 43.7 45 124.4 74.5 o5 i 7 5.8 io54 65 22 7 .3 i36.2 26 22.3 i3.4 86 7 3.8 44.2 46 125.2 76.1 06 176.7 io5 9 66 228.2 1 36.8 27 23.2 i3. 9 87 74.6 44-7 47 I26.I 7 5.6 7 177.5 106.4 67 229.0 i3 7 .3 28 24-0 i4.4 88 7 5.5 45.2 48 126.9 76.1 08 178.4 106 9 68 229.9 i3 7 .8 29 24.9 i4-9 89 7 6.3 45.8 49 127.8 76.6 09 179.3 1074 69 23o. 7 i38.3 3o 25. 7 i5.4 90 77.2 46.3 5o 128.7 77.1 10 180.1 108.0 7 23i.6 1 38.8 3i 26.6 i5.o 9 1 78.1 46.8 i5i 129.5 77-6 211 181.0 io8.5 271 232.4 i3 9 .3 32 27-4 i6.5 92 78.9 47.3 52 i3o.4 78.1 12 181.8 109.0 72 233.3 i3 9 .8 33 28.3 17.0 93 79.8 47.8 53 l3l .2 78.7 i3 182.7 109.5 73 234 . 2 1 4o.4 34 29.2 i 7 .5 94 80.6 48.3 54 I32.I 79.2 i4 i83.6 I 1 0.0 74 235.o 1 40.9 35 3o.o 18.0 95 8i.5 48.8 55 l32. 9 79-7 i5 i84.4 i io. 5 7& 2.35.9 i4i-4 36 30.9 i8.5 06 82.3 49.4 56 i33.8 80.2 16 i85.3 III 76 236. 7 141.9 37 3T.7 10. 97 83.2 49.9 5 7 i34. 7 80.7 17 186.1 1 1 1. 6 77 2,3 7 . 6 142.4 38 32.6 TO 5 84.i 5o.4 58 i35.5 81.2 18 187.0 112. 1 78 238.4 1429 3o 33.5 20.1 99 84-9 5o. 9 59 i36.4 81.7 19 187.8 II2.6 79 2 3 9 .3 1 43. 4 4o 34.3 20.6 100 85.8 5i.4 60 l3 7 .2 82.3 20 188.7 ii3.i bo 240 . 2 143-9 4i 35.2 21 . I 101 86.6 5i.o 161 i38.i 82.8 221 189.6 1 1 3.6 281 241 .0 i44-5 42 36.o 21.6 02 8 7 .5 52.4 62 139.0 83.3 22 190.4 n4-i 82 241.9 i45.o 43 36.9 22 . I o3 88.3 53.o 63 i3 9 .8 83.8 23 1QI .3 n4-6 83 242. 7 i45.5 44 3-4 22.6 o4 89.2 53,5 64 i4o.7 84.3 24 192.1 Il5.2 84 243.6 146.0 45 38.6 23.1 o5 90.1 54-0 65 i4i.5 84.8 25 193.0 u5. 7 8b 244.5 1 46. 5 46 47 48 g 3 9 .5 4o.3 41.2 42.0 42.9 23.6 24.2 24-7 25.2 25. 7 06 07 08 09 IO 90.9 9, .8 02.6 93.5 94.4 54-5 55.0 55.5 56.o 56.6 66 67 68 69 70 142.4 i43.2 i44-i 1 45.o i45.8 85.3 85.9 86.4 86.9 87.4 26 27 28 ? 9 3o i 9 3.8 194.7 i 9 5.6 196.4 197.3 116.2 116.7 117.2 117.7 118.2 8b 87 88 89 90^ 245.3 246.2 247-0 247.9 248.7 1 47-0 147-5 i48.i i48.6 149.1 5i 52 53 54 55 56 5 7 58 5 9 60 43.7 44-6 45.5 46.3 47-2 48.o 48.9 49.7 5o.6 5i.5 26.2 26.7 27.2 27.8 28.3 28.8 2 9 .3 29.8 3o.3 3o.8 1 1 1 12 i3 i4 i5 16 17 18 J 9 20 9 5.2 96.1 96.9 97.8 98.6 99.5 100.4 IOI .2 IO2 . I IO2.9 5 7 .i 5 7 .6 58.i 58.6 5 9 .i 5 9 .6 60.2 60.7 61.2 61.7 171 72 73 74 75 76 77 78 79 80 146.7 i4 7 .5 i48.4 149-2 iSo.i i5i .0 i5i.8 152.7 i53.5 i54-4 87.9 88.4 88.9 8 9 .5 90.0 9 o.5 91.0 9 i.5 92.0 92.5 a3i 32 33 34 35 36 37 38 3 9 4o 198.1 199.0 199.9 200.7 201 6 202.4 2o3.3 204 . i 205.0 205.9 118.8 119.3 119.8 1 20. 3 120.8 I 2 1. 3 I2I.8 122.4 122.9 123.4 291 9 l 9 3 9 4 95 96 97 98 99 3oo 249.6 aSo.S 2 5[.3 252.2 253.0 253-9 254-7 255.6 256.5 a5 7 .3 149-6 i5o.i 1 5o.fi iSi.i i5i. 7 i5a.a 1 52.7 i53.2 1 53.7 i54. 2 5iZ 1 Dep. Lat. Dist. Dep. Lat. Dist Dep. Lat. Dist. Dep. Lat. Dist Dep. ' Lat. N.E.byE.|E. S.E.byE^E. N.W.byW.|W. S W.byW.^W. [For 5J Points.^ Page 12] TABLE I. Difference of Latitude and Departure for 3 Points. N.E.byN. N.W.byN. S.E.byS. S.W.byS. Dist.l Lat. rloo.8 Dep. Dist. Lat. Dep. Dist. Lat. Dep. ""6772" Dist. Lat. ~i5oT Dep. Dist. Lat. Dep 00.6 61 5o. 7 33. 9 121 100.6 181 100.6 241 200.4 i33. 9 2 01 .7 01 . 1 62 5i.6 34-4 22 IOI .4 | 67.8 82 i5i.3 IOI. I 42 201 .2 1 34 .4 3 02.5 01 .7 63 52.4 35.o 23 102.3 68.3 83 l52.2 101.7 43 202.0 i35.o 4 o3.3 O2. 2 64 53.2 35.6 24 io3.i 68.9 84 i53.o 102.2 44 2O2 .9 i356 5 04.2 02. S 65 54.0 36.i 25 io3. 9 69.4 85 i53.8 102.8 45 2O3."7 i36i 6 o5.o o3 3 66 54-9 36. 7 26 io4.8 70.0 86 i54-7 io3.3 46 204.5 1 36. 7 7 o5.8 03.9 67 55. 7 3 7 .2 27 io5.6 70.6 87 i55.5 103.9 47 205.4 I3 7 .2 8 06.7 o4-4 68 56.5 3 7 .8 28 106.4 71.1 88 i56.3 104.4 48 206.2 137.8 9 07-5 o5.o 69 5 7 -4 38.3 2 9 107.3 71-7 89 i5 7 .i io5.o 49 207.0 1 38.3 10 08.3 o5.6 70 58.2 38.9 3o 108. i 72.2 90 i58.o io5.6 5o 207.9 i38-9 ii 09.1 06. i 71 59.0 39.4 i3i 108.9 72.8 191 i58.8 1 06. i 25l 268.7 1 3 9 .4 i a 10. 06.- 72 5 9 . 9 4o.o 32 109.8 7 3.3 92 159.6 106.7 52 209.5 i4o.o i3 10.8 07.2 73 60.7 4o.6 33 1 10.6 73-9 93 i6o.5 107.2 53 210.4 i4o.6 i4 ti.6 07.8. 74 6i.5 4i.i 34 111.4 74-4 94 i6i.3 107.8 54 211 .2 i4i.i 1 5 12.5 o8.3 75 62.4 41.7 35 112. 2 7 5.o 95 162 . i io8.3 55 212.0 i4i-7 16 i3.3 08.9 -6 63.2 42.2 36 ii3.i 75.6 96 i63.o 108.9 56 212.9 142.2 n i4-i 09.4 77 64.0 42.8 3 7 ii3. 9 76.1 97 i63.8 109.4 5^ 213.7 142.8 18 1 5.o 1 0.0 78 64-9 43.3 38 114.7 76.7 98 164.6 1 10.0 58 2i4.5 i43.3 1 9 i5.8 10.6 79 65. 7 43. 9 39 ii5.6 77.2 99 i65.5 1 1 0.6 59 2i5.4 143.9 :\o 16.6 ii . i 80 66.5 44-4 4o 116.4 77-8 200 i66.3 1 1 i.i 60 216.2 1 44-4 21 T7.5 11.7 81 6 7 .3 45.o i4i 117.2 7 8.3 201 i6 7 . i 111.7 261 217.0 i45.o 22 i8.3 12.2 82 68.2 45.6 42 118.1 78.9 02 168.0 112. 2 62 217.8 i45.6 23 19.1 12.8 83 69.0 46.i 43 118.9 79-4 03 168.8 II2.8 63 218.7 1 46. i 24 20.0 i3.3 84 69.8 46.7 44 119.7 80.0 o4 169.6 ii3.3 64 219.5 i46. 7 2.5 20.8 i3. 9 85 70.7 4 7 -2 45 120.6 80.6 o5 i 7 o.5 113.9 65 220.3 147.2 26 21 .6 i4-4 86 7 i.5 4 7 -8 46 121 .4 81.1 06 i7i.3 n4.4 66 221 .2 i4', B 27 22.4 i5.o 87 72.3 48.3 47 122.2 81.7 7 172.1 i i5.o 67 222 .O i48.3 28 23.3 i5.6 88 7 3.2 48.9 48 123. I 82.2 08 172.9 1 1 5.6 68 222.8 148.9 29 24.1 16.1 89 74-0 49.4 49 123.9. 82.8 09 173.8 1 16.1 69 223.7 149.4 3o 24.9 16.7 9 74-8 5o.o 5o 124.7 83.3 10 174-6 116.7 70 224.5 iSo.o 3i 25.8 17.2 9 1 75-7 5o.6 i5i 125.6 83.9 211 175.4 117.2 271 225.3 i5o.6 32 26.6 17.8 92 7 6.5 5i.i 52 126.4 84-4 12 176.3 117.8 72 226.2 i5i.i 33 27.4 i8.3 93 77-3 5i.7 53 127.2 85.o i3 i77-i 1 18.3 73 227.0 i5i. 7 34 28.3 18.9 94 78.2 52.2 54 128.0 85.6 i4 177-9 118.9 74 227.8 iSa.a 35 29.1 19.4 95 79.0 52.8 55 128.9 86.1 i5 178.8 119.4 75 228.7 i5a.8 36 29.9 20. o 96 79-8 53.3 56 129.7 86.7 16 1-79.6 120.0 76 229.5 i53.3 37 3o.8 20.6 97 80.7 53. 9 5 7 i3o.5 87.2 17 180.4 120.6 77 23o.3 1 53. 9 38 3i.6 21 .1 98 8i.5 54-4 58 i3i.4 87.8 18 i8i.3 121. 1 78 23I.I 1 54-4 39 32.4 21.7 99 82.3 55.o 5 9 I 32. 2 88.3 19 182.1 I2I.7 79 232.0 i55.o 4o 33.3 22.2 100 83.i 55.6 60 i33.o 88.9 20 182.9 122.2 80 232 ,8 i55.6 4i 34.i 22.8 IOI 84.0 56.i 161 i33. 9 89.4 221 i83.8 122.8 281 233.6 1 56.i 42 34-9 23.3 02 84.8 56. 7 62 1 34-7 90.0 22 184.6 123.3 82 234.5 1 56.7 43 35.8 23.9 o3 85.6 5 7 .2 63 i35.5 90.6 23 i85.4 123-9 83 235.3 137-2 44 36.6 24.4 04 86.5 5 7 .8 64 1 36.4 91.1 2,4 186.2 124-4 84 236.1 i5 7 8 45 3 7 .4 25.0 o5 8 7 .3 58.3 65 I3 7 .2 91.7 25 187.1 125.0 85 23 7 .0 1 58.3 46 38.2 25.6 06 88.1 58. 9 66- 1 38.o 92.2 26 187-9 125.6 86 23 7 .8 1 58.9 4? 3 9 .i 26.1 07 89.0 59.4 67 1 38.9 92.8 27 188.7 126.1 87 238.6 ,5 9 .4 48 39.9 26.7 08 89.8 60.0 68 139.7 9 3.3 28 189.6 126.7 88 2 3 9 .5 1 60.0 49 40.7 27.2 09 90.6 60.6 69 i4o.5 9 3. 9 29 190.4 12-^.2 89 24o.3 160.6 5o 4i.6 27.8 10 91.5 61.1 70 i4i.3 9 4-4 3o 191 .2 127.8 9 241.1 161.1 5i 42.4 28.3 III 92.3 61.7 171 142.2 95.0 23 I 192.1 1*8.3 291 242.0 161.7 52 43.2 28. Q 12 9 3.i 62.2 72 i43.o 95.6 32 192.9 128.9 92 242.8 162.2 53 44.i 29.4 i3 94.0 62.8 73 i43.8 96.1 33 198.7 129.4 93 243.6 162.8 54 44.9 3o.o 1 4 94-8 63.3 74 i44.7 96.7 34 194.6 i3o.o 94 244.5 1 63.3 55 45.7 3o.6 i5 95.6 63. 9 75 i45.5 97-2 35 i 9 5.4 i3o.6 95 ;45.3 i63. 9 56 46.6 3i.i 16 96.5 64.4 76 1 46.3 97-8 36 196.2 i3i.i 96 i46.i i64-4 5 7 47-4 3i. 7 17 97.3 65.o 77 147.2 98.3 3 7 197-1 i3i. 7 97 246.9 1 65.o 58 48.2 32.2 18 98.1 65.6 78 i48.o 98.9 38 197.9 132.2 98 247.8 1 65.6 5 9 49.1 3 2 .8 19 98.9 66.1 79 i48.8 99.4 3 9 198.7 i3 2 .8 99 248.6 1 66. i 60 49.9 33.3 20 99.8 66.7 80 149.7 roo.o 4o 199.6 i33.3 3oo 249.4 166.7 Dist. Dep. Lai. Dist. Dep. Lat. Dist. Dep. Lat. Dist/ Dep. Lat. Dist. Hep. Lat. N.E.byE. S.E.byE. N.W byW. S.W.byW. [For f, P,,int~. TABLE I. ii^u 1 Difference of Latitude and Departure for 3] Points. N ' E 4iN. N.W.3N. S . E-|S gw , s Dist : 4 5 6 7 B 9 10 00.fi 01.6 02 .i. 03.2 04.0 04.8 o5.6 106.4 07.2 08.0 joe. 6 01 .2 ni .8 02.4 o3.o o3.6 Io4.2 04.8 o5.4 06.0 Dist 6^ 6< 6C 67 68 69 70 . Lat. 4 9 .c 49.8 5o C 5i.4 52.2 53.o 53.8 54.6 55.4 56.2 Dep ~ : 36T3 36. 9 3;/) 38.i 38. 7 3 9 .3 3y.o 4o.5 4 1. 7 Dist. Lat. Dep. 72.1 72.7 733 7 3. 9 74-5 7 5.i 7 5. 7 76.2 76.8 77-4 Dis 181 82 8,3 84 85 86 87 88 89 90 . Lat. " 145.4 146.2 147.0 i48;< 149.4 i5o.2 iSi.o i5r.8 162.6 Dep Dist "241 42 43 44 45 46 4 7 48 4 9 5o . Lat. Dep. 143.6 M4.2 144.3 145.4 1 4'')- 9 146.5 i48J 148.9 121 22 23 24 2.5 26 2 7 2.8 29 3o 97.2 98.0 98.8 99.6 100.4 IOI . 102. 102. io3. 104. 107. 1 08. ' 109 109. 110. no. in.< 112. 112. u3. i 9 3.6 195.2 196!? 197.6 198.4 199.2 2OO. 200.8 1 1 12 i3 i4 10 08.8 09.6 10.4 I I .2 12.0 12 9 06.6 07- 07. 7 08.3 08.0 9 .5 71 57.0 72)57.6 73 58.6 74 1 59 4 70 6i!o 42.3 |4?..o 43.5 44-1 44-7 45.3 32. 33 34 35 36 105. 106. 106. 107. 108. 109. 78.0 78.6 79.2 79.8 80.4 8r.o 191 9? 9' i53.4 i54.2 i55.o i55.8 i56.6 i57 4 n3. u 5.6 116. 116.8 52 53 54 55 201 .6 202.4 203.2 204.0 2.04.8 2o5 6 149.5 iSo.i i5o. 7 i5i.3 l5l.o 1 62 5 17 18 '9 i3.7 i4.5 i5.3 10. I LO.7 II.: 77 78 79 61.8 62.7 63.5 45.9 46.5 47-1 3 7 38 3 9 IIO.O no. 8 1 1 1 .6 81.6 82.2 82.8 99 i58. 2 i5 9 .o i59.8 117.4 117.9 n8.5 5 7 58 206.4 207 . 2 208.0 1 53. i .53. 7 1 54.3 20 16.1 1 1 .9 80 64.3 47-7 4o 1 12.4 83.4 200 160.6 119. 6c 1 54 9 21 16.9 ia.5 81 65.i 48.3 i4i n3.j 84.0 201 161 .4 119.7 261 209.6 1 55.5 22 17-7 ! 1 3 . i 82 65.9 48.8 42 1 14- 84.6 02 162.2 I2O.3 62 2 IO 4 1 56 i 23 i8.5 i3. 7 83 66.7 49-4 43 114.9 85.2 o3 1 63. i 120.0 63 2M.2 166.7 24 i 9 .3 i4-3 84 6 7 .5 5o.o 44 ii5. 7 85.8 o4 i63. 9 121. 5 64 2 1 2 .O 167.3 25 20. I r4. 9 85 68.3 5o.6 45 n6.5 86.4 o5 164.7 122. 1 65 212.8 157.9 26 20.9 i5.5 8( 69.1 5i.a 46 117.3 87.0 06 1 65. 5 122.7 66 2 1 3 . 7 1 58.5 2 7 21. 7 16.1 87 69.9 5i.8 4 7 118. 8 7 .6 07 i66.3 123.3 67 214.5 iS^.i 28 22.5 i6. 7 88 70.7 52.4 48 118.9 88.2 08 167.1 I23. 9 68 2i5.3 159.6 2 9 23.3 17.3 89 71.5 53.o 49 119.7 88.8 09 167.9 124.5 ' 69 216. 1 i6o.a 3o 24.1 17.9 9< 7 2.3 53.6 5o 120.5 8 9 .4 10 168.7 125.1 70 216.9 160.8 3i 24.9 i8.5 9' 7 3.i 54.2 i5i 121 .3 90. r 21 I 169.5 125.7 271 217.7 161.4 32 '25.7 19.1 9 a 73.9 54.8 52 122. I 90.5 12 170.3 126.3 73 218.5 162.0 33 20.5 19.7 9 3 74.7 55.4 53 122. 91,1 I 3 171.1 126.9 7.3 219 3 162.6 34 27.3 20.3 94 7 5.5 56.o 54 123.7 9'-7 14 171.9 127.5 74 220. i i63.2 35 28.1 20.8 9 3 7 6.3 56.6 55 12.4.5 92.3 i5 172.7 128.1 75 220.9 .63.8 36 28.9 21.4 96 77. r 67.2 56 125. C 92.9 1 6 i 7 3.5 12.8.7 76 221 .7 164.4 37 29-7 22.0 97 77-9 5 7 .8 5 7 126. 1 9 3.5 17 '74-3 129.3 77 222.5 1 65.o 38 3o.5 22.6 98 78.7 58.4 58 126.9 94.1 18 i 7 5.i 129.9 78 223.3 i65.6 3o 3,. 3 23.2 99 79-5 59.0 59 127.7 94- 7 '9 175.9 i3o.5 79 224.1 166.2 4o 32. I I 23.8 IOO 8o.3 5 9 .6 60 128.5 9 5.3 20 i 7 6. 7 i3i.i 80 224.9 1 66.8 4i 32. 9 24.4 101 8r.i 60.2 161 129.3 95 9 221 177-5 i3r.6 281 225.7 167.4 4?. 33.7 25.0 02 81.9 60.8 62 i3o.i 96.5 22 178.3 32.2 8-2 226.5 168.0 43 3.4.5 25.6 o3 82.7 61.4 63 1 3o . 9 97.1 2.3 179-1 1 i3'?.S 83 22 7 .3 168.6 44 35.3 26.2 04 83.5 62.0 64 l3l. 7 97-7 24 '79-9 1 33. 4 84 ?'28.I 169.2 45 36 i 26.8 o5 84.3 62.5 65 i32.5 98.3 2.5 180.7 1 34.0 85 228.9 169.8 46 36 <; 27.4 06 85.i 63.i 66 i33.3 98.9 26 i8r.5 1 34.6 86 229.7 170.4 47 3 7 .8 28 .0 07 85. 9 63. 7 6 7 1 34. i QQ.5 2 7 182.3 i35.2 87 a3o.5 171.0 48 38.6 28.6 08 86,7 64.3 68 134.9 OO.l 28 i83.i 1 35.8 88 23. .3 1 7 1 .6 49 39.4 29.2 9 8 7 .5 64-9 69 i35. 7 00.7 a 9 183.9 36.4 89 23'2 . I 172.2 5o 4o . 2 29.8 10 88.4 65.5 70 i36.5 oi.3 3o i84. 7 i3 7 .o 90 2 b .9 I72.8 5i 4 1 .0 3o.4 III 89.2 66.1 71 i3 7 .3 01.9 23l .85.5 i3 7 .6 9' 233. 7 l?3.3 52 4i.8 3i.o 12 90.0 66.7 72 i38.2 02.5 3? i86.3 1 38. 2 92 234-^ 73-9 53 4^.6 3 1. 6 i3 90.8 67.3 73 39.0 o3.i 33 187.1 i38.8 9 3 235.3 i-4.5 54 43-4 32.2 i4 91.6 6 7 -9 74 39.8 o3.7 34 188.0 139.4 94 236.: i 7 5.i 55 32.8 i5 92.4 68.5 75 40.6 04.2 35 188.8 i4p.o 9 5 236.? i75. 7 56 45.o 33.4 16 93.2 69-1 76 4i-4 04.8 36 189.6 i4o.6 96 i3?.7 1 76.3 5 7 45.8 34.o 17 9 4o 69-7 77 42.2 o5.4 3 7 190.4 .41.2 97 1238.6 176.0 58 46.6 34.6 18 94-8 7 o.3 78 43.o 06.0 38 191 .2 i4i-8 98 >J 9 .4 177.$ 5 9 47-4 35.i 19 9 5.6 70.9 79 43.8 06.6 3 9 192.0 i4'2.4 99 >4o 2 178-1 60 48.2 35. 7 20 96.4 80 44-6 07.2 4o 192.8 i43.o oo ' >4i -o| 178.7 Dist., Dep.| Lat. ) St. Dep; Lat. tet.l Dep. .at. >ist.j Dep. Lat. St. Dip. Lat. N.E.3E. S.E^E. N.VV.^W. S.W. : i\V. [For 4J Points. Pagel4| TABLE I. Difference of Latitude and Departure for 3 Points. N.EN. N.W.iN. S.E.^S. S.W.^S. Dtst. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. i 00.8 00.6 61 47-2 38. 7 121 9 3.5 76.8 181 139.9 ii4-8 24 1 186 3 152.9 2 oi.5 oi.3 62 47-9 39.3 22 94.3 77.4 82 140.7 ii5.5 42 187 i *53-5 3 02.3 01 .0 63 48.7 4o.o 23 p.i 78.0 83 i4i.5 116.1 43 187.8 154.2 4 o3.i 02.5 64 49.5 4o.6 24 95.9 78.7 84 142.2 116.7 44 188.6 IS4.8 5 03.9 03.2 65 50.2 41.2 25 96.6 79.3 85 i43.o 117.4 45 189.4 1 55.4 6 04.6 o3.8 66 5i .0 4i.Q 26 97-4 79-9 86 i43.8 118.0 46 190.2 1 56. i 7 o5.4 o4.4 67 5i.8 42.5 27 98.2 80.6 87 i44.6 118.6 47 190.9 1 56. 7 8 06.2 o5.i 68 52.6 43.i 28 98.9 81.2 88 i45.3 IIQ.3 48 191.7 167.3 9 07.0 o5. 7 69 53.3 43.8 2 9 99-7 81.8 89 146.1 119.9 49 192.5 1 58.o 10 07.7 o6.3 _7_ 54.1 44-4 3o loo.S 82.5 9 146.9 120.5 5o i 9 3.3 1 58.6 ii o8.5'o 7 o 7i 54-9 45.o i3i 101 .3 83.i 191 147.6 121.2 25l 194.0 l5 9 .2 12 09.3 07.6 72 55. 7 45.7 32 102. 83. 7 92 i48.4 I 2 1. 8 52 194 8 i5 9 . 9 i3 10. 08.2 73 56.4 46.3 33 102.8 84-4 93 149-2 122.4 53 iy5.6 lool? i4 [0.8 08.9 74 5 7 .2 46.9 34 io3.6 85.o 94 iSo.o I 23. 1 54 , 9 6.3 161.1 i5 ii. 6 o 9 .5 75 58.o 47-6 35 io4-4 85.6 95 i5o.7 I23. 7 55 197.1 161.8 16 12.4 10.2 76 58. 7 48.2 36 io5. i 86.3 96 i5i.5 124.3 56 i97. 9 162.4 i? i3.i 10.8 77 5 9 .5 48.8 3 7 105.9 86.9 97 i52.3 125.0 57 198.7 i63.o 18 13.9 ii. 4 78 6o.3 49.5 38 106.7 8 7 .5 98 i53.i 125.6 58 199.4 1 63. 7 J 9 i4-7 12. I 79 61.1 5o.i 3 9 io 7 .4 88.2 99 i53.8 126.2 5 9 2OO. 2 1 64.3 20 i5.5 I2. 7 80 61.8 5o.8 4o 108.2 88.8 200 i54.6 126.9 60 2OI .O 164.9 21 16.2 i3.3 81 62.6 5i.4 i4i 109.0 89.4 201 i55.4 127.5 261 201.8 1 65. 6 22 17.0 14.0 '82 63.4 52.0 42 109.8 90.1 02 i56.i 128.1 62 202.5 166.2 23 17.8 14.6 83 64.2 52. 7 43 iio.S 90.7 o3 i56-9 128.8 63 2o3.3 1 66. 8 24 18.6 l5.2 84 64-9 53.3 44 1 1 1 .3 91.4 o4 i5 7 -7 129.4 64 204.1 i6 7 .5 25 i 9 .3 i5.o 85 65.? 53. 9 45 ii j. i 92.0 o5 i58.5 i3o.i 65 204.8 168.1 26 20.1 i6.5 86 66.5 54-6 46 1 12.9 92.6 06 159.2 i3o.7 66 2o5.6 168.7 2 7 20-9 17.1 87 6 7 .3 55.2 47 n3.6 9 3.3 07 160.0 i3i.3 67 206.4 169.4 28 21.6 17.8 88 68.0 55.8 48 114-4 93.9 08 160.8 l32.0 68 207.2 170.0 2 9 22.4 18.4 89 68.8 56.5 49 IlS.2 94-5 09 161.6 i32.6 69 207.9 170.7 3o 23.2 19.0 9 69.6 5 7 .i 5o 116.0 9 5.2 10 162.3 i33.2 70 208 . 7 i7i.3 3i 24.0 19.7 9 1 ~7oTT 57.7 i5i 1 16. 7 95.8 211 i63.i i33.o 271 209.5 1 7 1 .9 32 24.7 20.3 92 71.1 58.4 52 117.5 96.4 12 i63. 9 1 34.5 72 210.3 72.6 33 25.5 20. 93 71.9 59.0 53 ii8.3 97.1 i3 164.7 1 35.i 73 211 .0 73.2 34 26.3 21.6 94 72.7 5 9 .6 54 119.0 97-7 i4 i65.4 i35.8 74 211. 8 7 3.8 35 27.1 22.2 95 73.4 6o.3 55 119.8 9 8.3 i5 166.2 1 36.4 75 212.6 74-5 36 27.8 22.8 96 74.2 60.9 56 120.6 99.0 16 167.0 137.0 76 2i3.4 7 5.i 37 28.6 23.5 97 7 5.o 6i.5 5 7 121 .4 99.6 17 167.7 1 3 7 . 7 77 2l4-I 75.7 38 29.4 24.1 98 7 5.8 62.2 58 122. I 100.2 18 i68.5 i38.3 78 214.9 "6.4 39 3o.i 24.7 99 7 6.5 62.8 59 122.9 100.9 J 9 169.3 i38.o 79 215.7 77.0 4o 30.9 25.4 100 77-3 63.4 60 123.7 ioi.5 20 170.1 139.6 80 216.4 177.6 4i 3i. 7 26.0 101 78.1 64.1 161 124.5 102. 1 221 170.8 l4o.2 281 217.2 178.3 42 32.5 26.6 02 7 8.8 64-7 62 125.2 102.8 22 171 .6 t4o.8 82 218.0 178.9 43 33.2 27.3 o3 79.6 65.3 63 126.0 io3.4 23 172.4 i4i.5 83 218.8 179.5 44 34.o 27.9 o4 80.4 66.0 64 126.8 104.0 24 I 7 3.2 142.1 84 219.5 180.2 45 34.8 28.5 o5 81.2 66.6 65 127.5 104.7 25 173.9 142.7 85 220.3 180.8 46 35.6 29.2 06 81.0 67.2 66 128.3 io5.3 26 174.7 i43.4 86 221 .1 181.4 47 36.3 29.8 07 82.7 67.9 67 129.1 105.9 27 175.5 1 44-0 87 221 .9 182.1 48 3 7 .i 3o.5 08 83.5 68.5 68 129.9 1 06.6 28 176.2 1 44- 6 88 222.6 182.7 49 3 7 . 9 3i.i 09 84.3 69.1 69 1 3o . 6 107.2 29 177.0 i45.3 89 223.4 i83.3 5o 38.7 3i: 7 IO 85.o 69.8 70 i3i.4 107.8 3o 177.8 i45. 9 9 224.2 184.0 5i 3 9 .4 32.4 III 85.8 70.4 i 7 i l32.2 io8.5 23 1 178.6 M6.5 291 224*9 1 84 .6 52 40.2 33.o 12 86.6 71.1 72 1 33.o 109.1 32 179.3 147.2 92 225. 7 i85.2 53 4i .0 33.6 i3 87.4 71.7 73 i33. 7 109.8 33 180.1 147-8 93 226.5 185.9 54 4i. 7 34.3 i4 88.1 7 2.3 74 1 34.5 110.4 34 180.9 i48.4 94 227.3 186.5 55 42.5 34-9 i5 88.9 7 3.o 75 1 35. 3 IIl.O 35 181 7 149.1 9 5 228.0 187.1 56 43.3 35.5 16 89.7 7 3.6 76 1 36.o 111.7 36 182.4 149.7 96 228.8 187.8 57 44.i 36.2 17 90.4 74.2 77 136.8 II2.3 37 i83.a i5o.4 97 22 9 .6 188.4 58 44.8 36.8 18 91.2 74-9 78 i3 7 .6 112.9 38 184.0 iSi.o 98 2 3o.4 189.0 59 45.6 37-4 1 9 92.0 7 5.5 79 i38.4 n3.6 3 9 i84-7 i5i.6 99 23I.I 189.7 60 46.4 38.i 20 92.8 7 6.i 80 139.1 Il4-2 4o i85.5 i52.3 3oo 23i-9 190.3 Dist. Dep. Lat. Dist Dep. Lat. Dist Dep. Lat. Dist Dep. Lat. Dist Dep. Lat. N.E^E. S.E.^E. N.W.JW. S.W.^W. [For 4 Points. TABLE I. | Page 15 Difference of Latitude and Departure for 3| Points. N.E.iiY. N.W.iN. S.E.iS. S.W.JS. Dist . Lat. ' Dep. Dist Lat. Dep Dist Lat. Dep. Dist Lat. Dep Dist Lat. Dep. 2 3 oo. 7 oi.5 02.2 00.7 oi .3 02.0 61 62 63 45.2 45.9 46. 7 4i.o 4i.6 42.3 121 22 23 89.7 90.4 91.1 8i.3 81.9 82.6 181 82 83 i34.i 134.9 i35.6 I 2 1. 6 122.2 122.9 241 42 43 178.6 179-3 180 i 161.8 162,5 i63 2 4 5 6 8 ()3.0 o3. 7 o4.4 05.2 o5. 9 02.7 o3.4 04.0 04.7 o5.4 64 65 66 67 68 47-4 48.2 48. 9 49.6 5o.4 43.o 43. 7 44.3 45.o 45. 7 24 25 26 27 28 91.9 92.6 93.4 94.1 94-8 83.3 83. 9 84.6 85.3 86.0 84 85 86 87 88 i36.3 i3 7 .i i3 7 .8 i38.6 123.6 124.2 124.9 125.6 126.3 44 45 46 47 48 180.8 i8i.5 182.3 i83.o i83.8 163.9 1 64.5 i65.2 i65. 9 i66.5 9 10 06.7 07.4 06.0 06.7 69 70 5i. 9 46.3 47-0 I 9 3o 95.6 9 6.3 86.6 8 7 .3 89 90 i4o.o i4o.8 126.9 I2 7 .6 i 9 5o 184.5 i85.2 167.2 167.9 ti 08.2 o 7 .4 7i 52.6 47-7 i3i 97-1 88.0 191 i4i.5 128.3 757 186.0 168.6 12 i3 i4 08.9 09.6 10.4 08. i 08. 7 09.4 72 73 74 53.3 54.1 54.8 48.4 49.0 49-7 32 33 34 97.8 9 8.5 99 .3 88.6 89.3 90.0 P 94 142. 3 i43.o i43. 7 128.9 129.6 i3o.3 52 53 54 186.7 187.5 188.2 169.2 169.9 170.6 i5 1 1 .1 10. I 75 55.6 5o.4 35 100. 90.7 95 i44.5 i3i.o 55 188.9 171.2 ;6 ii .9 10. 7 76 56.3 5i.o 36 100.8 9 i.3 Q6 i45.2 i3i.6 56 r8o.7 171.9 '7 12.6 11. 4 77 5 7 .i 5i. 7 37 101 .5 92.0 97 i46.o i3 2 .3 5 7 190.4 172.6 18 i3.3 12. I 78 5 7 .8 52.4 38 IO2.3 92.7 Qb 146.7 i33.o 58 191 .2 173.3 19 14.1 12.8 79 58.5 53.i 3 9 io3.o 9 3.3 99 1 4 7 . / i33.6 191 .9 173.9 20 i4-8 i3.4 80 5 9 .3 53. 7 4o 103.7 9 4-o 200 148.2 1 34.3 60 192.6 174.6 21 i5.6 i4. i 81 60.0 54-4 i4i io4.5 94-7 201 148.9 i35.o 261 1 9 3.4 175 : 22 i6.3 14.8 82 60.8 55.i 42 105.2 95.4 02 149.7 i35. 7 62 194.1 175.9 23 17.0 i5.4 ' 83 6i.5 55. 7 43 106.0 96.0 o3 i5o.4 1 36.3 63 194.9 176.6 24 17.8 16.1 84 62.2 56.4 44 106.7 96.7 04 l5l.2 137.0 64 195.6 (T- _; 25 i8.5 16.8 85 63.o 5 7 .i 45 107.4 97-4 o5 i5i o l3 7 -7 65 196.4 178.0 26 i 9 .3 17.5 86 63. 7 5 7 .8 46 108.2 98.0 06 i5 2 .6 i38.3 66 197.1 178.6 27 2,0 . 18.1 87 64.5 58.4 47 108.9 98.7 07 i53.4 139.0 67 197.8 179.3 28 20.7 18.8 88 65.2 59.1 48 109.7 99.4 08 i54.i 139.7 68 198.6 1 8o.O 2 9 21.5 i 9 .5 89 65.9 5 9 .8 49 110.4 100. 1 09 i54-9 140.4 69 109.3 180.6 3o 22.2 20.1 9 66. 7 60.4 5o in .1 100.7 10 i55.6 i4i.o 70 200. i i8i.3 3 1 23.0 20.8 9 1 67.4 61.1 i5i 111.9 101.4 211 i56.3 i4i-7 271 200.8 i8a.: 32 23.7 21.5 92 68.2 61.8 52 112. 6 102. 1 12 i5 7 .i 142.4 72 201.5 182.7 33 24.5 22.2 93 68.9 62.5 53 u3.4 102-7 1 3 i5 7 .8 1 43.o 73 2O2.3 i83.3 34 25.2 22.8 94 69.6 63.i 54 ii4-i io3.4 i4 i58.6 i43. 7 74 2O3.O 1 84.o 35 25.9 23.5 95 70.4 63.8 55 u4.8 104.1 i5 I 9,3 i44.4 75 2o3.8 184.7 36 26. 7 24.2 96 71 .1 64.5 56 n5.6 104.8 16 160.0 i45.i 76 204.5 1 85. 4 37 27-4 24.8 97 7' -9 65. T 5 7 ii6.3 io5.4 17 160.8 145.7 77 205 2 1 86.0 38 28.2 25.5 98 72.6 65.8 58 117.1 1 06. i 18 i6i.5 i46.4 78 206 o 186.7 39 28.9 26.2 99 73.4 66.5 59 117.8 106.8 19 162.3 i47-i 79 206 7 187.4 4o 29.6 26.9 100 74.1 6 7 .2 60 118.6 107.4 20 i63.o 147-7 80 207.5 188.0 4i 3o.4 2 7 .5 IOI 74.8 67.8 161 119.3 1 08. i 221 i63.8 148.4 281 208 2 188.7 42 28.2 02 75.6 68.5 62 120.0 108.8 22 i64.5 149.1 82 208.9 189.4 43 31.9 28.9 o3 76.3 69.2 63 120.8 109.5 23 i65.2 149-8 83 209.7 190.1 44 3a.6 i 29.5 o4 77-1 60.8 64 121 .5 IIO.I 24 166.0 i5o.4 84 2io..f! 190.7 45 3 i 7 3o o5 70.5 65 122.3 1 10.8 25 166.7 i5i.i 85 211. 2 191.4 46 I 34 . i 3o. 9 06 78.5 71.2 66 123.0 iii.S 26 167.5 i5i.8 86 2 1 I . 9 192.1 47 '34. 8 3r.6 07 79-3 71.9 67 i23. 7 1 1 2. 2 27 168.2 1 52. 4 87 212.7 193.7 48 35.6 32.2 08 72.5 68 124.5 II2.8 28 168.9 i53.i 88 2l3.4 193.4 36.3 32.9 09 80.8 7 3.2 69 125.2 u3.5 29 169-7 i53.8 89 2l4.' 194.1 5o 3 7 .o 33.6 10 8i.5 73.9 70 I26.O Il4-2 3o 170.4 1 54-5 90 214.9 19l; 8 _ 5i 37.8 34.2 in 82.2 74-5 171 126.7 n4.8 a3i 171.2 i55.i 291 2 1 5. 6 195.4 52 38,5 34.9 12 83.o 7.5.2 7 2 127.4 1 1 5.5 32 171-9 i55.8 92 216.4 196.1 53 3o.3 35.6 83.7 75.Q 73 128.2 116.2 33 172.6 1 56.5 9 3 217.1 196.8 54 55 56 4o.o 4o.8 4i.5 36.3 36. 9 3 7 .6 i4 i5 16 84.5 85.2 86.0 76.6 77.2 77-9 74 75 76 128.9 129.7 i3o.4 1 16.9 117.5 118.2 34 35 36 173.4 i 7 4. i 174.9 5 7 .i 5 7 .8 58.5 94 9 5 96 217.8 218.6 219.3 197.4 198., 198.8 57 42.2 38.3 17 86.7 78.6 77 118.9 3 7 i 7 5.6 5 9 .2 97 220. i 199.5 58 59 60 43.o 43.7 44.5 39.0 3 9 .6 4o.3 18 '9 20 87.4 88.2 88.9 79.2 79-9 80.6 78 79 80 131.9 i32.6 i33.4 119.5 120.2 120-9 38 3o 4o I77-I 177-8 5 9 .8 6o.5 61.2 08 3oo 220. 8 221 .5 222.3 200.8 2OI.5 Dist., Den, Lat. Dist Dep. Lat. Dist. Dep. 1 Lat. Dist. Dep. Lat. Dist. Dep. 1 Lat. NE|E S.E.^E. N.VV4W. S.W.^W. [For 4^ Poml*. 1'agelCJ TABLE I. Difference of Latitude and Departure for 4 Points. N.E. N.W. S.E. S.W. Dist. Lat. Do p. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. B-sJ Lat. Dep ! 00.7 00.7 61 43.1 43.i 121 85.6 85.6 181 128.0 128.0 24 1 '70.4 170.4 2 CM .4 oi .4 62 43.8 43.8 22 86.3 86.3 82 128.7 128.7 42 171.1 171.1 'i o^.i O7. 1 63 44-5 44-5 ?3 8-.o 870 83 129,4 179.4 e. 171.8 I-l 4 02.8 02.8 64 45.3 45-3 24 87.7 87-7 84 i3o.i i3o.i 44 172.5 172.5 5 o3.5 o3.5 65 46.o 46.o 25 88.4 88.4 85 i3o.8 1 3o.8 45 173.3 173.2 6 04.2 04 . 2 66 46.7 46.7 26 89.1 89.1 85 iSi.5 i3i.5 46 173.9 '73-9 7 04.9 04.9 67 47-4 47-4 27 89.8 89.8 87 132.2 132.2 47 174-7 174.7 8 o5. 7 05.7 68 48.i 48.1 28 9 o.5 90.5 88 l32. 9 132.9 48 i 7 5.4 175.4 9 06.4 o6.4 69 48.8 48.8 29 91.2 91.2 89 i33.6 i33.6 49 176.1 176.1 10 07.1 07.1 70 49.5 49.5 3o 91.9 91.9 9 i34.4 1 34. 4 5o 176.8 176.8 1 1 07.8 07.8" 7i 50.2 50.2 i3i 92.6 92.6 191 1 35.i i35.i 25l 177.5 I7 7 .5 |2 o8.5 o8.5 72 50.9 50.9 32 9 3.3 9 3.3 92 i35.8 i35.8 52 178.2 178.2 i3 09.2 09.2 73 5i .6 5i.6 33 94.0 94.0 93 i36.5 1 36.5 53 178.9 178.9 i4 09.9 09.9 74 52.3 52.3 34 94.8 94.8 94 l3 7 .2 l3 7 .2 54 179.6 179.6 i5 10.6 10.6 75 53.o 53.0 35 9 5.5 9 5.5 9 5 1 37. 9 137.9 55 i8o.3 i8o.3 16 n.3 n.3 76 53. 7 53. 7 36 9 6.2 96.2 96 i38.6 1 38.6 56 181.0 181.0 i? 12.0 12 .O 77 54-4 54-4 3 7 9 6. 9 96.9 97 139.3 139.3 57 181 .7 181.7 18 12.7 I2. 7 78 55.2 55.2 38 97-6 97.6 9 8 i4o.o i'4o.o 58 182.4 182.4 9 13.4 ,3.4 79 55. 9 55. 9 39 9 8.3 9 8.3 99 140.7 i4o. 7 5 9 i83.i i83.i 20 i4-i i4-i 80 56.6 56.6 4o 99.0 99.0 200 i4i.4 i4i-4 60 1 83.8 i83.8 21 i4-8 14.8 ~8T 5 7 .3 5 7 .3 i4i 99-7 99-7 201 1 4?-. i 142.1 26, 184.6 1 84. 6 22 i5.6 i5.6 82 58.o 58.o 42 100.4 100.4 02 142.8 142.8 62 i85.3 i85>3 23 i6.3 ,6.3 83 58. 7 58. 7 43 101 . I 101. 1 03 i43.5 i43.5 63 1 86.0 1 86.0 24 17.0 17.0 84 5 9 .4 59.4 44 101.8 ioi.8 o4 i44.2 144.2 64 186.7 186.7 25 17-7 17.7 85 60. i 60. i 45 102.5 102.5 o5 i45.o i45.o 65 187.4 1874 ?.6 | 1 6 . 4 18.4 86 | 60. 8 60.8 46 103.2 1O3.2 06 i45. 7 i45-7 66 1 88. i 188. i 2" ly.l 19.1 87 61. 5l6i.5 47 103.9 108.9 07 146.4 1 46.4 67 188.8 188.8 281 19.8 19.8 88 02.2 1 O2. 2 48 104.7 104.7 08 i47-i i4 7 .i 68 189.5 .89.5 29 20 . 5 20.5 89 62.9 62.9 4 9 io5.4 io5.4 9 147-8 147.8 69 1 90 . 2 190.2 3o 21 .2 21.2 9 63. 6 | 63.6 5o 1 06. i 1 06. i IO i48.5 i48.5 70 190.9 12^9 3. 2J. 9 21. 9 9 1 64.3164.3 i5i 106.8 1 06.8 21 I 1 4 9 . 2 149-2 271 191 .6 191.6 32 22.6 22.6 92 65.i 65.i 52 1 07 . 5 107.5 12 149.9 149-9 72 192 .3 192.3 33 23.3 23.3 93 65.8 65.8 53 108.2 108,2 13 i5o.6 i5o.6 73 i o3 . o 193.0 34 24.0 24.0 94 66.5 66.5 54 108.9 108.9 i4 i5i.3 r5i.3 74 io3. 7 193.7 35 24-7 24.7 95 67.2 67.2 55 1 09 . 6 109.6 i5 l52.0 l52.0 1 94 . 5 194.5 36 25.5 25.5 96 67-9 67-9 56 i io.3 i io.3 16 i52. 7 l52. 7 76 1 95 . 2 195.2 37,26.2 26.2 97 68.6 68.6 57 I I 1 .0 11 1 .0 17 i53.4 i53.4 77 io5 .9 190.9 38 26.9 26.9 98 69.3 6 9 .3 58 111.7 111.7 18 i54-i 1 54. i 78 1 96 . 6 196.6 3 9 27.6 27.6 99 70 . o 70.0 5 9 I I 2 . 4 1 12.4 K ; i54-9 1 54-9 79 197.3 197.3 4o 28.3 28.3 100 70.7 70.7 60 ii3.i u3.i 20 i55.6 1 55.6 80 1 98 . o 198.0 4i 29.0 29.0 101 71-4" 71-4 161 n3.8 n3.8 221 i56.3 1 56.3 281 198.7 198.7 42 29.7 29.7 02 72.1 72.1 62 n4.6 u4.6 22 157.0 1 57.0 82 199.4 199.4 43 3o.4 3o.4 o3 72.8 72.8 63 H.5-.3 u5.3 2.3 1 5 7 .7 157.7 83 200 . I 200. i 44 3i .1 3i .1 04 7 3.5 7 3.5 64 1 16.0 1 16.0 24 i58.4 1 58.4 84 2.00.8 200 8 45 3i .8 3i.8 o5 74-2 74.2 65 1 16.7 1 16.7 25 i5 9 . i 1 5 9 . i 85 201 .5 20 1 .5 46 3^.5 32.5 06 7 5.o 7 5.o 66 1 17.4 1 17.4 2.6 159.8 159.8 86 202.2 2^2.2 47 33.2 33.2 07 75-7 7 5. 7 67 118.1 118.1 27 i6o.5 i6o.5 87 202 .9 202.9 48 33. 9 33.9 08 76.4 76.4 68 118.8 118.8 28 161 .2 161.2 88 203.6 203.6 4 9 34.6 34.6 09 77.1 77-i 69 1 19.5 1 19.5 2 9 161 .9 161.9 89 204.4 204.4 5o 35.4 35. .4 10 77.8 77.8 70 120.2 I 20. 2 3o 162.6 162.6 9 205.1 205.1 5i 36.i 36.i in 7 8.5 7 8.5 171 I2O-9 120-9 2.3 1 i63.3 i63.3 291 2C.5.8 2o5.8 52 36.8 36.8 12 79.2 79.2 72 121 .6 I 2 1. 6 32 164.0 164.0 92 206. 5 206.5 53 3 7 .5 37.5 i3 79-9 79-9 73 122.3 122.3 33 1 64. 8 164.8 9 3 207 .2 207.2 54 38.2 38.2 i4 80.6 80.6 74 123. O 123.0 34 i65.5 i65.5 94 207.9 2O--9 55 38. 9 38. 9 i5 8i.3 8i.3 75 123.7 i23. 7 35 166.2 166.2 95 208.6 208.6 , 56 3 9 .6 3 9 .6 16 82.0 82.0 76 1 2.4 . 5 124.5 36 166.9 166.9 96 209.3 209.3 57 4o.3 4o.3 17 82.7 82.7 77 125.2 125.2 3 7 167.6 16^.6 97 210.0 210.0 584i.o /I .0 18 83.4 83.4 78 125-9 125.9 38 i68.3 1 68.3 .98 2IO-7 210.7 5 9 41.7 41.7 J 9 84-i 84.i 79 1 26 . 6 126.6 3 9 169.0 169.0 99 21 I .4 211.4 60 42.4 4?. 4 20 84-9 84-9 80 127.3 I2 7 .3 4o 169.7 169.7 3oo 212.1 212.1 DISK; Dep. 1, a!.. [Dist. Dep. Lat. DiZ Dep. Lat. Dist. Do p. Lat. Dist. Dep. Lat." N K. N.W. S.E. S.W. [For 4 Points. TABLE II. [Pagel7 Difference of Latitude and Departure for 1 Degree. Dist 2 3 4 5 10 . Lat. Dep Dis Lat. Dep Dis 12 22 23 2.1 26 27 28 29 3o Lat. Dep Dis Lat. Dep Dist 02.0 o3.o 04.0 o5.o 06.0 07.0 08.0 09.0 10. 00. 00. I 00 I 00. I 00. I 00. I 00. I 00.2 00.2 6 62 63 64 65 6b 67 68 69 70 61 .0 62.0 63.o 64.o 65.o 66.0 67.0 68.0 69.0 70.0 01 .1 01 .1 OI . I OI .1 01. I 01 .2 01 .2 01 .2 01 .2 01 .2 121 .0 122.0 123.0 124.0 125.0 126.0 I2 7 .0 128.0 129.0 i3o.o 02.1 02.1 02.1 02.2 02.2 02.2 02.2 O2 .2 O2. C 02.3 18 8 8 84 85 86 8 7 88 89 90 181.0 182.0 i83.o 184.0 i85.o 186.0 187.0 188.0 189.0 190.0 03.2 03.2 03.2 03.2 03.2 03.2 o3.3 o3.3 o3.3 o3.3 241 42 43 44 45 46 47 48 g 241 .0 242.0 243.0 244 245.0 246,0 247.0 248.0 249.0 25o.o 04.2 04.2 04.2 04 3 o4.3 o4.3 o4.3 o4.3 04. 3 04 4 1 1 12 \i 16 i? 18 10 2C II .0 12. i3.o i4-o i5.o 16.0 17.0 18.0 19.0 20.0 OO.2 O0.2 00.2 00.2 00.3 oo.3 oo.3 oo.3 oo.3 oo.3 72 73 74 75 76 78 79 80 71.0 72.0 7 3.o 74-0 7 5.o 76.0 77.0 78.0 79.0 80.0 01 .2 01 ; 01 ' OI .C 01 .0 01 .3 01 .3 01.4 oi .4 oi .4 32 33 34 35 36 37 38 3 9 4o i3i ,o l32.0 i33.o i34.o i35.o i36.o i3 7 .o i38.o 139.0 i4o.o 02.,; O2.'; 02. C 02.3 02. , 02. t 02. L 02. i 02. i 02 ,i 9 92 9 3 94 95 96 97 98 99 200 191.0 19: i.o 193.0 i 9 4.o 195.0 196.0 197.0 198.0 199.0 200.0 o3.3 o3.4 o3.4 o3.4 o3.4 o3.4 o3.4 o3.5 o3.5 o3.5 25l 52 53 54 55 56 5 7 58 59 60 25l .0 252.0 253.o 254.0 255.o 256.o 25 7 .0 258.o 259.0 260.0 04. 04. 04. 04. 04. 04. 04. 04. 04. 04. 21 22 2J 25 26 2 7 28 21.0 22.0 23.0 24.0 25.0 26.0 27.0 28.0 00.4 00.4 00.4 00.4 00.4 oo.5 oo.5 oo.5 81 82 83 84 85 86 87 88 81.0 82.0 83.o 84.o 85.o 86.0 87.0 88.0 oi .4 oi .4 01 .4 oi.5 oi.5 oi.5 oi.5 oi.5 '42 43 44 45 46 47 48 i4i -o 142.0 i43.o i44-o i45.o i46.o i4 7 .o i48.o 02. 02. 02. 02. 02.5 02.5 02.6 02.6 2OI 02 o5 06 07 08 201 .0 202. 203.0 204.O 2O5.O 2O6.O 207.0 208.0 o3.5 o3.5 o3.5 o3.6 o3.6 o3.6 o3.6 o3.6 261 62 63 64 65 66 6 7 68 261 .0 262.0 263.o 264.0 265.o 266.0 267.0 268.0 04.6 04.6 04.6 04.6 04.6 04.6 04 7 o4 7 3o 29.0 3o.o oo.5 oo.5 89 9 90.0 oi .6 01.6 io 149.0 iSo.o 02.6 02.6 09 10 209.0 210.0 o3.6 o3. 7 69 70 269.0 270.0 o4'-7 04.7 3i 32 33 34 35 36 3i .0 32.0 33.o 34.o 35.o 36.o oo.5 jo. 6 00.6 00.6 00.6 00.6 9 1 S 94 95 96 91.0 92.0 9 3.o 94.o 9>5.o 96.0 01.6 01.6 01.6 01.6 01.7 01. 7 52 53 54 55 56 i5i .0 152.0 i53.o 1 54.0 i55.o i56.o 02.6 02. 7 02.7 02.7 02.7 02.7 211 12 l3 i5 16 211 .O 212. 213.0 214.0 215.0 216.0 o3. 7 o3. 7 o3. 7 o3. 7 o3.8 o3.8 271 7 ^ 7 4 75 76 271 .0 272.0 273.0 274.0 275.0 276.0 o4-7 o4. 7 o4.8 04.8 04.8 04.8 3 7 3 7 .o 00.6 97 97.0 01.7 5 7 i5 7 .o 02.7 17 217.0 o3.8 77 277.0 04.8 38 38.o 00.7 98 98.0 01.7 58 i58.o 02.8 id 218.0 o3.8 78 278.0 04.9 3 9 4o 39.0 4o.o 00.7 00.7 99 100 99.0 100. 01.7 01.7 59 60 159.0 160.0 02.8 02.8 J 9 20 219.0 22O.O o3.8 o3.8 79 80 279.0 280.0 / 04.9 04.9 4i 4i.o 00.7 IOI OI..O 01.8 161 161 .0 02.8 221 221 .0 o3.o 281 281.0 04.9 42 42.0 00.7 02 102.0 01.8 62 162.0 02.8 22 222.0 03,Q 82 282.0 04.9 43 43.o 00.8 o3 o3.o .8 63 i63.o 02.8 23 223.0 03.9 83 283.o 04.9 44 44.o 00.8 o4 04.0 .8 64 164.0 02.9 24 224.0 o3.9 84 284.0 o5.o 45 46.o 00.8 o5 o5.o .8 65 i65.o 02 .9 25 225.0 o3.9 85 285.0 o5.o 4b 46.0 00.8 06 06.0 o .8 66 66.0 02.9 26 226.0 o3. 9 86 286.0 o5.o 47 4 7 .o 00.8 07 07.0 o .9 6 7 6 7 .o 02.9 2 7 227.0 04.0 87 287.0 o5.o 48 48.o 00.8 08 08.0 o .9 68 68.0 02 .9 28 228.0 04.0 88 288.0 o5.o 49 49.0 00.9 09 09.0 o .9 69 69.0 02.9 2 9 229.0 04.0 89 289.0 o5.o *)0 5o.o 00.9 10 10. o .9 70 7 o.o o3.o 3o 230.0 04.0 9 290.0 o5.i 5i 5i .0 00.9 II I I .0 01.9 1-71 7 I.O o3.o 23l 23l.O 04.0 291 291 .0 o5.i 52 52.0 00.9 12 12.0 02.0 72 7 2.0 o3.o 32 232.0 04.0 92 292.0 o5.i 53 53.0 00.9 i3 i3.o 02.0 7 3 7 3.o o3.o 33 233.0 4. i 93 293.0 o5.i .54 54.0 00.9 i4 i4-o O2. 74 7 4-o o3.o 34 234.o 4.1 94 294.0 o5.i 55 65.0 OI .0 i5 i5.o 02.0 75 7 5.o 63.1 35 35.o 4. i 95 295.0 o5.i 56 56.o 01 .0 16 16.0 O2. 76 76.0 o3.i 36 36.o 4.1 96. 296.0 05.2 5? 7.0 01 .0 17 17.0 02.0 77 77 .0 o3.i 3 7 3 7 .o 4. i 97- 297.0 05.2 58 8.0 01 .0 18 18.0 O2. I 78 7 8.0 o3.i 38 38.o 4.2 98- 298.0 o5.2 59 9.0 01 .O 19 19.0 2.1 79 79.0 o3.i 39 39.0 4.2 99- 299.0 05.2 60 60.0 01 .O 20 20.0 2.1 80 80.0 o3.i 4o 4o.o 4.2 oo 3oo.o 05.2 D.st. )ep.| Lat. ist. Dep. Lat. )ist. Dep. Lat. Dist. Dep. ..at. ist: Dep. I Lat. . [For 89 Degrees. Page 18] TABLE II. Difference of Latitude and Departure for 2 Degrees. Dist . La'.. Deo. Dis Lat. Dep. Dist Lat. Dep Dis Lat. Dep Dist.| Lat. Dep. i OI 00.0 61 61.0 02.1 121 120. 04.2 18 180. o6.3 241 | 240.9 08.4 2 02. o 00. I 62 62.0 02.2 22 121. o4.3 82 181. 06. 42 241.9 08.4 3 o3.o 00. I 63 63. ) 02.2 23 122. o4.3 83 182. 06. 43 242. 9 o8,5 4 o4.o 00. I 64 64.o 02.2 24 123- o4.3 84 i83. 06. 44 243. 9 o8.5 5 o5.o OO.2 65 65.o 02.3 25 I2 4 . o4u 85 184. 06. 45 244.9 08 6 6 06.0 OO.2 66 66.0 O2. 3 26 125. 04.^ 86 i85. 06. 46 245. 9 08.6 7 07.0 O0.2 67 67.0 02.3 27 126. o4.4 8 7 186. 06. 47 246.8 08.6 8 08.0 oo.3 68 68.0 02.4 28 127. 04. 5 88 187. 06.6 48 247.8 08.7 9 09.0 oo.3 69 69.0 02.4 29 128. o4.5 89 188. 06.6 49 248.8 08.7 10 IO.O oo.3 70 70.0 02.4 3o I2 9 . 04. 5 90 189. 06.6 5o 249.8 08.7 ii II .0 00.4 71 71.0 02.5 ~r37 i3o. 04.6 191 190. 06.7 ?5i 25o.8 08.8 12 12.0 00.4 72 72.0 02.5 32 i3i. 04.6 92 191 . 06.7 52 25i.8 08.8 i3 i3.o oo.5 73 7 3.o 02:5 33 i3 2 . 9 04.6 9' 192. 06.7 53 252.8 08.8 i4 i4-o oo.5 74 74.o 02.6 34 133.9 04.7 9^ 193. 06.8 54 -53.8 08.9 i5 i5.o oo.5 75 7 5.o 02.6 35 i34. 9 04.7 9 5 i 9 4. 9 06.8 55 254.8 08.9 16 16.0 00.6 76 76.0 02.7 36 i35. 9 04.7 96 i 9 5. 9 06.8 56 255.8 08.9 17 17.0 00.6 77 77.0 02.7 37 i36. 9 o4.8 97 i 9 6. 9 06.9 57 256.8 09.0 18 18.0 00.6 78 78.0 02.7 38 137.9 04.8 98 i 9 7. 9 06. 9 58 257.8 09.0 r 9 19.0 00.7 79 79.0 02.8 39 i38. 9 04.9 99 i 9 8. 9 06.9 5 9 258.8 09.0 20 20. o 00.7 80 80.0 02.8 4o i3 9 . 9 04.9 200 i 99 . 9 07.0 60 25 9 .8 09.1 21 21 .0 00.7 81 81.0 02.8 i4i 140.9 04.9 201 200.9 07.0 261 260.8 09.1 22 22.0 oo. S 82 82.0 02.9 42 i4i .9 o5.o 02 201 .9 07.0 62 261.8 09.1 23 23.0 00.8 83 82.9 02.9 43 142.9 o5.o o3 202.9 07.1 63 262.8 9 .2 24 24.0 00.8 84 83. 9 02.9 44 i43. 9 o5.o o4 203.9 07.1 64 263.8 9 .2 25 a5.o 00.9 85 84.9 o3.o 45 i44-9 o5.i o5 204.9 07.2 65 264.8 9 .2 26 26.0 00.9 86 85. 9 o3.o 46 i45. 9 o5.i 06 205.9 07.2 66 265.8 9 .3 27 27.0 00.9 87 86.9 o3.o 47 146.9 o5.i 07 206.9 07.2 67 266.8 09.3 28 28.0 01 .0 88 87.9 o3.i 48 147-9 05.2 08 207.9 o 7 .3 68 26 7 .8 09.4 29 29.0 01 .0 89 88.9 o3.i 4 9 148.9 05.2 9 208.9 o 7 .3 6 9 268.8 9 .4 3o 3o.o 01 .0 9 89.9 o3.i 5o 149.9 05.2 TO 209.9 o 7 .3 70 269.8 9 .4 5i 3i.o 01. I 9 r 90.9 olTT i5i 150.9 o5.3 211 210.9 07.4 271 2 7 0.8 9 .5 32 3a.o 01. I 92 91.9 03.2 52 i5i .9 o5.3 12 21 I .9 07.4 72 2 7 1.8 09.5 33 33.o OI .2 93 92.9 03.2 53 i5 2 . 9 o5.3 i3 212.9 07.4 7 3 2 7 2.8 09.5 34 34.o 01 .2 94 93.9 o3.3 54 i53. 9 o5.4 i4 213.9 o 7 .5 74 2 7 3.8 09.6 35 35.o 01 .2 9 5 94.9 o3.3 55 i54. 9 o5.4 i5 214.9 o 7 .5 7 5 2 7 4.8 09.6 36 36.o 01.3 96 95.9 o3.4 56 155.9 o5.4 16 2 1 5 . 9' o 7 .5 7 6 2 7 5.8 09.6 3? 3 7 .o oi.3 97 96.9 o3.4 5 7 i56. 9 o5.5 17 216.9 07.6 77 2 7 6.8 09- 7 38 38.o oi.3 98 97-9 o3.4 58 157.9 o5.5 18 217.9 07.6 78 2 77 .8 09.7 39 39.0 01 .4 99 98.9 o3.5 5 9 158.9 o5.5 1 9 218.9 07.6 79 2 7 8.8 09.7 4o 4o.o oi .4 100 99-9 o3.5 60 r5 9 . 9 o5.6 20 219.9 7 . 7 80 279.8 09.8 4i 4i .0 oi .4 101 100.9 o3.5 161 160.9 o5.6 221 220.9 07. 7 281 280.8 09.8 42 4a.o o(.5 02 101 .9 o3.6 62 161 .9 >5. 7 22 221.9 7 . 7 82 281.8 09.8 43 43.o oi.5 o3 IO2 .9 o3.6 63 162.9 o5. 7 23 222.9 o 7 .8 83 282.8 09.9 44 44.o 01.5 04 103.9 o3.6 64 i63. 9 o5. 7 24 223.9 o 7 .8 84 283.8 09.9 45 45.o 01.6 o5 104.9 o3. 7 65 164.9 o5.8 25 224.9 7 -9 85 284.8 09.9 46 46.o 01 .6 06 05.9 o3. 7 66 :65. 9 o5.8 26 225.9 07.9 86 285.8 10.0 47 47.0 oi .6 07 [06.9 o3. 7 67 166.9 o5.8 27 226.9 o 7> 9 87 286.8 10.0 48 48.o 01.7 08 107.9 o3.8 68 167.9 o5. 9 28 227.9 08.0 88 28-7.8 i 10. i P 49.0 01.7 09 108.9 o3.8 69 168.9 05.9 29 228.9 08.0 8 9 1 288.8 10. i 5o 5o.o 01.7 10 109.9 o3.8 70 169. 9 o5. 9 3o 229.9 08.0 9 o ; 280.8 10. i ~5T 5i.o 01.8 III 110.9 o3. 9 171 170.9 06.0 23l 2 3o. 9 08. i 2 9 I 200.8 10.2 52 52.0 01.8 12 111.9 o3. 9 72 171-9 06.0 32 2 3i. 9 08. i 9 2 2 9 I .8 10.2 53 53.o 01.8 r3 12.9 o3. 9 73 172.9 06.0 33 232. 9 08. i 9 3 2 9 2.8 10.2 54 54.0 oi. 9 i4 13.9 04.0 74 173.9 06. i 34 33.9 08.2 94 293.8 10.3 55 55.o oi .9 i5 114.9 04.0 75 174.9 06. i 35 234.9 08.2 95 294.8 io.3 56 56.o 02.0 16 115.9 o4-o 76 175.9 06. i 36 35.9 08.2 ^ 2 9 5.8 10 3 57 5 7 .o 02 .0 17 110.9 04. i 77 176.9 06.2 37 36. 9 o8.3 97 296.8 10.4 58 58.o 02. o 18 117.9 04.1 78 177.9 06.2 38 37.9 o8.3 98 29 7 .8 10.4 ^ 59.0 02. i '9 118.9 04.2 79 178.9 06.2 3 9 38. 9 o8.3 99 208.8 10.4 ' 60 60.0 02.1 20 119.9 04.2 80 179.9 o6.3 4o 3 9 . 9 08.4 loo 299.8 io.5 Dist. Dep. Lat. Dist. Dep. Lat. )ist.| Dep. Lat. )ist. Dep. Lot Dist. Dep. Lat. [For 83 Degrees. TABLE II. [Page I9 Difference of Latitude and Departure for 3 Degrees. Dist 1 Lat. 01 .0 02.0 o3.o o4.o o5.o 06.0 07.0 08.0 o 9 .o IO.O Dep. 00. I OO. I 00.2 00 2 00.3 oo.3 00.4 00.4 oo.5 oo.5 Dist Lat. Dep. Dist Lat. Dep. Dist. Lat. Dep. Dist Lat. 1 Den. i 4 5 6 7 8 9 10 61 62 63 64 65 66 67 68 69 60.9 61.9 62.9 63.9 64.9 65.9 66.9 67-9 68.9 69.9 03.2 03.2 o3.3 o3.3 o3.4 o3.5 o3.5 .o3.6 o3.6 o3. 7 121 22 23 24 25 26 27 28 I 9 3o 120.8 121. 8 122.8 133.8 124.8 125.8 126.8 127.8 128.8 129.8 o6.3 06.4 06.4 o6.5 06.5 06.6 06.6 06.7 06.8 06.8 181 82 83 84 85 86 87 88 89 90 180.8 181.8 182.7 i83. 7 184.7 186.7 186.7 187.7 188.7 189.7 09.5 9 .5 09.6 09.6 09.7 09.7 09 8 09.8 09.9 09.9 24 1 42 43 44 45 46 47 48 g 240.7 242.7 243.7 244-7 245.7 246.7 247-7 248.7 12.6 12.7 12.7 12.8 12.8 12.9 i3.o i3.o ii II .0 00.6 7 1 70.9 03.7 i3i i3o.8 06.9 191 100.7 IO.O ?5i 25o. 7 i3 12 i3 i4 i5 1 6 12.0 i3.o i4-o i5.o 16.0 00.6 00.7 00.7 00.8 00.8 72 73 74 75 76 71-9 72.9 7 3. 9 74-9 75.9 o3.8 o3.8 03.9 03.9 04.0 32 33 34 35 36 i3i.8 i32.8 i33.8 i34.8 i35.8 06.9 07.0 07.0 07.1 07.1 P 1 06 191.7 i 9 3. 7 194.7 195.7 IO.O 10. 1 10.2 IO.2 TO. 3 52 53 54 55 56 251.7 252. 7 253. 7 254.7 255.6 13.2 13.2 i3.3 i3.3 i3 4 18 17.0 18.0 oo. 9 oo. 9 ' 77 78 76.9 77-9 04.0 04. i 38 i36.8 i3 7 .8 07.2 07.2 97 98 ^96.7 J 97-7 io.3 10.4 58 256.6 25 7 .6 i3.5 i3.5 1 9 19.0 OI .0 79 78.9 04.1 3 9 i38.8 7 .3 99 198.7 10.4 50 258.6 i3.6 20 20. 01 .0 80 79-9 04.2 4o 189.8 7 .3 200 199.7 io.5 60 25 9 .6 i3.6 21 21 .0 01. 1 81 80.9 04.2 i4i i4o.8 07.4 201 200 . 7 TO. 5 261 260.6 13.7 22 22.0 01 .2 82 81.9 04. 3 42 i4i.8 07.4 02 2OI .7 10.6 62 261.6 13.7 23 24 2-3.0 24.O 01.2 oi.3 83 84 82.9 83.9 04. 3 04.4 43 44 142.8 i43.8 7 .5 07.5 03 o4 202.7 203.7 10.6 10.7 63 64 262.6 263.6 i3.8 i3.8 25 26 25.0 26.0 oi.3 01.4 85 86 84.9 85. 9 04.4 o4.5 45 46 i44.8 i45.8 07.6 07.6 o5 06 204.7 205.7 10.7 10.8 65 66 264.6 265.6 i3. 9 l3.Q 27 27.0 01 .4 87 86.9 04.6 47 i46.8 07.7 07 206.7 10.8 67 266.6 14.0 28 28.0 oi.5 88 87-9 04.6 48 147-8 07.7 08 207.7 10.9 68 267.6 3o 2 9 .O 3o.o oi.5 01 .6 89 9 88.9 89.9 04.7 04.7 4.9 5o i48.8 149.8 07.8 07.9 09 10 208.7 209.7 10.9 II .0 69 70 268.6 26 9 .6 14.1 14.1 3i 3i.o 01 .6 9 1 90.9 04.8 i5i i5o.8 07.9 211 210.7 II. 271 270.6 14.2 3a 32.0 01.7 92 91.9 04.8 52 i5i.8 08.0 12 211.7 II .1 7 2 271 .6 14.2 33 33.o 01.7 93 92.9 04.9 53 i52.8 08.0 1 3 212.7 II .1 73 272.6 i4.3 34 34.o 01.8 94 93.9 04.9 54 i53.8 08. 1 i4 213.7 II .2 74 2 7 3.6 i4.3 35 35.o 01 .8 9 5 94-9 o5.o 55 i54.8 08. 1 1 5 214.7 IT. 3 75 274.6 \A.A 36 36.o 01 . 9 96 95.9 o5.o 56 i55.8 08.2 16 215.7 ii. 3 76 275.6 i4.4 37 36.9 01 .9 97 96.9 o5.i 57 i56.8 08.2 17 216.7 ii. 4 77 276.6 14.5 38 37.9 02.0 98 97-9 o5.i 58 167.8 08.3 18 217.7 11.4 78 277.6 i4.5 39 38.9 02. o 99 98.9 05.2 5 9 i58.8 08.3 X 9 218.7 ii. 5 79 278.6 i4.6 4o 3 9 . 9 02.1 100 99-9 05.2 60 i5 9 .8 08.4 20 219.7 ii. 5 80 279.6 14.7 4i 40.9 02.1 101 100.9 o5.3 161 160.8 08.4 221 220.7 11.6 281 280.6 14.7 42 4i. 9 O2. 2 02 101 .9 o5.3 62 161.8 08.5 22 221 .7 n. 6 82 281.6 14.8 43 42. 9 02.3 o3 102.9 o5.4 63 162.8 08.5 2.3 222.7 n .7 83 282.6 14.8 44 43. 9 02. 3 o4 103.9 o5.4 64 i63.8 08.6 223. 7 11.7 84 283.6 M-9 45 44. Q 02.4 o5 104.9 o5.5 65 164.8 08.6 25 224-7 TT.8 85 284.6 46 45. 9 02.4 06 105.9 o5.5 66 i65.8 08.7 26 225. 7 ii. 8 86 285.6 i5.o 47 46. 9 02. 5 07 106.9 o5.6 67 166.8 08.7 27 226.7 11.9 87 286.6 i5.o i 48 47-9 02. 5 08 107.9 o5. 7 68 167.8 08.8 28 227.7 11.9 88 287.6 i5. i 4 9 48. 9 02.6 09 108.9 o5. 7 69 168.8 08.8 29 228.7 12. 89 288.6 i5.i 5o 49-9 02.6 10 109.8 o5.8 70 169.8 08.9 3o 229.7 12.0 90 28 9 .6 l5.2 ' 5i 5o. 9 02.7 in no. 8 o5.8 171 170.8 08. 9 23l 230. 7 12. 1 291 290.6 15.2 52 5i.o 02.7 12 in. 8 o5. 9 72 171.8 09.0 32 23l. 7 12. I 92 291 .6 i5.3 53 02.8 i3 112. 8 o5. 9 73 172.8 09.1 33 232. 7 12.2 93 292.6 i5.3 54 53. 9 02.8 i4 ii3.8 06.0 74 173.8 09.1 34 233.7 12.2 94 2 9 3.6 i5.4 55 54. o 02.9 i5 n4.8 06.0 75 174.8 09.2 35 234.7 12.3 9 5 294.6 i5.4 56 55. 9 02.9 16 ii5.8 06. i 76 175.8 09.2 36 235. 7 12.4 96 2 9 5.6 i5.5 57 56. 9 o3.o 17 116.8 06. i 77 176.8 09.3 3 7 236.7 12.4 97 296.6 i5.5 58 57-9 o3.o 18 117.8 06.2 177-8 09.3 38 237.7 12.5 9 297.6 i5.6 59 58. 9 o3.i 19 118.8 06.2 79 178.8 09.4 39 238.7 12.5 99 298.6 i5.6 60 5 9 . 9 o3.i 20 119.8 o6.3 80 179.8 09.4 4o 239.7 12.6 3oo 299.6 i5. 7 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist.| Dep. Lat. Dist. Dep. Lat. [For 87 Degrees. Page 20] TABLE II. Difference of Latitude and Departure for 4 Degrees. Dist Lat. Dep. Dist Lat. Dep. Dist. Lat. Dep. Dist Lat. Dep. Dist. Lat. Dep. i 01 .0 OO.I 61 60.9 o4-3 121 120.7 08.4 181 180.6 12.6 24 1 240.4 IO 2 02. o 00. I 62 61.8 o4.3 22 121.7 o8.5 82 181.6 12.7 42 24i.4 16.9 3 o3.o 00.2 63 62.8 o4-4 23 122.7 08.6 83 182.6 12.8 43 242.4 17.0 4 o4.o oo.3 64 63.8 o4.5 24 123. 7 08.6 84 i83.6 12.8 44 243.4 17.0 5 o5.o oo.3 65 64-8 o4.5 25 124.7 08.7 85 i84.5 12.9 45 244-4 17.1 6 06.0 00.4 66 65.8 o4.6 26 125.7 08.8 86 i85.5 i3.o 46 245.4 17.2 7 07.0 oo.5 67 66.8 04.7 2 7 126.7 08.9 87 i86.5 i3.o 47 246.4 17.2 8 08.0 00.6 68 67.8 04.7 28 127.7 08.9 88 187.5 i3.i 48 247-4 i 7 .3 9 09.0 00.6 69 68.8 04.8 29 128.7 09.0 89 i88.5 13.2 4 9 248.4 17.4 10 10. 00.7 70 69.8 04.9 3o 129.7 09.1 90 189.5 i3.3 5o 249.4 17.4 ii II. 00.8 71 70.8 o5.o i3i i3o.7 09.1 191 190.5 i3.3 25l 25o.4 I 7 .5 12 12.0 00.8 7 2 71.8 o5.o 32 i3i. 7 09.2 92 191 .5 i3.4 52 25i.4 17.6 i3 i3.o 00.9 ?3 72.8 o5.i 33 l32. 7 09.3 93 192.5 i3.5 53 252.4 17.6 i4 i4.o 01 .0 74 7 3.8 05.2 34 i33. 7 09.3 94 193.5 i3.5 54 253.4 17.7 i5 i5.o or .0 75 74-8 05.2 35 i34- 7 09.4 95 i 9 4.5 i3.6 55 254.4 17.8 16 16.0 OI .1 76 7 5.8 o5.3 36 i35. 7 09.5 96 195.5 i3. 7 56 255.4 17.9 *7 17.0 01 .2 77 76.8 o5.4 37 i36. 7 09.6 97 196.5 13.7- 5 7 256.4 17.9 18 18.0 oi.3 78 77.8 o5.4 38 137.7 09.6 98 197.5 i3.8 58 267.4 18.0 1 9 19.0 oi.3 79 78.8 o5.5 3 9 i38. 7 09.7 99 198.5 i3. 9 5 9 258.4 18.1 20 20.0 01 .4 80 79.8 o5.6 4o 139. 7 09.8 200 199.5 14.0 60 259.4 18.1 21 20.9 oi.5 81 80.8 o5. 7 Mi i4o. 7 09.8 201 200.5 14.0 261 260.4 18.2 22 21.9 oi.5 82 81.8 o5. 7 42 i4i-7 09.9 02 2OI .5 14.1 62 261.4 i8.3 23 22.9 01.6 83 82.8 o5.8 43 l42. 7 IO.O 03 202.5 14.2 63 262.4 i8.3 24 23.9 01.7 84 83.8 05.9 44 i43.6 10. o4 203.5 14.2 64 263.4 18.4 25 24.9 01.7 85 84.8 05.9 45 i44-6 IO.I o5 204.5 i4.3 65 264.4 i8.5 26 .5.9 01.8 86 85.8 06.0 46 i45.6 IO.2 06 2o5.5 i4.4 66 265.4 18.6 27 26.9 01 .9 87 86.8 06. i 47 i46.6 io.3 07 206.5 i4.4 67 266.3 18.6 28 27.9 02 .0 88 87.8 06. i 48 147.6 io.3 08 207.5 i4.5 68 267.3 18.7 29 28.9 02. o 89 88.8 06.2 49 i48.6 10.4 09 208.5 14.6 69 268.3 18.8 3o 29.9 02.1 9 89.8 o6.3 5o 149-6 io.5 IO 209.5 14.6 70 269.3 18.8 3i 3o.o O2. 2 91 90.8 o6.3 161 i5o.6 io.5 211 210.5 14.7 271 270.3 18.9 32 31.9 02.2 92 91.8 06.4 52 i5i.6 10.6 12 211 .5 i4.8 72 271.3 19.0 33 32.9 02.3 93 92.8 o6.5 53 i52.6 10.7 13 212.5 14.9 73 272.3 19.0 34 33.9 02.4 94 93.8 06.6 54 i53.6 10.7 M 2i3.5 14.9 74 2 7 3.3 19.1 35 34.9 O2.4 95 94.8 06.6 55 i54.6 10.8 i5 2i4.5 i5.o 75 274.3 19.2 36 35.9 02.5 96 95.8 06.7 56 i55.6 10.9 16 ai5.5 i5.i 76 2 7 5.3 i 9 .3 37 36. 9 02. 6 97 96.8 06.8 57 i56.6 ii .0 17 216.5 i5.i 77 276.3 i 9 .3 38 3 7 . 9 02.7 98 97.8 06.8 58 i5 7 .6 ii .0 18 217.5 15.2 78 277-3 19.4 3 9 38.9 02.7 99 98.8 06.9 5 9 , i58.6 ii .1 J 9 218. 5 i5.3 79 278 3 19.5 4o 3 9 . 9 02.8 100 99.8 07.0 60 169.6 II .2 20 219.5 i5.3 80 279.3 i 9 .5 4i 40.9 02.9 101 100.8 07.0 161 160.6 II .2 221 220.5 i5.4 281 280.3 19.6 42 4i. 9 02.9 02 101.8 07.1 62 161.6 ii. 3 22 221 .5 i5.5 82 281.3 19.7 43 42.9 o3.o o3 102.7 07.2 63 162.6 ii. 4 23 222.5 i5.6 83 282.3 '9-7 44 43. 9 o3.i 04 io3.7 o 7 .3 64 i63.6 11.4 24 223.5 i5.6 84 283.3 19.8 45 44-9 o3.i o5 104.7 o 7 .3 65 164.6 ii. 5 25 224.5 i5.- 85 284.3 19.9 46 45. 9 o3.2 06 105.7 07.4 66 i65.6 ii. 6 26 225.4 i5.8 86 285.3 20.0 47 46. 9 o3.3 07 106.7 07.5 67 166.6 ii. 6 27 226.4 i5.8 87 286.3 20.0 48 47-9 o3.3 08 107.7 07.5 68 167.6 ii. 7 28 227.4 i5. 9 88 287.3 20. I 49 48. 9 o3.4 09 108.7 07.6 69 168.6 ii. 8 29 228.4 16.0 89 288.3 20.2 5o 49.9 o3.5 IO 109.7 07.7 70 169.6 11.9 3o 229.4 16.0 90 289 3 20.2 " 5i 5o. 9 o3.6 III 110.7 07.7 171 1-70.6 11.9 23l 23C.4 16.1 291 290.3 2o73~ 52 51.9 o3.6 12 111.7 07.8 72 i 7 i .6 12.0 32 a3i.4 16.2 92 291 .3 20.4 53 52.9 o3. 7 i3 111.7 07.9 73 I 7 2.6 12. 1 33 232.4 i6.3 93 292.3 20.4 54 53. 9 o3.8 i4 U3.7 08.0 74 173.6 12. I 34 233.4 i6.3 94 2 9 3.3 20.5 55 54-9 o3.8 i5 114.7 08.0 75 174.6 12.2 35 234.4 16.4 95 294. 3 20.6 56 55. 9 o3. 9 16 u5. 7 08. 1 76 175.6 12.3 36 235.4 i6.5 96 2 9 5.3 20.6 57 56. 9 04.6 17 116.7 08.2 77 176.6 12.3 37 236.4 i6.5 97 296.3 20. 7 58 5 7 . 9 04.0 18 117.7 08.2 78 177.6 12.4 38 23 7 .4 16.6 98 297.3 20.8 ^ 58. 9 04.1 '9 118.7 08.3 79 178.6 12.5 3 9 238.4 16.7 99 298.3 20.9 60 ^9^. 04.2 20 119.7 08.4 80 179.6 12.6 4o 2 3 9 .4 16.7 3oo 299.3 20.9 'list., Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. [For 86 Degrees. TABLE II. [Page 21 Difference of Latitude and Departure for 5 Degrees. Dist. Lat. Dep. Dist. Lat. Dep. Dist Lat. Dep. Dist. Lat. Dep. Dist.j Lat. Dep. i 01 .O OO.I 61 60.8 "bTT 121 120.5 io.5 181 i8o.3l i5. 24 1 240.1 21 ,O 2 02.0 00.2 62 61.8 o5.4 22 121 .5 10.6 82 i8i.3 iS.CJ 4a 24 1 . i 2 1 . 1 3 o3.o oo.3 63 62.8 o5.5 23 122.5 10.7 83 182.3 ^y i5.o 43 242. 21 .2 4 o4.o oo.3 64 63.8 o5.6 24 123.5 10.8 84 i83.3 y 16.0 44 243. 21.3 5 o5.o 00.4 65 64.8 o5. 7 25 124.5 10.9 85 184.3 16.1 45 244. 21 .4 6 06.0 oo.5 66 65. 7 o5.8 26 125.5 ii .0 86 i85.3 16.2 46 245. 21 .4 7 07.0 00.6 67 66.7 o5.8 27 126.5 ii .1 87 186.3 i6.3 47 246. 21.5 8 08.0 00.7 68 67.7 05.9 28 127.5 II .2 88 187.3 16.4 48 247. 21.6 9 09.0 00.8 69 68.7 06.0 ^9 128.5 II .2 89 i88.3 i6.5 49 248. 21 .7 10 10. 00.9 70 69.7 06. i 3o 129.5 II. 3 90 i8 9 .3 16.6 5o 249.0 21.8 ii II .0 01 .0 7i 70.7 06.2 i3i i3o.5 ii. 4 191 i 9 o.3 16.6 25l 250.0 21 . 9 1,2 12.0 01 .0 72 71-7 o6.3 32 i3i.5 ii. 5 92 i 9 i.3 16.7 52 25l .O 22 .O i3 i3.o OI .1 73 72.7 06.4 33 i3a.5 ii. 6 93 I 9 2.3 16.8 53 252 .O 27 . I i4 i3. 9 01 .2 74 73.7 06.4 34 i33.5 11.7 94 93.3 i6. 9 54 253.o 29 . 1 i5 14.9 oi.3 75 74-7 o6.5 35 i34.5 ii. 8 95 194.3 17.0 55 254.0 27. -2 16 i5. 9 oi .4 76 7 5. 7 06.6 36 i35.5 11.9 96 i 9 5.3 17.1 56 255.o 22.3 i? 16.9 oi.5 77 76. 7 06.7 3 7 i36.5 11.9 97 i 9 6.3 17.2 57 256.0 22.4 18 17.9 oi .6 78 77-7 06.8 38 i3 7 .5 12. 98 197-2 i 7 .3 58 257.0 22.5 '9 18.9 01.7 79 78.7 06.9 39 i38.5 12. I 99 I 9 8.2 i 7 .3 5 9 258.o 22.6 20 i9-9 Qi.7 80 79-7 07.0 4o 139.5 12.2 200 I 99 .2 17.4 60 259.0 22.7 21 20.9 01.8 81 80.7 07.1 i4i i4o.5 12.3 201 200.2 i 7 .5 261 260.0 22.7 22 21.9 oi .9 82 81.7 07.1 42 i4i.5 12.4 O2 2OI .2 17.6 62 261 .0 22.8 23 22.9 02. o 83 82.7 07.2 43 i42.5 12.5 o3 202.2 J 7-7 63 262.0 22. 9 24 23.9 02. i 84 83.7 o 7 .3 44 i43.5 12.6 o4 203.2 17.8 64 263.0 23.0 25 24.9 02.2 85 84-7 07.4 45 i44.4 12.6 o5 204.2 17.9 65 264.0 23.1 26 25.9 02.3 86 85. 7 o 7 .5 46 i45.4 12.7 06 205.2 18.0 66 265.0 23.2 27 26.9 02.4 87 86.7 07.6 47 i46.4 12.8 07 206 2 18.0 67 266.0 23.3 28 27.9 02.4 88 87.7 07.7 48 i4?-4 12.9 08 207.2 18. i 68 267.0 23.4 29 28.9 02.5 89 88.7 07.8 49 i48.4 i3.o 9 208.2 18.2 69 268.0 23.4 3o 29.9 02.6 90 89.7 07.8 5o 149.4 i3.i 10 209.2 i8.3 70 269.0 23.5 3i 3o.o 02.7 9 r 90.7 07.9 i5i i5o.4 13.2 211 210.2 18.4 271 270.0 23.6 32 3i. 9 02.8 92 91 .6 08.0 52 i5i.4 13.2 12 211 .2 i8.5 72 271.0 23.7 33 32.9 02.9 93 92.6 08. i 53 i5a.4 i3.3 13 212.2 18.6 ?3 272.0 23.8 34 35 33. 9 34.9 o3.o o3.i 9 i 95 93.6,08.2 94.6 o8.3 54 55 i53.4 i54.4 i3.4 i3.5 i4 i5 2l3.2 2l4.2 18.7 18.7 74 75 273.0 274.0 2 3. 9 24.0 36 35. 9 o3.i 96 o5.6 08.4 56 i55.4 i3.6 16 2l5.2 18.8 76 274.9 24.1 3 7 36. 9 03.2 97 96.6 o8.5 57 i56.4 i3. 7 17 2l6.2 18.9 77 275.9 24.1 38 37-9 o3.3 98 97.6 o8.5 58 i5 7 .4 i3.8 18 217.2 19.0 78 276.9 24.2 3 9 38. 9 o3.4 99 98.6 08.6 5 9 i58.4 i3. 9 J 9 218. 19.1 79 277.9 24.3 4o 3 9 .8 o3.5 IOO 99 - 6 08.7 60 159.4 i3. 9 20 2I 9 . 19.2 80 278.9 24.4 4. 4o.8 "oOT 10 1 100.6 "08.8 161 i6o.4 14.0 221 220. i 9 .3 281 279.9 24.5 42 4i.8 o3. 7 02 101 .6 08.9 62 161.4 14.1 22 221 . i 9 .3 82 280.9 24.6 43 42.8 o3. 7 o3 102.6 09.0 63 162.4 14.2 23 222. 19.4 83 281. 9 24.7 44 43.8 o3.8 o4 io3.6 09.1 64 i63.4 i4.3 24 223. i 9 .5 84 282. o 24.8 45 44.8 o3. 9 o5 104.6 09.2 65 i64.4 i4.4 25 224. 19.6 85 283. 9 24.8 46 45.8 04.0 06 io5.6 09.2 66 i65.4 i4.5 26 225. 19.7 86 284. 9 24. 9 47 46.8 04.1 07 106.6 09.3 67 166.4 i4.6 27 226. 19.8 87 285. 9 25.0 48 47-8 04.2 08 107.6 09.4 68 167.4 i4.6 28 227. 19.9 88 286. 9 25.1 49 48.8 o4.3 09 108.6 o 9 .5 69 168.4 i4. 7 2 9 228. 20.0 89 287. 9 25.2 5o 49.8 o4-4 10 109.6 09.6 70 169.4 i4.8 3o 22 9 . 20. 90 288. 9 25.3 5i 5o.8 o4.4 III i [-0.6 09.7 171 170.3 14.9 23 1 230. 20.1 291 28 9 . 9 25.4 52 5i.8 o4.5 12 ii i .6 09.8 72 i7i.3 i5.o 32 23l. 20.2 92 200. 9 25.4 53 52.8 o4.6 i3 112. 6 09.8 73 172.3 i5.i 33 232. 20.3 93 291.9 25.5 54 53.8 04.7 i4 n3.6 09.9 74 i 7 3.3 15.2 34 233. 2O.4 94 292.9 25.6 55 54.8 04.8 i5 if 4.6 10. 75 174.3 i5.3 3b 234. 20.5 9 5 293.9 25. 7 56 55.8 04.9 16 n5.6 10. I 76 175.3 i5.3 36 235. 20.6 96 294.9 25.8 57 56.8 o5.o 17 116.6 10.2 77 176.3 i5.4 37 236. 20.7 97 2 9 5. 9 2 5. 9 58 5 7 .8 o5.i 18 117.6 io.3 78 177-3 i5.5 38 23 7 . 20.7 98 2 9 6. 9 26.0 5 9 58.8 o5.i J 9 n8.5 10.4 79 178.3 i5.6 3 9 238. 20 8 99 2 9 7-9 26.1 60 5 9 .8 05.2 20 119.5 io.5 80 179.3 i5. 7 4o 23 9 . 20.9 3oo 2 9 8. 9 26.1 Dist. ttepT Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. [For 85 Degrees. i \ Page 22] TABLE II. Difference of Latitude and Departure for 6 Degrees. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. i 01 .0 00. I 61 60.7 o6.4 121 120.3 12.6 181 180.0 18.9 24 1 239.7 25.2 2 02 .0 00.2 62 61. 7 o6.5 22 131. 3 12.8 82 181.0 19.0 42 240,7 25.3 3 o3.o oo.3 63 62.7 06.6 23 r;2.3 12.9 83 182.0 19.1 43 24i-7 25.4 4 o4.o 00.4 64 63.6 06. 7 24 123.3 i3.o 84 i83.o 19.2 44 242.7 25.5 5 o5.o oo.5 65 64.6 6.8 25 j?4.3 i3.i 85 184.0 1 9 .3 45 243.7 1:5.6 6 06.0 00.6 66 65.6 06.9 ?6 >a5.3 l3.3 86 i85.o 19.4 46 244.7 25, 7 7 07.0 00.7 67 66.6 07.0 y~ t^t>.3 i3.3 87 186.0 19.5 4? 245.6 25.8 8 08.0 00.8 68 67.6 37. i 28 127.3 i3.4 8S 187.0 19.7 48 246.6 25 .9 9 09.0 00.9 69 68.6 07.2 29 128.3 i3.5 89 188.0 19.8 49 247.6 26.0 10 09.9 01 .0 70 69.6 07.3 3o 1:19.3 i3.6 9 i8 9 .o *9-9 5o 248.6 26.1 ii 10.9 01 .1 7i 70.6 07.4 i3i i3o.3 i3.7 191 1 9 0.0 20.0 25l 24 9 -6 26.2 12 11.9 oi.3 72 71.6 07. j 32 i3i.3 J.3.B 92 i 9 o. 9 20.1 5a 2 5o.6 26.3 i3 12.9 01 .4 73 72.6 07.6 33 i32.3 -.9 93 i 9 i. 9 20.2 53 a5i.6 26.4 i4 13.9 ci.5 74 7 3.6 07.7 34 i33.3 14.0 94 I 9 2. 9 20. 3 54 252.6 26.6 i5 14.9 01 .6 75 74.6 07.8 35 i34.3 4.i 95 i 9 3. 9 20.4 55 253.6 26.7 16 15.9 01.7 76 7 5.6 07.9 36 i35.3 14.2 96 194.9 20.5 56 254.6 26.8 *7 16.9 01.8 77 76.6 08.0 37 *35.2 i4.3 97 195.9 20. 6 5 7 255.6 26.9 18 17.9 01 .9 78 77-6 08.2 38 1 37. 2 i4.66.5 28.0 29 28.8 o3.o 89 88.5 09.3 49 148. i5.6 09 207.9 2!. 8 69 267.5 28.1 3o 29.8 o3.i 90 8 9 .5 09.4 5o 149- i5. 7 10 208.8 22.0 70 268.5 28.2 3i 3o.8 03.2 9 1 90.5 09.5 i Si i5o. i5.8 211 "20978" 22. 1 271 269.5 aO" 02 3i.8 o3.3 92 9.. 5 .x;.6 52 i5i. i5. 9 12 210.8 22.2 7 2 270.5 28.4 33 32.8 o3.4 9 3 92.5; 09.7 53 1 52. 2 16.0 i3 211.8 22.3 73 271 .5 28.5 34 33.8 o3.6 94 V 3.5:o 9 .8 54 i53.a 16.1 i4 212.8 22.4 74 272.5 28.6 35 34.8 o3. 7 95 94 5 1 09.9 55 i54.2 16.2 i5 2i3.8 22. r > 7 5 2 7 3.5 .8.7 36 35.8 o3.8 96 9 5 5 JO.O 56 i55. i6.3 16 -M4.8 22.1) 76 2-74.5 28.8 3 7 36.8 03:9 97 96.5 1O. 1 5 7 1 56, 16.4 17 ji5:tj ?a.7 77 2 7 5.5 29.0 38 3 7 .8 04.0 ^ 97-5 IO.2 58 i5 7 . i6.5 i5 ->3.8 23.5 85 283.4 20.8 46 45.7 04.8 06 io5.4 ii .1 66 i65. 17-4 26 aa4.8 23.6 86 284.4 | 29.9 47 46. 7 04.9 07 106.4 I I .2 67 166. i 7 .5 27 a:>5.3 23. 7 87 ao:>.4 ! 3o.o 48 47-7 o5.o 08 107.4 ii. 3 68 167. 17.6 a6 at>.8 23.8 88 286.4 3u.i P 48. 7 o5.i 09 108.4 ii. 4 69 168. 17.7 *9 rJrj.-i 2 3. 9 89 287.4 30.2 5o 49-7 05.2 10 109.4 ii. 5 70 169. 17.8 V) -.'28.7 24.0 90 j.88.4 3o.3 5i 5o. 7 "o5TI i ii 1 10.4 "n.6 171 170. 17.9 all 329.7 24.1 291 209.4 , 3o.4 52 5i. 7 o5.4 12 in .4 11.7 72 171. 18.0 32 230.7 24.3 92 290.4 3o.5 53 52. 7 o5.5 i3 112.4 n. 8 73 172. 18.1 33 23l .7 24-4 93 291 .4 3o.6 54 53. 7 o5.6 i4 ii3.4 11.9 74 173.0 18.2 34 232.7 24.5 94 292.4 30.7 55 54.7 o5. 7 i5 n4-4 12. 75 i74.o i8.3 35 233.7 24.6 95 2 9 3.4 3o.8 56 55. 7 05.9 16 n5.4 12. I 76 175.0 18.4 36 234-7 24.7 96 2 9 4-4 3o.o 57 56. 7 06.0 17 116.4 12.2 77 176.0 i8.5 37 235.7 24.8 97 2 9 5.4 3i.o 58 5 7 . 7 06. i 18 1 1 7 .4 12.3 78 177.0 18.6 38 236.7 24.9 93 2 9 6.4 3i.i J9 58. 7 06.2 '9 ii8.3 12.4 79 178.0 18.7 3 9 2*37.7 25.0 Q 9 297.4 3i.3 60 59.7 o6.3 20 119.3 12.5 80 179.0 18.8 4o 238.7 25.1 3oo 2 9 8.4 3i.4 Dist. Dep. j Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. |Dist. Dep. Lat. "" i [For 84 Degrees. TABLE II. [Page 23 Difference of Latitude and Departure for 7 Degrees. Dist Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. I 01 .0 00. 1 61 6o.5 07.4 121 120. 14.7 181 179.7 22.1 241 239.2 2 9 .4 2 02.0 00.2 62 6i.5 07.6 22 121 . i4-9 82 180.6 22.2 42 240.2 29.5 3 o3.o GO. 4 63 62.5 07.7 23 122. i5.o 83 181.6 22.3 43 24l .2 ~ ,. 29.0 4 o4.o oo.5 64 63.5 07.8 24 123. i.5. i 84 182.6 22.4 44 242 . 2 7 29.7 5 o5.o 00.6 65 64.5 07.9 25 124. 15.2 85 i83.6 22.5 45 243.2 7 i 20. 6 06.0 00.7 66 65.5 08.0 26 125. i5.4 86 184.6 22.7 46 244-2 3o.o 7 06.9 00.9 67 66.5 08.2 27 126. i5.5 87 i85.6 22.8 47 245.2 3o.i 8 07.9 01 .0 68 6 7 .5 o8.3 28 127.0 i5.6 88 186.6 22.9 48 246.2 30.2 9 08.9 01 . I 69 68.5 08.4 2 9 128.0 i5. 7 89 187.6 23.0 49 247. 3o.3 10 09.9 01 .2 70 6 9 .5 o8.5 3o 129.0 i5.8 9 188.6 23.2 56 248. 3o.5 1 1 10.9 oi.3 7i 7 o.5 08.7 i3i i3o.o 16.0 191 189.6 23.3 25l 249. 3o.6 12 11.9 oi.5 72 7 i.5 08.8 32 i3i .0 16.1 92 190.6 23.4 52 250. 3o. 7 i3 12.9 01 .6 73 7 2.5 08.9 33 l32.0 16.2 93 191 .6 2.3.5 53 25l. 3o.8 i4 i3. 9 01.7 74 73.4 09.0 34 i33.o i6.3 94 192.6 23.6 54 252. 3i.o i5 14.9 01.8 75 74-4 09.1 35 i34.o i6.5 95 193.5 23.8 55 253. 3i.i 16 i5. 9 01 .9 76 75.4 o 9 .3 36 i35.o 16.6 96 194.5 23.9 56 254. 3l.2 17 16.9 02. I 77 76.4 09.4 37 i36.o 16.7 97 195.5 24.0 5 7 255. 3i.3 18 17.9 02.2 78 77-4 09.5 38 137.0 16.8 98 i 9 6.5 24.1 58 256. 3i.4 1 9 18.9 02.3 79 78.4 09.6 3 9 i38.o 16.9 99 197.5 24.3 5 9 267.1 3i.6 20 19.9 02.4 80 79-4 09.7 4o 139.0 17.1 200 .98.5 24.4 60 258.i 3i. 7 21 20.8 02.6 81 80.4 09.9 i4i 139.9 17.2 201 199.5 24.5 261 269. i 3i.8 22 21.8 02.7 82 81.4 IO.O 42 140.9 i 7 .3 02 200.5 24.6 62 260.0 3i. 9 23 22.8 02.8 83 82.4 10. I 43 141.9 17-4 03 201 .5 24.7 63 261 .0 32.1 24 23.8 02 .9 84 83.4 10.2 44 142.9 i 7 .5 o4 2O2 .5 24.9 64 262.0 32.2 25 24.8 o3.o 85 84.4 10.4 45 i43.o 17.7 o5 2o3.5 25.0 65 263.0 32.3 26 a5.8 03.2 86 85.4 io.5 46 144.9 17.8 06 2o4.5 25.1 66 264.0 32.4 27 26.8 o3.3 87 86.4 10.6 4 7 i45. 9 17.9 07 205.5 25.2 67 265.o 32.5 28 27.8 o3.4 88 8 7 .3 10.7 48 146.9 18.0 08 206.4 25.3 68 266.0 32. 7 29 28.8 o3.5 89 88.3 10.8 49 147.9 18.2 09 207.4 25.5 6 9 267 . o 32.8 3o 29.8 o3. 7 9 8 9 .3 II .0 5o 148.9 i8.3 10 208.4 25.6 70 268.0 32. 9 3i 3o.8 o3.8 9 ! 90.3 1 1 . i i5i 149.9 18.4 211 209.4 25. 7 271 269.0 33.0 3? 3i.8 03.9 92 9 i.3 I I .2 52 i5o-9 i8.5 12 210.4 25.8 72 270.0 | 33. i 33 32.8 04.0 93 9P..3 ii. 3 53 i5i .9 18.6 i3 211 .4 26.0 78 271 .c | 33.3 34 33. 7 o4. i 94 9 3.3 n. 5 54 152.9 18.8 i4 212.4 26.1 74 272.0 33.4 35 34-7 o4.3 95 94.3 11. 6 55 i53.8 18.9 i5 2i3.4 26.2 75 273.0 33.5 36 35.7- o4-4 96 95.3 11.7 56 i54.8 19.0 16 214.4 26.3 76 273.9 33.6 37 36. 7 o4.5 97 96.3 11. 8 57 i55.8 19.1 17 2i5.4 26.4 77 274.9 33.8 38 37-7 04.6 98 97-3 11.9 58 i56.8 19.3 18 216.4 26.6 78 2 7 5. 9 33.9 3 9 38.7 04.8 99 98.3 12. I 59 167.8 19.4 J 9 217.4 26.7 79 276.9 34.o 4o 3 9 .7 04.9 100 99-3 12.2 60 i58.8 i 9 .5 20 218.4 2.6.8 80 277. 9. 34.i 4r 40.7 o5.o IOI 100.2 12.3 161 159.8 19.6 221 219.4 26.9 281 278. 9 34.2 42 4i-7 o5.i 02 IOI .2 12.4 62 160.8 19.7 22 220.3 27.1 82 279.9 34-4 43 42-7 05.2 o3 102.2 12.6 63 161.8 19.9 23 221.3 27.2 83 280 . 9 34.5 44 43. 7 o5.4 o4 103.2 12.7 64 162.8 20.0 24 222.3 27.3 84 281. 9 34.6 45 44-7 o5.5 o5 104.2 12.8 65 i63.8 20. I 25 223.3 27.4 85 282.9 34-7 46 45.7 o5.6 06 io5. 2 12-9 66 164.8 20.2 26 224.3 27.5 86 283. 9 34-9 47 46.6 o5. 7 07 106.2 i3.o 67 i65.8 20.4 27 225.3 27.7 87 284.9 35.o 48 47-6 o5.8 08 IO7.2 l3.2 68 166.7 20.5 28 226.3 27.8 88 285.9 35.i 49 48.6 06.0 09 108.2 r3.3 69 167.7 20.6 29 227.3 27.9 89 286.8 35.2 5o 49-6 06.1 10 109.2 i3.4 70 168.7 20-7 3o 228.3 28.0 9 287.8 35.3 5i 5o.6 06.2 in I 10.2 i3.5 171 169.7 20.8 23 I 229.3 28.2 29, 288.8 35.5 52 5t.6 o6.3 12 III .2 i3.6 72 170.7 21 .0 32 23o.3 28.3 92 289.8 35.6 53 52.6 o6.5 i3 I 12.2 i3.8 73 171.7 21 .1 33 2 3i.3 28.4 9 3 290.8 35.7 54 53.6 06.6 i4 II3.2 i3. 9 74 172.7 21 .2 34 232 3 28.5 94 291 .8 35.8 55 54.6 06.7 i5 Il4-I i4-o 7 5 ; 7 3.7 21.3 35 233.2 28.6 95 292.8 3i> . o 56 55.6 06.8 16 iiS.i i4.i 76 174-7 21.4 36 234.2 28.8 96 293.8 36 i 57 58 56.6 5 7 .6 06.9 07.1 17 18 116.1 117.1 i4-3 i4-4 77 78 175.7 176.7 21.6 21.7 37 38 235.2 236.2 28.9 29.0 97 98 294.8 2 9 5.8 36.2 36.3 59 60 58.6 5 9 .6 07.2 o 7 .3 9 20 118.1 1 19.1 i4.5 i4.6 79 80 177-7 178.7 21.8 21.9 3 9 4o 237.2 238.2 29.1 29.2 99 3oo 296.8 297.8 36.4 36.6 Wsu Dep. Lat. Dist, Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. [For 83 Degrees. Page 24] TABLE II. Difference of Latitude and Departure for 8 Degrees. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. 1 Lat. Dep. i 01 .0 00. 1 61 6o.4 o8.5 121 119.8 16.8 181 179.2 25.2 24 1 238.7 33.5 2 02. o oo.3 62 6i.4 08.6 22 120.8 17.0 82 180.2 25.3 42 239.6 33. 7 3 o3.o 00.4 63 62.4 08.8 23 121. 8 17.1 83 181.2 25.5 43 240.6 33.8 4 04.0 00.6 64 63.4 08.9 24 122.8 I 7 .3 84 182.2 25.6 44 241.6 34.o 5 o5.o 00.7 65 64.4 09.0 25 123.8 17-4 85 i83.2 25.7 45 242.6 34.i 6 o5 .0 00.8 66 65.4 09.2 26 124.8 I 7 .5 86 184.2 25.9 46 243.6 34.2 7 ., y 06.9 01 .0 67 66.3 09.3 27 125.8 17.7 87 i85.2 26.0 47 244.6 34-4 g 07.9 OI.I 68 6 7 .3 09.5 28 126.8 17.8 88 186.2 26.2 48 245.6 34.5 9 08.9 oi.3 69 68.3 09.6 2 9 127.7 18.0 89 187.2 26.3 49 246.6 34-7 10 09.9 01 .4 70 6 9 .3 09.7 3o 128.7 18.1 9 188.2 26.4 5o 247.6 34.8 ii 10.9 I oi .5 7i 70.3 09.9 i3i 129.7 18.2 191 189. 26.6 25l 248.6 34. 9 12 11.9 01 .7 7 2 7 i.3 IO.O 32 i3o.7 18.4 92 190. 26.7 52 249.5 35.i i3 12.9 01.8 73 7 2.3 IO.2 33 i3i .7 i8.5 93 191. 26.9 53 2 5o.5 35.2 i4 13.9 oi .9 74 7 3.3 io.3 34 i32. 7 18.6 94 192. 27.0 54 25i.5 35.3 i5 i4-Q 02.1 75 74.3 10.4 35 i33. 7 18.8 9 5 i 9 3. 27.1 55 252.5 35.5 16 i5.8 O2. 2 76 7 5.3 10.6 36 i347 18.9 96 i 9 4. 2 7 .3 56 253.5 35.6 i? 16.8 02.4 77 7 6.3 10.7 37 i35. 7 19.1 97 i 9 5. 27.4 57 254.5 35.8 18 17.8 02.5 78 77.2 10.9 38 i36.7 I9..2 98 196. 27.6 58 255.5 35. 9 19 18.8 02.6 79 78.2 II .0 3 9 137.7 i 9 .3 99 I 9 7- 27.7 5 9 256.5 36.o 20 19.8 02.8 80 79.2 ii .1 4o i38.6 i 9 .5 200 198. 27.8 60 2 5 7 .5 36.2 21 ?o.8 02.9 ~8T 80.2 11. 3 Mi i3 9 .6 19.6 201 1 99 .0 28.0 261 258.5 36.3 22 21.8 o3.i 82 81.2 ii. 4 42 i4o.6 19.8 O2 200.0 28 i 62 2 5 9 .5 36.5 23 22.8 03.2 83 82.2 ii. 6 43 i4i.6 19.9 o3 201 .O 28.3 63 260.4 36.6 24 23.8 o3.3 84 83.2 ii .7 44 142.6 20.0 o4 202. 28.4 64 261.4 36. 7 25 24.8 o3.5 85 84.2 ii. 8 45 i43.6 20.2 o5 203.0 28.5 65 262.4 36. 9 26 25.7 o3.6 86 85.2 12.0 46 i44-6 20.3 06 204.0 28.7 66 263.4 3 7 .o 27 26.7 o3.8 87 86.2 12. I 47 i45.6 20.5 07 205.0 28.8 67- 264.4 3 7 .2 28 27.7 03.9 88 87.1 12.2 48 i46.6 20.6 08 206.0 28.9 68 265.4 3 7 .3 29 28.7 04.0 89 88. 12.4 49 i47-5 2O.7 09 207.0 2 9 .I 69 266.4 3 7 -4 3o 29.7 04.2 9 89. 12.5 5o i48.5 20. 9 10 208.0 29.2 70 267.4 3 7 .6 3i 3o. 7 o4.3 9 1 90. 12.7 i5i i49.5 21 .0 211 208. 9 29.4 271 268.4 37-7 32 3i. 7 04. 5 92 91. 12 8 52 i5o.5 21 .2 12 | 209.9 2 9 .5 72 20 9 .4 37 9 33 32. 7 04.6 9 3 92. 12.9 53 i5i.5 21.3 13 210. 9 2 9 .6 73 270.3 38.o 34 33. 7 04.7 94 9 3. i3 i 54 i52.5 21.4 i4 211 . 9 2 9 .8 74 271 .3 38.i 35 34-7 04.9 95 94. 13.2 55 i53.5 21.6 i5 212. 9 29.9 75 272.3 38.3 36 35.6 o5.o 96 9 5. i3 4 56 i54.5 21.7 16 2i3. 9 3o.i 76 2 7 3.-3 38.4 37 36.6 o5.i 97 96. i3.5 57 i55.5 21. 9 17 214-9 30.2 77 274.3 38 6 36 3 7 .6 o5.3 98 97.0 i3.6 58 i56.5 22. 18 2i5. 9 3o.3 78 2 7 5.3 38. 7 3 9 38.6 o5.4 99 98.0 i3.8 5 9 i5 7 .5 22.1 r 9 216.9 3o.5 79 276.3 38.8 4o 3 9 .6 o5.6 IOO 99.0 i3. 9 60 t58.4 22.3 20 217-9 3o.6 80 277-3 3 9 .o 4i 4o.6 "BTy 101 IOO.O 14.1 161 75^7 ~22~7Z 221 TfO" ~3o78~ 281 278.3 3 9 .i 42 4i.6 o5.8 02 101 .0 .4.2 62 160.4 22.5 22 21 9 .8 30.9 82 27 9 .3 3$. 2 43 42.6 06.0 o3 1 02 .0 i 1 4. 3 63 161.4 22.7 23 220.8 3i .0 83 280.2 3$.4 44 43.6 06. i o4 io3.o i4.5 64 162.4 22.8 24 221.8 3l.2 84 281.2 39.5 45 44.6 o6.3 o5 104.0 i4 6 65 i63.4 23.0 25 222.8 3i.3 85 282.2 39.7 46 45.6 06.4 06 io5.o i4.8 66 i64.4 23.1 26 223.8 3i.5 86 283.2 39.8 4? 46.5 o6.5 07 106.0 i4.9 67 i65.4 23.2 27 224.8 3i.6 87 284.2 39.9 48 47-5 06.7 08 106.9 i5 o 68 166.4 23.4 28 225.8 3i. 7 88 285.2 4o.i 49 48.5 06.8 09 107.9 i5> 69 167.4 23.5 29 226.8 3i. 9 89 286.2 40.2 5o 49.5 07.0 10 108.9 1 5. 3 70 i68.3 23. 7 3o 227.8 32.0 90 287.2 4o.4 5i 5o.5 07.1 II I 109.9 i5.4 171 169.3 23.8 23l 228.8 32.1 291 288.2 4o.5 52 51-5 07.2 12 110.9 i5.6 72 170.3 23. 9 32 220.7 32.3 9 2 289.2 4o.6 53 52.5 07.4 i3 in .9 15.7 73 i 7 i.3 24.i 33 23o.7 32.4 9 3 2 9 0. 4o.8 54 53-5 o 7 .5 i4 112.9 i5. 9 74 172.3 24.2 34 23i. 7 32.6 94 2 9 I. 40.9 55 54-5 07.7 i5 113.9 16.0 75 i 7 3.3 24-4 35 232.7 32. 7 9 5 202. 4i.i 56 55-5 07.8 16 114.9 16 i 76 174.3 24.5 36 233.7 32.8 96 2 9 3. 41.2 57 56.4 07.9 17 u5.9 16 3 77 i 7 5.3 24.6 3 7 234.7 33.o 97 2 9 4. 4i.3 58 57-4 08. i 18 116.9 i6'4 78 176.3 24.8 38 235. 7 33.i 98 295. 4i.5 59 58.4io8.2 1 9 117. 8 16.6 79 177-3 24.9 3 9 236.7 33.3 99 296. 4i 6 60 59-4|8.4 20 118.8 16.7 80 I 78 . 2 25.1 4o 237.7 33.4 3oo 2 97 . 4i.6 Dist., 1 Dep. 1 Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat." [For 82 Degrees. TABLE II LPage25 Difference of Latitude and Departure for 9 Degrees. DistJ Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. I oi .0 00.2 61 60.2 o 9 .5 121 119.5 "18.9 181 178.8 28.3 24 1 238.0 3 7 . 7 2 02.0 oo.3 62 61.2 o 9 . 7 22 120.5 19.1 82 179.8 28.5 42 239.0 3 7 . 9 3 o3.o oo.5 63 62.2 9-9 23 121. 5 19.2 83 180.7 28.6 43 2.40.0 38.o 4 o4.o 00.6 64 63.2 10. 24 122.5 < 9 .4 84 181.7 28.8 44 24 1 .0 38.2 5 o4. 9 00.8 65 64.2 10.2 25 123.5 19. 6 85 182.7 28.9 45 242.0 38.3 6 o5.. 9 00.9 66 65.2 io.3 26 124.4 19.7 86 183.7 29.1 46 243.0 38.5 7 06. 9 01 .1 67 66.2 io.5 2 7 125.4 19.9 87 iS4-7 29.3 47 244.0 38.6 8 07- 9 oi.3 68 67.2 10.6 28 126.4 20.0 88 ifi5.7 29.4 48 244.9 38.8 9 08. 9 01 .4 6 9 68.2 10.8 2 9 127.4 20.2 89 186.7 29.6 49 245.9 3g.o 10 _9_-9_ oi .6 70 69.1 II .0 3o 128.4 20.3 90 187.7 29.7 5o 246.9 3 9 .i ii 10.9 oi. 7 7i 70. ii .1 i3i 129.4 20.5 191 188.6 29.9 5i 24-7.9 3 9 .3 12 11.9 oi .9 72 71- ii. 3 32 i3o.4 20. 6 92 189.6 3o.o 52 248.9 3 9 .4 i3 12.8 02. 73 72. ii. 4 33 i3i.4 20.8 93 190.6 30.2 53 249.9 3 9 .6 i4 i3.8 02.2 74 73. 11.6 34 i3a.4 21 .O 94 191 .6 3o.3 54 260.9 3 9 .7 i5 i4.8 02.3 75 74- 11.7 35 i33.3 21 .1 95 192.6 3o.5 55 25l .9 3 9 . 9 16 i5.8 02.5 76 75. ii. 9 36 i34.3 21.3 96 193.6 3o. 7 56 252.8 4o.o 17 16.8 02. 7 77 76. 12.0 3 7 i35.3 21.4 97 194.6 3o.8 57 253.8 40.2 18 i 7 .8 02.8 78 77.0 12.2 38 i36.3 21.6 98 195.6 3i .0 58 254-8 4o.4 1 9 18.8 o3.o 79 78.0 12.4 3 9 i3 7 .3 21. 7 99 196.5 3i.i 5 9 255.8 4o.5 20 19.8 o3.i 80 79.0 12.5 4o i38.3 21.9 200 197.5 3i.3 60 256.8 40.7 21 20. 7 o3~TT 81 80.0 12.7 MI "i3 9 .3 22.1 20 1 198.5 3i.4 261 25 7 .8 40.8 22 21.7 o3.4 82 81.0 12.8 42 i4o.3 22.2 02 199.5 3i.6 62 258.8 4i .0 23 22.7 o3.6 83 82.0 i3.o 43 i4i .2 22.4 o3 200.5 3i.8 63 2 5 9 .8 4i.i 24 23. 7 o3.8 84 83.o i3.i 44 142.2 22.5 o4 201 .5 3i. 9 64 260. 7 4i.3 25 24-7 o3. 9 85 84.0 i3.3 45 143.2 22. 7 o5 202 . 5 32.1 65 261 .7 4i.5 26 25. 7 04.1 86 84.9 i3.5 46 i44- 22.8 06 203.5 32.2 66 262.7 4t.6 27 26.7 04.2 87 85. 9 i3.6 4 7 i45. 23.0 07 204.5 32.4 67 263.7 4i.8 28 27.7 o4.4 88 86.9 i3.8 48 i46. 23.2 08 205.4 32.5 68 264.7 4i . 9 2 9 28.6 o4.5 8 9 87.9 i3. 9 49 i4 7 . a3.3 09 206.4 32. 7 69 265.7 42.1 3o 29.6 o4-7 9 88. 9 i4.i 5o 1 48. 23.5 10 207.4 32. 9 70 266.7 42.2 3i 3o.6 04.8 9 i 89-9 14.2 i5i 149. 23.6 21 I 208.4 33.o 271 267.7 42-4 32 3i.6 o5.o 9 2 9-9 i4.4 52 i5o. 23.8 12 209.4 33.2 72 268.7 42.6 33 32.6 05.2 9 3 9 i . 9 i4.5 53 iSi. 23. 9 13 210.4 33.3 7 3 269.6 42.7 34 33.6 o5.3 9 4 9 2.8 i4-7 54 152. 24.1 .14 211 .4 33.5 74 270.6 42. 9 35 34.6 o5.5 9 3.8 i4- 9 55 1 53. 24.2 i5 212.4 33.6 75 271 .6 43.o 36 35.6 o5.6 96 9 4-8 i5.o 56 1 54. 24-4 16 2i3.3 33.8 76 272.6 43.2 37 36.5 o5.8 97 9 5.8 l5.2 5 7 i55. 24.6 17 214.3 33. 9 77 2 7 3.6 43.3 38 3 7 .5 o5. 9 98 9 6.8 i5.3 58 1 56, 24. 7 18 2i5.3 34.i 78 274.6 43.5 3 9 38.5 06. i 99 97 .8 i5.5 5 9 i5 7 .o 24.9 '9 216.3 34.3 Z 9 2 7 5.6 43.6 4o 3 9 .5 o6.3 100 9 8.8 i5.6 60 1 58.o 25.0 20 217.3 34-4 80 276.6 43.8 4i 4o.5 06.4 IOI 99-8 7578" 161 169.0 25.2 221 2i8.3 34.6 ^8T 277.5 44.o 42 4i.5 06.6 02 100.7 16.0 62 160.0 25.3 22 219.3 34-7 82 278.5 44.1 43 42.5 06.7 o3 101 .7 16.1 63 161 .0 25.5 23 220.3 34-9 83 279.5 44.3 44 43.5 06. 9 o4 102.7 i6.3 64 162.0 25. 7 24 221 .2 35.o 84 280.5 44.4 45 44-4 07.0 o5 io3.7 16.4 65 i63.o 25.8 25 222.2 35.2 85 281.5 44.6 46 45.4 07.2 06 104.7 16.6 66 164.0 26.0 26 223.2 35.4 86 282.5 44-7 47 46.4 07.4 07 io5-7 16.7 6 7 164.9 26.1 27 224-2 35.5 87 283.5 44- 9 48 4 7 .4 c 7 .5 08 106.7 i6. 9 68 165.9 26.3 28 225.2 35. 7 88 284.5 45.i J9 5o 48.4 4 9 .4 07.7 07.8 9 10 107.7 108.6 17.1 17.2 69 70 166.9 16-7.9 26.4 26.6 ? 9 3o 226.2 227.2 35.8 36.o 89 90 285.4 286.4 45.2 45.4 ii 5o.4 08.0 in io 9 .6 17.4 i 7 i 168.9 26.8 23l 228.2 "36TT 291 287.4 45.5 52 5i.4 08. i 12 110.6 i 7 .5 72 169.9 26.9 32 22 9 . 36.3 9 l 288.4 45.7 53 52.3 o8.3 i3 in .6 17.7 ?3 1-70.9 2 7 .I 33 230. 36.4 93 289.4 45.8 54 53.3 08.4 i4 112. 6 17.8 74 171.9 2 7 .2 34 23l. 36.6 94 290.4 46.o 55 54.3 08.6 i5 u3.6 18.0 75 172.8 2 7 .4 35 232. 36.8 95 291 .4 46.1 56 55.3 08.8 16 n4.6 18.1 7 6 173.8 2 7 .5 36 233. 36.9 96 292.4 ** ** 46.3 57 58 1 56.3 5 7 .3 58.3 5.3_ 08. 9 09.1 9 .2 o 9 .4 *? 18 *9 20 u5.6 ii6.5 ii 7 .5 n8.5 co in , 291 .5 5i.4 5? 56.i 09.9 17 Il5.2 20. 3 77 174.3 3o. 7 37 233.4 41.2 97 292.5 5i.6 58 5 7 .i 10. I 18 I l6.2 20.5 78 175.3 3o.o 38 234.4 4i.3 98 2 9 3.5 5i. 7 r 9 58.i 10.2 T 9 117.2 20.7 79 176.3 3i.i 3 9 235.4 4i.5 99 2 9 4.5 5i. 9 60 5,., 10.4 20 118.2 20.8 80 177-3 3i.3 4o 236.4 41.7 3oo 2 9 5.4 52.1 Dist Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. [Fir 30 Degrees. TABLE II. [Pa at . 27 Difference of Latitude and Departure for 11 Degrees. Dist. Lat. Dep. Dist. Lat. Dep. Dist Lat. Dep. Dist Lat. Dep. Dist Lat Dep. i oi .0 00.2 ~~6T -59^9 ii. 6 121 n'8,8 23.1 787 177.7 34.5 241 236.6 46.0 2 3 4 5 6 02. o 02.9 o3. 9 04.9 05.9 00.4 00.6 00.8 01 .0 01 .1 62 63 64 65 66 60.9 61.8 ' 62.8 63.8 64.8 n. 8 12.0 12.2 12.4 12.6 22 2.3 24 25 26 119.8 120.7 121.7 122.7 123.7 23.3 23.5 23. 7 23. 9 24.0 82 83 84 85 86 178.7 179.6 180.6 181.6 182.6 34. 7 34-9 35.i 35.3 35.5 43 44 45 46 23 7 .6 238.5 209.5 240.5 24i.5 46.2 46.4 46.6 46. 7 46 o 7 8 9 06.9 o 7 . 9 08.8 oi .3 oi.5 oi. 7 67 68 69 65.8 66.8 67- 7 12.8 i3.o 13.2 2 7 28 o 9 124.7 125.6 126.6 24.2 24.4 24.6 87 88 89 i83.6 i84.5 i85.5 35. 7 35. 9 36. i 4 7 48 49 242.5 243.4 244.4 <-\j .y 47.1 4 7 .3 4 7 .5 10 09.8 oi .9 70 68. 7 i3.4 3o 127.6 24.8 90 i86.5 36.3 5o j 245.4 4 7 . 7 n ~io.8 02.1 71 69. 7 i3.5 i3i 128.6 25.0 191 187.5 36.4 257 246.4 4 7 .Q 12 11. 8 02.3 72 70.7 i3. 7 32 129.6 25.2 92 i88.5 36.6 52 2 4 7 .4 *- / y 48.i 1 3 12.8 02. 5 73 71-7 i3. 9 33 i3o.6 25.4 9 3 189.5 36.8 53 248.4 48.3 i4 i5 i3. 7 1.4.7 02.7 02.9 74 75 72.6 7 3.6 14.1 i4.3 34 35 i3i.5 i32.5 25.6 25.8 94 95 190.4 191 .4 3 7 .o 3 7 .2 54 55 249.3 25o.3 48.5 48 7 16 i5. 7 o3.i 76 74.6 i4.5 36 i33.5 26.0 96 192.4 37-4 56 25i.3 *-l*J * / 48.8 17 i6. 7 03.2 77 7 5.6 i4. 7 3 7 134.5 26.1 193.4 3 7 .6 5 7 252.3 4o o 18 i?.? o3.4 78 76.6 14.9 38 1 35.5 26.3 98 194.4 3 7 .8 58 253.3 fy - 4 9 . 2 '9 20 18.7 19.6 o3.6 c3.8 lo 77-5 78.5 1 5. '3 3 9 4o 1 36.4 i3 7 .4 26.5 26.7 99 200 '11 i 9 6.3 38.o 38.2 59 60 254.2 255.2 49.4 49.6 21 20.6 04.0 81 79-5 i5.5 141 i38.4 26.9 201 197.3 38.4 261 256.2 4o.8 -2 21.6 04.2 82 8o.5 i5.6 42 i3 9 .4 27.1 02 198.3 38.5 62 25 7 .2 y/ 5o.o 23 22.6 04.4 83 8i.5 i5.8 43 i4o.4 27.3 03 199.3 38. 7 63 258.2 50.2 24 23.6 04.6 84 82.5 16.0 44 i4i.4 27.5 04 ~ 200.3 38. 9 64 259. 1 5o.4 25 24.5 04.8 85 83.4 16.2 45 i4a.3 27.7 o5 201 .2 3 9 .i 65 260. 1 5c.6 26 25.5 o5.o 86 84.4 16.4 46 1 43. 3 2 7-9 06 202.2 3 9 .3 66 261 . 1 5o 8 2 7 26.5 05.2 87 85.4 16.6 47 i44.3 28.0 07 203.2 3 9 .5 67 262.1 5o. 9 28 2 7 .5 o5.3 88 86.4 16.8 48 i45.3 28.2 08 204.2 39. 7 68 2.63 . i 5i i 2 9 28.5 o5.5 89 87.4 I 7 .0 49 i46.3 28.4 9 205.2 39.9 69 264 I 5i.3 3o 29.4 o5. 7 90 88.3 I 7 .2 5o 147.2 28.6 10 206. I 4o i 70 265.o 5i.5 ~3T 3o.4 05.9 9 l 8 9 .3 17.4 i5i i48.2 "2O" 211 207. I 4o.3 271 266.0 ? 32 3i.4 06. i 9 2 90.3 17.6 52 149.2 2 9 .0 12 208. I 4o.5 7 2 267.0 5i.*9 33 32.4 o6.3 93 9 i.3 17.7 53 i5o.2 2 9 .2 i3 209.1 4o.6 73 268.0 34 33.4 o6.5 94 92.3 17-9 54 l5l .2 29.4 i4 210. I 4o.8 74 269.0 52^3 35 34.4 06.7 95 9 3.3 18.1 55 152.2 29.6 i5 211 .0 4i .0 75 269.9 52.5 36 35.3 06.9 96 94-2 i8.3 56 i53.i 29.8 16 212.0 41.2 76 270. 9 52. 7 3 7 36.3 07.1 97 9 5.2 i8.5 5 7 i54.i 3o.o 17 2l3.0 4i.4 77 271. 9 52. 9 38 3 7 .3 o 7 .3 98 96.2 18.7 58 i55.i 3o.i 18 214.0 4i.6 78 272. 9 53.o 3 9 38.3 07.4 99 97.2 18.9 5 9 1 56.i 3o.3 1 9 2 I 5 . 4i.8 79 2-73.9 53.2 4o 3 9 .3 07.6 100 98.2 19. i 60 i5 7 .i 3o.5 20 216.0 42.0 80 2 7 4-9 53.4 4i 40.2 07.8 I0 99.1 i 9 .3 161 i58.o 3o. 7 221 216.9 42.2 281 2 7 5.8 53.6 42 41.2 08.0 02 100. I i 9 .5 62 159.0 30.9 22 217. Q 42.4 82 2 7 6.8 53.8 43 42.2 08 2 o3 101 . I 19-7 63 160.0 3i . i 23 218.9 42.6 83 277.8 54.o 44 43.2 08.4 o4 102. I i 9 .8 64 161 .0 3i.3 24 219.9 42. 7 84 278.8 54.2 45 44.2 08.6 o5 io3.i 20. o 65 162.0 3i.5 25 220.9 42.9 85 279.8 54-4 46 45.2 08.8 06 104. 1 2O. 2 66 i63.o 3i. 7 26 221.8 43. i 86 280.7 54.6 4 7 46.i 09.0 7 io5.o 20.4 6 7 i63. 9 3i. 9 27 222.8 43.3 8 7 281 .7 54.8 48 4 7 .i 09.2 08 1 06.0 20.6 68 164.9 32.1 28 223.8 43.5 88 282.7 55.o 4 9 48.i 9 .3 09 107.0 20.8 69 165.9 32.2 2 9 224.8 43. 7 89 283. 7 55.i 5o 49. i 9 .5 10 108.0 21 .0 _ 7 _o_ 166.9 32.4 3o 225.8 43.9 90 284.7 55.3 5i 5o.i 09-7 1 1 1 109.0 21 .2 i 7 i 167,9 32.6 23l 226.8 44.i 291 285 7 55.5 52 5i.o 09.9 13 109.9 21.4 72 168.8 32.8 32 227. 7 44-3 92 2.86.6 55. 7 53 52.0 IO. I i3 110.9 21.6 73 169.8 33.0 33 228.7 44.5 93 287.6 55. 9 54 53.o io.3 i4 111.9 21.8 74 170.8 33.2 34 229.7 44.6 94 288.6 56. i 55 54.0 io.5 i5 112.9 21.9 75 171.8 33.4 35 230.7 44-8 95 289.6 56.3 56 55.o 10. 7 16 1 13.9 22. I 76 172.8 33.6 36 2 3i. 7 45.o 96 200.6 56.5 5 7 56.o 10.9 17 ii4.c 22.3 77 i73. 7 33.8 37 232.6 45.2 97 2 9 i.5 56. 7 58 56. 9 1 1 . i 18 n5.8 22.5 78 174-7 34.o 38 233.6 45.4 98 2 9 2.5 56. 9 59 5 7 -9 n. 3 Z 9 116.8 22. 7 79 175-7 34.2 39 234.6 45.6 99 2 9 3.5 5 7 .i 60 58. 9 n. 4 20 117.8 22.9 80 176.7 34.3 4o 235.6 45.8 3oo 2 9 4.5 5 7 .2 Dist. Hep. Lat. Dist. Dep. Lat. Dist. Dep. 1 Lat. Dist. Dep. Lat. Dist. Dep. Lat. [F; 79 Degrees. Page 28] TABLE II. Difference of Latitude and Departure for 12 Degrees. Hist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist.| Lat. Dep. 7" 01 .0 OO.2 6l 5 9 -7 12.7 121 118.4 l572~ 181 177.0 3 7 .6 241 235.7 5o.i 2 02. o 00.4 62 60.6 12.9 22 119.3 25.4 82 178.0 3 7 .8 42 236.7 5o.3 3 02 .9 00.6 63 61.6 i3.i 23 120.3 25.6 83 179.0 38.o 43 23 7 . 7 5o.5 4 03.9 00.8 64 62.6 i3.3 24 121. 3 2 5.8 84 180.0 38.3 44 238. 7 5o. 7 5 04.9 01 .0 65 63.6 i3.5 25 122.3 26.0 85 181.0 38.5 45 2 3 9 .6 5o.o 6 05.9 01.2 66 64.6 i3. 7 26 123.2 26.2 86 i8i. 9 38. 7 46 240.6 5i.i 7 06.8 oi.5 67 65.5 i3. 9 27 124-2 26.4 87 182.9 38. 9 47 241.6 5i.4 8 07.8 01.7 68 66.5 14.1 28 125.2 26.6 88 i83. 9 3 9 .T 48 242.6 5i.6 9 08.8 01 .9 69 6 7 .5 i4.3 29 126.2 26.8 89 i84.Q 3 9 .3 49 243.6 5i.8 10 09.8 02.1 70 68.5 14.6 3o 127.2 27.0 90 i85.8 3 9 .5 5o 244.5 52.0 ii ~io.8 02.3 7i 69.4 14.8 i3i I28.I 27.2 191 1 86.8 3 9 . 7 25l 245.5 52.2 12 11.7 02.5 72 70.4 i5.o 32 I2 9 .I 27-4 92 187.8 39.9 52 246.5 52.4 i3 12.7 02.7 73 71-4 15.2 33 i3o.i 27.7 93 188.8 4o.i 53 24 7 .5 52.6 i4 i3. 7 02.9 74 72.4 i5.4 34 i3i.i 27.9 94 189.8 4o.3 54 248.4 52.8 i5 14-7 o3.i 75 73.4 i5.6 35 l32.0 28.1 95 190-7 4o.5 55 240.4! 53.o 16 i5. 7 o3.3 76 74.3 i5.8 36 i33.o 28.3 96 191.7 4o.8 56 25o.4 53.2 i? 16.6 o3.5 77 7 5.3 16.0 37 i34.o 28.5 97 192.7 4i .0 57 25i.4 53.4 18 17.6 o3. 7 78 7 6.3 16.2 38 i35.o 28.7 98 193.7 41.2 58 252.4 53.6 1 9 18.6 04.0 79 77-3 16.4 3 9 i36.o 28.9 99 194.7 4i.4 5 9 253.3 53.8 20 19.6 04.2 80 7 8.3 16.6 4o i36. 9 _ 2 9 J _i_ 200 195.6 4i.6 60 254.3 54-1 21 20.5 04.4 ~8T 79.2 16.8 i4i 137. 9 29.3 2OI 196.6 4i.8 261 255.3 54.3 22 21.5 04.6 82 80.2 17.0 42 i38. 9 29.5 02 197-6 42.0 62 256.3 54-5 23 22.5 04.8 83 81.2 i 7 .3 43 i3 9 . 9 29.7 03 198.6 42.2 63 25 7 .3 54. 7 24 23.5 o5.o 84 82.2 i 7 .5 44 i4o. 9 29.9 o4 i 99 .5 42.4 64 258.2 54.9 25 24.5 05.2 85 83.! 17.7 45 i4i.8 3o.i o5 200. 5 42.6 65 25 9 .2 55.i 26 25.4 o5.4 86 84.i 17.9 46 142.8 3o.4 06 201.5 42.8 66 260.2 55.3 27 26.4 o5.6 87 85.i 18.1 47 i43.8 3o.6 07 202.5 43.o 67 26l.2 55.5 28 27.4 o5.8 88 86.1 i8.3 48 i44.8 3o.8 08 2o3.5 43.2 68 262.1 55. 7 29 28.4 06.0 89 87.1 i8.5 49 i45. 7 3i .0 09 204.4 43.5 69 263.1 55. 9 3o 29.3 06.2 90 88.0 18.7 5o i46. 7 3l.2 10 205.4 43. 7 70 264.1 56. i 3i 3o.3 06.4 9 1 89.0 18.9 i5i 147-7 3i.4 211 206.4 43.9 271 265.1 56.3 32 3i.3 06.7 92 90.0 19.1 52 148.7 3i.6 12 207.4 44.i 72 266.1 56.6 33 32.3 06.9 93 91 .0 19.3 53 149.7 3i.8 i3 208.3 44-3 73 267.0 56.8 34 33.3 07.1 94 91.9 i 9 .5 54 i5o.6 32.0 i4 20 9 .3 44.5 74 268.0 5 7 .o 35 34.2 o 7 .3 95 92.9 19.8 55 i5i.6 32.2 i5 210.3 44.7 75 26 9 .0 5 7 .2 36 35.2 o 7 .5 96 93.9 20. o 56 i52.6 32.4 16 211 .3 44-9 76 270.0 5 7 .4 3? 36.2 07.7 97 94.9 2O. 2 57 i53.6 32.6 17 212.3 45. i 77 270. 9 5 7 .6 38 3 7 .2 07.9 98 95.9 2O.4 58 i54.5 32. 9 18 2l3.2 45.3 78 2 7 I- 9 5 7 .8 3,9 38.i 08. i 99 96.8 20.6 5 9 i55.5 33.i J 9 2l4-2 45.5 79 2 7 2. 9 58.o 4o 3 9 .r o8.3 IOO 97.8 20.8 60 i56.5 33.3 20 2l5.2 45. 7 80 2 7 3. 9 58.2 4i 4o.i o8.5 101 98.8 21 .0 161 i5 7 .5 ITT 221 2l6.2 45. 9 281 2 7 4- 9 ~5lM 42 4i.i 08.7 02 99.8 21 .2 62 i58.5 33.7 22 217.1 46.2 82 2 7 5.8 58.6 43 42.1 08.9 o3 i oo . 7 21.4 63 159.4 33. 9 23 218.1 46.4 83 276.8 58.8 44 43.o 09.1 o4 101 .7 21.6 64 160.4 34.i 24 219.1 46.6 84 2 77 .8 59.0 45 44-0 09.4 o5 102.7 21.8 65 161.4 34.3 25 220.1 46.8 85 278.8 59.3 46 45.o 09.6 06 103.7 22. 66 162.4 34.5 26 221. I 47.0 86 2 79 .8 59.5 4? 46.o 09.8 07 104.7 22.2 67 i63.4 34.7 27 222.0 47-2 87 280.7 5 9 .7 48 47-0 10. 08 io5.7 22.5 68 i64.3 34-9 28 223. 47-4 88 281.7 59.9 i 9 1Z' 9 10.2 09 106.6 22.7 69 i65.3 35. i 29 224.0 47-6 89 282.7 60. i 5o 48.9 10.4 IO 1.07.6 22. 9 70 i66.3 35.3 3o 225. 47-8 9 283.7 6o.3 ~"sT 49.9 10.6 III 108.6 23.1 171 167.3 35.6 23 1 226.O 48.o 291 284.6 6o75~ 52 5o. 9 10.8 12 109.6 23.3 72 168.2 35.8 32 226.9 48.2 92 285.6 60. 7 53 5i.8 ii .0 i3 iio.S 23.5 73 169.2 36.o 33 227.9 48.4 93 286.6 60.9 54 52.8 II .2 i4 in. 5 23. 7 74 170.2 36.2 34 228.9 48.7 94 287.6 61.1 55 53.8 ii. 4 i5 112. 5 2 3. 9 75 171.2 36.4 35 229.9 48.9 95 288.6 6i.3 56 54-8 u.6 16 i>3.5 24.1 76 172.2 36.6 36 2 3o.8 49.1 96 2 8 9 .5 6i.5 57 55.8 11.9 17 n4.4 24.3 77 i 7 3.i 36.8 37 23i.8 49.3 97 2 9 0.5 61.7 58 56.7 12. I 18 n5.4 24.5 78 i74.i 37.0 38 232.8 49.5 98 291.5 62 .0 59 57.7 60 j 58. 7 12.3 12.5 19 20 116.4 117.4 24.7 24.9 79 80 i75.i 176.1 3 7 .2 3 7 .4 3 9 4o 233.8 234.8 49-7 49.9 99 3oo 292.5 293.4 62.2 62.4 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Deo. Lat. Dist. Dep. TaT [For 78 Degrees TABLE II. l^age 29 Difference of Latitude and Departure for 13 Degrees. Dist. Lat. Dep. Dis;. Lat. (Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. ] Dep. I 01 .0 00.2 61 5 9 .4 i3. 7 121 117.9 27.2 181 176.4 4o. 7 24 1 234.8 54.2 2 o; 9 OO.4 62 6o.4 i3. 9 22 118.9 2 7 .4 82 177.3 40.9 42 235.8 54-4 3 02.9 00.7 63 61.4 14.2 23 119.8 27.7 83 i 7 8.3 41.2 43 236.8 54.7 4 03.9 00.9 64 62.4 i4.4 24 120.8 27.9 84 179-3 4i.4 44 23 7 -7 54. 9 b 04.9 01 .1 65 63.3 i4.6 25 121. 8 28.1 85 i8o.3 4i.6 45 238. 7 55.; 6 oh. 8 oi.3 66 64.3 14.8 26 122.8 28.3 86 181.2 4r.8 46 239.7 55.3 7 06.8 01 .6 67 65.3 i5.i 27 123.7 28.6 87 182.2 42.1 47 240.7 55.6 8 o 7 .8 01.8 68 66.3 i5.3 28 124.7 28.8 88 i83.2 42.3 48 241.6 55.8 9 08.8 02.0 69 67.2 i5.5 29 125.7 29.0 89 184.2 42.5 49 242.6 56.o 10 09-7 02.2 70 68.2 i5. 7 3o 126.7 29.2 9 i85.i 42.7 5o 243.6 56.2 n 10.7 02.5 71 69.2 16.0 i3i 127.6 2 9 .5 i 9 i 186.1 43.o 25l 244.6 56.5 12 11.7 02.7 72 70.2 16.2 32 128.6 29.7 92 187.1 43.2 52 245.5 56. 7 i3 12.7 02.9 73 71.1 16.4 33 129.6 29.9 93 188.1 43.4 53 246.5 56. 9 i4 i3.6 o3.i 74 72.1 16.6 34 i3o.6 3o.i 94 i8 9 .o 43.6 54 247-5 5 7 .i i5 14.6 o3.4 75 7 3.i 16.9 35 i3i.5 3o.4 9 5 I 9 0.0 43. 9 55 248.5 5 7 .4 16 i5.6 o3.6 76 74.i 17.1 36 i32.5 3o.6 96 i 9 i .0 44.i 56 249.4 5 7 .6 17 16.6 o3.8 77 75.o i 7 .3 3 7 i33.5 3o.8 97 I 9 2.0 44.3 57 25o.4 5 7 .8 18 i 7 .5 04.0 78 76.0 i 7 .5 38 i34.5 3i.o 98 I 9 2. 9 44.5 58 25i.4 58.o jo i8.5 o4.3 79 77.0 17.8 3 9 i35.4 3i.3 99 193.9 44-8 59 252.4 58.3 20 i 9 .5 o4.5 80 77,9 18.0 4o i36.4 3i.5 200 194.9 45.o 60 253.3 58.5 21 20.5 04.7 81 78.9 18.2 i4i i3 7 .4 3i.7 201 195.8 45.2 261 254-3 58.7 22 21.4 04.9 82 79-9 18.4 42 i38.4 3i. 9 02 I 9 6.8 45.4 62 255.3 58. 9 23 22.4 05.2 83 80.9 18.7 43 i3 9 .3 32.2 03 197-8 45.7 63 256.3 5 9 .2 24 23.4 o5.4 84 81.8 18.9 44 i4o.3 32.4 o4 198.8 45.9 64 257.2 5 9 .4 25 24.4 o5.6 85 82.8 19.1 45 i4i.3 32.6 o5 199.7 46.i 65 258.2 5 9 .6 26 25.3 o5.8 86 83.8 19.3 46 i42.3 32.8 06 200.7 46.3 66 259.2 5 9 .8 27 26 3 06. i 87 84.8 19.6 47 i43.2 33.i 07 201 .7 46.6 67 260.2 60. i 28 27.3 o6.3 88 85. 7 19.8 48 i44.2 33.3 08 202.7 46.8 68 261 .1 6o.3 29 28.3 o6.5 89 86.7 20. o 49 i45.2 33.5 09 2o3.6 47.0 69 262.1 6o.5 3o 29.2 06.7 9 87.7 20. 2 5o 146.2 33. 7 10 204.6 47.2 70 263.1 60.7 3: 30.2 07.0 9 i 88.7 20.5 i5i 147-1 34.o 211 2o5.6 47-5 271 264.1 61.0 32 3l.2 07.2 9 2 89.6 20.7 52 i48.i 34.2 12 206.6 47-7 72 265.0 61.2 33 32. 07.4 93 90.6 20.9 53 149.1 34.4 i3 207.5 47-9 73 266.0 61 4 34 33. 07.6 94 91.6 21 .1 54 i5o.i 34.6 i4 2o8.5 48.i 74 267.0 161 .6 35 34. 07.9 95 92.6 21.4 55 i5i .0 34- 9 i5 209.5 48.4 75 268.0(61.9 36 35, 08.1 9 6 93.5 21.6 56 l52.O 35.i 16 2IO.5 48.6 76 268.9 62.1 3 7 36. o8.3 97 94.5 21.8 57 i53.o 35.3 17 211. 4 48.8 77 269.9 62.3 38 3 7 .o o8.5 08 9 5.5 22.0 58 i54.o 35.5 18 212.4 4 9 .o 78 270.9 62.5 3 9 38. D 08.8 99 96.5 22.3 59 i54-9 35.8 19 2i3.4 49-3 79 271.8 62.8 4o 39.0 09.0 IOO 97-4 22.5 60 i55.9 36.o 20 214.4 49-b 80 272.8 63.o 4i 3 9 , 9 oo . 2 101 98.4 22.7 161 i56. 9 J6.2 221 2i5.3 49.7 281 273.8 63.2 4a 43 40.9 4i .9 09.4 9-7 02 o3 y / 99.4 IOO.4 22. 9 23.2 62 63 i5 7 .8 i58.8 36.4 36. 7 22 23 2i6.3 217.3 49.9 50.2 82 83 274.8 275.7 63.4 63.7 44 42.9 9-9 o4 23.4 64 159.8 36. 9 24 2i8.3 5o.4 84 276.7 63.9 45 43.8 IO.I o5 102.3 23.6 65 160.8 3 7 .i 25 219.2 5o.6 85 277-7 64.1 46 44.8 io.3 06 io3.3 23.8- 66 161 .7 3 7 .3 26 220.2 5o.8 86 278.7 64-3 47 48 45.8 46.8 10.6 10.8 07 08 io4.3 IO5.2 24.1 24.3 67 68 162.7 i63. 7 3 7 .6 3 7 .8 27 28 221 .2 222.2 5i'.3 87 88 279.6 280.6 64-6 64.8 49 5o 47-7 48. 7 II .0 II .2 9 10 106.2 107.2 24.5 24.7 69 70 164.7 i65.6 38.o 38.2 8 223.1 224.1 sl! 7 89 9 281.6 282.6 65 o 65.2 5i 52 53 54 55 56 57 58 59 60 49-7 50.7 5i.6 52.6 53.6 54.6 55.5 56.5 5 7 .5 58.5 ii. 5 11.7 11.9 12 I 12.4 12.6 12.8 i3.o i3.3 ,i3.5 in 12 i3 i4 i5 16 17 18 20 IOS.2 109.1 no. i in .1 112. 1 n3.o u4.o i:5.c 116.0 116.9 25.0 25.2 25.4 25.6 25.9 26.1 26.3 26.5 26.3 27.0 171 72 73 I 77 78 L 9 166.6 167.6 168.6 169.5 170.5 I7I.5 172.5 i 7 3.4 174.4 175.4 38.5 38. 7 38. 9 3 9 .i 3 9 .4 3 9 .6 3 9 .8 4o.o 4o.3 4o.5 23l 32 33 34 35 36 37 38 225.1 226. I 227.O 228.0 229.0 230.0 23o-9 23l .9 232.9 233.8 52 .O 52.2 52.4 52.6 52.9 53.i 53.3 53.5 53.8 54-0 291 93 94 95 96 1 283.5 284-5 285.5 286.5 287.4 288.4 289.4 290.4 291 .3 292 . 3 65.5 65.7 65.9 66.1 66.4 66.6 66.8 67.0 6 7 .3 67JL Dist. Dep. ' Lat. Dist. Dep Lat. Dist Dep. Lat. Dist Dep. Lat. Dist Dep. 1 Lat. [For 77 Degrees. 1 Page 30] TABLE II. Difference of Latitude and Departure for 14 Degrees. Dist Lat. Dep. Dist Lat. Dep. Dist Lat. Dep. Dis Lat. Dep. Dist Lat. Dep. i 01 .0 00.2 61 5 9 .2 "14.8 121 117.4 29.3 181 i 7 5.6 43.8 24 1 233.8 58.3 01 .9 oo.5 62 60.2 i5.o 22 u8./ 2 9 .5 82 176.6 44-0 42 234.8 58.5 : 02.9 00.7 63 01. 1 15.2 23 119. c 29.8 83 177.6 44.3 43 235.8 58.8 4 o3. 9 OI .O 64 62.1 i5.5 24 120. C 3o.o 84 178.5 44-5 44 236.8 5 9 .o f. 04.9 OI .2. 65 63.i i5. 7 25 121 .C 30.2 85 179.5 44.8 45 23 7 -7 59.3 6 o5.8 oi.5 66 64.o 16.0 26 122.3 3o.5 86 i8o.5 45.o 46 238.7 59.5 j 06.8 01.7 67 65.o 16.2 27 123.2 3o. 7 87 181.4 45.2 47 239.7 5 9 .8 8 07.8 oi .9 68 66.0 i6.5 28 124.2 3i.o 88 182.^ 45.5 48 240.6 60.0 9 08.7 02.2 69 67.0 16.7 29 125.2 3l.2 89 i83.4 45. 7 49 241.6 60.2 10 09.7 02.4 70 67.9 16.9 3o 126. I 3i.4 90 i84.4 46.o 5o 242.6 6o.5 ii 10.7 02.7 71 68.9 17.2 i3i I27.I 3i. 7 191 i85.3 46.2 25l 243.5 "GoTy" 12 ii. 6 02.9 72 69.9 17-4 32 I28.I 3i. 9 92 i86.3 46.4 52 244.5 61.0 i3 12.6 o3'i 73 70.8 17-7 33 129.0 32.2 9^ 187.3 46. 7 53 245.5 61.2 i4 i3.6 o3.4 74 71.8 17.9 34 i3o.o 32.4 94 188.2 46.9 54 246.5 61.4 i5 i4.6 o3.6 75 72.8 18.1 35 i3i.o 32. 7 95 189.2 4 7 .2 55 247-4 61.7 16 i5.5 03.9 76 7 3. 7 18.4 36 iSa.o 32. 9 96 190.2 47-4 56 248.4 61.9 i? i6.5 04.1 77 74-7 18.6 3 7 i3 2 . 9 33.i 97 191 .1 47-7 57 249.4 62.2 18 i 7 .5 o4.4 78 75-7 18.9 38 i33. 9 33.4 98 192. i 47-9 58 25o.3 62.4 *9 18.4 04.6 79 76.7 19.1 39 i34.o 33.6 99 193.1 48. i 5 9 25i.3 62.7 20 19.4 04.8 80 77-6 19.4 4o i35.8 33. 9 200 194.1 48.4 60 252.3 62.9 21 20.4 ~o57T 81 78.6 19.6 i4i i36.8 34.1 2OI 195.0 48.6 261 253.2 63.i 22 21.3 o5.3 82 79.6 19.8 42 i3 7 .8 34.4 O2 196.0 48.9 62 254.2 63.4 23 22.3 o5.6 83 8o.5 20.1 43 i38.8 34.6 o3 197.0 49. i 63 255.2 63.6 24 23.3 o5.8 84 8i.5 20.3 44 139.7 34.8 o4 197.9 49-4 64 256.2 63. 9 25 24.3 06.0 85 82.5 20.6 45 140.7 35.i o5 198.9 49.6 65 267.1 64.1 26 25.2 o6.3 86 83.4 20.8 46 i4i. 7 35.3 06 199.9 49.8 66 258 . i 64-4 27 26.2 o6.5 87 84-4 21.0 47 142.6 35.6 07 200.9 56.i 67 2{J 9 .I 64.6 28 27.2 06.8 88 85.4 21.3 48 i43.6 35.8 08 201.8 5o.3 68 260.0 64.8 29 28.1 07.0 89 86.4 21.5 49 i44.6 36.o 09 202.8 5o.6 69 261 .0 65.i 3o 29.1 o 7 .3 9 8 7 .3 21.8 5o i45.5 36.3 10 2o3.8 5o.8 70 262.0 65.3 '17 3o.i o 7 .5 9 1 88.3 22.0 i5i M6.5 36.5 211 204.7 5i.o 271 263.o 65.6 32 3i.o 07.7 92 8 9 .3 22.3 52 147-5 36.8 12 205.7 5i.3 72 263.9 65.8 33 32.0 08.0 9 3 90.2 22.5 53 i48.5 3 7 .o 13 206.7 5i.5 73 264.9 66.0 34 33.o 08.2 94 91.2 22.7 54 149.4 3 7 .3 i4 207.6 5i.8 74 265. 9 66.3 35 34.0 o8.5 9 5 92.2 23.0 55 i5o.4 3 7 .5 i5 208.6 52.0 75 266.8 66.5 36 34-9 08.7 96 9 3.i 23.2 56 i5i.4 37-7 16 209.6 52.3 76 267.8 66.8 3 7 35. 9 09.0 97 94.1 23.5 57 i52.3 38.o 17 210.6 52.5 77 268.8 67.0 38 36.9 09.2 98 9 5.i 23. 7 58 i53.3 38.2 18 211. 5 52. 7 78 269.7 6 7 .3 3 9 3 7 .8 o 9 .4 99 96.1 24.0 5 9 i54.3 38.5 J 9 212.5 53.o 79 270.7 6 7 .5 4o 38.8 09.7 100 97.0 24.2 60 i55.2 38. 7 20 2i3.5 53.2 80 271.7 6 7 . 7 4i 3 9 .8 09.9 IOI 98.0 24.4 161 i56.2 38. 9 221 214.4 53.5 281 272.7 68.0 42 4o.8 IO.2 02 99.0 24-7 62 I5 7 .2 3 9 . 2 22 2i5.4 53. 7 82 2 7 3.6 68.2 43 4i.7 IO.4 o3 99-9 24.9 63 i58.2 3 9 .4 23 216.4 53. 9 83 274.6 68.5 44 42.7 10.6 04 100.9 25.2 64 159.1 39.7 24 217.3 54.2 .84 2 7 5.6 68. 7 45 43. 7 10.9 o5 IOI .9 25.4 65 160.1 39.9 25 218. 3 54-4 85 276.5 68.9 46 44.6 II. I 06 102.9 25.6 66 161 .1 40.2 26 219.3 54-7 86 277.5 69.2 4? 45.6 ii. 4 07 io3.8 25.9 67 162.0 40.4 27 220. 3 54.9 87 2 7 8.5 69.4 48 46.6 ii. 6 08 104.8 26 i 68 i63.o 4o.6 28 221 .2 55.2 88 2*79.4 69-7 49 47-5 11.9 09 io5.8 26.4 69 164.0 40.9 29 222.2 55.4 89 280.4 69.9 5o 48.5 12. I 10 106.7 26.6 70 i65.o 4i.i 3o 223.2 55.6 90 281.4 70.2 5i i 9 ' 5 * 12.3 in 107.7 26.9 171 i65.o 4i-4 23l 224.1 55. 9 291 282.4 70.4 52 5o.5 12.6 12 108.7 27.1 72 166.9 4i.6 32 225.1 56.i 92 283.3 70.6 531 5i.4 12.8 i3 109.6 27.3 73 167.9 41.9 33 226.1 56.4 9 3 284.3 70.9 54 5 2 .4 i3.r M no. 6 27.6 74 168.8 42.1 34 227.0 56.6 9* 285.3 7 i.i 55 53.4 i3.3 i5 in .6 27 8 75 169.8 42.3 35 228.0 56. 9 95 286.2 7i.4 56 54.3 i3.5 16 I I 2. 6 28.1 76 170.8 42.6 36 229.0 57.1 96 28-7.2 71.6 5? 55.3 i3.8 17 ii3.5 28.3 77 171.7 42.8 37 23o.o 5 7 .3 97 288.2 71.9 58 56.3 i4.o 18 u4.5 28.5 78 172.7 43.i 38 2 3o. 9 5 7 .6 98 289.1 72.1 5 9 57.2 i4.3 1 9 ii5.5 28.8 79 173-7 43.3 3 9 231.9 5 7 .8 99 290.1 72.3 60 58 . 2 i4-5 20 116.4 29.0 80 174.7 43.5 4o 232.5 58.i 3oo 291 .1 72.6 Dist.l Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. )ist. Dep. Lat. Dist. Dep. "LaiT [For 76 Degrees. TABLE 11. [Page 3] Difference of Latitude and Departure for 15 Degrees. Dist Lat. Dep. Dist Lat. Dep. Dist Lat. Dep. Dist Lat. Dep. Dist. Lat. Dep. i 2 3 4 5 6 7 8 9 10 01 .0 01 .9 02 .9 o3. 9 04.8 o5.8 06.8 07.7 08.7 p_9_._7 oo.3 oo.5 00.8 or .0 oi.3 01 .6 01.8 02.1 02. 3 02 .6 61 62 63 64 65 66 6 7 68 69 70 59^ 60.9 61.8 62.8 63.8 64-7 65. 7 66.6 67.6 i5.8 16.0 i6.3 16.6 16.8 17.1 i 7 .3 17.6 17.9 18.1 121 22 23 24 25 26 27 28 116.9 117.8 118.8 119.8 120.7 121.7 122 .7 123.6 124.6 125.6 3i.3 3i.6 3i.8 32.1 32.4 32.6 32. 9 33. i 33.4 33.6 181 82 83 84 85 86 87 88 89 90 174.8 176.8 176.8 '77-7 178.7 i8o!e 181.6 182.6 i83.5 46.8 47-1 47-4 47.6 47-9 48.i 48.4 48. 7 48.9 49.2 24 1 42 43 44 45 46 4 7 48 i 9 5o 232.8 233.8 234.7 235. 7 236. 7 23 7 .6 238.6 239.6 240 5 241 .5 62.4 62.6 62.9 63.2 63.4 63. 7 63. 9 64.2 64-4 64- 7 ii 12 i3 M i5 10.6 n. 6 12.6 i3.5 i4.5 02.8 o3.i o3.4 o3.6 o3. 9 72 73 74 75 68.6 6 9 .5 70.5 7i.5 72.4 18.4 18.6 18.9 19.2 19.4 32 33 34 35 126.5 127.6 128.5 120.4 i3o.4 33. 9 34.2 34-4 34.7 34.9 191 93 i84.5 i85.5 186.4 187.4 188.4 49.4 49.7 5o.o 60.2 5o.5 261 52 53 54 55 242.4 243.4 244.4 245.3 246.3 65. D 65.2 65.5 65. 7 66 o 16 i5.5 04. i 76 7 3.4 19.7 36 i3i.4 35.2 96 189.3 5o. 7 56 247.3 66 3 17 18 '9 20 16.4 17-4 18.4 i 9 .3 04.4 04.7 04.9 05.2 77 78 79 80 74.4 7 5.3 7 6.3 77-3 19.9 2O. 2 2O.4 20.7 3 7 38 3o 4o i3 2 .3 i33.3 i34.3 i35. 2 35.5 35. 7 36.o 36.2 97 98 99 200 190.3 191 .3 192.2 193.2 5i.o 5l.2 5i.5 5i.8 5 7 58 59 60 248.2 249.2 250.2 25I.I 66.5 66.8 67.0 6 7 .3 21 20.3 o5.4 81 78.2 21 .0 i4i i36.2 36.5 201 194.2 5?.o 261 252.1 67 6 22 21.3 o5. 7 82 79.2 21 .2 42 137.2 36.8 02 i 9 5.i 52.3 67 253.1 67 8 23 22.2 06.0 83 80.2 21.5 43 i38.i 3 7 .o 03 1(^6.1 5^.5 63 264.0 68 i 24 23.2 06. * 84 81.1 21.7 44 139.1 3 7 .3 o4 197.0 5?. 8 255.o 68 3 25 24.1 o6.5 85 82.1 22.0 45 i4o.i 3 7 .5 o5 198.0 53.i 65 256.o 68 6 26 25.1 06. 7 86 83.i 22.3 46 i4i .0 3 7 .8 06 199.0 53.3 66 266.9 68 8 27 26.1 7 .0 87 84.o 22.5 47 142.0 38.o 07 199.9 53.6 67 7570 60 i 28 27.0 7 .2 88 85.o 22.8 48 i43.o 38.3 08 200.9 53.8 68 268.9 6o.4 29 28.0 o 7 .5 89 86.0 23.0 49 143.9 38.6 09 201.9 54.i oo 269.8 69.6 3o 29.0 o 7 .8 90 86.9 23.3 5o 144.9 38.8 10 202 .8 54-4 70 260.8 69.9 3i 29.9 08.0 9' 87.9 23.6 161 145.9 3o.i 211 2o3.8 54.6 271 261.8 70.1 32 3o. 9 o8.3 9 2 88.9 23.8 52 i46.8 3 9 .3 12 204.8 54-9 7 2 262.7 70.4 33 3.1-9 o8.5 93 89.8 24.1 53 147.8 3 9 .6 i3 206.7 55. f 73 263. 7 7-7 34 32.8 08.8 94 90.8 24.3 54 i48.8 39.9 i4 206.7 55.4 74 264.7 7.Q 35 33.8 09. i 95 91.8 24.6 55 149.7 4o.i i5 207.7 55.6 76 71 .2 36 34.8 09.3 96 92.7 24.8 56 i5o. 7 4o.4 16 208.6 55.9 76 266.6 71.4 3 7 35. 7 09.6 97 93.7 25.1 57 i5i .7 4o.6 17 209.6 56.2 77 267.6 71 .7 38 36.7 09.8 98 94-7 25.4 58 162.6 40.9 18 210 6 56.4 78 268.5 7 2.0 39 37-7 10. I 99 9 5.6 25.6 5 9 i53.6 41.2 19 211. 5 56.7 79 269.5 72.2 4o 38.6 10.4 IOO 96.6 25.9 60 1 54. 5 4i-4 20 212.5 56. 9 80 2 7 O.5 7 2.5 4i 3 9 .6 10.6 101 97.6 26.1 161 i55.5 4i. 7 221 2i3.5 5 7 .2 281 2-71.4 72.7 42 4o.6 10.9 02 98.5 26.4 62 166.6 4i .9 22 214.4 5 7 .5 82 272.4 7 3.o 43 4i.5 1 1 . i o3 99-5 26.7 63 167.4 42.2 23 216.4 5 7 . 7 83 273.4 7 3.2 44 42.5 n. 4 04 100. 5 26.9 64 168.4 42.4 24 216.4 58.o 84 274.3 73.5 45 43.5 n. 6 o5 101 .4 27.2 65 169.4 42. 7 25 217.3 58.2 85 2 7 5.3 7 3.8 46 44.4 n .9 06 102.4 27.4 66 i6o.3 43.o 26 218.3 58.5 86 2 7 6.3 74-0 4 7 45.4 12.2 07 io3.4 27.7 67 i6i.3 43.2 27 219.3 58.8 87 2 77 .2 74.3 48 46.4 12.4 08 io4.3 28.0 68 162.3 43.5 28 220.2 69.0 88 2 7 8.2 74.5 49 47-3 12. 7 9 io5.3 28.2 6 9 i63.2 43. 7 2 9 221 .2 5 9 .3 89 2-79.2 74-8 5o 48.3 I2. 9 10 io6.3 28.5 70 164.2 44.o 3o 222.2 5 9 .5 90 280.1 7 5.i 5i 49-3 13.2 in 107.2 28. 7 171 i65.2 44.3 23l 223.1 69.8 291 28I.I 7 5.3 52 5o.2 i3.5 12 108.2 29.0 72 166.1 44.5 32 224.1 60.0 92 282.1 7 5.6 53 5l .2 13.7 i3 109.1 29.2 73 167.1 44.8 33 225.1 6o.3 93 283.0 7 5.8 54 5a .2 14.0 i4 IIO. I 29.5 74 168.1 45.o 34 226.0 60.6 94 284.0 76.1 55 53.i 14.2 i5 II 1 .1 29.8 75 169.0 45.3 35 227.O 60.8 95 284.9 76.4 56 54.i i4.5 16 I 12 .O 3o.o 76 170.0 45.6 36 228.0 61 .1 96 285.9 76.6 57 55.i i4.8 17 i i3.o 3o.3 77 171 .0 45.8 37 228.9 6i.3 97 286.9 76.9 58 56.o i5.o 18 n4-o 3o.5 78 171.9 46.i 38 229.9 61.6 98 28-7.8 5 9 67.0 1 5. 3 X 9 1 14 9 3o.8 79 172.9 46.3 39 230.9 61.9 99 288.8 77-4 60 58.o i5.5 20 n5. 9 3i.i 80 173.9 46.6 4o 23i.8 62.1 3oo 289.8 77-6 Dist. Dep. Lat. Dist-l Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. [For 75 Degrees. Fage32j TABLE II. Difference of Latitude and Departure for 16 Degrees Dist Lat. Dep. Dist Lat. Dep. Dist. Lat. Dep. Dist Lat. Dep. Dist Lat. Dep. i OI .0 oo.3 61 58.6 16.8 121 n6.3 33.4 181 174.0 49.9 241 23l .7 66.4 2 01 .9 00.6 62 59.6 17.1 22 n 7 .3 33.6 82 174.9 5o.? 42 232.6 66.7 3 0.9 DO. 8 63 60.6 17-4 23 118.2 33. 9 83 175.9 5o.4 43 233.6 67.0 4 o3.8 01 .1 64 6i.5 17.6 24 119.2 34.2 84 176.9 5o. 7 44 234.5 6 7 .3 5 04.8 01 .4 65 62.5 17.9 25 120.2 34.5 85 177-8 5i.o 45 235.5 67.5 6 o5.8 01.7 66 63.4 18.2 26 121 .1 34. 7 86 178.8 5i.3 46 236.5 67.8 7 06.7 oi .9 67 64.4 i8.5 27 122. I 35.o 87 179.8 5i.5 47 23 7 .4 68.1 8 07.7 02.2 68 65.4 ,8.7 28 123.0 35.3 88 180.7 5i.8 48 238.4 68.4 9 08.7 02.5 69 66.3 19.0 29 I24.O 35.6 89 181.7 52.1 49 239.4 68.6 10 09.6 02.8 7Q 6 7 .3 i 9 .3 3o 125.0 35.8 9 182.6 52.4 5o 24o.3 68.9 n 10.6 ~bTo~ 7i 68.2 19.6 i3i 125-9 36.i 191 i83.6 52.6 25l 24i.3 69.2 12 n. 5 o3.3 72 69.2 19.8 32 126.9 36.4 92 184.6 52. 9 52 242.2 6 9 .5 i3 12.5 o3.6 73 70.2 20.1 33 127.8 36 7 9 3 i85.5 53.2 53 243.2 69.7 i4 i3.5 03.9 74 71.1 20.4 34 128.8 36.9 94 i86.5 53.5 54 244.2 70.0 i5 i4-4 04. i 75 72.1 2O.7 35 129.8 3 7 .2 95 187.4 53. 7 55 245.1 70.3 16 i5.4 o4.4 76 7 3.i 20.9 36 i3o.7 3 7 .5 96 188.4 54.o 56 246.1 70.6 17 i6.3 04.7 77 74.0 21.2 37 i3i. 7 3 7 .8 97 189.4 54.3 57 247.0 70.8 18 i 7 .3 o5.o 78 7 5.o 21.5 38 l32.7 38.o 98 190.3 54.6 58 248.0 71.1 1 9 i8.3 O5.2 79 75-9 21.8 3 9 i33.6 38.3 99 191 .3 54.9 5 9 249.0 7i.4 20 19.2 o5.5 80 76.9 22.1 4o i34.6 38.6 200 192.3 55.i 60 249-9 71.7 21 20.2 o5.8 81 77-9 22.3 i4i i35.5 38.9 201 193.2 55.4 261 2.50.9 71.9 22 21. I 06.1 82 78.8 22.6 42 i36.5 3 9 .i 02 194.2 55.7 62 25l .9 72.2 23 22.1 o6.3 83 79.8 22.9 43 i3 7 .5 39.4 o3 i 9 5.i 56.o 63 252.8 72.5 24 23.1 06.6 84 80.7 23.2 44 i38.4 39.7 o4 196.1 56.2 64 253.8 72.8 25 24.O 06.9 85 81.7 23.4 45 i3 9 .4 4o.o o5 197.1 56.5 65 254.7 7 3.o 26; 25.0 07.2 86 82.7 23. 7 46 i4o.3 40.2 06 198.0 56.8 66 255.7 7 3.3 27 26.0 07.4 87 83.6 24.0 47 i4i-3 4o.5 07 199.0 5 7 .i 67 256.7 7 3.6 28; 26. 9 07.7 88 84.6 24.3 48 i42.3 4o.8 08 199.9 5 7 .3 68 25 7 .6 73-9 29,27.9 08.0 89 85.6 24.5 49 i43.2 4i.i 09 200.9 5 7 .6 69 258.6 74.i 3oJ28.8 o8.3 90 86.5 24.8 5o i44-2 4i.3 10 2OI .9 5 7 . 9 70 25 9 .5 74-4 3i 29.8 o8.5 9 1 8 7 .5 25.1 i5i i45.2 4i.6 211 202.8 58.2 271 260.5 74-7 3 2 l3o.8 08.8 92 88.4 25.4 52 i46, i 41.9 12 203.8 58.4 72 261.5 7 5.o 33.3r. 7 09.1 93 89.4 25.6 53 i47- 1 42.? i3 204.7 58. 7 73 262.4 7 5.2 34 ; 32. 7 09.4 94 90.4 25.9 54 i48.o 42.4 i4 205.7 59.0 74 263.4 7 5.5 35.33.6 09.6 95 9 i.3 26.2 55 149.0 42.7 i5 206.7 59.3 7 5 264.3 7 5.8 36 134.6 09.9 96 92.3 26.5 56 i5o.o 43.0 16 207.6 59.5 76 265.3 76.1 3? 35.6 10.2 97 9 3.2 26.7 57 150.9 43.3 17 208.6 5 9 .8 77 266.3 76.4 38 36.5 io.5 98 94.2 27.0 58 i5i .9 43.6 18 209.6 60. i 78 267.2 76.6 39 3 7 .5 10.7 99 9 5.2 27.3 59 i52.8 43.8 1 9 210.5 60.4 79 268.2 76.9 4o 38.5 ii .0 100 96.1 27.6 60 i53.8 44.i 20 211. 5 60.6 80 269.2 77 .2 4i 3 9 .4 u. 3 101 97.1 27.8 161 i54.8 44.4 22! 212.4 60.9 281 270.1 77-5" 42 4o.4 11. 6 02 98.0 28.1 62 i55. 7 44-7 22 2i3.4 61 .2 82 271.1 77-7 43 4i.3 11.9 o3 99.0 28.4 63 i56. 7 44.9 23 214.4 6i.5 83 272.0 78.0 44 42.3 12. I o4 IOO.O 28.7 64 i5 7 .6 45.? 24 2i5.3 61.7 84 273.0 7 8.3 45 43.3 12.4 o5 100.9 28.9 65 1 58. 6 45.5 25 216. 3 62.0 85 274.0 78.6 46 44.2 12.7 06 101 .9 29.2 66 i5 9 .6 45.8 26 217.2 62.3 86 2-74.9 78.8 47 45.2 i3.o 07 102.9 29.5 67 i6o.5 46.o 27 218.2 62.6 87 275.9 79.1 48 46.i 13.2 08 io3.8 29.8 68 i6i.5 46.3 28 219.2 62.8 88 276.8 79-4 49 47.1 i3.5 09 104.8 3o.o 69 162.5 46.6 29 220. i 63.i 89 277.8 79-7 5o 48.i i3.8 10 io5.7 3o.3 7 i63.4 46.9 36 22 I. I 63.4 90 278.8 79-9 5i 49.0 i4.i III 106.7 3o.6 171 i64.4 47.1 23l 222.1 63. 7 291 279.7 80.2 52 5o.o i4.3 12 107.7 30.9 72 i65.3 4 7 -4 32 223. 63. 9 92 280.7 8o.5 53 50.9 i4.6 i3 108.6 3i.i 73 i66.3 47.7 33 224.0 64.2 93 281.6 80.8 54 5i. 9 14.9 i4 109.6 3i.4 74 i6 7 .3 48.o 34 224.9 64.5 94 282.6 81.0 55 52. 9 15.2 i5 110.5 3i. 7 75 168.2 48.2 35 225.9 64.8 95 283.6 8i.3 56 53.8 i5.4 16 in. 5 32.0 76 169.2 48.5 36 226.9 65.i 96 284.5 81.6 57 54.8 i5. 7 17 112. 5 32.2 77 170. i 48.8 37 227.8 65.3 97 285.5 81.9 58 55.8 16.0 18 n3.4 32.5 78 171.1 49.1 38 228.8 65.6 98 286.5 82.1 69 56. 7 i6.3 J 9 "4.4 32.8 79 172.1 49.3 3 9 229.7 65. 9 99 287.4 82.4 60 5?-7 i6.5 20 n5.4 33.i 80 i 7 3.o 49.6 4o 230.7 66.2 3oo 288.4 82.7 biZ Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. ^ist. Dep. Lat. [For 74 Degrees, TABLE II. [Page 33 Difference of Latitude and Departure for 17 Degrees. Di*t.| Lat. Dep. Disft. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. f Dep. i ! 01 .0 00.3 61 58.3 17.8 121 n5. 7 35.4 181 i 7 3.i 52. 9 24 1 23o.5 70.5 2 oi .9 00.6 62 59.3 18.1 22 M6.7 35.7 82 174.0 53.2 42 23i.4 70.8 3 02.9 00.9 63 60.2 18.4 23 117.6 36.o 83 175.0 53.5 43 232.4 71.0 4 o3.8 01 .2 64 61.2 18.7 24 118.6 36.3 84 176.0 53.8 44 233.3 71.3 5 04.8 oi.5 65 62.2 19.0 25 119.5 36.5 85 176.9 54.i 45 234.3 71.6 6 o5. 7 01.8 66 63.i i 9 .3 26 120.5 36.8 86 177-9 54-4 46 235.3 71.9 7 06.7 02.0 67 64.i 19.6 2 7 121. 5 37.1 87 178.8 54-7 47 236.2 72.2 8 07.7 02.3 68 65.o 19.9 28 122.4 3 7 -4 88 179-8 55.o 48 237.2 72.5 9)08.6 02.6 69 66.0 20.2 29 123.4 3 7 . 7 89 180.7 55.3 4 9 238.1 72.8 10 j 09.6 02 .9 70 66.9 20.5 3o 124.3 38.o 9 181.7 55.6 56 23 9 .I 7 3.i , j io.5 03.2 7 1 07.9 20.8 i3i 125.3 38.3 191 182.7 55.8 25l 240.0 73.4 I 2 u. 5 o.3.5 72 68.9 21 . I 32 126.2 38.6 92 i83.6 56.i 52 24 1 .0 -3. 7 i3 12.4 o3.8 73 69.8 21.3 33 127.2 38. 9 9 3 184.6 56.4 53 241 .9 74-0 i4 i3.4 04.1 74 70.8 21.6 34 I28.I 3 9 .2 94 i85.5 56. 7 54 242 .9 74.3 i5 i4.3 o4-4 75 71-7 21.9 35 129.1 3 9 .5 95 i86.5 5 7 .o 55 243. q 74.6 1 6 i5.3 04.7 76 72.7 22.2 36 i3o.i 3 9 .8 96 187.4 5 7 .3 56 244.8 74-8 17 i6.3 o5.o 77 7 3.6 22.5 3 7 i3i .0 4o.i 97 188.4 5 7 .6 57 245.8 7 5.i 18 17.2 o5.3 78 74-6 22.8 38 l32.0 4o.3 98 189.3 5 7 . 9 58 246.7 75.4 19 18. a o5.6 79 7 5.5 23.1 39 l32 .9 4o.6 99 190.3 58.2 5 9 247-7 75. 7 20 19.1 o5.8 80 7 6.5 23.4 4o i33.9 40.9 200 191 .3 58.5 60 248.6 76.0 21 20. I 06.1 81 77.5 23. 7 i4i i34-8 41.2 201 192 .2 58.8 261 249.6 7 6.3 22 21.0 06.4 82 78.4 24.0 42 i35.8 4i.5 02 193.2 5 9 .i 62 2 5o.6 76.6 a3 22.0 06.7 83 79-4 24.3 43 i36.8 4i.8 03 194.1 5 9 .4 63 25i .5 76.9 24 23.0 O 7 .O 84 8o.3 24.6 44 i3 7 . 7 42.1 o4 i 9 5.i 5 9 .6 64 252.5 77-2 95 07.3 85 8i.3 24-9 45 i38.7 42.4 o5 196.0 59.9 65 253.4 77-5 26 24.G 07.6 86 82.2 25.1 46 i3 9 .6 4a .7 06 197.0 60.2 66 254-4 77-8 27 258 07.9 87 83.2 25.4 47 i4o.6 43.o 07 198.0 6o.5 67 255.3 78.1 28 26 8 08.2 88 84.2 25.7 48 i4i.5 43.3 00 198.9 60.8 63 256.3 78.4 2 9 27.7 08.5 89 85.i 26.0 4 9 43.6 09 199.9 61.1 6g 257.2 78.6 3o 28.7 08.8 90 86.1 26.3 5o i43.4 43.9 10 200.8 5: .4 70 258.2 78.9 3i 29.6 09. 1 91 87.0 26.6 i5i i44-4 44.i 211 201 .8 61.7 271 269.2 79.2 32 3A.fi oq 4 92 88.0 26.9 52 i45.4 44-4 12 2O2 .7 02 .0 72 260. I 79. b 33 3 1. 6 09.6 93 88.9 27.2 53 i46.3 44. 7 13 203.7 62.3 73 26l.I 79.8 34 32.5 09.0 89.9 2 7 .5 54 i4 7 .3 45.o i4 204.6 62.6 74 262.0 80. i 35 33.5 IO.2 o5 90.8 27.8 55 148.2 45.3 i5 2o5.6 62 .9 75 263.0 8o.4 36 34.4 ro.5 96 91.8 28.1 56 149.2 45.6 16 206.6 63.2 76 263.9 80.7 37 35.4 10.8 92.8 28.4 57 iSo.i 45.9 17 207.5 63.4 77 264.9 81.0 38 36.3 1 1 . i 08 Q3.7 28.7 58 iSi.i 46.2 18 208.5 63. 7 78 266.9 8i.3 3o 37 3 u. 4 99 94.7 28.9 iSa.i 46.5 19 209.4 64.o 79 266.8 81.6 4o 38.3 11.7 100 95.6 29.2 60 i53.o 46.8 20 210.4 64.3 80 267.8 81 .9 4i 30.2 12.0 101 96.6 29. t> 161 1 54.o 4 7 .i 221 21 I .3 64.6 281 268.7 82.2 42 40.2 17 3 02 97.5 29.8 62 i54-9 4 7 -4 22 212.3 64-9 82 269.7 82.4 43 4 i. i I? 6 03 98.5 3o.i 63 i55. 9 47-7 23 2i3.3 65.2 83 270.6 82.7 44 45 42.1 43.o I2. 9 l3.2 o4 o5 99.5 100.4 3o.4 3o. 7 64 65 i56.8 i5 7 .8 47-9 48.2 24 25 2l4-2 215.2 65.5 65.8 84 85 271 .6 272.5 83.0 83.3 46 44-0 i3.4 06 101 .4 3i .0 66 i58. 7 48.5 26 216.1 66.1 86 273.5 83.6 47 48 44-9 45. 9 i3. 7 14.0 07 08 102.3 io3.3 3i.3 3i.6 6 7 68 159.7 i6o. 7 48.8 49.1 27 28 217.1 218.0 66.4 66. 7 87 88 274.5 276.4 83.9 84.2 49 46.9 i4-3 09 104.2 3i. 9 6 9 161.6 49-4 29 219.0 67.0 9 276.4 84.5 5o 4 7 .8 14.6 IO 105 2 32.2 70 162.6 49.7 3o 220.0 07.2 9 277.3 84.8 5i 48.8 "14.9 1 I I 106. i 32.5 171 i63.5 5o.o 23l 220.9 6 7 .5 291 278.3 85.i 52 53 4 9 .7 5o. 7 15.2 i5.5 12 1 3 107. i 108.1 32. 7 33.o 7 2 73 i64.5 i65.4 5o.3 5o.6 32 33 221 .9 222.8 67-8 68 . i 279.2 280.2 85.4 85. 7 54 55 5i.6 52.6 r5.8 16. i i4 109.0 I 10. 33.3 33.6 74 75 166.4 i6 7 .4 60.9 5l .2 34 35 223.8 224.7 68.4 68.7 9 4 9 5 281.2 282.1 86.0 86.2 56 57 58 53.6 54.5 55.5 56.4 5 7 .4 16.4 16.7 17.0 17.2 17.5 16 17 18 '9 20 1 10.9 111.9 1.2.8 n3.8 n4.8 33. 9 34.2 34.5 34-8 35.i 76 78 79 80 169.3 170.2 171 .2 172.1 5i.5 5i. 7 52.0 52.3 52.6 36 3 7 38 39 4o 22b. 7 226.6 227 .6 228.6 229.5 69.0 69.3 69.6 69.9 70.2 90 97 98 ,99 3oo 283.1 284.0 285.o 285.9 286.9 86.5 86.8 87.1 87.4 87-7 Uist. Dep. Lr.l. Dist Dep. Lat. Dist Dep. Lat. Dist. Dep. Lat. Dist. Den. Lat. [For 73 Degrees. i'ugeM TABLE II. Difference of Latitude and Departure for 18 Degrees. Dist. Lat. Dep. Dist. Lat. D>p. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. ) Dep. I 01 .0 oo.3 61 58.0 18.9 121 n5.i 3 7 .4 181 172.1 55.9 24 1 229.2 74.5 2 01.9 00.6 62 59.0 19.2 22 116.0 3 7 . 7 82 1 7 3.I 56.2 42 230.2 7 4.8 3 02 .9 00.9 63 59.9 I 9 .5 23 117.0 38.o 83 174.0 56.6 43 23I.I 7 5.i 4 o3.8 01 .2 64 60.9 19.8 24 117.9 38.3 84 175.0 56. 9 44 232.1 7 5.4 5 o4-8 01.5 65 61.8 20.1 25 118.9 38.6 85 175.9 5 7 .2 45 233.0 75. 7 6 o5.7 oi .9 66 62.8 20.4 26 119.8 38. 9 86 176.9 5 7 .5 46 234.0 76.0 7 06.7 02.2 67 63.7 20. 7 2~ 1 20. 8 i 39.2 87 177-8 5 7 .8 47 234.9 7 6.3 8 07.6 02.5 68 64-7 21 .0 28 121.7 3 9 .6 88 178.8 58.i 48 235. 9 76.6 9 08.6 02.8 69 65.6 21.3 2 9 122.7 39-9 8 9 179.7 58.4 49 236.8 76.9 10 09.5 o3.i 70 66.6 21.6 3o 123.6 40.2 9 180.7 58. 7 5o 23 7 .8 77.3 ii loT5~ o3.4 7i 6 7 .5 21. 9 i3i 124.6 4o.5 i 9 i 181.7 D 9 .0 25l 238. 7 77-6 12 ii. 4 o3. 7 72 68.5 22.2 32 125.5 4o.8 92 182.6 5 9 .3 52 239.7 77-9 i3 12.4 04.0 73 69.4 22.6 33 126.5 4i.i 9 3 i83.6 5 9 .6 53 240.6 78.2 i4 i3.3 o4.3 74 70.4 22. 9 34 127.4 4i-4 94 i84.5 5 9 .o 54 241.6 7 8.5 i5 i4.3 04.6 75 71.3 23.2 35 128.4 4i. 7 95 i85.5 6o.3 55 242.5 78.8 16 15.2 04.9 76 72 .3 23.5 36 129.3 42.0 96 186.4 60.6 56 243.5 79.1 17 16.2 o5.3 77 7 3.9 23.8 37 i3o.3 42.3 97 187.4 60. 9 57 244-4 79-4 18 17.1 o5.6 78 74.2 24.1 38 l3l.2 42.6 98 i88.3 61.2 58 245.4 79-7 1 9 18.1 05.9 79 7 5.i 24-4 3 9 i3a.a 43.o 99 189.3 6i.5 5 9 246.3 80.0 20 19.0 06.2 80 76.1 24-7 4o 1 33.i 43.3 200 190.2 61.8 60 24 7 .3 8o.3 21 20. o o6~5~ ~8T 77.0 25.0 Mi 1 34.i 43.6 201 I 9 I .2 62.1 261 248.2 80. 7 22 20.9 06^8 82 78.0 25.3 42 1 35.1 43.9 O2 I92.I 62.4 62 249.2 81.0 23 21 .9 07.1 83 78.9 25.6 43 1 36.o 44.2 o3 I93.I 62.7 63 250.1 8i.3 24 22.8 07 4 84 79-9 26.0 44 137.0 44.5 04 194.0 63.o 64 a5i.i 81.6 25 23.8 07 7 85 80.8 26.3 45 137.9 44.8 o5 I95.O 63.3 65 252.0 81.9 26 24.7 08 'o 86 81.8 26.6 46 1 38.0 45.i 06 195.9 63. 7 66 253.0 82.2 27 25.7 o8.3 87 82.7 26.9 47 139.8 45.4 07 196.9 64.o 67 253.9 82.5 28 26.6 08.7 88 83. 7 27.2 48 i4o.8 45. 7 08 197.8 64.3 68 254.9 82.8 29 27.6 09.0 89 84-6 27.5 49 141.7 46.o 09 198.8 64.6 69 255.8 83.i 3o 28.5 09.3 9 85.6 27.8 5o 142.7 46.4 10 199.7 C4- 9 70 256.8 83.4 ~3T 29.5 09.6 9 1 86.5 28.1 i5i i43.6 46.7 211 200.7 65.2 2 7 I 25 7 . 7 83. 7 3s 3o.4 09.9 92 8 7 .5 28.4 52 144.6 47.0 12 201 .6 65.5 7 2 258. 7 84.i 33 3i.4 10.2 9 3 88.4 28.7 53 i45.5 47-3 13 202.6 65.8 73 259.6 84.4 34 32.3 io.5 94 89.4 29.0 54 i46.5 47-6 i4 2o3.5 66.1 74 260.6 84-7 35 33.3 10.8 95 90.4 29.4 55 i47-4 47-9 i5 204.5 66.4 75 26i.5 85.o 36 34.2 ii . i 96 9 i.3 29.7 56 i48.4 48.2 16 205.4 66.7 76 262.5 85.3 3 7 35.2 ii. 4 97 92.3 3o.o 57 i49.3 48.5 17 206.4 67.1 77 263.4 85.6 38 36.i ii. 7 98 9 3.2 3o.3 58 i5o.3 48.8 18 207.3 67.4 78 264.4 85. 9 3 9 3 7 .i 12 I 99 94.2 3o.6 5 9 l5l.2 4 9 .i 1 9 208.3 67.7 79 265.3 86.2 4o 38.o 12.4 100 9 5.; 3o. 9 60 iSa.a 49.4 20 209.2 68.0 80 266.3 86.5 4i 39.0 I2. 7 IOI 96.1 3l.2 161 i53.i 49.8 221 210.2 68.3 281 267 . 2 86.8 42 3 9-9 i"3.o 02 97.0 3i.5 62 i54.i 5o.i 22 211 . I 68.6 82 268.2 87.1 43 40.9 i3.3 o3 98.0 3i.8 63 i55.o 5o.4 23 212. I 68.9 83 269.1 8 7 .5 44 4i.8 i3.6 o4 98. 9 32.1 64 r56.o 50.7 24 2i3.q 69.2 84 270.1 87.8 45 42.8 ,3. 9 o5 99-9 32.4 65 i56. 9 5i.o 25 214.0 6 9 .5 85 27I.I 88.1 46 43. 7 14.2 06 100.8 32.8 66 i5 7 .o 5i.3 26 214.9 69.8 86 2 7 2.O 88.4 47 44-7 i4.5 07 101. 8 33.i 67 1 58.8 5i.6 27 215.9 70.1 87 2 7 3.0 88.7 48 45. 7 14.8 08 102.7 33.4 68 159.8 5i. 9 2.8 216.8 7 o.5 88 2 7 3.9 89.0 P 46.6 i'5.i 09 103.7 33. 7 69 160.7 52.2 29 217.8 70.8 89 2 7 4-9 8 9 .3 5o 47.6 i5.5 10 104.6 34.o 70 161 .7 52.5 3o 218.7 71.1 90 2 7 5.8 89.6 ~5T 48.5 i5.8 III io5.6 34.3 171 162.6 5a. B ^3T 219.7 71.4 291 2 7 6 8 89.9 5 a 49.5 16.1 12 io6.5 34.6 72 i63.6 53.2 32 220.6 7i-7 92 2 77 . 7 90.2 53 5o.4 16.4 i3 107.5 34. 9 73 i64.5 53.5 33 221 .6 72.0 93 2 7 8. 7 90.5 54 5i.4 16.7 i4 108.4 35.2 74 i65.5 53.8 34 222.5 7 2.3 94 2 7 9.6 90.9 55 52.3 17.0 i5 109.4 35.5 75 166.4 54.i 35 223.5 72.6 95 280.6 91.2 56 53.3 i 7 .3 16 no. 3 35.8 76 167.4 54-4 36 224.4 72-9 96 281.5 91 !5 57 54.2 17.6 17 ill. 3 36.2 77 i68.3 54-7 37 225.4 7 3.? 97 282.5 91.8 58 55.2 17.9 18 I 12.2 36.5 78 169.3 55.o 38 226.4 7 3.5 98 283.4 92.1 5 9 56.i 18:2 1 9 II3.2 36.8 79 170.2 55.3 3 9 227.3 73-9 99 284 4 92.4 60 67. i i8.5 20 114. i 3 7 .i 80 171.2 55.6 4o 228.3 74.2 3oo 285.3 92.7 j D!~|L Dep. Lat. Dist Dep. Lat. Dist. Dep. Lat. Dist. -Dep. Lat. Dist. Dep. Lat. _ , . _ |_ [For 72 l)egres. TABLE II. [Page 35 Difference of Latitude and Departure for 19 Degrees. Dist Lat. Dep. Dist. Lat. Dep. Dist Lat. Dep. Dist Lat. Dep. Dist. Lat. Dep I 00.9 oo.3 61 57-7 19.9 121 ii4-4 39.4 ii 171.1 58. 9 24 1 22-7.9 78.5 2 01 .0 oo. 7 62 58.6 2O. 2 22 n5.4 39.7 82 I 7 2.I 42 228.8 78.8 3 02.8 01 .O 63 59.6 20.5 23 ii6.3 4o.o 83 1 7 3.o 5o.6 43 220.8 70 i 4 o3.8 oi.3 64 6o.5 20.8 24 117.2 4o.4 84 i 7 4.o SQ Q 44 236. 7 /y 70.4 .*> o4-7 01 .6 65 6i.5 21 .2 25 118.2 4o. 7 85 174.9 60! 2 45 23i.7 /y * 79-8 6 o5.7 02. o 66 62.4 21.5 26 ii 9 .i 4i .0 86 I75.Q 60.6 46 232.6 80., 7 06.6 02.3 67 63.3 21.8 2 7 I 20. I 4i.3 8 7 176.8 60.9 4 7 233.5 80.4 8 o 7 .6 02.6 68 64.3 22.1 28 121 .0 4i-7 88 177-8 61.2 48 234.5 80. 7 9 )ob.5 O2 .0 69 65.2 22.5 2 9 122.0 42.0 8 9 178.7 61.5 4 9 235.4 81.1 10 Q9-5 o3.3 70 66.2 22.8 3o 122.9 42.3 9 179-6 61.9 5o 236.4 81.4 ii 10.4 o3.6 71 67.1 23.1 i3i 123. 9 42.6 191 180.6 62.2 a5i 237.3 gj 12 ii. 3 o3. 9 72 68.1 23.4 32 124.8 43.o 9? i8i.5 62.5 52 238.3 82!o i3 12.3 04.2 73 69.0 23.8 33 125.8 43.3 9 3 182.5 62.8 53 239.2 82.4 c4 13.2 04.6 74 70.0 24.1 34 I26. 7 43.6 94 i83.4 63.2 54 240.2 82.7 i5 14.2 04.9 75 70.9 24.4 35 127.6 44.o 95 184.4 63.5 55 241 . i 83.o 16 i5. i 05.2 76 71.9 24.7 36 128.6 44.3 96 i85.3 63.8 56 242. i 83.3 17 16.1 o5.5 77 72.8 25.1 3 7 I2 9 .5 44-6 97 i86.3 64.i 5 7 243.0 83. 7 .8 17.0 05.9 76 7 3.8 25.4 38 i3o.5 44- 9 98 187.2 64.5 58 243.9 84.0 '9 18.0 06.2 79 74.7 25.7 3 9 i3i.4 45.3 99 188.2 64.8 5 9 244.9 84.3 20 18.9 o6.5 80 7 5.6 26.0 4o i32.4 45.6 200 189.1 65.i 60 245.8 84.6 21 19.9 06.8 81 7 6.6 26.4 Mi i33.3 45.9 201 190.0 65.4 261 246.8 85.o 22 20.8 07.2 82 77-5 26.7 42 i34.3 46.2 02 191 .0 65.8 62 247.7 85.3 23 21. 7 o 7 .5 83 7 8.5 27.0 43 i35.2 46.6 o3 191.9 66.1 63 248^7 85.6 24 22.7 07.8 84 79.4 27.3 44 i36.2 46. 9 o4 192. 9 66.4 64 24 9 .6 86.0 25 23.6 08. i 85 8o.4 2 7 - 7 45 i3 7 .i 47.2 o5 193.8 66. 7 65 25o.6 86.3 26 24.6 o8.5 86 8i.3 28.0 46 i38.o 4 7 .5 06 194.8 67.1 66 25i.5 86.6 27 25.5 08.8 87 82.3 28.3 4 7 i3 9 .o 4 7 .9 07 195.7 67.4 252.5 86. 9 28 26.5 09.1 88 83.2 28. 7 48 139.9 48.2 08 196.7 67-7 68 253.4 8 7 .3 29 27-4 09.4 89 84.2 29.0 49 146.9 48.5 9 197.6 68.0 Go 254.3 87.6 3o 28.4 09.8 90 85.i 2 9 .3 5o i4i.8 48.8 10 198.6 68.4 70 255.3 8 7 . 9 3i 2 9 .3 10. I 9 r 86.0 29.6 i5i 142.8 4 9 .2 211 i 99 .5 68.7 271 256.2 88.2 32 3o.3 10.4 02 8 7 .o 3o.o 52 i43. 7 4 9 .5 12 200.4 69.0 73 25 7 .2 88.6 33 3l.2 10.7 93 8-7.9 3o.3 53 i44.7 4 9 .8 i3 201.4 6 9 .3 73 258.1 88. 9 34 32. I ii. i 94 88.9 3o.6 54 i45.6 56.i i4 202.3 69.7 74 25 9 .I 89.2 35 33.i ii. 4 9 5 89.8 3o. 9 55 j.46.6 5o.5 i5 2o3.3 70.0 75 260.0 8 9 .5 36 34.o 11.7 96 90.8 3i.3 56 5o.8 16 204.2 70.3 /6 261.0 89-9 3 7 35.o 12.0 97 91.7 3i.6 5-7 i48!4 5i .1 17 2O5.2 70.6 77 261 . 9 00.2 38 35. 9 12.4 98 92. 7 3i .9 58 i4 9 .4 5i.4 18 206. 1 71.0 78 262. 9 9 o.5 3 9 36 9 12.7 99 93.6 32.2 5 9 i5o.3 5i.8 19 207. 1 7i.3 79 263.8 90.8 4o 3 7 .8 i3.o 100 94.6 32.6 60 i5i.3 52.1 20 208.0 71.6 80 264. 7 4i 38.8 i3.3 101 9 5.5 32.9 161 l52.2 52.4 221 20 9 .0 72.0 281 265.7 91.5 42 39.7 i3. 7 02 96.4 33.2 62 i53.2 52. 7 22 20 9 . 9 82 266.6 91.8 43 40.7 i4.o o3 97-4 33.5 63 i54.i 53.i 23 210. 9 7^6 83 267.6 92.1 44 4i.6 i4.3 o4 98.3 33. 9 64 i55.i 53.4 24 211. 8 72. 9 84 268.5 92.5 45 42.5 14.7 o5 99-3 34.2 65 i56.o 53. 7 2.5 212-7 7 3.3 85 2 6 9 .5 9 2.8 46 43.5 i5.o 06 IOO. 2 34.5 66 157.0 54.o 26 2l3. 7 7 3.6 86 270.4 93.1 47 44.4 i5.3 07 [OI .2 34.8 67 '57-9 54-4 27 214.6 73. 9 87 271.4 9 3.4 4'8 45.4 i5.6 08 102. I 35.2 68 i58.8 54.7 28 2i5.6 7 4-2 88 272.3 9 3.8 49 46.3 16.0 09 io3.i 35.5 6 9 159.8 55.o 29 216. 5 7 4.6 89 2 7 3.3 94.J 5o 47.3 i6.3 10 104.0 35.8 7 160.7 55.3 3o 2I 7 .5 74- 9 9 2 7 4.2 94.4 ' 5i 48.2 16.6 in io5.o 36.i 171 161 .7 ~55. 7 23l 218.4 7 5.2 291 2 7 5.1 94- 7 52 49.2 16.9 12 105.9 36.5 72 162.6 56.o 32 ^19.4 7 5.5 9 2 276.1 95.1 53 56.i 17.3 i3 106.8 36.8 73 i63.6 56.3 33 220. 3 75. 9 9 3 277.0 9 5.4 54 17.6 i4 107.8 3 7 .i 74 i64.5 56.6 34 221.3 7 6.2 94 278.0 9 5.7 55 52 !o 17.9 i5 108.7 3 7 -4 75 i65.5 5 7 .o 35 222.2 7 6.5 95 278.9 06.0 56 52.9 18.2 16 109.7 3 7 .b 76 166.4 5 7 .3 36 223.1 7 6.8 96 2 79 . 9 06.4 5 7 53.o 18.6 17 no. 6 38.i 77 167.4 5 7 .6 3 7 224.1 77-2 97 280.8 96.7 58 54.8 18.9 18 in. 6 38.4 78 i68.3 58.o 38 225.0 77-5 98 281.8 97.0 5 9 55.8 19 112. 5 38. 7 79 169.2 58.3 3 9 226.0 77.8 99 282. 7 97.3 60 56. 7 19.5 W 20 n3.5 3 9 .i 80 170.2 58.6 4o 226.9 78.1 3oo 283. 7 97.7 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. [For ?i Degrees. I>age36] TABLE II. Difference of Latitude and Departure for 20 Degrees. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. l).st. Lat. Dep. Dist. Lat. Dep. i oo.o 00.3 ~6T 5 7 .3 20.9 121 ii3.7 4.1.4 181 170.1 61.9 241 226.5 82.4 2 7 01 .9 00.7 62 58.3 21.2 22 114.6 41.7 82 171 .0 i 62.2 42 227.4 82.8 3 02.8 01 .0 63 5Q.2 21.5 23 n5.6 42.1 83 172.0 626 43 228.3 83.i 4 o3.8 01 .4 64 66. i 9I. 9 24 n6.5 42.4 84 172.9 62.9 44 229 3 83.5 5 04.7 01.7 65 61.1 22.2 25 ii 7 .5 42.8 85 173.8 633 45 230 2 83.8 6 o5.6 02. I 66 62.0 22.6 26 118.4 43.i 86 174.8 63.6 46 231.2 84.1 7 c6.6 02.4 67 63.o 22.9 27 n 9 .3 43.4 87 I 7 5. 7 64.0 4 7 232.1 84.5 8 o 7 .5 02.7 68 63. 9 23.3 28 120.3 43.8 88 176.7 64-3 48 233.0 84.8 9 o8.5 o3.i 69 64.8 23.6 29 121 .2 44.i 89 177.6 64-6 49 234.0 85.2 10 09.4 o3.4 70 65.8 23.9 3o 122.2 44.5 90 178.5 65.o 5o 234. 9 85.5 ii io.3 o3.8 ?i 66.7 24.3 i-3-i 123. I 44.8 191 179.5 65.3 25l 235. 9 85.8 12 n. 3 04. i 72 67.7 24.6 32 124.0 45.i 92 180.4 65. 7 52 236.8 86.2 i3 12.2 o4-4 73 68.6 25.0 33 125.0 45.5 93 181.4 66.0 53 237.7 86.5 i.4 l3.2 04.8 74 69.5 25.3 34 125.9 45.8 94 182.3 66.4 54 238.7 86.9 i5 14.1 o5.i 75 7P.5 25. 7 35 126.9 46.2 95 1 83. a 66.7 55 23 9 .6 87.2 16 i5.o o5.5 76 71-4 26.0 36 127.8 46.5 96 184.2 67.0 56 240.6 87.6 17 16.0 o5.8 77 72.4 26.3 3 7 128.7 46.9 97 i85.i 67.4 5 7 241.5 87.9 18 16.9 06.2 78 7 3.3 26.7 38 129.7 4 7 -2 98 1 86. i 67.7 58 242.4 88.2 *9 17.9 o6.5 79 74-2 27.0 3 9 i3o.6 47-5 99 187.0 68.1 5 9 243.4 88.6 20 18.8 06.8 80 7 5.2 27.4 4o i3i.6 47-9 200 187.9 68.4 60 244.3 88.9 21 19.7 07.2 ~8T 76.1 27.7 i4i i32.5 48.2 201 188.9 68.7 261 245.3 8 9 .3 22 20.7 o 7 .5 82 77.1 28.0 42 i33.4 48.6 02 189.8 69.1 62 246.2 89.6 23 21.6 07.9 83 78.0 28.4 43 i34.4 48.9 03 1 9 o. 8 69.4 63 247-1 90.0 24 22.6 08.2 84 78.9 28.7 44 i35.3 49-3 o4 i 9 i .7 69.8 64 248.1 90.3 25 23.5 08.6 85 79-9 29.1 45 i36.3 49-6 o5 192.6 70.1 65 24 9 .O 90.6 26 24.4 08.0 86 80.8 29.4 46 l3 7 .2 49.9 06 193.6 70.5 66 250.O 91.0 27 25.4 09.2 87 81.8 29.8 47 i38.i 5o.3 07 194.5 70.8 6 7 25o. 9 91.3 28 26.3 09.6 88 82.7 3o.i 48 139.1 5o.6 08 195.5 71.1 68 a5i.8 91.7 29 27.3 09.9 89 83.6 3o.4 49 i4o.o 5i.o 09 196.4 7 i.5 69 252.8 92.0 3o 28.2 io.3 9 84.6 3o.8 5o MI .0 5i.3 10 197.3 71.8 70 253. 7 $2j " 3i 29.1 10.6 9 1 85.5 "3T7T i5i "14^9" 5i.6 211 198.3 72.2 271 254.7 92.7 32 3o.i IO.O 92 86.5 3i.5 52 1 42. 8 52.0 12 199.2 72.5 72 255.6 93.0 33 3i .0 n .3 93 87.4 3i.8 53 i43.8 52.3 i3 2OO. 2 72.9 73 256.5 9 3.4 34 3i.9 11.6 94 88.3 32.1 54 i44.7 52. 7 i4 201 .1 7 3.2 74 25 7 .5 9 3. 7 35 32. 9 12.0 9 5 8 9 .3 32.5 55 i45. 7 53.o i5 202.0 7 3.5 75 258.4 94.1 36 33.8 12.3 96 90.2 32.8 56 i46.6 53.4 16 2O3.0 73-9 76 259.4 94-4 37 34.8 12.7 97 91.2 33.2 57 i47-5 53. 7 17 203.9 74-2 77 260.3 94.7 38 35.7 i3.o 98 92.1 33.5 58 i48.5 54.o 18 204-9 74.6 78 J.6l .2 95.1 3 9 36.6 i3.3 99 93.0 33.9 5 9 149.4 54-4 ! 9 2o5.8 74-9 79 262.2 95.4 4o 3 7 .6 i3. 7 100 94.0 34.2 60 i5o.4 54-7 20 206.7 7 5.2 80 263.1 9 5.8 4.i 38.5 i4.o 101 94.9 34.5 161 i5i.3 55.i 221 207.7 7 5.6 281 264.1 96.1 42 3 9 .5 i4-4 02 95.8 34.9 62 l52.2 55.4 22 208.6 75-9 82 265.0 9 6.4 43 4o.4 14.7 o3 96.8 35.2 63 i53.2 55.7 23 209 . 6 -6.3 83 265.9 9 6.8 44 4i.3 r5.o o4 97-7 35.6 64 1 54.1 56.i 24 210.5 76.6 84 266.9 97.1 45 42.3 i5.4 o5 9-7 35. 9 65 i55.o 56.4 25 21 I .4 77-o 85 267.8 97-5 46 43.2 i5. 7 06 99.6 36.3 66 i56.o 56.8 26 212.4 77-3 86 268.8 97-8 47 44.2 16.1 07 i oo . 5 36.6 67 i56. 9 5 7 .i 27 2i3.3 77-6 8 7 269. 7 98.2 48 45.i 16.4 08 101 .5 36.9 68 i5?.9 5 7 .5 28 2 I 4 2 78.0 88 2 7 0.6 98.5 P 46.o 16.8 09 102.4 3 7 .3 69 i58.8 5 7 .8 2 9 215.2 7 8.3 89 271 .6 98.8 So 47-0 17.1 10 io3.4 3 7 .6 70 159.7 58.i 3o 2 1 6 . 1 78.7 GO 272.5 99.2 ~5T 47-9 17-4 II I io4.3 38.o 171 160.7 58.5 a3i 217.1 79.0 291 2 7 3.5 99-5 52 48. 9 17.8 12 I05.2 38.3 72 161.6 58.8 32 218.0 79-3 9 2 2 7 4-4 99.9 53 49.8 18. i i3 106.2 38.6 73 162.6 5 9 .2 33 218.9 79-7 93 2 7 5.3 100.2 54 5o.7 i8.5 i4 107. 1 39.0 74 i63.5 59.5 34 219.9 80.0 9 4 2 7 6.3 100.6 55 5i 7 18.8 i5 108.1 3 9 .3 75 164.4 59.9 35 220.8 80.4 9 5 277.2 100.9 56 52.6 19.2 16 109.0 397 76 i65.4 _ ' ' 60.2 36 221.8 80.7 96 278.1 IO1 .2 57 53.6 i 9 .5 17 109.9 4o.o 77 i66.3 6o.5 37 222 .7 81.1 97 279.1 101.6 58 54.5 n;.8 18 1 10.9 40.4 78 167.3 60.0 38 223.6 8i.4 98 280.0 101.9 A 9 55.4 2U.2 19 in. 8 40.7 79 168.2 6, .2 3 9 224.6 81.7 99 281.0 102.3 60 56.4 20.5 20 112. 8 4i .0 80 169. i 61.6 4o 22^.5 82.1 3oo 281.9 1 02. 6 bist Dep. Lat. Dist. Hep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Li. [For 70 Degrees. TABLE II. t p age37 Difference of Latitude and Departure for 21 Degrees. Dist. Lat. Dep. Dist. Lat. Dep. )ist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. I 00.9 00.4 61 56. o 21.9 121 i i3.o 43.4 181 6 9 .o 64 - 9 24 1 25.0 86.4 2 01.9 00. 7 62 57,0 22.2 22 1 13.9 43.7 82 6 9 . 9 65.2 42 25. 9 86.7 3 02.8 OI .1 63 58.8 22.6 23 ii4.8 44.i 83 70.8 65.6 43 26.0 87.1 4 o3. 7 01.4 64 5 9 .7 22.9 24 ii5.8 44-4 84 71.8 65. 9 44 27.8 87.4 5 o4-7 01.8 65 60.7 23.3 25 116.7 44-8 85 72.7 66.3 45 28.7 87.8 6 o5.6 02.2 66 61.6 23. 7 26 117.6 45.2 86 i 7 3.6 66.7 46 29.7 88.2 7 o6.5 02.5 67 62.5 24.0 27 118.6 45.5 87 7 4-6 67.0 4 7 3o.6 88.5 8 o 7 .5 02.9 68 63.5 24.4 28 119.5 45.9 88 i 7 5.5 67.4 48 23i.5 88.9 9 08.4 03.2 69 64-4 24.7 2 9 120.4 46.2 89 176.4 67.7 49 232.5 89.2 10 o 9 .3 o3.6 65.4 25.1 3o 121.4 46.6 90 177-4 68.1 5o 233.4 89.6 ii io.3 o3. 9 7 1 66.3 25.4 i3i 122.3 46.9 191 7 8.3 b8.4 25l 234.3 90.0 12 I I .2 o4.3 72 67.2 25.8 32 123.2 4 7 .3 92 179.2 6S.8 52 235.3 9 o.3 i3 12. I 04.7 73 68.2 26.2 33 124.2 47-7 93 180.2 6 9 .2 53 236 2 9-7 i4 l3 . I o5.o 74 69. i 26.5 34 125. I 48.o 94 181.1 6 9 .b 54 23 7 .I 9 i.o i5 14.0 o5.4 75 70.0 26.9 35 126.0 48.4 9 5 182.0 9-9 55 238.1 9 i.4 1 6 14.9 o5. 7 76 71.0 27.2 36 127.0 48. 7 96 i83.o 70.2 56 239.0 91.7 '7 1,5.9 06. i 77 71.0 27.6 3 7 127.9 97 183.9 70.6 5 7 23 9 . 9 9 2.1 18 16.8 o6.5 78 72.8 28.0 38 128.8 4 9 .5 98 184.8 71.0 58 240.9 9 2.b 19 17.7 06.8 79 7 3.8 28.3 39 129.8 49.8 99 i85.8 7 i.3 59 241.8 92.8 20 18.7 07.2 80 74-7 28.7 4o i3o.7 50.2 iOO 186.7 71.7 60 242.7 93.2 21 19.6 o 7 .5 81 7 5.6 29.0 i4i i3i.6 5o.5 201 187.6 72.0 261 243.7 9 3.5 22 20.5 07.9 82 76.6 29.4 42 i32.6 DO. 9 02 188.6 72-4 62 244.6 9 3. 9 43 21.5 08.2 83 77-5 29. 7 43 i33.5 5l.2 03 189.5 72.7 63 245.5 9 4-3 24 22.4 08.6 84 7 8.4 3o.i 44 i34.4 5i.6 o4 190.5 7 3.i 64 246.5 9 4-6 23.3 09.0 85 79-4 3o.5 45 i35.4 52.0 o5 191 .4 7 3.b bb 247-4 o5.o 26 24.3 09.3 86 8o.3 3o.8 46 i36.3 52.3 06 192.3 7 3.8 66 248.3 9 b.3 27 25.2 09.7 87 81.2 3l.2 47 137.2 52.7 07 i 9 3.3 7 4-2 67 249.3 (p. 7 28 26.1 IO.O 88 82.2 3i.5 48 i38.2 53.o 08 I 9 4-2 7 4-b 68 250.2 9 6.o 27.1 10.4 89 83.i 3i. 9 139.1 53.4 09 i 9 5. i 74- 9 69 25l.I 9 6.4 3o 28.0 10.8 90 84.0 32.3 5o i4o.o 53.8 IO 196.1 7 b.3 70 252.1 9 b.8 3i 28.9 1 1 . i 91 85.o 32.6 i5i i4i.o 54-1 211 197.0 7 5.6 271 253.0 97.1 32 33 29.9 3o.8 ii. 5 ii. 8 9? c3 85. 9 86.8 33.o 33.3 52 53 141.9 142.8 54.5 54.8 12 K 197.9 198.9 76.0 76.3 7 2 2b3. 9 254.9 97 .5 97-8 34 3l. 7 12.2 94 8 7 .8 33. 7 54 i43.8 55.2 1^ 199.8 76.7 74 255.8 98.2 35 32.7 12.5 95 88. 7 34.o 55 i44-7 55.5 i5 200.7 77.0 7 5 2bb. 7 98.6 36 33.6 12.0 9* 89.6 34-4 56 i45.6 55.9 16 201 .7 77-4 76 2b 7 . 7 98.9 37 38 34.5 35 . 5 i3.3 i3.6 97 98 90.6 91 .5 34.8 35.i 57 58 i46.6 i47.5 56.3 56.6 17 1 8 2O2.6 2o3.5 77.8 78.1 78 258.6 259.5 99.3 99-6 3 9 4o 36.4 3 7 .3 i4.o i4.3 99 IOO 92.4 93.4 35.5 35.8 59 60 i48.4 149.4 5 7 .o 5 7 .3 i 9 20 204.5 7 8.b 7 8.8 79 80 260.5 261.4 IOO.O ioo.3 4i 38.3 14.7 101 94-3 36.2 161 1 5o . 3 5 7 . 7 221 206.3 79 .2 281 262.3 100.7 42 3 9 .2 02 36.6 62 l5l.2 58.i 22 207.3 79.6 82 263.3 101. 1 43 4o. i i5.4 03 06 2 36.9 63 152.2 58.4 23 208.2 79-9 83 264.2 101.4 44 i5.8 9 7 .I 3 7 .3 64 i53.i 58.8 24 209.1 80.3 84 265.1 101.8 42.0 16.1 o5 98.0 3 7 .6 65 i54.o 5 9 .i 25 210. I 80.6 8b 266.1 102.1 46 42. 9 i6.5 06 99.0 38.o 66 i55.o 5 9 .5 26 211 .0 81.0 8b 2.6 7 .0 102.5 47 48 4 9 5o 43. 9 44-8 45.7 46. 7 16.8 17.2 17.6 17.9 07 08 09 10 99 . 9 100.8 101.8 102. 7 38.3 38.7 3 9 .i 3 9 .4 67 68 69 70 i55.9 i56.8 i5 7 .8 i58.7 5 9 .8 60.2 60.6 60.9 27 28 2 9 3o 211 .Q 212.0 2i3.8 214.7 8i.3 81.7 82.1 82.4 88 89 90 267.9 268.9 269.8 270.7 102.9 <03.2 io3.6 io3. 9 "5? 52 53 54 55 56 57 58 4 7 .6 48.5 4 9 .5 5o.4 5i.3 52.3 53.2 54.i i8.3 18.6 19.0 19.4 19.7 20.1 20.4 20.8 12 i3 i4 i5 16 17 18 io3.b io4.6 io5.5 106.4 1 0-7.4 io8.3 109.2 IIO. 2 3 9 .8 4o.i 4o.5 4o. 9 41.2 4i.6 42.3 171 72 73 74 75 76 77 78 159.6 160.6 i6i.5 162.4 i63.4 i64.3 i65.2 166.2 6i.3 61.6 62.0 62.4 62.7 63.i 63.4 63.8 2.3 I 32 33 34 35 36 37 38 215.7 216.6 217.5 218. 5 2I 9 .4 220.3 221 .3 222.2 82.8 83.i 83.5 83. 9 84.2 84.6 84-9 85.3 291 92 9 3 94 9 5 96 97 98 271.7 272.6 27 3.5 2 7 4-5 2 7 5.4 2 7 6.3 2-77.3 278.2 io4-3 io4.6 io5.o io54 io5. 7 106.1 106.4 1 06 .8 l 9 55.i 56.o 21 .1 21.5 20 II I .1 112. 42.6 43.o 167.1 64.i 64.5 3 9 4o 22.3.1 224.1 85.6 86.0 3oo 279.1 280.1 I0 7 .2 I0 7 .5 Dist. Dep. Lat. Dist Dep. Lat. Dist Dep Lat. Dis Dep. Lat Dis Dep. Lat. [For 69 Degrees. Page38J TABLL II. Difference of Latitude and Departure for 22 Degrees. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. OO.Q oo.4 61 56.6 22.9 121 112.2 45.3 181 167.8 67.8 24 1 223.5 90.3 2 w . y OI .Q 00.7 62 5 7 .5 23.? 22 II3.I 45.7 82 168.7 68.2 42 224.4 90.7 3 * 7 02.8 OI.I 63 58.4 23.6 23 i i 4 . o 46.i 83 169.7 68.6 43 225.3 91.0 4 o3.7 oi.5 64 5 9 .3 24.0 24 n5.o 46.5 84 170.6 68.9 44 226.2 9' -4 o4.6 01 .9 65 6o.3 24.3 25 1 1 5 . 9 46.8 85 I7I.5 69.3 45 227.2 91.8 6 o5.6 02.2 66 61.2 24.7 26 1 16. 8 47-2 86 172.5 69.7 46 228.1 92.2 7 02.6 67 62.1 25.1 27 1 17. b 47-6 87 173.4 70.1 47 229.0 . 92.5 3 07.4 o3.o 68 63.o 25.5 28 i-8. 7 47-9 88 174.3 70.4 48 229.9 Q o8.3 o3.4 69 64.o 25.8 29 119.6 48.3 89 I 7 5.2 70.8 49 230.9 o3 3 y 10 o 9 .3 o3. 7 70 64-9 26.2 32 120.5 48. 7 90 176.2 71.2 5o 23i.8 93.7 n 10.2 04.1 71 65.8 26.6 i3i J21 .5 49.1 191 i 77 .i 7 i.5 a5i 232.7 94.0 12 II .1 o4.5 72 66.8 27.0 32 122 4 49.4 92 i 7 8.o 71.9 52 233.7 94.4 i3 12. I 04.9 73 6 7 . 7 27.3 33 123.3 4 9 .8 93 178.9 72.3 53 234-6 94.8 i4 i3.o 05.2 74 68.6 27.7 34 124.2 50.2 94 179.9 72.7 54 235.5 95.2 i5 13.9 o5.6 7 5 6 9 .5 28.1 35 125.2 5o.6 180.8 7 3.o 55 236.4 95.5 16 i4.8 06.0 76 7 o.5 28.5 36 I26.I 5o.o 96 181.7 73-4 56 237.4 17 i5.8 06.4 77 71-4 28.8 37 127.0 5i.3 97 182.7 7 3.8 5 7 238.3 96.3 18 16.7 06.7 78 72.3 29.2 38 128.0 5i. 7 98 i83.6 74-a 58 239.2 96.6 19 17.6 07.1 79 7 3.2 29.6 3 9 128.9 52.1 99 J84.5 7 4.5 59 240.1 97.0 20 i8.5 07.5 80 74.2 3o.o 4o 129.8 52.4 200 i85.4 74-9 60 241.1 97-4 21 ~io.5 07.9 81 7 5.i 3o.3 i4i i3o. 7 52.8 20J 186.4 7 5.3 261 242.0 97.8 22 20^4 08.2 82 76.0 3o. 7 42 i3i. 7 53.2 02 187.3 75-7 62 242.9 98.1 23 21.3 08.6 83 77.0- 43 i3a.6 53.6 o3 188.2 7 6.o 63 243.8 98.5 24 22.3 09.0 84 77-9 3i!5 44 i33.5 53.0 o4 189.1 76.4 64 344.8 98.9 25 23.2 09.4 85 78.8 3i.8 45 i34.4 54.3 o5 190.1 76.8 65 245.7 99.3 26 24.1 09.7 86 79-7 32.2 46 i35.4 54.7 06 191 .0 77-2 66 246.6 99.6 27 25.0 10. 1 87 80.7 32.6 47 i36.3 55.i 07 191.9 77.5 6 7 247-6 100.0 28 26.O io.5 88 81.6 33.o 48 l3 7 .2 55.4 08 192.9 77-9 68 248.5 100.4 29 26.9 10.9 89 82.5 33.3 49 i38.2 55.8 09 193.8 7 8.3 69 249.4 100.8 3o 27.8 11 .2 90 83.4 33. 7 5o i3 9 .i 56.2 10 78.7 70 25o.3 101. 1 3i "28^7" 11.6 9 1 84-4 34.i i5i i4o.o 56.6 211 195.6 79.0 271 25i.3 101.5 32 29.7 12.0 92 85.3 34.5 52 140.9 56. 9 12 196.6 79-4 72 252.2 101.0 33 3o.6 12.4 93 86.2 34.8 53 i4i.o 5 7 .3 i3 197.5 79.8 73 253.1 102.3 34 3i.5 12.7 94 87.2 35.2 54 142.8 5 7 . 7 i4 198.4 80.2 74 254.0 102.6 35 32.5 88.1 35.6 55 i43.7 58.i i5 199.3 8o.5 255.0 io3.o 36 33.4 13^5 96 89.0 36.o 56 i44-6 58.4 16 200.3 80.9 ?6 .}55.O io3.4 37 34.3 i3. 9 97 89.9 36.3 57 i45.6 58.8 17 201 .2 81.3 77 256.8 io3.8 38 35.2 14.2 98 90.9 36. 7 58 i46.5 5 9 .2 18 2O2 . 1 81.7 7* 257.8 104.1 3 9 36.2 14.6 99 91.8 37.1 59 147.4 5 9 .6 19 203.1 82.0 79 258.7 io4.5 4o 3 7 .i i5.o 100 92.7 3 7 .5 60 i48.3 5 9 . 9 20 204.0 82.4 80 259.6 104.9 4, 38.o i5.4 101 93.6 3 7 .8 161 149.3 6o.3 221 204.9 82.8 yt 260.5 io5.3 4a 38. 9 i5,7 02 94.6 38.2 62 150.2 60.7 22 205.8 83.2 te 261.5 i5.6 43 39.9 16.1 o3 95.5 38.6 63 iSi.i 61.1 23 206.8 83.5 83 262.4 106.0 44 4o.8 i6.5 o4 96.4 39.0 64 I52.I 61.4 24 207.7 83.9 84 263.3 106.4 45 4i-7 16.9 o5 97-4 39.3 65 i53.o 61.8 25 208.6 84.3 85 264.2 1 06.8 46 42.7 17.2 06 9 8.3 3 9 .7 66 i53. 9 62.2 26 209.5 84-7 86 265.2 107.1 47 43.6 17.6 07 99.2 4o.i 67 i54.8 62.6 27 210.5 85.o 87 266.1 107.5 48 .44.5 18.0 08 IOO.I 4o.5 68 i55.8 62.9 28 211 .4 85.4 88 267.0 107.9 49 45.4 18.4 09 IOI.I 4o.8 69 i56. 7 63.3 29 212.3 85.8 89 268.0 io8.3 5o 46.4 18.7 IO 102.0 41.2 7 i5 7 .6 63. 7 3o 2.3.3 86.2 9 268.9 108.6 5i 47-3 i 9 .i III 1O2 .9 4i.6 171 i58.5 64.i 23 1 214.9 86.5 291 269.8 109.0 52 48.2 i 9 .5 12 io3.8 42.0 72 169.5 64.4 32 2l5.1 86.9 92 270.7 109.4 53 4 9 -i i 9 . 9 i3 104.8 42.3 73 160.4 64-8 33 2)6. 8 7 .3 93 271-7 109.8 54 5o.i 20.2 i4 io5.7 42. 7 74 i6i.3 65.2 34 217.0 87.7 94 272.6 1 JO. I 55 5i.o 20. 6 i5 106.6 43.i 7 5 162.3 65.6 35 217.9 88.0 95 2 7 3.5 i io.5 56 5i.o 21.0 16 107.6 43.5 76 i63.2 65. 9 36 218.8 88.4 96 274.4 1 1 0.0 57 52.8 21.4 17 io8.5 43.8 77 1 64.1 66.3 37 219.7 88.8 97 275.4 in.3 58 53.8 21.7 18 109.4 44.2 78 i65.o 66.7 38 22.0.7 89.2 98 276.3 1 1 1.6 59 54-7 22.1 10 110.3 44.6 79 166.0 67.1 3 9 221 .6 89.5 99 277.2 112.0 60 55,6 22.5 20 in. 3 45.o 80 166.9 67.4 4o 222.5 89.9 3oo 278.2 112.4 Dist. De_>. | Lat. DisT Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. [For 68 Degrees. TABLE II. [Pae33 Difference of Latitude and Departure for 23 Degrees. Disi. Lat. Dep. )ist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat: Dep. i 00.0 00.4 61 56.2 23.8 121 ii. 4 47-3 181 166.6 70.7 24 1 221.8 94.2 2 01.8 00.8 62 57. i 24.2 22 12.3 47-7 82 167.5 71.1 42 222.8 94-6 3 02.8 01 .2 63 58.o 24.6 23 13.2 48.i 83 i68.5 71.5 43 223.7 94-9 4 o3. 7 01.6 64 58. 9 25.0 24 14.1 48.5 84 169.4 44 224.6 95.^ 5 04.6 O2. 65 5 9 .8 25.4 25 i5. i 48.8 85 170.3 72.3 45 225.5 6 o5.5 02.3 66 60.8 25.8 26 16.0 49 2 86 171.2 72.7 46 226.4 96 i 7 06.4 02.7 67 61.7 26.2 27 16.9 49-6 87 172.1 7 3.i 47 227.4 96.5 8 07.4 o3.i 68 62.6 26.6 28 117.8 5o.o 88 i 7 3.i 73.5 48 228.3 96.9 9 o8.3 o3.5 6 9 63.5 27.0 2 9 18.7 5o.4 89 i74.o 73.8 49 229.2 97-3 10 09.2 o3. 9 70 64.4 27.4 3o 119.7 5o.8 90 174. 9 74.2 5o 230. I 97-7 ii 10. I o4.3 ji 65.4 27.7 i3i 120.6 5l.2 191 175.8 74-6 25l 2-3 I .0 98.5 12 II .0 04.7 72 66.3 28.1 32 121. 5 5i.6 92 176.7 7 5.o 52 232.0 98.5 i3 12.0 o5.i 73 67.2 28.5 33 122.4 52.0 93 177-7 ?5.4 53 232 .9 98.9 i4 12.9 o5.5 74 68.1 28.9 34 123.3 52.4 94 178.6 7 5.8 54 233.8 99.2 i5 i3.8 o5.9 75 69.0 29.3 35 124.3 52.7 95 179.5 76.2 55 234-7 99.6 16 i4.7 o6.3 76 70.0 29.7 36 125.2 53.i 96 180.4 76.6 56 235.6 100.0 17 i5.6 06.6 77 70.9 3o.i 3 7 126. 1 53.5 97 i8i.3 77.0 5 7 236.6 100.4 18 16.6 07.0 78 71.8 3o.5 38 127.0 53.9 98 182.3 77-4 58 2 3 7 .5 100.8 19 17-5 07.4 79 72.7 30.9 39 128.0 54.3 99 i83.2 77-8 5 9 238.4 101.2 20 18.4 07.8 80 7 3.6 3i.3 4o 128.9 54-7 200 184.1 78.1 60 2 3 9 .3 1 01. 6 21 .9-3 08.2 81 74.6 3i.6 i4i 129.8 55.i 201 i85.o 78.5 261 24o.3 IO2.O 22 20.3 08.6 82 7 5.5 32.0 42 i3o. 7 55.5 O2 185.9 78-9 62 24 1 .2 102.4 23 24 21 .2 22.1 09.0 09.4 83 84 76.4 77.3 32.4 32.8 43 44 i3i.6 i32.6 55. 9 56.3 o3 o4 186.9 187.8 79-3 79-7 63 64 242.1 243.0 1O2.8 103.2 25 'j3 O 09.8 85 78.2 33.2 45 i33.5 56. 7 o5 188.7 80. i 65 243. 9 io3.5 20 23.9 10.2 86 79-2 33.6 46 i34-4 5 7 .o 06 189.6 8o.5 66 244-9 103.9 27 24.9 io.5 87 80. i 34.o 47 i35.3 5 7 -4 07 , 9 o.5 80.9 67 245.8 io4-3 28 25.8 10.9 88 81.0 34-4 48 i36.2 5 7 .8 08 i 9 ,.5 8i.3 68 246.7 104.7 29 26.7 ii .3 89 81 .9 34.8 49 l3 7 .2 58.2 09 192.4 81.7 69 24-7.6 io5.i 3o 27.6 11.7 9 82.8 35.2 5o i38.i 58.6 10 i 9 3.3 82.1 70 248.5 io5.5 3i 28 5 12 . I 91 83.8 35.6 i5i i3 9 .o 5o o 211 194.2 82.4 271 249.5 io5.o 3a 90.5 12.5 84.7 35.9 52 i3 9 . 9 5 9 .4 12 i 9 5 i 82.8 72 2 5o.4 i o6.3 33 S^ 12 .9 93 85.6 36.3 53 i4o.8 5 9 .8 13 196.1 83.2 73 25i.3 106.7 34 3i.3 t3.3 86.5 36. 7 54 i4i.8 60. 2 i4 197.0 83.6 74 252.2 107.1 35 3? ? i3.7 95 87.4 37.1 55 142.7 60.6 i5 197.9 84.0 75 253.1 107.5 36 33 i 96 88.4 37.5 56 M3.6 61 .0 16 198.8 84-4 76 254.1 107.8 37 34.i i4-5 97 89.3 37-9 5 7 i44.5 6i.3 17 199.7 84.8 77 255.0 108.2 38 35.o 14.8 98 90.2 38.3 58 i45.4 61.7 18 200.7 85.2 78 255.9 1 08. 6 39 35.o 15.2 99 91 .1 38. 7 59 i46.4 62.1 19 201 .6 85.6 79 256.8 109.0 4o 36.8 i5.6 100 92.1 3 9 .i 60 147-3 62.5 20 202.5 86.0 80 257-7 109.4 4i 42 43 3 7 . 7 38.7 3o 6 16.0 16.4 16.8 101 02 o3 9 3.o 9 3. 9 94.8 3 9 .5 3 9 . 9 40.2 161 62 63 148.2 149.1 i5o.o 62 .y 63.3 63. 7 221 22 23 203.^ 204.^ 2o5.3 86.4 86.7 87.1 281 82 83 258.7 25 9 .6 26o.5 109.8 I 10.2 1 1 0.6 44 4o.5 17.2 04 95.7 4o.6 64 i5i .0 64.i 24 206. y 87.5 84 261.4 1II.O 45 41.4 17.6 o5 96.7 4i.o 65 i5i .9 64-5 25 207. i 87.9 85 262.3 1 1 1. 4 46 42 .3 18.0 06 07.6 4i.4 66 i52.8 64-9 26 208.0 88.3 8b 263.3 111.7 47 43 3 18 4 07 08.5 4i.8 67 i53. 7 65.3 27 209.0 88.7 87 264.2 112. 1 48 i 9 5o 44.2 45.i 46.o 18.8 19. i i 9 .5 08 09 10 99.4 ioo.: 101 .3 42.2 42.6 43.o 68 69 70 1 54- 6 i55.6 i56.5 65.6 66.0 66.4 28 29 3o 209.9 2IO.C 211.7 89.1 8 9 .5 89.9 88 89 9 265 . i 266.0 266.9 112. 5 112.9 n3.3 5i 52 53 54 55 46.0 47-9 48.8 49.7 5o.6 i 9 . 9 20.3 20.7 21 .1 21.5 1 1 1 12 i3 i4 i5 102.2 io3.i 104.0 104.9 105.9 43.4 43.8 44.2 44.5 44.9 171 72 73 74 75 157.4 i58.3 159.2 160.2 161 .1 66.8 67.2 67.6 68.0 68.4 23l 32 33 34 35 212.6 2i3.6 2i4-5 2i5.4 2i6.3 90.3 90.6 91.0 91.4 9.. 8 291 93 267 .9 268.8 269.7 270.6 271.5 n4-i ii4-5 1 14.9 ii 5.3 56 58 59 60 5i.5 52.5 53.4 54.3 55.2 21.0 22.3 22.7 23.1 23.4 16 17 18 T 9 20 1 06. 8 107.7 1 08 .6 109.5 i io.5 45.3 45.7 46.i 46.5 46.9 76 78 79 8< 162.0 162.9 163.8 164.8 1 65. 7 68.8 69.2 69.6 69.9 70.3 36 37 38 3 9 217.2 218.2 219.1 22O.O 22O-9 92.2 $.0 93.4 9 3.8 9 97 98 o" 3oo 272 .5 2 7 3.4 2 7 4.3 2 7 5.2 2 7 6.2 M6.o 116.4 1 1 6.8 117.2 Dist. Dep. Lat. Dist Dep. Lat. Disl Dep. Lat. Dis Dep. Lai Dist Dep. Lat. [For 07 Degrees. Page 40] TABLE II. Difference of Latitude and Departure for 24 Degrees. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. i 00.9 00.4 6l 55. 7 '24.8 121 no. 5 49.2 181 i65.4 7 3.6 24 1 220.2 98.0 2 01.8 00.8 62 56.6 25.2 22 in. 5 49.6 82 i66.3 74.0 42 221 .1 98.4 3 02 .7 OI .2 63 5 7 .6 25.6 23 112.4 5o.o 83 167.2 74-4 43 222.0 9 8.8 4 03.7 oi .6 64 58.5 26.0 ?-4 n3.3 5o.4 84 168.1 74-8 44 222.9 99.2 o4-6 C2.0 65 59.4 26.4 25 r i4-2 5o.8 85 169.0 7 5.2 45 223.8 99-7 6 o5.5 02.4 66 6o.3 26.8 26 u5.i 5l.2 86 169.9 75-7 -46 2-24.7 1 00. 1 06.4 02.8 67 61.2 27.3 27 1 16.0 5i. 7 87 170.8 76.1 47 22D.6 100.5 8 o 7 .3 o3.3 68 62.1 27.7 28 116.9 52.1 88 171.7 76.5 48 226.6 100.9 9 08.2 o3. 7 69 63.o 28.1 29 117.8 52.5 89 172.7 76.9 49! 227.5 ioi.3 10 09.1 04. i 70 63-9 28.5 3o 118.8 52. 9 9 173.6 77.3 5o 228.4 101.7 1 1 10. o4.5 71 64.9 28.9 i3i 119.7 53.3 191 174.5 77-7 25 1 229.3 102. 1 12 I I .0 04.9 72 65.8 29.3 32 120.6 53. 7 92 175.4 78.1 62 230.2 102.5 i3 II .9 o5.3 73 66.7 29.7 33 121 .5 54.1 93 176.3 7 8.5 53 23l.I 102.9 i4 12.8 o5. 7 74 67.6 3o.i 34 122.4 54.5 94 177.2 78-9 54 232.0 io3.3 i5 .3.7 06.1 75 68.5 3o.5 35 123.3 54.o 95 178.1 79.3 55 233.0 103.7 16 14.6 o6.5 76 69.4 3o.9 36 124.2 55.3 96 179.1 79-7 56 2.33.9 io4-i T 7 i5.5 06.9 77 70.3 3i.3 37 125.2 55. 7 97 186.0 80. i 5 7 234.8 io4-5 18 16.4 07.3 78 7 i.3 3i. 7 38 I26.I 56.i 98 180.9 8o.5 58 235.7 104.9 19 17-4 07.7 79 72.2 32.1 3 9 127.0 56.5 99 181.8 80.9 5 9 236.6 io5.3 20 i8.3 08. i 80 7 3.i 32.5 4o 127.9 56. 9 200 182.7 8i.3 60 23 7 .5 io5.8 21 19.2 o8.5 81 74.o 3 2 . 9 i4i 128.8 5 7 .3 201 i83.6 81.8 261 2.38.4 106.2 22 20. I 08.9 82 74-9 33.4 42 129.7 5 7 .8 O2 1 84.5 82.2 62 23 9 .3 106.6 23 21 .0 09.4 83 7 5.8 33.8 43 i3o.6 58. 2 03 i85.4 82.6 63 24o.3 107.0 24 21 .9 09.8 84 76.7 34.2 44 i3i.6 58.6 o4 !86.4 83.o 64 24l .2 107.4 25 22.8 10.2 85 77-7 34.6 45 i3 2 .5 59.0 o5 187.3 83.4 65 242.1 107.8 26 23.8 10.6 86 78.6 35.o 46 i33.4 59.4 06 188.2 83.8 66 243.0 108.2 27 24.7 II .0 87 79-5 35.4 47 i34.3 5 9 .8 07 189.1 84.2 67 243.9 108.6 28 25.6 11. 4 88 80.4 35.8 48 i35.2 60.2 08 190.0 84.6 68 244.8 109.0 29 26.5 ii. 8 89 8i.3 36.2 49 i36.i 60.6 09 190.9 85.o 69 245.7 109.4 3o 27.4 12.2 00 82.2 36.6 5o 137.0 61 .0 10 191 .8 85.4 70 246.7 109.8 3i 28.3 12.6 91 83.i 3 7 .o i5i 137.9 61.4 211 192.8 85.8 271 247-6 II0.2 3; 29.2 i3.o 92 84.0 3 7 -4 52 i38. 9 61.8 12 193.7 86.2 73 248.5 no. 6 3J 3o.i i3.4 9 3 85.o 3 7 .8 53 139.8 62.2 i3 194.6 86.6 73 249.4 III.O 34 3i.i i3.8 94 85.9 38.2 54 140.7 62.6 i4 io5.5 87.0 74 25o.3 111.4 35 32.0 14.2 95 86.8 38.6 55 i4i.6 63.o i5 196.4 87.4 75 25l .2 in 9 36 32.9 14.6 96 87.7 3 9 .o 56 i42.5 63.5 16 197.3 87.9 76 252.1 II7.3 3 7 33.8 i5.o 97 88.6 3 9 .5 57 i43.4 63. 9 17 198.2 88.3 77 253.1 112.7 38 34.7 i5.5 98 89.5 3 9 . 9 58 i44.3 64.3 18 199.2 88.7 78 254.0 ii3.i 3 9 35.6 i5. 9 99 90.4 4o.3 5 9 i45.3 64-7 *9 200.1 89. i 79 254.9 n3.5 4o 36.5 i6.3 IOO 91.4 40.7 60 i46.2 65.i 20 201 .0 89.5 80 255.8 1 13. 9 4i 3 7 .5 16.7 101 92.3 4i.i 161 147-1 65.5 221 201 , 9 89.9 281 256.7 u4.3 42 38.4 17.1 02 9 3.2 4i.5 62 148.0 65.9 22 202.8 9 o.3 82 25 7 .6 114.7 43 3 9 .3 i 7 .5 o3 94.1 41.9 63 148.9 66.3 23 203.7 oo .7 83 258.5 ii5.i 44 40.2 17.9 o4 95.0 42.3 64 149.8 66.7 24 204.6 01. 1 84 25 9 .4 n5.5 45 4i.i i8.3 o5 95.9 42.7 65 i5o.7 67.1 25 2o5.5 9i.5 85 260.4 n5. 9 46 42.0 18.7 06 96.8 43.i 66 i5i.6 6 7 .5 26 206.5 91.9 86 261.3 ii6.3 4v 42.9 19.1 07 97-7 43.5 67 i5a.6 67.9 27 207.4 92.3 87 262.2 116.7 48 43-9 I9 .5 08 98.7 43.9 68 i53.5 68.3 28 2 8.3 92.7 88 263.1 117.1 49 44.8 19.9 09 99.6 44.3 69 i54.4 68.7 29 2O 9 .2 9 3., 89 264.0 ii 7 .5 5o 45. 7 20.3 IO ioo.5 44-7 70 i55.3 69.1 3o 210. I 9 3.5 9 264.9 118.0 5i 46.6 20.7 III 101 .4 45.i 171 i56.2 69.6 23l 21 1 .0 94.0 291 265.8 118.4 52 47 5 21 .2 12 102.3 45.6 72 .5 7 .i 70.0 32 211 . 9 94-4 92 266.8 118.8 53 48.4 21.6 i3 103.2 46.o 73 i58.o 70.4 33 212.9 94.8 93 267.7 1 19.2 54 49-3 22.0 1 4 104.1 46.4 74 i5 9 .-o 70.8 34 2i3.8 95.2 94 268.6 1 1 9 .6 55 60.2 22.4 i5 io5.i 46.8 75 159.9 71.2 35 214.7 95.6 95 269.5 I2O.O 56 5l.2 22.8 16 106.0 47-2 76 160.8 71.6 36 2i5.6 96.0 96 270.4 120.4 57* 52. ( 23.2 17 106.9 47-6 77 161 . 7 72.0 3 7 216. 5 96.4 97 271 .3 120.8 58 53.o 23.6 18 107.8 48.o 78 162.6 72.4 38 217.4 96.8 98 272.2 121. 2 59 53. 9 24.0 '9 108.7 48.4 79 1 63. 5 72.8 3 9 2I&.3 97.2 99 273.2 1 2 1. 6 60 54.8 24.4 20 109.6 48.8 80 164.4 7 3.2 4o 219.3 97.6 3oo 274.1 122.0 Dbt. Dcp. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. i Lat. [For 66 Degrees. TABLE II. [Page 41 Difference of Latitude arid Departure for 25 Degrees. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. i 00.9 00.4 61 55.3 25.8 121 109.7 5i . i 181 164.0 7 6.5 24 1 218.4 IOI.O 2 DI.fi 00.8 62 56.2 26.2 22 no. 6 5i,6 82 164.9 76. 9 42 219.3 102.3 3 02. 7 oi.3 63 5 7 .i 26.6 23 in. 5 52.0 83 i65. 9 77-3 43 220.2 102. 7 4 o3.6 01. 7 64 58.o 2-7.0 24 112. 4 52.4 84 1 66.8 77.8 44 221. 1 io3.i 5 o4.5 02. I 65 58. 9 27. 5 25 n3.3 52.8 85 167.7 78.2 45 222.0 io3.5 6 o5.4 02.5 66 5 9 .8 27.9 26 Il4-2. 53.2 86 168.6 78.6 46 223.0 104.0 7 o6.3 o3.o 67 60.7 28.3 27 iiS.i 53. 7 8 7 169.5 7 9 .o 47 223.9 104.4 8 o 7 .3 o3.4 68 61.6 28.7 28 1 16.0 54.i 88 170.4 79-5 48 224.8 104.8 9 08 . 2 o3.8 69 62.5 29.2 29 116.9 54.5 89 i 7 i.3 79-9 49 225.7 105.2 IO 09. 1 04.2 70 63.4 29.6 3o 117.8 54-9 9 172.2 8o.3 5o 226.6 io5. 7 1 1 IO.O 04.6 7 1 64.3 3o.o i3i 118.7 55.4 191 i 7 3.i 80.7 25l 227-5 1 06. i ra 10.9 o5.i 7 2 65.3 3o.4 32 119.6 55.8 92 i 7 4.o 81.1 52 228.4 i o6.5 1 3 ii. 8 o5.5 73 66.2 3o. 9 33 120.5 56.2 93 174-9 81.6 53 229.3 106.9 i4 12.7 05.9 74 67.1 3i.3 34 121 .4 56.6 94 175.8 82.0 54 230.2 107.3 i3,6 o6.3 75 68.0 3i. 7 35 122.4 5 7 '.i 95 176.7 82.4 55 23l.I 107.8 16 i4.5 06.8 76 68.9 32.1 36 123.3 5 7 .5 96 177.6 82.8 56 232.0 108.2 17 1.5.4 07.2 77 69.8 32.5 3 7 124.2 57-9 97 178.5 83.3 57 2.32.9 1 08 .6 18 i6.3 07.6 78 70.7 33.o 38 125. I 58.3 98 179.4 83. 7 58 233.8 109.0 19 17.2 08.0 79 71.6 33.4 39 126.0 58. 7 99 180.4 84.1 59 234.7 109.5 20 18.1 o8.5 80 72.5 33.8 4o 126.9 5 9 .2 200 i8i.3 84.5 60 235.6 109.9 21 IO.O 08.9 81 73.4 34.2 i4i 127.8 5 9 .6 201 182.2 84-9 261 236.5 i io.3 22 IO.O 09.3 82 74.3 34- 7 42 128.7 60.0 O2 i83.i 85.4 62 23 7 .5 110.7 23 20.8 9-7 83 7 5.2 35.i 43 129.6 60.4 o3 184.0 85.8 63 238.4 in. i 24 21.8 10. I 84 76.1 35.5 44 i3o.5 60.9 o4 184.9 86.2 64 23 9 .3 1 1 1. 6 25 22 . 7 10.6 85 77.0 35. 9 45 i3i.4 6i.3 o5 i85.8 86.6 65 240.2 112.0 76 23.6 ii .0 86 77-9 36.3 46 i3a.3 61.7 06 186.7 87.1 66 241.1 II2.4 27 24.5 ii. 4 87 78.8 36.8 47 i33.2 62.1 7 187.6 8 7 .5 67 U42.0 I I 2.8 28 25.4 u. 8 88 79.8 3 7 .2 48 i34.i 62.5 08 i88.5 87-9 68 242-9 it3.3 29 26,3 12.3 89 80.7 3 7 .6 49 i35.o 63.o 09 189.4 88.3 69 243.8 ii3. 7 3o 27.2 12.7 90 81.6 38.o 5o 135.9 63.4 10 190.3 88.7 70 244. 7 i i4-i 3i 28 i i3 i QI 82.5 38.5 i5i i36.9 63.8 211 191.2 8 9 .2 271 245.6 u4-5 32 33 29.0 i3.5 l3 Q 92 93 83.4 84.3 38. 9 3 9 .3 52 53 137.8 i38.7 64-2 64-7 12 13 I 9 2.I i 9 3.o 8 9 .6 9 o.o 72 73 246.5 24 7 .4 1 1 5.o ii 5.4 34 3o 8 i4-4 9 4 85.2 39-7 54 139.6 65.i i4 193.9 00.4 74 248.3 1 1 5.8 35 31.7 i4-8 86 i 4o.i 55 i4o.5 65.5 i5 194.9 90.9 75 249.2 116.2 36 3? 6 1 5. a 96 87.0 4o.6 56 i4i-4 65. 9 16 i 9 5.8 91.3 76 aSo.i 1 16.6 37 38 33.5 34.4 i5.6 16.1 97 08 87-9 88.8 4i .0 4i-4 57 58 i42.3 i43.2 66.4 66.8 17 18 190.7 19-7.6 91.7 92.1 77 78 25 1. 252.0 I I "7. 1 II7-5 3 9 4o 35.3 36.3 i6.5 i6. 9 99 IOO 89.7 90.6 4i.8 42.3 59 60 i44.i i45.o 67.2 67.6 '9 20 198.5 199-4 92.6 93.0 79 80 252-9 253.8 u 7 -9 ii8.3 4i 37.2 17.3 IOI 91.5 42.7 161 145.9 68.0 221 200.3 93.4 281 254- 7 118.8 42 38.i 17.7 02 92.4 43.i 62 146.8 68.5 22 201.2 9 3.8 82 255.6 119.2 43 44 45 39.0 3 9 . 9 4o.8 18.2 18.6 I 9 .0 o3 o4 o5 9 3.3 94-3 43.5 44.o 44-4 63 64 65 147.7 148.6 149.5 68.9 6 9 .3 69.7 23 24 25 202.1 203.0 203.O 94.2 94-7 95-1 83 84 85 256.5 25 7 .4 258.3 119.6 I2O.O 120.4 46 47 48 4i-7 42.6 43.5 i 9 .4 i 9 . 9 20. 3 06 07 08 96.1 97.0 97.9 44-8 45.2 45.6 66 67 68 i5o.4 i5i.4 i5a.3 70.2 70.6 71.0 26 27 28 204.8 205. 7 206.6 9 5.b 9 5. 9 9 6.4 86 87 88 259.2 260. i 261.0 120.0 I 2 1. 3 I21. 7 4 9 5o 44.4 45.3 20.7 21 . I 09 IO 98.8 99-7 46.i 46.5 69 70 i53.2 i54.i 71-4 71.8 3o 2O 7 .5 208.5 96.8 97.2 89 90 261.9 262.8 122. 1 122.6 5i 52 53 54 55 56 57 58 59 60 46.2 47.1 48.o 48.9 49.8 5o.8 5i. 7 52.6 53.5 54-4 21.6 22.0 22.4 22.8 23.2 23.7 24.1 24.5 24. 9 25.4 III 12 i3 i4 i5 16 17 18 20 100.6 ior.5 102U io3.3 104.2 io5.i 1 06.0 106.9 107.9 108.8 46.9 47-3 47.8 48.2 48.6 49.0 49.4 49.9 5o.3 5o. 7 171 72 73 74 75 76 3 B i55.o i55.9 i56.8 i5 7 .7 i58.6 159.5 160.4 i6i.3 162.2 i63.i 7 2.3 72.7 7 3.i 7 3.5 7 4.o 7 4-4 7 4.8 7 5.2 7 5.6 76.1 23l 32 33 34 35 36 3 7 38 20 9 .5.4 02 6 66 5 9 .3 28.9 26 II3.2 55.2 86 167.2 8i.5 46 221.1 107.8 7 o6.3 o3.i 67 60.2 29.4 27 114.1 55. 7 8 7 168.1 82.0 47 222.0 io8.3 8 07.2 o3.5 68 61.1 29.8 28 u5.o 56.i 88 169.0 82.4 48 222. 9 I 08. -7 9 08. i 03.9 69 62.0 30.2 29 115.9 56.5 89 169.9 82.9 4 9 223.8 IO 9 .2 10 09.0 o4-4 70 62.9 3o. 7 3o 116.8 5 7 .o 90 170.8 83.3 5o 224. 7 io 9 .6 II OQ . Q 04.8 7 63.8 3i.i i3i 117.7 5 7 .4 191 171.7 83. 7 25l 225.6 I 1 0.0 12 16.8 o5.3 72 64-7 3i.6 32 118.6 57.9 02 172.6 84.2 52 226.5 1 10.5 i3 11.7 o5. 7 73 65.6 32.0 33 119.5 58.3 93 i 7 3.5 84.6 53 227.4 I I0. 9 t4 12.6 06. i 74 66.5 32.4 34 120.4 58. 7 94 174-4 85.o 54 228.3 1 1 1.3 i5 i3.5 06.6 75 67.4 3 2 . 9 35- 121 .3 5 9 .2 95 i 7 5.3 85.5 55 22 9 .2 Hi. 8 16 i4.4 07.0 76 68.3 33.3 36 122.2 5 9 .6 96 176.2 85. 9 56 230.1 I 12. 2 17 i5.3 o 7 .5 77 69.2 33.8 3 7 123. I 60. i 97 177.1 86.4 57 23l.O 112.7 18 16.2 07.9 78 70.1 34.2 38 124.0 6o.5 98 178.0 86.8 58 23l. 9 ii3.i 1 9 17.1 08 J 79 71.0 34.6 3 9 124.9 60.9 99 178.0 87.2 5 9 232.8 n3.5 20 18.0 08.8 80 71.9 35.i 4o 125.8 61.4 200 179.8 87.7 60 233.7 i i4o 21 18.9 09.2 81 72.8 35.5 i4i 126.7 61.8 201 180.7 88.1 261 234.6 n4.4 22 19.8 09.6 82 73-7 35. 9 42 127.6 62.2 O2 181.6 88.6 62 235.5 114.9 23 20.7 10. I 83 74.6 36.4 43 128.5 62.7 03 182.5 89.0 63 236.4 n53 24 21.6 io.5 84 7 5.5 36.8 44 129.4 63.i 04 i83.4 89.4 64 2 3 7 .3 ii 5. 7 25 22.5 ii .0 85 76.4 3 7 .3 45 i3o.3 63.6 o5 i84.3 89.9 65 238.2 116.2 26 23.4 11.4 86 77 .3 3 7 .7 46 l3l.2 64.0 06 i85.2 9 oJ 66 23 9 .I 1 1 6.6 27 24.3 ii. 8 87 78.2 38.i 47 I32.I 64-4 07 186.1 90.7 67 240.0 117.0 26 25.2 12.3 88 79.1 38.6 48 i33.o 64.9 08 186.9 91.2 68 240.9 ii 7 .5 29 26.1 12.7 89 80.0 39.0 49 i33. 9 .65.3 09 187.8 91.6 69 241.8 117-9 3o 27.0 13.2 90 80.9 3 9 .5 5o E.34.8 65.8 10 188.7 92.1 70 242.7 118.4 3i 27.9 i3.6 9 1 8i-.8 3 9 .o 161 i35. 7 66.2 211 189.6 92.5 271 243.6 118.8 32 28.8 i4.o 92 82.7 4o.3 52 i36.6 66.6 12 190.5 9 2 -9 72 244-5 119.2 33 29.7 i4.5 93 83.6 4o.8 53 i3 7 .5 67.1 i3 191.4 9 3.4 73 245.4 119.7 34 3o.6 14.9 94 84.5 41.2 54 1 38.4 6 7 .5 i4 192.3 9 3.8 74 246.3 I20.I 35 3i.5 i5*3 85.4 4i.6 55 i3 9 .3 67.9 i5 193.2 9 4-2 75 247.2 120.6 36 3 2 .4 i5.8 96 86.3 4?. i 56 140.2 68.4 16 194.1 94.7 76 248.1 I 21.0 37 33.3 16.2 97 87.2 42.5 57 i4i .1 68.8 17 195.0 95.1 77 249.0 I2I.4 38 34.2 16.7 98 88.1 43. o 58 142.0 6 9 .3 18 195.9 9 5.6 78 249.9 121.9 3 9 35.i 17.1 99 89.0 43.4 59 142.9 69.7 r 9 196.8 9 6.o 79 25o.8 122.3 4o 36.o i 7 .5 100 89.9 43.8 60 i43.8 70.1 20 I97-7 06.4 80 251.7 122.7 4i 36.9 18.0 101 90.8 44.3 TeT 144.7 70.6 221 198.6 9 6. 9 281 252.6 123.2 42 37-7 18.4 02 91.7 44.7 62 i45.6 71.0 22 199.5 97-3 82 253.5 123.6 43 38.6 1 8. 8 o3 92.6 45.2 63 i46 5 7i.5 23 200.4 97-8 83 254-4 124.1 44 3 9 .5 i 9 .3 o4 93.5 45.6 64 147-4 7L9 24 201.3 98.2 84 255.3 124.5 45 40.4 19.7 o5 9 4.4 46.o 65 i48.3 72 .3 25 2O2.2 98.6 85 256.2 124.9 46 4i.3 20.2 06 95.3 46.5 66 149.2 72.8 26 2O3.I 99.1 86 257.1 125.4 47 42.2 20.6 07 96.2 46. 9 67 iSo.i 7 3.2 2 7 204.0 99-5 87 268.0 125.8 48 43.i 21 .0 08 97.1 47-3 68 i5i .0 7 3.6 28 204.9 99-9 88 258. 9 126.3 4 9 44.o 21.5 09 98.0 47.8 69 i5i .9 74-1 20 2o5.8 100.4 89 25 9 .8 126.7 5o 44-9 21. 9 IO 98.9 48.2 70 i5a.8 74-5 3o 206.7 100.8 9 260.7 127.1 ~sT 45.8 22.4 1 1 1 99.8 48. 7 171 i53.7 7 5.o 23l 207.6 ioi.3 201 261.5 127.6 52 46. 7 22.8 12 100.7 49.1 72 i54.6 75.4 32 208.5 101.7 0'2 262.4 128.0 53 47-6 23.2 i3 101 .6 49.5 73 i55.5 7 5.8 33 209.4 102. 1 93 2633 128.4 54 48'. 5 23. 7 i4 102.5 5o.o 74 1 56.4 7 6.3 34 210.3 102.6 94 264.2 128.9 55 49.4 24.1 i5 io3.4 5o.4 75 i5 7 .3 76.7 35 21 1.2 io3.o 95 265.1 129.3 56 5o.3 24.5 16 io4.3 5o.o 76 i58.2 77.2 36 212. 1 io3.5 96 266.0 129.8 57 5l.2 25.0 17 1O5.2 5i.3 77 i5 9 .i 77.6 3 7 2l3.0 io3. 9 97 266.9 I 36.2 58 52.1 25.4 18 106.1 5i. 7 78 160.0 78.0 38 2 I 3-9 io4-3 98 267.8 i3o.6 59 53.o 25.9 1 9 107.0 52.2 79 160.9 78.5 3 9 2 1 4.8 104.8 99 268.7 i3i.i 60 53.9 26 3 20 107.9 52.6 80 161.8 78.9 4o 2l5. 7 105.2 3oo 260.6 i3i.5 Dist. Dep. 1 La.. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lai. Dist. Dep. Lat. [For CA Degrees. TABLE II [Pago 43 Difference of Latitude and Departure for 27 Degrees. Dial. Lat. Dep Di'st Lat. Dep % Dist Lat. Dep. Dist Lat. Dep. Dist Lat. Dep. I 2 3 4 5 6 8 9 ro 00.9 or. 8 02.7 o3.6 o4.5 o5.3 06.2 07.1 08.0 08.9 oo.5 00.9 01 .i. 01.8 02. 3 02.7 03.2 o3.6 04.1 o4.5 61 62 63 64 65 66 67 68 6 9 . 7 54-4 55.2 56.i 5 7 .o 5 7 . 9 58.8 5 9 . 7 60.6 6i.5 62.4 2 7.7 28.1 28.6 29.1 29.5 3o.o 3o.4 3o. 9 3i.3 3i.8 121 22 23 24 25 26 27 28 ? 3o 107.8 108.7 io 9 .6 no. 5 in ./ 112.; II3.2 n4.o ii4. 9 n5.8 54-9 55.4 55.8 56.3 56. 7 5 7 .2 5 7 . 7 58.i 58.6 5 9 .o i8r 82 83 84 85 86 87 88 8 9 9 i6i.3 162.2 i63.i r63. 9 164.8 165.7 1 66 .6 167.5 168.4 169.3 82.2 82.6 83.i 83.5 84.0 84.4 84- 9 85.4 85.8 86.3 34] 42 43 44 45 46 47 48 g 214.7 2r5.6 2i6.5 217.4 2i8.3 21 9 .2 22O.r 221.0 221.9 2228 109.4 109.9 I 10.' 1 1 0.8 1 1 1. a 111.7 112. 1 I I 2.6 ii3.o ii3.5 ii 12 i3 i4 i5 16 09.8 10.7 n.6 12.5 i3.4 r4.3 o5.o o5.4 -5-9 06.4 06.8 07.3 7i 72 73 74 75 76 63.3 64.a 65.o 65. 9 66.8 67.7 32.2 si? 33.6 34.o 34.5 r3i 32 33 34 35 36 116.7 117.6 ii8.5 u 9 .4 I20.J 121 .2 5 9 .5 5 9 . 9 60.4 60.8 6i.3 61.7 191 9 2 9 3 94 9 4 170.2 171.1 172.0 172.9 173.7 174-6 86.7 87.2 87.6 88.1 88.5 8 9 .o 25l 52 53 54 55 56 2236 224.5 225.4 226.3 227.2 228. r 114.0 ii4-4 114.9 n5.3 1 1 5.8 n6.a 17 18 '9 20 r5.i 16.0 r6. 9 17.8 07.7 08.2 08.6 09. r 77 78 11 68.6 6 9 .5 70.4 7 i.3 35.o 35.4 35. 9 36.3 37 38 3 9 4o 122. I 123.0 123.8 124.7 62.2 62.7 63.i 63.6 97 98 99 200 i 7 5.5 176.4 177-3 178.2 8 9 .4 89-9 9 o.3 90.8 57 58 59 60 22 9 .O 22 9 . 9 23o.8 23.. 7 116.7 117.1 117-6 1 18.0 21 22 23 18.7 19.6 20.5 o 9 .5 ro.o 10.4 8r 82 83 72.2 7 3.i 74.o 36.8 3 7 .2 3 7 . 7 i4i 42 43 125.6 126.5 127.4 64.o 64.5 64.9 201 02 o3 179-1 1 80.0 180.9 9 i.3 91.7 92.2 261 62 63 232.6 233.4 234-3 n8.5 118.9 I IQ.4 24 25 21.4 22.3 10.9 11. 3 84 85 74.8 75-7 38.i 38.6 44 45 128.3 120.2 65.4 65.8 04 o5 181.8 182.7 92.6 93.i 64 65 235.2 236.1 119.0 12O.3 26 23.2 11. 8 86 76.6 J 9 .o 46 i3o. i 66.3 06 i83.5 Q3.5 66 237.0 1 20. 8 27 24.1 12.3 87 77-3 3 9 .5 47 i3i .0 66.7 07 i84-4 94.0 67 1 237.0 121.2 28 24-9 12.7 88 78.4 4o.o 48 i3i.o 67.2 08 i85.3 Q4.4 68 238.8 I2I-7 ? 9 3o 25.8 26.7 13.2 i3.6 89 9 79-3 80.2 4o.4 4o. 9 i 9 5o i32.8 i33. 7 67.6 68.1 9 10 186.2 187.1 9 4. 9 9 5.3 69 70 23 9 . 7 240.6 122. 1 122.6 3i 27.6 i4.i 9 1 81.1 4i.3 i5i i34.5 68.6 211 188.0 9 5.8 271 24i.5 I23.O 32 28.5 i4.5 02 82.0 4i.8 52 i35.4 6 9 .o 12 188.9 9 6.2 7 2 242.4 123.5 33 34 29.4 3o.3 i5.o i5.4 93 94 82.9 83.8 42.2 42.7 53 54 i36.3 137.2 6 9 .5 6 9 . 9 i3 i4 189.8 190.7 96-7 97.2 73 74 243.2 244.1 123.9 124.4 35 3l.2 i5. 9 9 5 84.6 43.i 55 i38.i 70.4 i5 191.6 97.6 75 245.0 124.8 36 32.1 i6.3 9 6 85.5 43.6 56 i3 9 .o 70.8 16 192.5 98.1 76 245. 9 125.3 ^7 33.o 16.8 97 86.4 44-0 57 189.9 7i.3 17 ip3.3 98.5 77 246.8 125.8 38 33. 9 i 7 .3 98 8 7 .3 44-5 58 i4o.8 71-7 18 194.2 99- 78 247.7 126.2 3 9 34.7 17-7 99 88.2 44. 9 ^9 141.7 72.2 19 195.1 99-4 79 248.6 126.7 4o 35.6 18.2 100 89.1 45.4 60 i4a.6 72.6 20 196.0 99-9 80 24 9 .5 127.1 4i 36.5 18.6 roi 90.0 45. 9 161 i43.5 7 3.i 221 196.9 100.3 281 25o.4 127.6 42 3 7 .4 19. i 02 90.9 46.3 62 i44.3 7 3.5 22 197-8 100.8 82 25i.3 128.0 43 38.3 19.5 o3 91.8 46.8 63 r45.2 74-0 23 198.7 loi.a 83 252.2 128.5 44 3 9 .2 20. o o4 9 2.7 47-2 64 i46.r 74.5 24 199.6 101.7 84 253.0 128.9 45 4o.i 20.4 o5 9 3.6 47-7 65 147-0 74. 9 25 200.5 IO2.I 85 2 53. 9 129.4 4b 4i.o 20. 9 06 9 4-4 48.i 66 147.9 75.4 26 201.4 102.6 86 254-8 129.8 47 41.9 21 .3 07 9 5.3 48.6 67 i48.8 7 5.8 27 202.3 io3.i 87 255.7 i3o.3 4 42.8 21.8 08 Ctf.2 4 9 .o 68 149.7 76.3 28 203.1 io3.5 88 256.6 i3o.7 4 9 43. 7 22.2 09 97-1 4 9 .5 69 i5o.6 76.7 2 9 204.0 104.0 8 9 2 5 7 .5 l3l.2 5o 44-6 22.7 10 9 8.o 49.9 70 i5i.5 77.2 3o 2o4- 9 io4-4 9 258.4 .3i. 7 5i 45.4 23.2 i ii 9 8 -9 5o.4 171 162.4 77-6 a3i 2o5.8 104.9 201 2 5 9 .3 i3a.i 52 46.3 23.6 12 99-8 5o.8 72 i53.3 78.1 32 206.7 io5.3 9 2 260.2 i3a.6 53 47-2 24.1 i3 100.7 5i.3 73 i54.i 78 5 33 207.6 io5.8 93 261.1 i33.o 54 48.i 24.5 i4 roi .6 5r.8 74 i55.o 79 o 34 208.5 106.2 94 262.0 i33.5 55 49.0 25.0 r5 02.5 52 .2 75 i55. 9 79 4 35 200.4 106.7 95 2628 i33. 9 56 49.9 25.4 16 o3.4 52.7 76 i56.8 79 9 36 210.3 107.1 96 263.7 i34.4 i>7 5o 8 25.Q 17 104.2 53.i 77 i57-7 80 4 3 7 211. 2 107.6 97 264.6 1 34 .8 58 5i. 7 26.3 18 io5.i 53.6 78 i58.6 80 8 38 212. 1 1 08.0 98 265.5 i35.3 5 9 52.6 26.8 19 106.0 54-O 79 159.5 81 3 3 9 213.0 1 08. 5 99 2664 i35, 7 bo 53.5 27.2 20 io6. 9 54.5 80 160.4 81 7 4o 2i3.8 io 9 .o 3oo 267.3 1 36. 2 Dist. Dep. 1 Lat Dist. Dep. Lat.' Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. [For G3 Degrees. Page 44] TABLE II. Difference of Latitude and Departure for 28 Degrees. Dist. i 2 Lat. 1 Dep. oo . 9 oo . 5 01.8 oo. o Dist. Lat. Dep. 28.6 29.1 Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 61 62 53. 9 54-7 121 22 106.8 I0 7 . 7 56.8 5 7 .3 181 82 1 59.8 160.7 85.o 85.4 241 42 212.8 2l3. 7 u3 i 1 1 3.6 3 02.6 01 .4 63 55.6 29.6 23 108.6 5 7 . 7 83 161.6 85. 9 43 214.6 i i4-i 4 o3.5 01 .9 64 56.5 3o.o 24 109.5 58.2 84 162.5 86.4- 44 2i5.4 u4-6 5 o4.4 02.3 65 5 7 .4 3o.5 25 110.4 58. 7 85 i63.3 86.9 45 2i6.3 1 1 5.o 6 o5.3 02.8 66 58.3 3i.o 26 in. 3 59.2 86 164.2 8 7 .3 46 217.2 n5.5 7 06.2 o3.3 67 5 9 .2 3i.5 27 112. I 59.6 87 i65.i 87.8 47 218. i 116.0 8 07.1 o3.8 68 60.0 3!. 9 28 ii3.o 60. i 88 166.0 88.3 48 219.0 116.4 g 07.9 04.2 69 60.9 32.4 2 9 n3. 9 60.6 89 166.9 88.7 49 219.9 1 16.9 7 10 08.8 04.7 70 61.8 32. 9 3o 114.8 61 .0 9 167.8 89.2 5o 220.7 117.4 1 1 09.7 05.2 71 62.7 33.3 i3i n5. 7 6i.5 191 168.6 89.7 25l 221.6 117.8 12 >. 10.6 o5.6 72 63.6 33.8 32 ii6.5 62.0 92 169.5 90.1 52 222.5 n8.3 i3 n. 5 06. i ?3 64.5 34.3 33 117.4 62.4 93 170 4 90.6 53 223.4 118.8 i4 12.4 06.6 74 65.3 34.7 34 n8.3 62.9 9 4 i 7 i.3 91.1 54 224.3 1 19.2 i5 l3.2 07.0 75 66.2 35.2 35 119.2 63.4 95 172.2 9I.S 55 225.2 119.7 16 i4-i o 7 .5 76 67.1 35. 7 36 I 20. I 63.8 96 i 7 3.i 92.0 56 226.0 I2O.2 17 i5.o 08.0 77 68.0 36.i 37 121 .O 64.3 97 173.9 92.5 5 7 226.9 I2O.7 18 i5.o o8.5 78 68.9 36.6 38 121. 8 64.8 98 174.8 93.0 58 22 7 .8 121. 1 IQ 16.8 08.9 79 69.8 3 7 .i 3 9 122.7 65.3 99 175.7 93.4 5 9 228.7 I 2 1. 6 7 20 17-7 09.4 80 70.6 3 7 .6 4o 123.6 65. 7 200 176.6 9 3. 9 60 229.6 122.1 21 i8.5 09.9 81 7 i.5 38.o i4i 124.5 66.2 201 i 77 .5 94-4 261 23o.4 122.5 22 19.4 l6.3 82 72.4 38.5 42 125.4 66. 7 02 178.4 9 4.8 62 23i.3 123.0 23 20.3 10.8 83 7 3.3 3 9 .o 43 126.3 67.1 03 179.2 9 5.3 63 232.2 123.5 24 21 .2 11. 3 84 74.2 3 9 .4 44 127.1 67.6 o4 180.1 9 5.8 64 233.1 123.9 25 22.1 ii .7 85 7 5.i 39.9 45 128.0 68.1 o5 181.0 96.2 65 234-0 124.4 26 23 12.2 86 7 5. 9 4o.4 46 128.9 68.5 06 181.9 96-7 66 234-9 124.9 27 23.8 12.7 87 76.8 4o.8 47 129.8 69.0 07 182.8 97.2 67 235. 7 125.3 28 2^. 7 i3.i 88 77-7 4i.3 48 i3o-7 6 9 .5 08 i83/7 97-7 68 236.6 125.8 20 25.6 i3.6 89 78.6 4i.8 49 :3i.6 70.0 09 184.5 98.1 69 2.3 7 .5 126.3 3o 26.5 14.1 90 79-5 42.3 5o i32.4 7^-4 10 i85.4 98.6 70 238.4 126.8 3i 27.4 i4-6 91 8o.3 42.7 i5i i33.3 70.9 211 7861" 99- ! 271 "alp 127.2 32 28.3 i5.o 92 8i.a 43.2 52 i34.2 71.4 12 187.2 99-5 72 240.2 127.7 33 29. i i5.5 93 82.1 43. 7 53 i35.i 71.8 13 188.1 1 00.0 73 241.0 128.2 34 3o.o 16.0 94 83.o 44.i 54 i36.o 72.3 i4 189.0 loo.S 74 241-9 128.6 35 3o.9 16.4 95 83. 9 44.6 55 i36. 9 72.8 i5 189.8 ioo. 9 75 242.8 1 29.1 36 3i.8 16.9 96 84.8 45.i 56 i3 7 . 7 7 3.2 16 190.7 101.4 76 243.7 129.6 3y 3 2 . 7 17-4 97 85.6 45.5 5 7 i38.6 73.7 17 191.6 ioi. 9 77 244.6 i3o.o 38 33.6 1.7.8 98 86.5 46.o 58 i3 9 .5 7 4.2 18 192.5 102.3 78 245.5 i3o.5 3 9 34-4 i8.3 99 8 7 .4 46.5 5 9 i4o.4 7 4.6 J 9 193.4 102.8 79 246.3 i3i.o 4o 35.3 18.8 100 88.3 46.9 60 i4i.3 7 5.i 20 194.2 io3.3 80 247.2 i3i.5 4i 36.2 19.2 101 89.2 47-4 161 142.2 7 5.6 221 195.1 io3.8 281 248.1 1 3 1. 9 4s- 3 7 .i 19.7 02 90.1 47-9 62 143.0 7 6.i 22 196.0 104.2 82 249.0 i32.4 43 38.o 2O. 2 o3 90.9 48.4 63 143.9 7 6.5 23 196.9 104.7 83 249.9 132.9 44 38.8 20.7 04 91.8 48.8 64 144-8 77-0 24 197.8 105.2 84 25o.8 i33.3 45 3 9 . 7 21 . I o5 92.7 49-3 65 i45. 7 77-5 25 198.7 io5.6 85 25 1. 6 i33.8 46 4o.6 21.6 06 9 3.6 49.8 66 i46.6 77-9 26 199.5 106.1 86 252.5 1 34. 3 4? 4i.5 22.1 07 94.5 50.2 67 i4 7 .5 78.4 27 200.4 1 06.6 87 253.4 1 34-7 48 43.4 22.5 08 95.4 5o. 7 68 148.3 78.9 28 201.3 107.0 88 254-3 i35.2 49 43.3 23.0 09 96.2 5i.a 69 149.2 79-3 29 202.2 107.5 8 9 255.2 i35. 7 5o 44.i 23.5 10 97.1 5i.6 70 i5o.i 79.8 3o 203.1 1 08.0 90 256.1 1 36. i 5i 45.o 73^" III 98.0 52.! 171 i5i .0 "8o.3 23l 204-0 108.4 291 256.9 1 36.6 52 45-9 24.4 12 98.9 52.6 72 i5i .9 80.7 32 204.8 108.9 92 2 5 7 .8 137.1 53 46.8 24.9 i3 99.8 53.i 73 l52. 7 81.2 33 205.7 109.4 93 258. 7 137.6 54 47-7 25.4 i4 100.7 53.5 74 i53.6 81.7 34 206.6 109.9 94 25 9 .6 i38.o 55 48.6 25.8 i5 loi.S 54.0 7 5 i54.5 82.2 35 207.5 no 3 9 5 260.5 i38.5 56 49.4 26.3 16 102.^ 54-5 76 i55.4 82.6 36 208.4 1 10.8 96 261.4 139.0 5? 5o.3 26.8 17 io3.3 54-9 77 i56.3 83.i 37 209.3 iu.3 97 262.2 139.4 58 5l.2 27.2 18 104.2 55.4 78 l5 7 .2 83.6 38 2IO.I 111.7 9 8 263.1 i3 9 . 9 5 9 52.1 27.7 1 9 io5. i 55. 9 79 i58.o 84.0 3 9 2II.O 112. 2 99 264.0 i4o.4 60 53.o 28.2 20 106.0 56.3 80 i58. 9 84.5 4o 2II. 9 II2.7 3oo 264.9 i4o.S Dist Dep. Lat. Dist Dep. Lat. Dist Dep. Lat. Dist Dep. Lat. Dist Dep. Lai. [For 62 Degrees. TABLE II. fP-s- * Difference of Latitude and Departure for 29 Degrees. Dist. Lat. Dep. ist. Lat. Dep. Dist. Lat. Dep. ist. Lat. Dep. Dist. Lat. Dep. i )O.Q o.5 61 53.4 2 9 .6 121 106.8 58. 7 8l 1 58.3 87.8 24 1 H0.8 1 16.8 2 JI.7 I .0 62 54-2 3o.i 22 106.7 69.1 82 1 5 9 .2 88.2 42 211.7 II7-3 3 02.6 i .5 63 55.i 3o.5 23 107.6 5 9 .6 83 160.1 88. 7 43 212.5 1 17.8 4 o3.5 1.9 64 56.o 3i.o 24 108.5 60. i 84 160.9 8 9 .2 44 2i3.4 n8.3 5 o4.4 2.4 65 56.9 3i.5 25 109.3 60.6 85 161.8 89.7 45 214.3 1 18.8 6 05.2 02.9 66 57-7 32.0 26 no. 2 61.1 86 162.7 90.2 46 215.2 119.3 7 06. i o3.4 6 7 58.6 32.5 27 in .1 61.6 87 i63.6 90.7 47 216.0 119.7 8 07.0 o3. 9 68 59.5 33.o 28 112. 62. i 88 1 64. 4 91.1 48 216.9 I 20. 2 9 07.9 o4-4 69 6o.3 33.5 29 112. 8 62.5 89 i65.3 91.6 49 217.8 120-7 10 08.7 04.8 70 61.2 33. 9 3o ii3. 7 63.o 90 166.2 92.1 5c> 218.7 121. 2 1 1 9.6 o5.3 71 62.1 34-4 i3i 114.6 63.5 9 1 167.1 92.6 25l 2I 9 .5 121.7 12 o.5 ,5.8 72 63.o 34-9 32 n5.4 64.o 92 167.9 93.1 52 220.4 122.2 i3 i .4 o6.3 73 63.8 35.4 33 u6.3 64.5 93 168.8 9 3.6 53 221.3 I22. 7 2.2 06.8 74 64-7 35.9 34 117-2 65.o 94 169.7 94.1 54 222.2 123.1 i5 3.1 07-3 75 65.6 36.4 35 118.1 65.4 95 170.6 94-5 55 223.0 23.6 16 4.0 07.8 76 66.5 36.8 36 118.9 65. 9 9 6 171.4 95.0 56 223. 9 24.1 17 4.9 08.2 77 6 7 .3 3 7 .3 3 7 119.8 66.4 97 172.3 95.5 57 224.8 24.6 18 5.7 08.7 78 68.2 3 7 .8 38 120.7 66.9 98 173.2 96.0 58 225-7 125.1 6.6 09.2 79 69.1 38.3 3 9 121 .6 6 7 .4 99 174.0 9 b.i> 59 226.5 125.6 20 7.5 09.7 80 70.0 38.8 4o 122.4 67.9 200 174.9 97.0 bo 227.4 126.1 21 8.4 IO.2 81 70.8 3 9 .3 i4i 123.3 68.4 201 i 7 5.8 97-4 261 228.3 126.5 22 9.2 10.7 82 71.7 3 9 .8 42 124.2 68.8 O2 176.7 97-9 62 22 9 .2 I2 7 .0 23 20. i I I .2 83 72.6 40.2 43 125. I 69.3 O-: 177.5 98.4 63 230.0 1*7.5 24 21 .0 ii. 6 84 7 3.5 40.7 44 125.9 69.8 oz 178.4 98-9 64 23o. 9 128.0 25 21 .9 12. I 85 74-3 41.2 45 126.8 70.3 o5 179.3 99.4 bb 23 1. 8 128.5 26 22 .7 12.6 86 4i-7 46 127.7 70.8 06 180.2 99-9 bb 232.6 129.0 27 23.6 i3. i 87 76.1 42.2 47 128.6 71.3 07 181.0 100.4 67 233.5 129.4 28 2.4.5 i3.6 88 77.0 42.7 48 12Q.4 71.8 08 181.9 100.8 68 234-4 129.9 29 ?5.4 14.1 89 77-8 43.i 49 i3o.3 72.2 09 182.8 IOI.3 69 235.3 i3o.4 3o 96 ? i4-5 90 78.7 43.6 5o l3l.2 72.7 10 i83.7 101.8 70 236.1 i3o. 9 3i 27.1 i5.o 91 79.6 44.i i5i i3a.i 7 3.2 211 i84-5 102.3 271 237.0 i3i.4 32 33 28.0 28.9 i5.5 16 o 9* od 8i!3 44-6 45.i 53 i3a.o ,33.8 73.7 74-2 12 i3 i85.4 i86.3 102.8 io3.3 ? 73 23 7 -9 238.8 i3i-9 i32.4 34 29.7 i6.5 94 82.2 45.6 54 i34. 7 74-7 i4 187.2 io3.7 74 2 3 9 .6 i32.8 35 3o .6 170 o5 83.i 46.i 55 i35.6 7 5.t i5 188.0 io4-2 7 5 24o.5 i33.3 36 3i.5 i 7 .5 84.0 46.5 56 i36.4 7 5.6 16 188.9 104.7 76 241.4 1.33.8 37 38 39 4o 32.4 33.2 34.i 35.o 17.9 18.4 18.9 19.4 i 99 I GO 84.8 85. 7 86.6 .8 7 .5 47-0 4 7 .5 48.o 48.5 58 59 60 i3 7 .3 i38.a i3 9 .i i3 9 . 9 76.1 76.6 77-1 77-6 17 18 20 189.8 190.7 191.5 192.4 IOD.2 106.7 1 06. 2 106.7 77 78 Z 9 80 242.3 243.1 244.0 1 34-3 1 34.8 i35.3 i35. 7 4i 42 43 44 35. 9 36.7 3 7 .6 38,5 19.9 20.4 20.8 21 .3 101 O2 o4 88.3 89.2 90.1 91 .0 49.0 49.5 49.9 5o.4 161 62 63 64 i4o.8 i4i-7 142.6 i43.4 78.1 7 8.5 79.0 79.5 221 22 23 24 193.3 19-4.2 i 9 5.o i 9 5. 9 107.1 107.6 108.1 108.6 281 82 83 84 245.8 246.6 247-5 248.4 i36.2 1 36.7 l3 7 .2 1 37-7 45 46 47 48 3 9 .4 40.2 42^0 21.8 22.3 22.8 23.3 o5 06 7 08 91.8 92.7 o3.6 94-5 50.9 5i.4 61.9 52.4 65 66 67 68 i44-3 i45.2 i46.i i46. 9 80. c 8o.5 81.0 8i.4 25 26 27 28 196.8 I97-7 ijfc 199.4 109.1 109.6 I 10. 1 1 10. 5 85 86 87 88 25o'.I 261.0 25l. 9 r A i38.2 i38.7 1 39. i 139.6 49 5o 42.9 43. 7 23.8 24.2 09 10 9 5.3 96.2 53 '.3 69 70 148.7 81.9 82.4 29 3o 200. 3 201.2 III.O 1 1 1. 5 69 9 252.8 253.6 i4o.6 5i 44.6 24.7 n 97.1 53.8 171 149.6 82.9 23 I 202.0 I 12.0 29. 254-5 >4i.j 52 53 45.5 46.4 25.2 25.7 i i3 98.0 98.8 54-3 54.8 72 73 160.4 i5i.3 83.4 83.9 32 33 202.9 203.8 1 12.5 1 1 3.o % 23.). 4 256.3 142.0 54 55 56 57 58 47-2 48.i 49.0 49.9 50.7 26.2 26.7 27. 1 27.6 28.1 it i ' i i i 99-7 100.6 101.5 102.3 103.2 55.3 55.8 56.2 56. 7 5 7 .2 74 75 76 77 78 162. a i53.i 1 54 '.8 166.7 84.4 84.8 85. 85. 86. 34 35 36 3 7 38 204-7 2o5.5 206.^ 207.: 208.2 1 13.4 ii 3. 9 1 14-9 1 1 5.4 94 2.57.1 258.o 2.58.9 1 43.o ,43.5 i44.c i44-5 5g 6c 61.6 52.5 28.6 2 9 . 2 104.1 io5.c 57.7 58.2 Zj i56.C 167.4 86. 87- 3 9 4o 209.0 20 9 . 9 1 15.9 1 16.4 3oo 2.b i .!: 26 2. i 145-4 Dis DCD Lat Dis Dep. Lat. Dst Dep. Lat Dist Dep. Lat. Dist Dep Lai. [For Gl Degrees. l'ae4G] TABLE II Difference of Latitude and Departure for 30 Degrees. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dop. Dist. Lat. Dep. Dist. Lat Dep. i 00.9 7xT5 ~6T 52.8 ~3oT5" 121 io4.8 6o.5 181 1 56.8 90.5 "air 208.7 1 20. 5 2 01 7 01 .0 62 53. 7 3i,o 22 io5.7 61 .0 82 1 57.6 91.0 42 209.6 121. 3 oa 6 oi.5 63 54.6 3i.5 2.3 io6.5 6i.5 83 i58.5 91.5 43 210.4 I2I.5 4 o3.5 02. o 64 55.4 32.0 24 107.4 62.0 &4 i5 9 .3 Oi.O 44 2 I 1. 3 122.0 5 o4-3 02.5 65 56.3 32.5 25 108.3 62.5 85 160.2 92.5 45 212.2 122.5 6 05.2 o3.o 66 5 7 .2 33.o 26 109.1 63.o 86 161.1 9 3.o 46 2l3.0 123.0 7 06. i o3.5 67 58.o 33.5 27 IIO.O 63.5 87 161.9 9 3.5 47 2l3. 9 123.5 8 06.9 04.0 68 58. 9 34.o 28 110.9 64.0 88 162.8 94.0 48 214.8 124.0 9 07.8 o4.5 69 5 9 .8 34-5 29 111.7 64.5 89 i63.7 9 4.5 49 2 1 5.6 124.5 10 08.7 o5.o 7" 60.6 35.o 3o 112. 6 65.o 90 1 64. 5 95.0 5o 2i6.5 125.0 ii o 9 .5 ~o575~ 71 ~6i~!ir 35.5 i3i n3.4 65.5 191 i65.4 9 5.5 a5i 217.4 125.5 12 io.4 06.0 72 62.4 36.o 32 n4.3 66.0 92 1 66.3 96.0 52 218.2 126.0 i3 ii. 3 o6.5 73 63.2 36.5 33 Il5.2 66.5 93 167.1 96.5 53 2I 9 .1 126.5 i4 12. I 07.0 74 64.i 3 7 .o 34 116.0 67.0 94 168.0 97.0 54 220.0 127.0 i5 i3.o o 7 .5 75 65.o 3 7 .5 35 116.9 6 7 .5 168.9 97-5 55 220.8 127.5 16 13.9 08.0 76 65.8 38.o 36 117.8 68.0 96 169.7 98.0 56 221.7 128.0 17 1.4.7 o8.5 77 66.7 38.5 37 118.6 68.5 97 170.6 98.5 57 222.6 128.5 18 i5.6 09.0 78 6 7 .5 39.0 38 1 19.5 69.0 98 i 7 i.5 99.0 58 223.4 129.0 1 9 i6.5 o 9 .5 79 68.4 3 9 .5 3 9 120.4 6 9 .5 99 172.3 99.5 5 9 224.3 129.5 20 i 7 .3 IO.O 80 6 9 .3 4o.o 4o 121 .2 70.0 200 I 7 3.2 IOO.O 60 225.2 i3o.o 21 i8.a io.5 81 70.1 4o.5 i4i 122 . I "7^5 20i 174.1 ioo. 5 261 226.0 i3o.5 22 19.1 11 .0 82 71.0 4i .0 42 123.0 71.0 02 174.9 IOI.O 62 226. 9 i3i.o 23 19.9 ii. 5 83 71.9 4i.5 43 123.8 7 i.5 03 i 7 5.8 ioi.5 63 227.8 i3i.5 24 20.8 12. O 84 72.7 42.0 44 124-7 72.0 04 176.7 I02.O 64 228.6 1 32.0 25 21.7 12.5 85 7 3.6 42.5 45 125.6 72.5 o5 177.5 102.5 65 22 9 .5 i3 2 .5 26 22.5 i3.o 86 74.5 43.o 46 126.4 7 3.o 06 178.4 io3.o 66 230.4 1 33.o 27 23.4 i3.5 87 7 5.3 43.5 47 127.3 7 3.5 07 179.3 io3.5 67 23l.2 i33.5 28 24.2 14.0 88 76.2 44-0 48 128.2 74-0 08 1 80. i 104.0 68 232.1 1 34.o 29 25.1 i4.5 89 77-i 44-5 49 129.0 74-5 09 181.0 io4.5 69 233.0 i34.5 3o 26.0 i5.o 9 77-9 45.o 5o 129.9 7 5.o 10 181.9 io5.o 70 233.8 i35.o 3i 26.8 i5.5 9 1 78.8 45.5 i5i i3o.S |75.5 211 182.7 io5.5 271 234.7 i35.5 32 27.7 16.0 92 79-7 46.0 52 i3i.6 76.0 12 1 83.6 1 06.0 72 235.6 1 36.o 33 28.6 i6.5 93 8o.5 46.5 53 !32.5 7 6.5 13 i84-5 io6.5 73 236.4 i36.5 34 29.4 17.0 94 81.4 47.0 54 i33.4 77.0 i4 i85.3 107.0 74 2 3 7 .3 137.0 35 3o.3 i 7 .5 95 82.3 47-5 55 1 34. a 77-5 i5 186.2 107.5 75 238.2 137.5 36 3l.2 18.0 96 83.i 48.o 56 i35.i 78.0 16 187.1 108.0 76 23 9 .0 i38.o 3? 32.0 i8.5 97 84.0 48.5 5 7 1 36.o 7 8.5 17 187.9 io8.5 77 239.9 i38.5 38 3 2 . 9 19.0 98 84.9 49-0 58 1 36.8 79.0 18 188.8 109.0 78 240.8 139.0 3 9 33.8 i 9 .5 99 85.7 49-5 5 9 i3 7 . 7 79-5 J 9 189.7 109.5 79 241.6 139.5 4o 34.6 20. o IOO 86.6 5o.o 60 1 38.6 80.0 20 190.5 11O.O 80 242.5 i4o.o 4r 35.5 20.5 101 8 7 .5 5o.5 161 139.4 ~8o75" 221 191.4 i io.5 281 243.4 i4o.5 42 36.4 21 .O 02 88.3 5i.o 62 i4o.3 81.0 22 192.3 III.O 82 244.2 i4i-o 43 3 7 .2 21.5 o3 89.2 5i.5 63 i4i .2 8i.5 23 193.1 iii.S 83 245.1 i4i.5 44 38.i 22.0 o4 90.1 52.0 64 142.0 82.0 24 194.0 I I 2.0 84 246.0 142.0 45 3 9 .o 22.5 o5 90.9 52.5 65 142.9 82.5 25 194.9 I I 2.5 85 246.8 i4a.5 46 3 9 .8 23.0 06 91.8 53.o 66 i43.8 83.o 26 r 195.7 n3.o 86 247.7 1 43.o 47 40.7 23.5 07 92.7 53.5 67 i44.6 83.5 27 196.6 n3.5 87 248.5 i43.5 48 4i.6 24.0 08 9 3.5 54.o 68 i45.5 84.0 28 197.5 i i4-o 88 249.4 1 44.0 J9 42.4 24.5 09 94-4 54.5 69 i46.4 84.5 29 198.3 n4.5 89 25o.3 i44-5 5o 43.3 25.0 10 9 5.3 55.o 70 147.2 85.o 3o 199.2 1 1 5.o 9 25l.I 1 45.o ~~5T 44-2 ~2~575~ in 90.1 bb.b 171 148.1 85.5 23l 200.1 n5.5 291 252.O i45.5 52 45.o 26.0 12 1 97.0 56.o 72 149.0 86.0 32 200-9 1 16.0 92 252.9 1 46.o 53 45.9 26.5 i3 97-9 56.5 73 149.8 86.5 33 201.8 n6.5 93 253.7 i46.5 54 46.8 27.0 i4 98.7 5 7 .o 74 i5o.7 87.0 34 202.6 117.0 94 254-6 147.0 55 47-6 27.5 i5 99.6 5 7 .5 75 i5t.fi 8 7 .5 35 203.5 ii 7 .5 95 255.5 147-5 56 48.5 28.0 16 100.5 58.o 76 i52.4 88.0 36 204.4 1 1 8.0 96 256.3 1 4S.o 57 49.4 28.5 17 101 .3 58.5 77 i53.3 88.5 37 205.2 n8.5 97 257.2 i48.5 58 5o.2 29.0 18 102.2 59.0 78 i54.2 89.0 38 206. 1 119.0 98 258.1 149.0 59 60 5i.i 52.0 29.5 3o.o 1 9 20 io3.i 103.9 5 9 .5 60.0 79 80 i55.o 1 55. 9 8 9 .5 90.0 39 4o 207.0 207.6 119.5 I2O.O .99 ooo 268.9 259.8 .i49.5 150.0 Dist. DepT Lat. Di^u Dep. | Lat. Dist. Dep. 1 Lat. Dist. Den. Lat. Disi Dep. Lat. [For 60 Degrees. TABLE II. irse4? Difference of Latitude and Departure for 31 Degrees. Dist. Lat. Dep. Dst. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. )ist. Lat. j Dep. i 00.9 oo.5 61 52.3 1-4 2, o3. 7 2.3 81 I55.I Q 3.2 24 1 206.6 1 124.1 2 01.7 o. .0 62 53.i 1.9 22 04.6 2.8 82 ,56.0 93-7 207.4' 124.6 3 02.6 oi.5 63 54-0 2.4 23 o5.4 63.3 83 1 56.9 9^.3 43 208.3- 125.2 4 o3.4 02 . i 64 54-9 3.o 24 o6.3 63. 9 84 157.7 9 4-8 44 209.1 125.7 5 o4.3 02 .6 65 55.7 3.5 25 07.1 64.4 85 ,58.6 9 5.3 45 210.0 ,26.2 6 o5.i o3.i 66 1 56.6 4.0 26 08.0 64. 9 86 159.4 9 5.8 46 210.9 126.7 7 06.0 o3.6 67 57.4 4.5 27 08.9 65.4 87 i6o.3 9 6.3 47 21I. 7 127.2 8 06.9 04. i 68 58.3 35.o 28 09.7 65. 9 88 ,6,. i 9 6.8 48 212.6 127.7 9 07 7 04.6 69 5 9 .i 35.5 29 i .0.6 60.4 89 162.0 97-3 49 2 I 3.4 128.2 10 08.6 05.2 60.0 36., 3o i . i. 4 67.0 9 162.9 97-9 5o 214.3 128.8 1 1 09.4 o5. 7 7i 60.9 36.6 ,3, 112. 3 6 7 .5 191 ,63. 7 98.4 25l 2l5.I 129.3 12 .o.3 06.2 7 2 61.7 37., 32 i j3. i 68.0 92 ,64.6 98-9 52 2IO.O 129.8 i3 1 1 . i 06.7 73 62.6 3 7 .6 33 n4-o 68.5 93 ,65.4 99-4 53 216.9 ,3o.3 14 12.0 07.2 74 63.4 38.i 34 1,4.9 69.0 94 i66.3 99-9 54 217.7 i3o.8 .5 12.9 07.7 75 64.3 38.6 35 ,,5. 7 6 9 .5 95 ,67.1 100.4 55 218.6 i3i.3 16 .3.7 08.2 76 65.i 3 9 .i 36 1.6.6' 70.0 96 168.0 100.9 56 219.4 ,3i.8 17 i4-6 08.8 77 66.0 3 9 . 7 3 7 ii7-4 70.6 97 168.9 101.5 57 220.3 ,32.4 18 .5.4 09.3 78 66.9 40.2 38 i,8.3 7i -i 98 169.7 102.0 58 221.1 ,32.9 19 .6.3 09.8 79 67.7 4o.7 39 1,9.1 71.6 99 ,70.6 102.5 59 222.O ,33.4 20 17. i ,o.3 80 68.6 4l.2 4o ,20.0 72. , 200 171.4 io3.o 60 222-9 ,33.9 21 18.0 10.8 8, 69.4 41.7 14, 120-9 72.6 20, 172.3 io3.5 261 223-7 i34.4 22 18.0 1 1 .3 8? 70.3 42 2 42 12, .7 73. , 02 , 7 3.i 104.0 62 224-6 i34.Q IQ-7 u. 8 83 71.1 42. 7 43 122.6 73-7 03 104.6 63 225.4 135.5 24 * L 20.6 ,2.4 84 72.0 43.3 44 123.4 74-2 o4 174.9 io5.i 64 226.3 1 36.o 2.5 21 .4 . 2 .O 85 72.9 43.8 45 124.3 74.7 o5 175.7 io5.6 65 0.27.1 i36.5 26 86 73.? 44.3 46 125.1 7 5.2 06 176.6 1 06. i 66 228.0 137.0 27 23. I 3. 9 87 74.6 44.8 47 126.0 75.7 07 177.4 106.6 67 228.9 i3 7 .5 28 24 <> 4.4 88 75.4 45.3 48 126.9 76.2 08 i 7 8.3 107.1 68 229.7 1 38.o 29 3o 94.9 14.9 .5.5 89 90 70.3 77.1 45.8 46.4 127.7 128.6 76.7 77-3 09 10 I7 9 .i 1 80.0 107.6 108.2 69 70 23o.6 23i.4 i38.5 1 39. i 3. 26.6 16.0 91 78.0 46.9 i5i 129.4 77-8 21, 180.9 108.7 27, 232.3 i3 9 .6 32 27 4 .6 5 78.9 47-4 52 i3o!a 7 8.3 12 181.7 109.2 72 233.1 i4o.i 33 28.3 17 o 93 79-7 47-9 53 78.8 i3 182.6 109-7 73 234.0 i4o.6 34 35 29., JO O ,7-5 .8 o 94 o5 80.6 81.4 48.4 48.9 54 55 132.0 i3 2 . 9 79-3 79-8 i4 1 5 ,83.4 ,84-3 ,10.2 II0.7 74 75 234.9 235.7 i4i-6 36 3o.g i8.5 96 82.3 4 9 .4 56 i33. 7 8o.3 1.6 ,85., 1 1 1. 2 76 236.6 142.2 3, 7 I O 1 Q7 83.i DO.O 57 ,34.6 80.9 17 186.0 n.8 77 237.4 l42-7 38 32.6 iy. i 10. 6 98 84.o 5o.5 58 i35.4 81.4 18 186.9 II2.3 78 238.3 i43.2 3a 33 4 2O 1 go 84.9 5,.o 5 9 i36.c 81.9 ,9 187-7 I I 2.8 79 239.1 i43. 7 4o 34.3 20.6 JOO 85. 7 5i.5 60 ,3 7 .i 82.4 20 ,88.6 1,3.3 80 240.0 i44-2 ii 35 i 2 1 I 1OI 86.6 52.0 .6. i38.o 82.9 221 189.4 n3.8 28, 240.9 i44-7 42 36.o 21.6 G2 87.4 52.5 62 i38. 9 83.4 22 , 9 o.3 ii4.3 82 241.7 ,45.2 {3 36 o 88.3 53.o 63 139.7 84.0 2.3 191.1 1 14.9 83 242.6 ,45.8 4 '4 3V? 29 .7 o4 89.1 53.6 64 ,40.6 84.5 24 , 9 2.0 1 1 5.4 84 243.4 i46.3 45 38 6 23.2 o5 90.0 54.! 65 ,4, .4 85.o 25 192.9 ,i5. 9 85 244-3 1 46.8 46 47 48 49 5o 3 9 .4 4o.3 4L.I 42 .0 42.9 23. 7 24.2 24-7 25.2 25.8 06 07 08 09 H 90.9 91.7 *L 94.3 54-6 55.i 55.6 56.i 56. 7 66 67 . 68 6 9 70 i42.3 i43.i i44.c 144.9 i45.7 85.5 86.0 86.5 87.0 87.6 26 27 28 194.6 195.4 196.3 197.1 ,16.4 116.9 117-4 117.9 ,,8.5 86 87 88 89 9 245.1 246.0 246. 9 247-7 248.6 147-3 i47-8 ,48.3 1 48 .8 149.4 5i 43 7 ~2~6~3~ I I I 57.2 171 i46.6 88., 23, 198.0 , 19 o 201 24 9 .4 149-9 5? 44.6 26.8 12 9^.0 5 7 -7 72 i47-4 88.6 32 198.9 119.5 9? 25o.3 ,5o.4 53 54 55 56 57 58 59 60 45.4 '46.3 47.1 48.0 48. 9 49-7 5o.6 5i.4 2 7 .3 27.8 28.3 28.8 29.4 59.9 3o.4 30.9 i3 u .5 .6 17 18 ! 9 20 96.9 97-7 98.6 99., ,01 . ,02.0 102.9 58.2 58. 7 5 9 .2 ^9-7 6o.3 60.8 6,.3 61.8 73 74 75 76 77 78 79 8( ,48.3 ,49. ,5o.o ,5o. 9 i5,. 7 i5a.6 ,53.4 i54. 89.1 89.6 9 0. T 90.6 91.2 91.7 9 2.2 92.7 33 34 35 36 37 38 39 4o 199.7 200. 6 201.4 202.3 203.1 204-0 2o4- 9 I2O.O 120.5 I2I.O I2I.5 122. 1 122.6 123.1 123.6 9 3 9 4 95 96 97 98 99 3oo 25l.2 252.O 252.9 253.7 254.6 255.4 256.3 257.1 i5M ,5i.o i5a.5 1 53.o ,53.5 ,54.o i54-5 Dist De... TaiT Disi Dep Lat Dis Dep Lai Dist Dep. Lat. Dist Dep. Lat. [For 50 Degrees. Puge48] TABLE II. Difference of Latitude and Departure for 32 Degrees. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Let. Dep i 00.8 co. 5 61 5i. 7 32.3 121 102 .6 64.1 "787 i53.5 95.9 241 204.4 127.7 2 01 .7 01 . I 62 52.6 32. 9 22 io3.5 64. 7 82 i54-3 96.4 42 205.2 128.2 3 02.5 01 .6 63 53.4 33.4 23 io4.3 65.2 83 i55.2 97.0 43 206. 1 128.8 4 o3.4 02. i 64 54-3 3'3. 9 24 IO5.2 65. 7 84 1 56.o 97-5 44 206.9 I2 9 .3 5 04.2 02 .6 65 55.i 34.4 25 106.0 66.2 85 1 56. o 98.0 45 207.8 129.8 6 o5.i 03.2 66 56.o 35.o 26 106.9 66.8 86 i5 7 .7 98.6 46 208.6 i3o.4 7 05.9 o3.7 67 56.8 35.5 2 7 107.7 6 7 .3 8 7 i58.6 99.1 4 7 209.5 i3o. 9 8 06.8 04.2 68 5 7 -7 36.o 28 108.6 67.8 88 1 5 9 .4 99.6 48 210.3 i3i.4 9 07.6 04.8 69 58.5 36.6 29 109.4 68.4 89 i6o.3 1OO.2 49 21 I .2 I3..G 10 o8.5 o5.3 70 59.4 3 7 .i 3o 110.2 68.9 9 161.1 100. 7 5o 212.0 j32.5 ii 09.3 o5.8 7i 60.2 3 7 .6 i3i III .1 69.4 191 162.0 101.2 261 21 2.9 1 33.o 12 10.2 06.4 72 61.1 38.2 32 III .9 69.9 92 162.8 101-7 52 2.1 3.7 i33.5 i3 II .0 06.9 73 61 .9 38. 7 33 112.8 70.5 9 3 i63. 7 102.3 53 214.6 ,34.i i4 II .9 07.4 74 62.8 3 9 .2 34 ii3.6 71.0 94 i64.5 102.8 54 21 5.4 1 34 .6 i5 12.7 07.9 75 63.6 3 9 .7 35 n4.5 7i.5 P i65.4 io3.3 55 216.3 i35.i 16 i3.6 o8.5 76 64.5 4o.3 36 n'5.3 72.1 96 166.2 103.9 56 217.1 i35. 7 17 i4-4 09.0 77 65.3 4o.8 3 7 116.2 72.6 97 167.1 io4-4 5 7 217.9 i3'6.2 18 i5.3 09.5 78 66.1 4i.3 38 117.0 7 3.i 98 167.9 104.9 58 2l8.8 1 36.7 19 16.1 10. I 79 67.0 41.9 3 9 117,9 7 3. 7 99 168.8 io5.5 5 9 219.6 l3 7 .2 20 17.0 10.6 80 67.8 42.4 4o ,18.7 74-2 200 169.6 1 06.0 60 220.5 i3 7 .8 21 17.8 ii .1 81 68.7 42.9 Mi 1 19.6 74-7 201 170.5 io6.5 261 T 2 ~iTJ i3-8.3 22 18.7 11.7 82 6 9 .5 43.5 42 120.4 7 5.2 02 i 7 i.3 107.0 62 222.2 i38.8 23 19.5 12.2 83 70.4 44.o 43 121. 3 7 5.8 o3 I 7 2.2 107.6 63 223.0 i3 9 .4 24 20.4 I2. 7 84 71.2 44.5 44 I 22. I 7 6.3 o4 i 7 3.o 108. i 64 2.23-9 i3 99 25 21.2 13.2 85 72.1 45.o 45 123.0 7 6.8 o5 i 7 3.8 1 08 .6 65 224-7 1 4o-4 26 22.0 i3.8 86 72.9 45.6 46 123.8 77 -4 06 174.7 109.2 66 225.6 i4i-o 27 22.9 i4.3 87 7 3.8 46.i 4 7 124.7 77-9 7 175.5 109.7 6 7 226.4 i4i.5 28 23.7 i4.8 88 74.6 46.6 43 125.5 78.4 08 176-4 I IO.2 68 227.3 142.0 29 24.6 i5.4 89 7 5.5 47-2 49 126.4 79- 09 177.2 1 10.8 69 228.1 142.5 3o 25.4 i5. 9 9 7 6.3 47-7 5o 127.2 79-5 10 178. i iii.3 70 229.0 i43.i 3j 26.3 16.4 9 1 77.2 48.2 i5i 128.1 80.0 211 178.9 ii i. 8 271 229.8 i43.6 32 27.1 17.0 92 78.0 48.8 52 128.9 8o.5 12 179.8 112.3 72 230.7 1 44.i 33 28.0 I-.5 93 78.9 49-3 53 129.8 81.1 13 180.6 112.9 73 23i.5 144.7 34 28.8 18.0 94 79-7 49.8 54 i3o.6 81.6 i4 i8i.5 ii3.4 74 232.4 i45.2 35 29.7 i8.5 9 5 80.6 5o.3 55 i3i.4 82.1 i5 182.3 1 13.9 75 233.2 i45. 7 36 3o.5 19.1 96 8i.4 5o.o 56 1 31.3 82.7 16 i83.2 1 14-5 76 234.1 1 46.3 3 7 3i.4 19.6 97 2.3 5i.4 5 7 i33.i 83.2 i? 184.0 1 1 5.0 77 234.9 1 46. 8 38 32.2 20. I 98 83.i 5i. 9 58 1 34.o 83. 7 18 184.9 n5.5 78 2.35.8 1.47.3 3 9 33.i 20.7 99 84.0 52.5 5 9 1 34.8 84.3 1 9 185.7 1 1 6. i 79 236.6 i4 7 -8 4o 33. 9 21 .2 100 84.8 53.o 60 i35. 7 84.8 20 186.6 ii 6.6 80 23 7 .5 i48.4 4i 34.8 21. 7 101 85. 7 53.5 161 1 36. 5 "85TT 221 187.4 117.1 281 238.3 148.9 42 35.6 22.3 02 86.5 54.1 62 i3 7 .4 85.8 22 i88.3 1 1 7 .6 82 239.1 149.4 43 36.5 22.8 o3 8 7 .3 54.6 63 i38.2 86.4 23 189.1 I I 8. 2 83 240.0 1 5o.o 44 3 7 .3 23.3 04 88.2 55.i 64 1 3 9 . i 86.9 24 190.0 ii8. 7 84 240.8 i5o.5 45 38.2 23.8 o5 89.0 55.6 65 i3 9 . 9 87.4 25 190.8 119.2 85 a4i-7 iSi.o 46 39.0 24.4 06 89.9 56.2 66 i4o.8 88.0 26 191.-; 119.8 86 242.5 i5i.6 4? 39.9 24.9 07 90.7 56. 7 67 i4i.6i88.5 2 7 192.5 1 20. 3 87 243.4 I52.I 48 40.7 25.4 08 91 .6 5 7 .2 68 i42.5 89.0 28 1 9 3.4 120.8 88 244.2 i52.6 49 4i.6 26.0 09 92.4 5 7 .8 69 143.3 89.6 29 194.2 I 2 I .4 89 245.1 1 53.i 5o 4'->. 4 26.5 10 9 3.3 58.3 7 144.2 90 . i 3o 195.1 I2I-9 9 245.9 ,53. 7 5i 43.3 27.0 1 1 1 94.1 58.8 171 i45.o 90'. 6 23l 195.9 122.4 291 246.8 i54,2 52 44.i 27.6 12 95.0 59.4 72 i45. 9 91.1 32 1 96-7 122.9 92 247.6 .54-7 53 44-9 28.1 i3 9 5.8 59.9 7 3 i46. 7 91 .7 33 19-7.6 123.5 9 3 248.5 i55.3 54 45.8 28.6 i4 96.7 60.4 7 4 i47-6 92.2 34 198.4 124.0 94 249.3 i55.8 55 46.6 29.1 i5 97-5 60.9 7 5 148.4 92.7 35 199.3 124.5 9 5 25O.2 1 56.3 56 4?-5 29.7 16 98.4 6i.5 76 149.3 9 3.3 36 200.1 125. I 9 6 25l .0 i56. 9 5 7 48.3 3o.2 17 99.2 62 .0 77 i5o. i 93.8 3 7 2O I .O 125.6 97 25l . 9 i5 7 .4 58 49.2 So.? 18 100. I 6*. 5 7 8 i5i .0 94-3 38 201.8 126.1 98 252.7 157.9 59 5o.o 3i.3 '9 100.9 63.i 79 i5i.8 94.9 3 9 2O2. 7 I26. 7 99 253.6 i58.4 60 50.9 3i.8 20 101 .8 63.6 80 1 52. 6 95-4 4o 2o3.5 I2 7 .2 3oo 254-4 159.0 Dial; Do p. Lat Dist Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. [For 58 Degrees. TABLE II. [Page 10 Difference of Latitude and Departure for 33 Degrees. Dist Lat. Dep. Dist Lat. Dep. Dist Lat. Dep. Dist Lat. Dep. Dist. Lat. Dep. 2 3 4 5 6 8 00.8 01.7 02.5 o3.4 04.2 c5.o o5. 9 06.7 oo.5 01 . I 01 .6 02.2 O2 .7 o3.3 o3.8 o4-4 6l 62 63 64 65 66 67 68 5i.a 52.0 52.8 53. 7 54.5 55.4 56.2 5 7 .o 33.2 33.8 34-3 34-9 35.4 35. 9 36.5 3 7 .o 22 23 24 25 26 2-7 28 iOI .5 102.3 103.2 104.0 .04.8 105.7 io6.5 107.3 65. 9 66.4 67 . o 6 7 .5 68.. 68.6 69.2 69.7 181 82 83 84 85 86 87 88 i5..8 1 52. 6 i53.5 1 54.3 i55.2 1 56.o i56.8 .57.7 98.6 99.1 99-7 100.2 100.8 ioi.3 101.8 102.4 42 43 44 45 46 47 202. i 2O3.O 2o3.8 204.6 2o5.5 206.3 207.2 208.0 ~i~37.3 i3i.8 .32.3 132.9 1 33.4 .34.0 1 34.5 i35.i 9 07.5 04.9 69 57-9 3 7 .6 29 108.2 70.3 89 1 58. 5 102.9 49 208.8 1 35. 6 10 08.4 o5.4 70 58. 7 38.i 3o 109.0 70.8 9 i5 9 .3 io3.5 5o 209.7 1 36. 2 1 1 39.2 06.0 7' 5 9 .5 38. 7 i3i 109.9 71.3 19. 160.2 104.0 25. 210.5 .36.7 12 10. I o6.5 72 60.4 3 9 .2 32 1 10.7 71.9 92 161.0 104.6 57 211.3 .37.2 i3 10.9 07.1 73 61.2 39.8 33 u i .5 72.4 93 161 .9 io5.i 53 212.2 .37.8 i4 u. 7 07.6 74 62.1 4o.3 34 112.4 7 3.o 162.7 105.7 54 2 I 3.0 i38.3 i5 16 12.6 i3.4 08.2 08.7 76 62 o 63.? 4o.8 4i.4 35 36 II3.2 n4.i 7 3.5 74.i $ i63.5 164.4 106.2 106.7 55 56 2i3. 9 214.7 .38. 9 139.4 1 7 t4.3 09.3 77 64.6 4i .9 3 7 114.9 74.6 97 i65.2 107.3 5 7 2i5.5 i4o.o 18 i5. i 09.8 78 65.4 42.5 38 ii5. 7 7 5.2 98 166. i 107.8 58 216.4 i4o.5 19 I5.Q io.3 Z 9 66.3 43.o 3 9 116.6 75.7 99 166.9 108.4 59 217.2 20 16.8 10.9 80 67.1 43.6 4o 117.4 76.2 200 167-7 108.9 60 2.8.1 i4i.6 21 17.6 u. 4 81 S' 9 44.i i4i ii8.3 76.8 201 168.6 109.0 26. 218.9 .42.2 22 i8.5 12.0 82 68.8 44-7 42 119.. 77-3 O2 169.4 I 10.0 62 219.7 142.7 23 19.3 12.5 83 69.6 45.2 43 119.9 77-9 o3 170.3 1 10.6 63 22O.6 143.2 24 20.1 i3.i 84 70.4 45. 7 44 120.8 78.4 o4 171.1 jii.i 64 221.4 i43.8 25 21 .0 i3.6 85 71.3 46.3 45 121 .6 79.0 o5 171.9 111.7 65 222.2 i44-3 26 21.8 14.2 86 72.1 46.8 46 122.4 79-5 06 172.8 112. 2 66 223.1 144.9 27 22 ,6 '4.7 87 7 3.o 47-4 47 123.3 80. i 07 i 7 3.6 II2.7 67 223-9 i45.4 28 23.5 15.2 88 7 3.8 47-9 48 124.1 80.6 08 174.4 u3.3 68 224-8 1460 29 24.3 i5.8 89 74-6 48.5 49 125.0 81.2 09 i 7 5.3 u3.8 69 225.6 i46.5 3o 25.2 i6.3 90 7 5.5 49 .0 5o 125.8 81.7 10 176.1 114.4 70 226.4 147.1 3i 26.0 16.9 9 1 7 6.3 49.6 i5. 126.6 82.2 21 I 177.0 114.9 271 227.3 147.6 32 26.8 17-4 92 77-2 5o.i 52 127.5 82.8 12 177.8 u5.5 7 2 228.1 1 48. i 33 27-7 18.0 93 78.0 5o. 7 53 128.3 83.3 i3 178.6 1 1 6.0 73 229.0 1 48. 7 34 28.5 i8.5 94 78.8 51:2 54 129.2 83. 9 i4 179.5 116.6 74 229.8 149.2 35 29.4 19.1 9 5 79-7 5l.7 55 i3o.o 84-4 i5 i8o.3 117.1 75 23o.6 149.8 36 JO. 2 19.6 96 8o.5 52.3 56 i3o.8 85.o 16 181.2 117.6 76 23i.5 i5o.3 37 Jt.O 20.2 97 81.4 52.8 57 i3i. 7 85.5 17 182.0 118.2 77 232.3 i5o. 9 38 Ji. 9 20.7 98 82.2 53.4 58 i3 2 .5 86.1 18 182.8 118.7 78 233.2 i5..4 09 32.7 21 .2 99 83.o 53.9 59 i33.3 86.6 in 183.7 119.3 79 234.0 l52.0 4o 33.5 21.8 100 83. 9 54.5 60 i34.2 87.1 20 i84.5 119.8 80 234-8 .52.5 4i 34-4 22.3 IOI 84-7 55 o .6. i35.o 87.7 221 i85.3 120.4 281 235.7 1 53.o 42 35.2 22.9 02 85.5 55.6 67 i35. 9 88.2 22 186.2 120.9 82 236.5 1 53.6 43 36.i 23.4 63 86.4 56., 6.3 i36. 7 88.8 2.3 187.0 121.5 83 2 3 7 .3 1 54. i 44 36.9 24.0 o4 87.2 56.6 64 i3 7 .5 89.3 24 18.7.9 122.0 84 238.2 1 54.7 45 3 7 -7 24.5 o5 88.1 5 7 .2 65 i38.4 89.9 25 188.7 122.5 85 239.0 i55.2 40 38.6 25.1 06 88.9 57.7 66 l3 9 .2 90.4 26 189.5 123.1 86 23 9 -9 1 55.8 47 3 9 -4 25.6 07 89-7 58.3 67 91.0 2 7 190.4 123.6 87 240.7 1 56.3 48 4o.3 26.1 08 90.6 58.8 68 140.9 9 i.5 28 191.2 124.2 88 241.5 i56. 9 49 4i . i 26.7 9 91 .4 5 9 -4 69 1*1.7 92.0 29 192.1 124.7 89 2^42.4 i5 7 .4 5o 4i .9 27.2 10 92.3 5 9 . 9 7<> 142.6 92.6 3o 192.9 125.3 9 243.2 i5 7 -9 5i 42.8 27.8 i . i 9 3.i 6o.5 171 i43.4 93.1 23l 193.7 125,8 29. 244-1 .58.5 52 43.6 28.3 12 93.9 6. .0 72 i44.3 9 3.7 32 194.6 126.4 92 244.9 i5 9 .o 53 44-4 28.9 r3 94.8 61 5 73 i45.i 94.2 33 . 9 5.4 126.9 93 245.7 169.6 54 45.3 29.4 i4 9 5.6 62.1 74 94.8 34 196.2 127.4 94 246.6 1 60. i 55 46.i 3o.o i5 96.4 62 6 75 .46.8 95.3 35 197.1 128.0 95 247-4 160.7 56 47.0 3o.5 .6 97-3 63.2 76 i47-6 36 197.9 128.5 96 248.2 161.2 5 7 58 47.8 48.6 3i.o 3.. 6 17 18 98., 99.0 63.7 64 . 3 77 78 i48.4 .49.3 9 6.4 96.9. 37 38 198.8 199.6 ,29.1 129.6 97 98 249-1 2499 161.8 162.3 6? 49.5 5o.3 32.1 3 2 . 7 '9 20 99.8 100.6 64.8 65.4 79 80 iSo.i iSi.o 97-5 98.0 3 9 4o 200.4 201.3 l3o.2 i3o.7 99 3oo 25o.8 2S..6 162.8 1 63. 4 Dist.l Dep. Lat. )ist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. [For 57 Degrees. I'aguaOj TABLE 11. Difference of Latitude and Departure for 34 Degrees. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. i 00.8 00.6 61 5o.6 34.1 121 i oo . 3 67.7 181 iSo.i I O I . 2 241 199.8 134.8 2 01 .7 01 . I 62 5i.4 34-7 22 101 . 1 68.2 82 i5o. 9 101.8 4? 200 .6 135.3 3 02.5 01.7 63 52.2 35.2 2.3 102.0 68.8 83 i5i .7 102 .3 43 201.5 136.9 4 o3.3 02.2 64 53.i 35.8 24 102.8 6 9 .3 84 iSa.5 102.9 44 202.3! i36.4 5 04. i 02.8 65 53.9 36.3 25 io3..6 69.9 85 i53.4 io3.5 45 2O3.I 1 37.0 6 o5.o o3.4 66 54.7 36. 9 26 ic4.5 70.5 86 i54.2 104.0 46 203.9 1 37.6 7 o5.8 o3 . 9 67 55.5 3 7 -5 2 7 io5.3 71.0 87 1 55.o io4-6 47 204.8 i38.i 8 06.6 o4-5 .68 56.4 38.o 28 106.1 71.6 88 i55. 9 io5.i 48 2o5.6 1 38. 7 9 07.5 o5.o 69 5 7 .2 38.6 ?9 106.9 72.1 89 1 56. 7 105.7 49 206.4 139.2 IP o8.3 o5.6 7" 58.o 3 9 .i 3o 107.8 72.7 90 :5 7 .5 100.2 5o 207.3 i3 9 .8 1 1 09.1 06.2 7 1 58.9 39-7 i3i 108.6 7 3.3 191 i58.3 1 06.8 25l 208.1 i4o.4 12 09.9 06.7 7 2 59-7 4o.3 32 109.4 7 3.8 92 l5 9 .2 107.4 52 208.9 140.9 i3 10.8 07-3 73 6o.5 4o.8 33 no. 3 74-4 93 160.0 107.0 53 209.7 i4i.5 i4 n. 6 07.8 74 6i.3 4i.4 34 n i .1 74-9 94 160.8 i o8.5 54 210.6 142.0 i5 12.4 08.4 75 62.2 41.9 35 in .9 75.5 95 161.7 109.0 55 21 1.4 142.6 16 i3.3 08. 9 76 63.o 42.5 36 112. 7 76.1 96 162.5 109.6 56 212.2 i43.2 17 14.1 09-5 77 63.8 43.i 3 7 n3.6 76.6 97 .63,3 I 10.2 57 2l3.I i43. 7 18 14.9 10. I 78 64.7 43.6 38 u4-4 77-2 98 164.1 1 10.7 58 2i3. 9 144.3 19 i5.8 10.6 79 65.5 44.2 39 II5.2 77-7 99 i65.o ui.3 59 214.7 144.8 20 16.6 II .2 80 66.3 44-7 4o 1 16. i 7 8.3 200 i65.8 1 1 1. 8 6o'2i5.5 i45.4 21 17-4 II.7 81 67.2 45.3 i4i 1 16.9 78.8 201 1 66.6 1 12.4 261 216.4 145.9 22 18.2 12.3 82 68.0 45.9 42 117.7 79-4 02 167.5 n3.o 62 217.2 i46.5 23 19.1 12.9 83 68.8 46.4 43 118.6 80.0 03 i68.3 ii3.5 63 218.0 147.1 24 19.9 i3.4 84 69.6 47.0 44 119.4 8o.5 o4 169.1 n4.i 64 218.9 147.6 25 20.7 i4-o 85 7 o.5 47-5 45 120.2 81.1 o5 170.0 n4.6 65 219.7 148.2 26 21 .6 i4.5 86 7i.3 48.1 46 121 .0 81.6 06 170.8 11 5. 2 66 ' 220.5 148.7 27 22.4 87 72.1 48.6 47 121 . 9 82.2 7 171.6 ii5.8 67 221.4 149.3 28 23.2 i5. 7 88 7 3.o 49.2 48 122.7 82.8 08 172.4 n6.3 68 222.2 149.9 29 24.0 16.2 69 7 3.8 49.8 49 123.5 83.3 09 173.3 116.9 69 223.0 i5o.4 3o 24.9 16.8 90 74-6 5o.3 5o 124-4 83. 9 10 174.1 II7-4 70 223.8 iSi.o 3i 25. 7 17. 3 : 91 75.4 5o. 9 i5i 125.2 84-4 211 174.9 118.0 271 224. 7 i5i.5 32 26.5 17.9 92 7 6.3 5i.4 52 I26.O 85.o 12 175.8 ii8.5 72 225.5 iSa.i 33 27.4 18.5: 93 77-i 52.0 53 126.8 85.6 i3 176.6 119.1 73 226.3 l52. 7 34 28.2 19.0 94 77-9 52.6 54 127.7 86.1 i4 177.4 119.7 74 227.2 i53.2 35 29.0 19.6 95 78.8 53.i 55 128.5 86.7 i5 178.2 120.2 228.0 i53.8 36 29.8 20. I 96 79.6 53. 7 56 12 9 .3 87.2 16 179.1 120.8 76 228.8 i54.3 37 3o. 7 2C). 7 97 80.4 54-2 5 7 130.2 87.8 17 179.9 I2I.3 77 229.6 1 54-9 38 3i.5 21.2 98 81.2 54.8 58 i3i .0 88.4 18 180.7 121.9 78 23o.5 i55.5 39 32.3 21.8 99 82.1 |55.4 59 i3i.8 88.9 19 181.6 122.5 79 23 1.3 1 56.o 4o 33.2 22.4 IOO 82.9 55. 9 60 i3a.6 8 9 .5 20 182.4 123.0 80 232.1 i56.6 4i 34-0 22.9 101 83.7 56.5 161 1 33. 5 90.0 221 i83.2 i 23.6 281 233.o 1 5 7 .i 42 34.8 23.5 02 84.6 5 7 .o 62 1 34. 3 90.6 22 184.0 124.1 82 233.8 1 5 7 . 7 43 3b.6 24.0 o3 85.4 67.6 63 1 35. i 91.1 23 184.9 124.7 83 234.6 1 58.3 44 36.5 24.6 04 86.2 58.2 64 1 36.o 91.7 24 185.7 125.3 84 235.4 1 58.8 45 3 7 .3 25.2 o5 87.0 58. 7 65 1 36.8 9 2 -3 25 i86.5 125.8 85 236.3 159.4 46 38.i 25. 7 06 87.9 5 9 .3 66 i3 7 .6 92.8 26 187.4 126.4 86 23 7 .I 47 3 9 .o 20.3 07 88.7 5 9 .8 67 1 38. 4 93.4 2 7 188.2 126.9 87 23 7 .9 i6a1 48 3 9 .8 26.8 08 89.5 60.4 68 139.3 y3.o 28 i8 9 .o 127.5 88 238.8 161.0 4 9 4o.6 27.4 9 90.4 61 .0 69 i4o. i 94.5 2 9 i8 9 .8 128.1 89 239.6 161.6 5o 4 (.5 28.0 to 91.2 6i.5 7 140.9 9 5.i 3o 190.7 128.6 9 240.4 162.2 5i 42.3 28.5 ii i 92.0 62.1 171 i4i.8 9 5.6 23l 191.5 1 29.2 291 24l.2 l62. 7 52 43.i 2 9 .1 12 92.9 62.6 72 142.6 96.2 32 192.3 1 29.7 92 242.1 i63.3 53 43.9 29.6 i3 63.2 73 i43.4 96.7 33 193.2 i3o.3 93 242-9 1 63 .8 b4 44.8 3() . 2 i4 94.5 63. 7 74 i44.3 97.3 34 194.0 130.9 243. 7 i64.4 55 45.6 3o.8 i5 9 5.3 64.3 75 i45.i 97-9 35 194.8 i3i.4 9 5 244.6 i65.o 56 46.4 3i.3 47-3l3i. 9 16 '7 96.2 97.0 64-9 65.4 76 77 i45.9 1 46. 7 98.4 99.0 36 3 7 196!? l32.O 96 97 245.4 246.2 i65.5 166. i 58 48.i 32.4 18 97-8 66.0 78 147.6 995 38 197.3 i33.i 98 247.1 , 1 66.6 69 48. 9 33.o '9 98.7 66.5 79 148.4 IOO. I 39 198.1 1 33. 6 99 2479 l6 7 .2 60 4 9 -7 33.6 20 99.5 6 7 .i 80 149.2 100.7 4o 199.0 1 34.2 3oo 248.7 167.8 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. 1 Lat. Dist. Dep. Lat Dist. De P . Lat. [For 56 Degrees. TABLE IL fp 8 g;i Difference of Latitude and Departure for 35 Degrees. Disl. Lat. Dep. Dist. Lat. Dep. Dist. Lat Dep. Dist. Lat. De r . Dist. Lat. Dep. I 00.8 00.6 61 5o.o 3b.o 121 99.1 69.4 181 i48.3 io3.8 24. 197.4 1 38. 2 2 ot .6 01 .1 62 5o.8 35.6 22 99.9 70.0 82 i4 9 -i 1044 42 198.2 i38.8 3 4 02. 5 o3.3 01.7 02.3 63 64 5i.6 52.4 36.i 36. 7 23 24 100.8 loi .6 7 o.5 71.1 83 84 i4 9 - 9 i5o.7 io5.o io5.5 43 M 199.1 '99-9 139.4 i4o.o i> o4.i 02.9 65 53.2 3 7 .3 25 102.4 71.7 85 i5i.5 106.1 45 200.7 i4o.5 b 04.9 o3.4 66 64.1 3 7 -9 26 103.2 7 2.3 86 i52.4 106.7 46 201.5 i4i.i 7 8 ot>. 7 06.6 o4.o o4-6 b7 68 54.9 55. 7 38.4 3 9 .o 27 28 104.0 104.9 72.8 73.4 87 88 i53.2 i54-o 107.3 107.8 47 48 202.3 203.1 i4'-7 l4^.2 9 07.4 05.2 69 56.5 39.6 29 105.7 74-0 89 1 54-8 108.4 4o 204.0 1 42. 8 10 08.2 05/7 70 57.3 40.2 3o io6.5 74.6 9 1 55.6 109.0 5o 204.8 i43.4 ii 09.0 o6.3 7i 58.2 40.7 i3i 107.3 75.1 191 i56.5 109.6 2.5 I ao5.6 1 44-0 12 09.8 06.9 72 5 9 .o 4i.3 32 108.1 75-7 92 57.3 I IO.I 52 206.4 i44-5 r3 10.6 07.5 73 5 9 .8 4i. 9 33 108.9 7 6.3 9 3 i58.[ 1 10.7 53 207.2 i45.i i4 n.5 08.0 74 60.6 42.4 34 109.8 76.9 94 i58. 9 1 1 1.3 54 208.1 i45 7 i5 12.3 08.6 75 61.4 43.o 35 no. 6 77-4 95 i5 9 -7 1 1 1. 8 55 2.08.9 i46.3 16 i3.i 09.2 76 62.3 43.6 36 in .4 78.0 96 160.6 1 12.4 56 2007 1 46.8 '7 i3. 9 09.8 77 63.i 44.2 37 112. 2 78.6 97 161.4 1 1 3.o 57 210.5 147.4 18 '4-7 io.3 78 63.9 44-7 38 u3.o 79.2 98 162.2 1 1 3.6 58 2II.3 1 48.o '9 i5.6 IO.O 79 64-7 45.3 3 9 113.9 79-7 99 1 63.o i i4-i 5 9 212.2 1 48. 6 20 16.4 ii. 5 80 65.5 45.9 4o 114.7 8o.3 200 i63.8 114.7 60 2 1 3.0 149.1 21 17.2 12.0 81 66.4 46.5 i4i ii5.5 80.9 201 164.6 ii5.3 261 213.8 i4 9 -7 22 18.0 12.6 82 67.2 /i-.o 42 ii6.3 81.4 O2 i65.5 1 1 6.9 67 214-6 i5o.3 23 18.8 13.2 83 68.0 47-6 43 117.1 82.0 o3 i66.3 116.4 63 2i5.4 i5o. 9 24 19.7 i3.8 84 68.8 48.2 44 118.0 82.6 o4 167.1 1 17.0 64 216.3 :5i.4 25 20.5 i4.3 85 69.6 48.8 45 118.8 83.2 o5 l67- 9 117.6 65 217.1 1 52.0 26 2C.3 14.9 86 70.4 49.3 46 119.6 83. 7 06 168.7 118.2 66 217-9 i5 2 6 27 22 . I i5.5 87 7i.3 49.9 47 12.0.4 84-3 07 169.6 118.7 67 218.7 1 53.i 28 22. 9 16.1 88 72.1 5o.5 48 121 .2 84.9 08 170.4 ii 9 .3 68 2I 9 .5 i53. 7 29 23.8 16.6 89 72.9 5i.o 4 9 122. I 85.5 09 171.2 11 9-9 69 220.4 1 54-3 3o 24.6 17.2 90 7 3. 7 5i.6 5o 122.9 86.0 10 172.0 120.5 70 221.2 1 54-9 3i 25.4 17.8 9i 74.5 52.2 i5i 123.7 86.6 211 172.8 I 21.0 271 222.0 i55.4 32 26.2 18.4 92 75-4 52.8 52 124.5 87.2 12 173.7 I 2 1. 6 72 222.8 1 56.o 33 27.0 18.9 9 3 76.2 53.3 53 125.3 87.8 i3 174-5 122.2 73 223.6 1 56.6 34 27.9 19.5 94 77.0 53.9 54 126.1 88.3 i4 i 7 5.3 122.7 74 224.4 157.2 35 28.7 20. i 95 77-8 54.5 55 127.0 88.9 i5 176.1 123.3 75 225.3 157.7 36 29.5 20.6 96 78.6 55-. i 56 127.8 8 9 .5 16 176.9 123.9 76 226.1 i58.3 3 7 3o.3 21.2 97 79-5 55.6 5 7 128.6 90.1 17 177-8 J24.5 77 226.9 i58. 9 38 3i.i 21.8 98 8o.3 56.2 58 129.4 90.6 18 178.6 125.0 78 227.7 i5 9 .5 3 9 3i.o 22.4 99 81.1 56.8 59 i3o.2 91.2 X 9 179.4 125.6 79 228.5 1 60.0 4o 32.8 22. 9 IOO 81.9 5 7 -4 60 i3i.r 91.8 20 180.2 126.2 80 229.4 160.6 4i 33.6 23.5 IOI 82.7 5 7 -9 161 i3i .9 9 2.3 221 181.0 126.8 281 230.2 161.2 4:* 34-4 24.1 02 83.6 58.5 62 132.7 92.9 22 181.9 I27 .3 82 23 1. 161.7 43 35.2 24.7 o3 84.4 5 9 .i 63 i33.fi 9 3.5 23 182.7 127.9 83 2 3i.8 162.3 44 36.o 25.2 o4 85.2 59-7 64 i34.3 94.1 2.4 i83.5 128.5 84 232.6 162.9 45 36.9 25.8 o5 86.0 60.2 65 i35.2 94.6 25 i84.3 129.1 85 233.5 1 63.5 46 37.7 26.4 06 86.8 60.8 66 i36.o 9 5.2 26 i85.i 129.6 86 234.3 1 64-c 47 38.5 27.0 07 87.6 6l.4 67 i36.8 9 5.8 2 7 i65. 9 i3o.2 87 235.i 164.6 48 3 9 .3 27.5 08 88.5 61 .9 68 i3-r.6 96.4 28 186.8 i3o.8 88 235.9 i65.2 49 4o. i 28.1 9 89.3 62.5 69 i38.4 96.9 29 187.6 i3i.3 89 236.7 1 65 .8 5o 4i .0 28. 7 10 90.1 63.i 70 139.3 97-5 3o 188.4 i3i-9 9 237.6 i66.3 Si 4i.8 29-3 n i 90.9 63. 7 171 i4o. i 98.1 23 I 189.2 102.5 291 238.4 166.9 52 42.6 29.8 12 91 .7 64.2 72 i4o. 9 98-7 3?. I OO.u 1 33.i 92 239.2 167.5 53 43.4 3o.4 i3 92.6 64.8 73 MI -7 99.2 33 100.9 1 33.6 93 240.0 168.1 54 44-2 3i.o i4 93.4 65.4 74 i42.5 99.8 34 191.7 i34-2 94 240.8 1 68 .6 55 45.i 3t.5 T5 94.2 66.0 75 i43.4 100.4 35 192.5 .34-8 9 5 24 1. 6 169.2 56 45.9 32.1 16 95.0 66.5 76 144-2 100. o 36 i 9 3.3 135.4 96 24? 5 169.8 5? 46.7 32.7 17 95.8 67.1 77 i45.o loi .5 37 i 9 4.i i35.o 97 243.3 170.4 58 47.5 33.3 18 96,7 67.7 78 i45.8 102. I 38 i 9 5.o 1 36.5 98 244.1 170.9 59 48.3 33.8 T 9 97-5 68.3 79 i46.6 102.7 3o . 9 5.8 l3 7 .T 39 a44-9 171 5 60 49.1 34.4 20 9 8.3 68.8 80 i47-4 103.2 4o 196.6 137-2 5oo 245:7 172.1 Dist. Den. Lat. Dist. Den. Lat. Dist. Dep. | Lat. Dist. Dep. Lat. Dist.'' Dep. 1 Lat. [For 5r> Degrees Page 52] TABLE II. Difference of Latitude and Departure for 36 Degrees. DM. Lat. Dep. Dist. Lat. Dep. Dist Lat. Dep. Dist.! Lat i Dep. !)ist Lat. } Dep. i 00.8 00.6 61 "4b,4 35. 9 121 97-9 71.1 181 i46.4 i 106.4 24 1 195.0! 141.7 2 oi .6 01 .2 62 5o.2 36.4 22 98.7 71 .7 82 l4?'2 IO 7 .O 4a i 9 5.8i 142.2 3 02.4 01.8 63 5i.o 3 7 .o 23 99.5 7 2.3 83 148.1 io 7 .6 43 '196.6 | 142.8 4 03.2 02.4 64 5i.8 3 7 .6 24 ioo.3 7 2. 9 84 1 48. 9 108.2 44 ! i 97-4 i43.4 5 o4-o 02.9 65 52.6 38.2 25 IOI .1 7 3.5 85 1^9.7 108. 7 45 198.2 1 44.0 6 o4-9 o3.5 66 53.4 38.8 26 101 .9 7 4.i 86 l5o.5 109.3 46 199.0 144.6 7 o5. 7 o4.i 67 54-2 39.4 2 7 102.7 74-6 8 7 i5i.3 109.0 47 199.8 145.2 8 o6.5 o4-7 68 55.o 4o.o 28 io3.6 7 5.2 88 152.1 i io.5 48 200 6 i45.8 9 o 7 .3 o5.3 69 55.8 4o.6 2 9 io4-4 7 5.8 89 152.9) in. i 49 201.4 i46.4 10 08. i 05.9 70 56.6 4i.i 3o 105.2 7 6.4 9 53.7 111.7 5o 202.3 146.9 ii 08. 9 o6.5 71 ~5 7 .4 41.7 i3i 106.0 77.0 191 154.5 I 1 2.3 25 1 203.1 147-5 12 09.7 07.1 72 58.2 42.3 32 106.8 77-6 92 155.3 I I 2. 9 52 203.9 i48.i i3 io.5 07.6 73 5 9 .i 42.9 33 107.6 7 8.2 93 1 56.i u34 53 204.7 148.7 i4 ii. 3 08.2 74 5 9 . 9 43.5 34 108.4 7 8.8 94 1 56. 9 1 14^> 54 2 5.5 149.3 i5 12. I 08.8 75 60.7 44.i 35 109.2 79-4 95 i5 7 .8 114.6 55 206.3 149.9 16 12.0 09.4 76 6i.5 44-7 36 I IO.O 79-9 96 1 58.6 I I 5.2 56 207.1 i5o.5 17 i3.8 IO.O 77 62.3 45.3 3 7 no.8 8o.5 97 1 5 9 .4 110.8 5 7 207-9 1 5i.i 18 i4-6 10.6 78 63.i 45.8 38 in .6 81.1 98 160.2 116.4 58 208.7 i5i!e 1 9 i5.4 II .2 79 63.9 46.4 3 9 112. 5 8i. 7 99 161.0 I1 7 .0 5 9 209.5 i5a.a 20 16.2 ii. 8 80 64-7 47-0 4o n3.3 82.3 200 161.8 1 1 7 .6 60 210.3 1 52 8 31 17.0 12.3 81 65.5 47-6 i4i 1 14.1 82.9 201 162.6 118.1 261 21 1.2 53-4 22 17.8 12.0 82 66.3 48.2 42 114.9 83.5 02 163.4 118.7 62 2120 1 54.0 23 18.6 i3.5 83 67.1 48.8 43 n5.7 84.1 o3 164.2 119.3 63 212.8 (54.6 24 19.4 14.1 84 68.0 49-4 44 n6.5 84.6 o4 1 65.o I 19.0 64 213.6 1 55. 2 25 2O. 2 14.7 85 68.8 5o.o 45 117.3 85.2 o5 i65.8 120.5 65 2,4-4 1 55.8 26 21 .0 i5.3 86 69.6 5o.5 46 118.1 85.8 06 166.7 121. 1 66 2l5.2 1 56.4 27 21.8 i5. 9 87 70.4 5i . i 47 118.9 86.4 7 i6 7 .5 121. 7 67 2160 1 56. 9 28 22.7 i6.5 88 71.2 5i. 7 48 119.7 8 7 .o 08 1 68. 3 122.3 68 2 1 6.8 157,5 2 9 23.5 17.0 89 72.0 52.3 49 120.5 8 7 .6 09 169.1 122.8 6 9 , 217.6 1 58. i 3o 24.3 17.6 9 72.8 52. 9 5o 121 .4 88.2 10 169.9 123.4 70 ' 218.4 1 58. 7 3i 25.1 18.2 9 1 7 3.6 53.5 i5i 122.2 88.8 211 I70-7 124.0 271 219.2 i5 9 .3 32 25.9 18.8 92 74.4 54.i 52 123. 8 9 .3 12 I 7 i.5 124.6 72 220.1 159.9 33 26.7 19.4 93 7 5.2 54-7 53 123.8 89.9 i3 I 7 2.3 125.2 220.9 i6o.5 34 27.5 20.0 94 76.0 55.3 54 124.6 90.5 i4 i 7 3.i 125.8 74 221.7 161.1 35 28.3 20.6 95 76.9 55.8 55 125.4 91.1 i5 173.9 126.4 75 222.5 ' l6l.6 36 29.1 21 .2 96 77-7 56.4 56 126.2 91.7 16 174.7 I2 7 .0 76 223.3 162.2 37 29.9 21.7 97 7 8.5 5 7 -o 5 7 127.0 92.3 ij 175.6 127.5 77 224.1 162.8 38 3o. 7 22.3 98 79-3 5 7 .6 58 127.8 92.9 18 176.4 128.1 78 224.9 1 63 .4 3 9 3i.6 22.9 99 80. i 58.2 59 128.6 93.5 19 177-2 128.7 79 225.? 164.0 4o 3 2 .4 23.5 100 80.9 58.8 60 129.4 9 4-o 20 178.0 129.3 80 226.5 164.6 4i 33.2 147T IOI 81.7 5 9 -4 161 i3o.3 94.6 221 178.8 1 29.9 281 227.3 "J65.2 42 34.o 24.7 02 82.5 60.0 62 i3i . i 9 5.2 22 179-6 i3o.5 82 228.1 i65^8 43 34.8 25.3 o3 83.3 6o.5 63 131.9 95.8 23 180.4 i3i .1 83 22.9.0 i663 44 35.6 25. 9 o4 84.1 61.1 64 132.7 96.4 24 181.2 i3i! 7 84 229.8 166.9 45 36.4 26.5 o5 84.9 61.7 65 i33.5 97-o 25 182.0 i32.3 85 23o.6 167.5 46 3 7 -2 27.0 06 85.8 62.3 66 i34.3 ' ' _ 97-6 2.6 182.8 1 32.8 86 23 1.4 168.. 47 38.o 27.6 07 86.6 62.9 67 i35.i 98.2 27 i83.6 1 33.4 87 232.2 168.7 48 38.8 28.2 08 87-4 63.5 68 i35. 9 98.7 28 i84.5 i34.o 83 233.0 169.3 49 39.6 28.8 09 88.2 64.1 69 i36. 7 99.3 29 1.85.3 1 34. 6 89 233.8 169.9 5o 4o.5 29.4 10 89.0 64. 7 70 i3 7 .5 99-9 3o 186. i i35.2 9 234.6 170.5 5i 4i.3 3o.o I II 89.8 65.2 171 i38.3 i oc> . 5 2 3, 186.9 i35.8 291 235.4 1 7 1 .0 52 42.1 3o.6 12 90.6 65.8 72 l3 9 .2 IOI . I 32 187.7 1 36.4 92 236.2 171.6 53 42.9 3l.2 i3 91 .4 66.4 73 i4o.o 101 .7 33 .88.5 i3 7 .o 93 237.0 172.2 54 43. 7 3. -7 r4 92.2 6 7 .o 74 i4o.8 102.3 34 189.3 t3 7 .5 94 237.9 172.8 55 44.5 3 2 .3 i5 93.0 6 7 .6 7 5 i4i.6 IO2 . 9 35 190.1 i38.i 95 238.7 173.4 56 45.3 32.0 16 9 3.8 68.2 76 142.4 io3.5 36 190.9 i38. 7 96 2 3 9 .5 174.0 57 58 46.i 46. 9 33.5 34.i 17 18 94-7 9 5.5 68.8 69.4 77 78 i43.2 i44.o i o4 . o 104.6 3 7 38 191-7 192.5 ,3 9 .3 i3 9 .o 97 98 24o.3 241.1 174.6 I 7 5.2 5 9 47-7 34-7 '9 96.3 69.9 79 i44.8 105.2 3 9 i 9 3.4 i4o.5 99 241.9 175.7 60 48.5 35.3 20 97.1 7 o.5 80 i45.6 io5.8 4o 194.2 r4i.i 3oo 242.7 1-6.3 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lai. Dist. Dep. 1 Lat. Dist.| Dep. La? [For 54 Degrees. TABLE 11. [I'agesa Difference of Latitude and Departure for 37 Degrees. Dist.! Lat. Dep. Dist. Lat. Dcp. Dist. Lat. Dep. Dist. Lat. Dcp. Dist. Lat. Dep. i 00.8 00.6 61 48. 7 36.7 121 96.6 72.8 181 1 44 -6 108.9 241 192.6 i45.o 2 01 .6 OI .2 62 49.5 37.3 22 97-4 73.4 82 i45.4 109.5 42 193.3 i45.6 3 02.4 01.8 63 5o.3 37-9 23 98.2 74.o 83 i46.2 I 10. 1 43 194.1 146.2 4 03.2 02.4 64 61 . i 38.5 24 99.0 74.6 84 146.9 110.7 44 194.9 i46.8 5 04.0 o3.o 65 5i .9 3 9 .i 25 99.8 7 5.2 85 I47.7 ii i.3 45 196.7 1*7-4 6 04.8 o3.6 66 52. 7 39.7 26 100.6 75.8 86 i48.5 II 1.0 46 196.5 i48.o 7 o5.6 04.2 67 53.5 4o.3 27 101 /4 76.4 87 i4 9 .3 112. 5 47 197.3 i48.6 8 06.4 04.8 68 54.3 4o. 9 28 102.2 77-0 88 i5o.i n3.i 48 198.1 9 07.2 06.4 69 55.i 4i .5 29 io3.o 77.6 89 i5o 9 Ii3. 7 49 198.9 149-9 10 08.0 06.0 70 55.9 42.1 3o io3.8 7 8.2 90 161.7 ii4.3 5o 199.7 i5o.5 ii 08.8 06.6 7' 56. 7 42.7 i3i 104.6 78.8 191 162.6 114.9 2.5 T 200.5 iSi.i 12 09.6 07.2 72 5 7 .5 43.3 32 106.4 79-4 92 1 53.3 ii5.5 62 201.3 161.7 i3 10.4 07.8 7 3 58.3 43.9 33 106.2 80.0 93 164.1 116.2 53 202.1 162. J i4 II .2 08.4 74 69.1 44.5 34 107.0 80.6 94 164.9 1 1 6.8 54 202-9 162.9 i5 12. 09.0 75 59.9 45.i 35 107.8 81.2 95 i55. 7 II7-4 55 203.7 1 53.5 16 12.8 09.6 60.7 45. 7 36 108.6 81.8 96 i56.5 1 1 8.0 56 2o4.5 i54-i 17 i3.6 IO.2 77 61 .5 46.3 3 7 109.4 82.4 97 167.3 118.6 5 7 20D.2 i54. 7 18 14.4 10.8 78 62.3 46. 9 38 II0.2 83.i 98 168.1 119.2 58 206.0 i55.3 1 9 15.2 11.4 79 63.i 47.5 39 II I .O 83. 7 99 168.9 119.8 5 9 206.8 166.9 20 16.0 12. 80 63.9 48.i 4o in. 8 84.3 200 159.7 120.4 60 207.6 1 56.5 21 16.8 12.6 81 64. 7 48-7 i4i 1 12.6 84-9 201 i6o.5 I 21.0 261 208.4 i5 7 .i 22 17.6 13.2 82 6'... 5 49-3 42 n3.4 85.5 02 i6i.3 I 2 1. 6 62 209.2 1 5 7 .7 23 18.4 i3.8 83 66.3 5o.o 43 I l4-2 86.1 03 162.1 122.2 63 210.0 i58.3 2.4 19.2 i4.4 84 67.1 5o.6 44 i i5.o 86. 7 o4 162.9 122.8 64 210.8 1 58 .9 25 20. i5.o 85 6 7 .9 61.2 45 116.8 8 7 .3 o5 163.7 123.4 65 211.6 ,5o.5 26 20.8 i5.6 86 68.7 5i.8 46 116.6 87.9 06 i64.5 124.0 66 212.4 160.1 27 21 .6 16.2 8 7 6 9 .5 62.4 47 117.4 88.5 07 i65.3 124.6 67 2l3.2 160.7 28 22.4 16.9 88 7 o.3 53.o 48 118.2 89. i 08 1 66. i 125.2 68 2l4-O i6i.3 23.2 17.5 89 71.1 53.6 119.0 89 7 09 166.9 126.8 69 214.8 161.9 3o 24.O 18.1 90 71.9 54.2 5o 119.8 90.3 10 167.7 126.4 70 216.6 162.6 3i 24.8 18.7 91 72.7 54.8 i5i 120.6 00.0 211 i68.5 127.0 271 216.4 163.1 37 2.5.6 19-3 92 7 3.5 55.4 62 121 .4 91.6 12 169.3 127.6 72 217.3 i63. 7 33 ?6.4 10. 03 74.3 56.o 53 122.2 92.1 i3 170.1 128.2 73 218.0 i64.3 34 27.2 20.5 94 7 5.i 56.6 54 123.0 92.7 i4 170.9 128.8 74 218.8 164.9 35 28.0 21 . I 95 75-9 5 7 .2 55 123.8 o3.3 i5 171.7 129.4 75 219.6 i65.5 36 28.8 21 .7 06 76.7 5 7 .8 56 124.6 93.9 16 172.6 i3o.o 76 220.4 1 66.1 37 29.5 22.3 97 77-5 58.4 57 126.4 94.5 17 173.3 i3o.6 77 221.2 166.7 38 3o.3 22.0 98 78.3 So.ti 58 126.2 o5.i r8 I74-I l3l.2 78 222.0 167.3 3 9 4o 3i . i 3, .9 23.5 .24.1 99 100 79.1 79-9 5 9 .6 60.2 59 60 127.0 127.8 9 5.7 9 6.3 1 9 20 174.9 176.7 i3i.8 i3a.4 79 80 222.8 223.6 167.9 i68.5 4i 32.7 24.7 101 80.7 60.8 161 128.6 96.9 221 176.5 i33.o 281 224-4 169.1 42 33.5 25.3 02 81.6 61.4 6? 129.4 97.5 22 177-3 i33.6 82 225.2 169.7 43 31.3 2 5-9 o3 82.3 62.0 63 l3o.2 98.1 23 178.1 i34-2 83 22.6.0 170.3 44 35.i 26.6 o4 83.i 62.6 64 i3i .0 98.7 24 178.9 i34.8 84 226.8 170.9 45 35,o 27.1 o5 83.o 63.2 65 j3i.8 99-3 25 179-7 i35.4 85 22 7 .6 171.6 46 36.7 27.7 06 84-7 63.8 66 i3a.6 00.0 26 i8o.5 1 36.o 86 228.4 172.1 47 48 3 7 .5 38 3 28.3 7 08 85.5 86.3 64-4 65.o 67 68 i33.4 i34.2 100.5 101 .1 27 28 i8i.3 182.1 1 36.6 l3 7 .2 87 88 229.2 230.0 172.7 i 7 3.3 49 5o 3 9 .i 3 9 . 9 g;f 09 10 87.1 87.8 65.6 66.2 69 70 i35.o i35.8 101 .7 102.3 1 3o 182.9 i83. 7 i3 7 .8 1 38 .4 89 9 23o.8 23 1.6 173.9 174.6 5i 40.7 3o 7 1 1 1 88.6 66.8 171 i36.6 102.9 23l 184.6 1 39.0 291 232.4 176.1 52 53 54 4i.5 42.3 43.i 3i.3 31.9 32.5 12 i3 i4 89.4 90.2 91 .0 6 7 .4 68.0 68.6 72 73 74 i3 7 .4 i38.2 139.0 io3.5 104.1 io4-7 32 33 34 i85.3 1 86. i 186.9 139.6 140.2 i4o.8 9 ? 9 3 233.2 234.0 234.8 176.7 1763 176.9 55 56 57 58 43.9 44-7 45.5 46.3 47-1 47-9 33.i 33. 7 34-3 34-9 35.5 36.i i5 16 17 18 20 91.8 92.6 93.4 94-2 93.0 9 5.8 69.2 69.8 70.4 71 .0 71.6 72.2 75 76 77 78 79 80 139.8 i4o.6 i4i-4 142.2 i43.o i43.8 io5.3 io5-9 io6.5 107.1 107.7 to8.3 35 36 37 38 3 9 4o 187.7 188.6 189.3 190.1 190.9 191.7 i4i.4 142.0 142.6 143.2 i43.8 1 44- 4 96 97 98 99 3oo 235.6 236.4 23 7 .2 238.0 238.8 2 3 9 .6 177.5 178.1 178.7 179.3 179-9 i8o.5 Dist.: Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lai. [For 53 Degrees. Page 54] TABLE II. Difference of Latitude and Departure for 38 Degrees. Dist. Lat. Dep. Disi. Lat. Dep. Dist. Lat. Dep. Dist. Lat.. Dep. Dist. 1 Lat. Dep. I 00.8 00.6 61 48.i 3 7 .6 121 9 5.3 74.5 181 142.6) iu-4 24' } 189.9 i4-4 2 01 .6 OI .2 62 48.9 38.2 22 96.1 7 5.i 82 i43.4 112. 1 42 190.7 j49-o 3 02.4 01.8 63 49-6 38.8 23 90.9 7 5. 7 83 i44-2 112. 7 43 191.5! i49-6 4 03.2 02.5 64 5o.4 39.4 24 97-7 7 6.3 84 i45.o i 4 3.3 44 192.3 l5o.2 o3-9 o3.i 65 5i.2 4o.o 25 98.5 -77-0 85 i45-8 11 3.9 45 utf.i >5oJ 6 04.7 o3. 7 66 52.0 4o.6 26 v3 77-6 86 M6-6 ii4-5 46 193.9 i5i.5 7 o5.5 o4.3 67 52.8 41.2 27 too. i 78.2 87 147.4 i*5.i 47 194.6 i5aj 8 ,o6.3 04.9 68 53.6 41.9 28 ! 100.9 78.8 88 *4&J ii5. 7 48 19S.4 i5a.7 9 07.1 o5.5 69 54.4 42.5 29 101 .7 79-4 89 148.9 1*64 49 196.2 1 53.3 *o 07.9 06. a TO 55.2 43.i 3o 102.4 80.0 9 149.7 JI 7 .0 5o 197.0 53.9 ii 08.7 06.8 7i 55. 9 43.7 i3i 103.2 80.7 591 i5o.5 117.0- 5a 1978 *54.5 12 o 9 .5 07.4 72 56.7 44.3 32 104.0 Si. 3 02 j5t.3 Ii8-2 52 198.6 i55.i 1 3 10.2 08.0 73 5 7 .5 44-9 33 104.8 81.9 9 3 t52.I 1*8.8 53 199,4 i55.8 M II .0 08.6 74 58.3 45.6 34 io5.6 82.5 94 1 52 .9 1194 54 200.2 i56.4 5 ii. 8 09.2 75 5 9 .i 46.2 35 106.4 83.i 95 i53. 7 I2O.J 55 200-9 1 57.0 16 12.6 09.9 -76 59-9 46.8 36 107.2 83.7 96 j54-5 120.7 56 201-7 i57.6 I 7 i3.4 io.5 77 60.7 47-4 3 7 108.0 84.3 97 i55.2 121.3 57 202. D 58.2 1 8 14.2 ii .1 78 6i.5 48.o 38 108.7 85.o 98 1 56.o 121-9 58 2o33 1 58.8 19 i5.o 11.7 79 02.3 48.6 39 109.5 85.6 99 1 56 .8 122.5 5 9 ao4-i 59.5 io i5.8 12.3 80 63.o 49.3 4<> 110.3 86.2 200 *5 7 .6 i23.1 00 2^-9 160.1 21 i6.5 12.9 81 63.8 49.9 MI in . i 86.8 201 i58.4 V23. 7 261 2o5 7 160.7 22 i 7 .3 i3.5 82 64.6 56.5 42 111.9 87.4 02 l5q.a 124.4 6a 2o6.5 . i6i.3 23 18. i 14.2 83 65.4 5i.i 43 112.7 88.0 o3 1 60.0 125.0 63 2t>7-2 >6i .9 24 18.9 i4.8 84 66.2 Si.? 44 n3.5 88.7 04 160.8 125.6 64 5HJ8.0 i6i.5 25 19.7 i5.4 85 67.0 52.3 45 ii4.3 89.3 o5 i6i.5 126.2 65 a8.8 63.a 26 20.5 16.0 86 67.8 52. 9 46 n5.o 89.9 06 162.3 126.8 66 209.6 63.8 27 21.3 16.6 87 68.6 53.6 47 ii5.8 90.5 07 i63.i 127.4 67 210.4 1 64 .4 28 22.1 17. > 88 6 9 .3 54.2 48 116.6 91.1 08 163.9 128.1 68 21 1 .2 i65.o 29 22.9 17.9 89 70.1 54.8 49 117.4 91.7 09 164.7 128.7 69 2J2.0 t65.6 3o 23.6 i8.5 9 70.9 55,4 DO 1*8.2 9 2.3 10 i65.5 129.3 70 212.8 i66.a 3} 24.4 19.1 9 1 71.7 56.o i5i 119.0 93 .0 211 166.3 129.9 271 213.6 166.8 32 25.2 19.7 92 72.5 56.6 52 119.8 9 3.6 12 i6 7 .i i3o.5 72 ai4.3 167.6 33 26.0 20.3 93 7 3.3 5 7 .3 53 120.6 94.2 i3 i6 7 .8 i3i.i 73 2l5.1 >68.i 34 26.8 20.9 94 74 . i 5 7 .9 54 121 .4 94.8 J4 168.6 i3i.8 74 21 5.9 168-7 35 27.6 M.5 95 74-9 58.5 55 122. I 95.4 i5 169.4 1 33.4 _H / 2*6-7 169.3 36 28.4 22.2 96 7 5.6 59.1 56 122-9 96.0 16 I 7 0.2 i33.o 7<> ?I7.5 169.9 3? 29.2 22.8 97 76.4 5 9 . 7 5 7 123.7 96-7 17 I 7 I.O 1 33.6 7~ ^i8.3 170.5 38 29.9 23.4 98 77.2 6o.3 58 124.5 97 .3 18 171.8 134.2 -78 219.1 171.2 39 3o. 7 24.0 99 78.0 61.0 59 125.3 97-9 19 1 7 2.6 i348 79 a 9- 171.8 4o 3i.5 24.6 1OO 78.8 61.6 60 126.1 9 8.5 20 173.4 i35.4 &> 22U.6 172.4 4< 32.3 25.2 101 79.6 62.2 16) 126.9 99.1 221 174.2 i36.i afc 22 K4 170.0 42 33.i 25. 9 02 8o.4 02.8 62 127.7 99-7 22 174.9 1 36. 7 222.2 i 7 3.6 43 33.Q 26.5 o3 81.2 63.4 63 128.4 100.4 23 175.7 i3 7 .3 83 223-0 174.2 44 34. 7 27.1 o4 82.0 64.0 64 129.2 101 .0 24 176.5 i3 7 . 9 84 223.8 J74.8 45 35.5 27.7 o5 82.7 64.6 65 i3o.o 101 .6 25 177-3 1 38. 5 85 224.6 175-5 46 36.2 28.3 06 83.5 65.3 66 i3o.8 102.2 26 178.1 139.1 86 225.4 176.1 4? 3 7 .o 28.9 07 84.3 65.9 67 i3i.6 102.8 37 178.9 139.8 87 226.2 176.7 48 37.8 29.6 08 85.i 66.5 68 i3a.4 io3.4 28 179-7 l4o.4 88 226.9 7-.3 49 38.6 30.2 9 85.9 67.1 69 i33.a 104.0 29 180.5 i4i-o 80 227.7 177 9 5o 3 9 .4 -3o.8 JO 86.7 67.7 70 i34.o io4-7 3.. ifij.a i4i-6 9 228.5 i-8.5 5i 40.2 3i.4 1 1 1 8 7 .5 68.3 i34-7 io5.3 23. iha.o > i4;..2 2QI ?29-3 179.2 52 4i .0 32.0 12 88.3 69.0 72 i35.5 105.9 3-> l8?.8 i4u.8 9 y s3o.i 179.8 53 4i.8 32.6 i3 89.0 69.6 7 3 i36.3 io6.5 33 1 83.6 143.4 93 230.9 18-0.4 54 42.6 33.2 i4 89.8 70.2 74 i3 7 .i 107.1 34 i84-4 144-1 94 a3i.7 181.0 55 43.3 33. 9 i5 90.6 70.8 75 137.9 107.7 35 i85.2 i44-7 95 23a.5 181.6 56 44.i 34.5 16 91 .4 71 .4 76 138.7 108.4 36 186.0 i45.3 96 233.3 182.2 5 7 44.9 35. i 17 92.2 72.0 77 139.5 109.0 3 7 186.8 145.9 97 234-O 182.9 58 45.7 35. 7 18 93.0 73 6 78 i4o.3 109.6 38 187.5 i46.5 98 234.8 i83.5 59 J46.5 36.3 '9 9 3.8 73 3 79 i4i . i 1 IO.2 39 i88.3 i47-< 99 235.6 184.1 60 47-3 36.9 20 94.6 73.; 80 i4i.8 uo.8 4o 189.1 147-8 3oo | 236.4 184.7 Dist. Di-p. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist.! Dep Lat. [For 52 Degrees. TABLE 11. [Paga5>| Difference of Latitude and Departure for 39 Degrees. Disl. Lat. Dcp. Dist. Lat. Dep. Dist. Lat. Dep. ">ist. Lat. Dep. )ist.j Lat. TW i 00.8 00.6 6. 47-4 38.4 121 94-0 76.. 181 140.7 li3. 9 24. ' i8i.3 f5i .7 2 01 .6 oi.3 62 48.2 39.0 22 94.8 76.8 82 i4i.4 n4.5 49. .88.1 .52.3 3 02.3 01 .9 63 49.0 3 9 .6 23 9 5.6 77-4 83 142.2 II5.2 43 188.8 l52. 9 4 o3.i 02.5 64 49-7 4o.3 24 96.4 78.0 84 .43.0 1 1 5.8 44 189.6 .53.6 5 o3-9 o3.i 65 5o.5 40.9 25 97.1 78.7 85 i43.8 116.4 45 190.4 .54-2 6 o4.7 o3.8 66 5i.3 4i.5 26 97-9 79-3 86 >44.5 1.7.1 46 191.2 .54-6 7 o5.4 o4.4 67 62. i 42.2 27 9 8.7 79-9 87 i45.3 117.7 47 192.0 1 55.4 8 06.2 o5.o 68 5a.8 42.8 28 99 .5 80.6 88 146.1 1.8.3 48 192. - 1 .56.. 9 07.0 o5. 7 69 53.6 43.4 29 ioo.3 81.2 89 .46.9 118.9 49 , 9 3.5 1 56.7 1C) 07-8 o6.3 70 54. 4 1 44.i 3o 101 .0 81.8 9 "47-7 . 19.6 5o 194.3 157.3 1 1 o8.5 06.9 7i 55.2 44-7 i3i 101.8 82.4 191 148.4 120.2 a5i 195.1 1 58.o 19 09.3 07.6 72 56.o 45.3 32 102.6 83.i 92 149-2 120.8 52 195.8 .58.6 i3 10. 1 08.2 73 56.7 45. 9 33 io3.4 83. 7 93 . 5o.o .21.5 53 196.6 159.; i4 10.9 08.8 74 5 7 .5 46.6 34 104.1 84.3 94 .5o.8 .22.1 54 .97.4 i5 9 .8 i5 11.7 09.4 75 58.3 47-2 35 104.9 85.o 95 i5i.5 122.7 55 ,98.? i6o.5 16 12.4 1 . I 76 59.1 4 7 .8 36 105.7 85.6 96 i5a.3 .23.3 56 .98.9 161.1 17 13.2 10.7 77 5 9 .8 48.5 37 1 06.5 86.2 97 .53.. 124.0 5 7 199.7 .61.7 18 1 4.0 n.3 78 60.6 49.1 38 107.2 86.8 98 1 53. 9 124.6 58 200.5 .62.4 19 14.8 12.0 79 61.4 49. 7 3 9 108.0 8 7 .5 99 1 54. 7 125.2 59 201.3 i63.o 20 i5.5 12.6 80 62.2 5o.3 4o 108.8 88.1 200 .55.4 .25-9 60 202.1 1 63. 6 2J i6.3 13.2 81 62.9 5 i.o i4i 109.6 88.7 20. i56.2 I 26.5 26. 202.8 i64.3 22 17.1 i3.8 82 63.7 5..6 42 1 10.4 89.4 Q2 157.0 127.1 62 2o3.6 164.9 2.3 17.9 .4.5 83 64.5 52.2 43 1 1 1 .1 90.0 o3 157.8 127.8 63 2o4-4 .65.5 24 ,8.7 i5.i 84 65.3 52.9 44 111.9 90.6 o4 1 58.5 128.4 64 205.2 166.1 ?5 19.4 .5.7 85 66.1 53.5 45 112.7 9 i.3 o5 i5 9 .3 129.0 65 205.9 .66.8 26 20.2 16.4 86 66.8 54.1 46 ii3.5 91.9 06 1 60. i 129.6 66 206.7 167.4 27 21 .0 17.0 87 67.6 54.8 4 7 i .4.2 9 2.5 07 .60.9 i3o.3 67 207.5 168.0 98 21.8 .7.6 88 68.4 55.4 48 u5.o 93.1 08 161.6 i3o.9 68 208.3 168.7 30 72.5 .8.3 89 69.2 56.o 49 ii5.8 93.8 09 162.4 i3i.5 69 209.1 169.3 3o 23.3 18.9 9 69.9 56.6 56 116.6 94-4 10 i63.2 132.2 70 209.8 .69.9 3 1 24.1 .9-5 $ 70.7 5 7 .3 .5. 1.7.3 95.0 211 164.0 i3 2 .8 271 2.0.6 ,70.5 3 a 24 .Q 2C). 1 92 7. .5 57. Q 52 118. i 95.7 12 164.8 i33.4 72 211.4 171.2 33 2.5.6 20.8 9 3 72.3 58.5 53 118.9 9 6.3 i3 .65.5 1 34-0 73 212.2 171.8 34 26.4 21.4 94 7 3. 5 9 .2 54 119.7 96.9 i4 .66.3 i34-7 74 212-9 172.4 35 27 . 2 22 .O 95 73.8 59.8 55 120.5 97.5 i5 167.1 i35.3 75 2i3.7 . 7 3.i 36 28.0 22.7 9* 74-6 60.4 56 12. .2 08.2 16 167.9 i35. 9 76 2.4-5 173.7 3 7 v8 8 ?3 3 97 75.4 61 .0 57 122.0 98.8 17 1 68. 6 i36.6 77 2 1 5.3 174.3 38 ?0 5 23.9 08 76.2 61 7 58 122.8 99.4 18 169.4 137.2 78 216.0 175.0 39 3o.3 2.4.5 99 76.9 62.3 5 9 123.6 too. i 19 170.2 .3 7 .8 79 216.8 175.6 4o 3i .1 25.2 100 77-7 6.2.9 60 124.3 100.7 20 171 .0 1 38.5 80 2.7.6 176.2 4i 3i.9 25.8 101 78.5 63.6 .61 125.1 ioi .3 221 171.7 i39.x 28. 218.4 176.8 42 32.6 26.4 02 70.3 64.2 62 125.9! ioi .9 22 172.5 138-7 82 219.2 177-5 43 33.4 27 . i o3 80.0 64.8 63 126.7 102.6 23 i 7 3.3 i4o.3 83 219.9 178.1 44 3A . > 27 7 o4 80,8 65.4 64 I2 7 .5 103.2 24 i74.i i4i-o 84 220.7 178.7 45 .i5.o 28.3 o5 81.6 66.1 65 128.2 io3.8 25 174.9 i4i-6 85 221.5 179.4 46 35.7 28 9 06 82.4 66.7 66 129.0 io4.5 26 175.6 142.2 86 222.3 .80.0 47 48 36.5 37 3 20.6 3o . 07 08 83.2 83.9 6 7 .3 68.0 6 7 68 129.8 .3o.6 io5. i io5.7 27 28 176.4 177.2 142.9 i43.5 87 88 223.0 223.8 180.6 181.2 4 9 5o 38.i 38. 9 3o.8 3.. 5 09 lo 84-7 85.5 68.6 69.2 69 70 i3i.3 i3a.i 106 4 . 07 . < i ? 9 3<> .78.0 178.7 .44.1 i44-7 89 9 1 224.6 225.4 181.9 182.5 ~5T 52 "39.6 4o 4 32.1 32.7 1 1 1 I 2 86.3 87.0 69.9 70.5 171 72 .32.9 ,33.7 .07.6 .08.2 23. 32 179.5 i8o.3 i45.4 i46.o 29. 92 226.1 226.9 i83.i .83.8 53 54 55 56 57 i 58 60 4i.2 42.0 42.7 43.5 44-3 45.i ^9 | O.O 33.4 34.0 34.6 35.2 35. 9 36.5 3 7 .i 3 7 .8 IZ i5 16 17 18 19 20 87.8 88.6 89.4 90.1 90.9 91.7 92.5 93.3 71.1 7i-7 72.4 ? 3.o 7 3.6 74-3 gi 73 74 75 76 78 79 80 .34.4 j i3'5.2 .36.0 .36.8 i3 7 .6 1 38.3 ,3 9 .. i3 9 . 9 108.9 109.3 1 10. 1 I IO.fi 1 1 1 .4 ..2.0 .12.6 1.3.3 33 34 35 36 37 38 39 4o .81.1 181.9 182.6 i83.4 184.2 i85.o 585.7 ,86.5 1 46.6 147-3 !33:S 1 49-1 149.8 i5o.^ 161.0 9 3 9 4 95 96 97 98 99 3oo 227.7 228.5 229.3 230.0 a3o.8 23 1. 6 232.4 233.1 .84.4 i85.o i85.6 .86.3 186.9 18-7.5 188.2 188.8 l>tst Dc^ T^uT Dist Dep. Lat. Dist Dep. Lat. Dist Dep. Lat. Dist Dep. Lat. [For 51 Degrees rs56] TABLE 11. Difference of Latitude and Departure for 40 Degrees. Dist. Lat. Dep. Dist.| Lai. Dep. Dist. Lat. Dep. Dist Lat. Dep. Dist. Lat. Dep. j 00.8 00.6 61 46-7 3 9 .2 121 92.7 77-8 181 1 38.7 1 16.3 24 1 184.6 1 54 .9 2 oi.5 oi.3 62 47-5 39.9 22 9 3.5 78.4 82 i3 9 .4 1 17.0 42 , i85.4 1 55. 6 3 02 3 01 .9 63 48.3 4o.5 23 9 4-2 79.1 83 l4o.2 117.6 43 186. i i56.2 4 o3 i 02.6 64 49.0 4i.i 24 9 5.o 79-7 84 i4i.o ii8.3 44 186.9 1 56. 8 5 o3.8 03.2 65 49.8 4i.8 25 9 5.8 8o.3 85 i4i-7 118.9 45 187.7 i5 7 5 6 o4-6 o3.9 66 5o.6 42.4 26 9 6.5 81.0 86 1 42. 5 1 19.6 46 188.4 i58.i o5.4 o4.5 67 St. a 43.i 2 7 9 7-3 81.6 87 i43.3 120.2 47 189.2 1 58. 8 8 06. i o5.i 68 52.1 43.7 28 9 8.. 82.3 88 1 44.0 120.8 48 190.0 i5 9 .4 9 06.9 o5.8 69 5 2 . 9 44-4 2 9 98.8 82.9 89 144.8 f I2I.5 4 9 190.7 1 60. i 10 07-7 06.4 70 53.6 45.0 3o 99.6 83.6 90 i45.5 122.1 5o 191 .5 i6o. 7 1 1 08.4 07.1 7i 54-4 45.6 i3i 100.4 84.2 191 i46.3 122.8 25l J 9 ?.3 i6i.3 12 09.2 07-7. 72 55.2 46.3 32 101 . 1 84.8 02 147-1 123.4 52 jy3.o 162.0 i3 IO.O 08.4 73 55. 9 46.9 33 101 .9 85.5 9 3 147.8 I24.I 53 193.8 162.6 i4 10.7 09.0 74 56. 7 47-6 34 102.6 86.1 94 i486 124.7 54 194.6 1 63. 3 .5 11.5 09.6 75 5 7 .5 48.2 35 io3.4 86.8 95 149.4 125.3 55 195.3 i63. 9 16 12.3 io.3 76 58.2 48. 9 36 104-2 87.4 96 i5o.i 126.0 56 i 9 6.i 164.6 '7 i3.o 10.9 77 59.0 49.5 3 7 104.9 88.1 97 i5o. 9 126.6 57 i 9 6. 9 i65.2 18 i3.8 11. 6 78 59.8 5o.i 38 io5.7 88.7 98 1 5 1. 7 127.3 58 197.6 i65.8 '9 14.6 12.2 79 6o.5 5o.8 39 fo6.5 8 9 .3 99 i52.4 127.9 5 9 198.4 1 66.5 20 i5.3 I2. 9 80 6i.3 5,. 4 4o 107.2 90.0 200 i53.2 128.6 60 199.2 i6 7 .i 21 [6.1 i3.5 81 62.0 52.1 i4i 108.0 90.6 201 1 54.o 129.2 261 199.9 167.8 22 16.9 14.1 82 62.8 5 2 . 7 42 108.8 9 i.3 02 1 54-7 129.8 62 200.7 168.4 23 17.6 14.8 83 63.6 53.4 43 109.5 91 .9 o3 i55.5 i3o.5 63 201.5 169.1 24 18.4 i5.4 84 64.3 54.0 44 iio.3 92.6 o4 1 56.3 i3i.i 64 202.2 169.7 25 19.2 16.1 85 65.i 54.6 45 i ii .1 03.2 o5 157.0 i3i.8 65 y.o3.o 170.3 26 19.9 16.7 86 65.9 55.3 46 in. 8 9 3.8 06 i5 7 .8 i32.4 66 2.o3.8 171.0 27 20.7 17-4 87 66.6 55. 9 47 112. 6 94-5 07 1 58 .6 1 33. i 67 2o4.5 171.6 28 21.4 18.0 88 67.4 56.6 48 n3.4 9 5.i 08 1 5 9 .3 i33. 7 68 2o5.3 I 7 2.3 29 22.2 18.6 89 68.2 5 7 .2 49 n4-i 95.8 09 1 60. i i34.3 6 9 206. 1 172.9 JO 23.0 . 9 .3 90 68.9 5 7 . 9 5o 114.9 96.4 10 160.9 i35.o 70 206.8 173.6 3i 3 .3. 7 19.9 9 1 69.7 58.5 i5i 1 i5. 7 97.1 211 161.6 i35.6 271 207.6 174.2 32 24.5 20.6 92 70.5 69.1 52 116.4 97-7 12 162.4 1 36.3 72 208.4 174-8 33 25.J 21 .2 93 71.2 59.8 53 117.2 98.3 13 i63.a 1 36. 9 73 209.1 i 7 5.5 34 26.0 21 .9 94 72.0 60.4 54 118.0 99.0 i4 1 63. 9 i3 7 .6 74 209.9 176.1 35 26.8 22.5 95 72.8 61.1 55 118.7 99.6 i5 164.7 i38.a 75 210.7 176.8 36 27.6 23.1 96 7 3.5 61.7 56 119.5 100.3 1 6 i65.5 i38.8 76 21 1.4 177-4 3 7 28.3 23.8 97 74.3 62.4 5 7 120.3 100.9 17 166.2 139.5 77 212.2 178.1 38 29.1 24.4 98 7 5.i 63.o 58 121 .0 101 .6 18 167.0 140.1 78 2l3.0 178.7 3 9 29.9 25.1 99 7 5.8 63.6 5 9 121. 8 102.2 19 167.8 i4o.8 79 213.7 179.3 4o 3o.6 25.7 100 76.6 64.3 60 122.6 102.8 20 168,5 i4i.4 80 214.5 1 80.0 4i 3, .4 26.4 101 77-4 64.9 161 123.3 io3.5 221 169.3 142.1 281 21 5.3 180.6 4s 32.2 27.0 02 78.1 65.6 62 124.1 104.1 22 170.1 142.7 82 216.0 i8i.3 43 32. 9 27-6 o3 78.9 66.2 63 124.9 104.8 23 170.8 143.3 83 216.8 181.9 44 3^.7 28.3 o4 79-7 66.8 64 125.6 io5.4 24 i 7 i.6 1 44-o 84 217.6 182.6 45 34.5 28.9 o5 80.4 6 7 .5 65 126.4 1 06. i 25 172.4 i44.6 85 218.3 i83.2 46 35.2 29.6 06 81.2 68.1 66 127.2 106.7 2.6 I73.I i45.3 86 219.1 i83.8 47 36.o 30.2 07 82.0 68.8 6 7 127.9 107.3 27 173.9 145.9 87 219.9 i84.5 48 36.8 3o. 9 08 82.7 69.4 68 128.7 108.0 28 174-7 1 46.6 88 220.6 1 85.i 49 3 7 .5 3i.5 09 83.5 70.1 69 129.5 108.6 29 175.4 147-2 8 9 221.4 iss.e 5b 38.3 32.1 10 84.3 70.7 70 i3o.2 109.3 3o 1 7 6.2 1 47 -8 90 222.2 186.4 5i 39.1 32.8 III 85.o 7 i.3 I 7 I i3i .0 109.9 23l i77-o M8.5 291 222. 9 187.1 52 3 9 .8 33.4 12 85.8 72.0 72 i3i.8 1 10.6 32 177.7 149.1 92 223. 7 187.7 53 4o.6 34.i i3 86.6 72.6 73 i3 2 .5 II I .2 33 178.5 149.8 93 224.5 188.3 54 4i-4 34. 7 i4 8 7 .3 7 3.3 74 i33.3 in. 8 34 179.3 i5o.4 94 225.2 189.0 55 42.1 35.4 i5 88.1 73.9 75 i34.i 112. 5 35 1 80.0 i5i.i 95 226.0 189.6 5b 42 .9 36.o 16 88.9 74-6 76 1 34. 8 n3.i 36 180.8 l5l. 7 06 226.7 190.3 5? 43. 7 36.6 17 89.6 7 5.2 77 i35.6 ii3.8 37 181.6 i5a.3 97 227.5 190.9 58 44.4 3 7 .3 18 90.4 7 5.8 78 i36.4 n4.4 38 182.3 1 53.o 98 228.3 191.6 5 9 45.2 37-9 19 91.2 76.5 79 i3 7 .i n5.i 39 i83.i 1 53.6 99 229.0 192.2 60 46.o 38.6 20 91.9 77-i 80 137.9 ii5.7 4o 183.9 i54.3 3oo 229.8 1928 I)C Lat. Dist. Dep. L.at. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. [For 50 Degrees. TABLE II. rPuses? Difference uf Latitude and Departure for 41 Degrees Dist. Lat. Dep. Dist. Lat. Dep. )ist. Lat. Dep. Dist Lat. Dep. Dist. Lat. Dep. I 00.8 00.7 61 46.0 4o.o 21 9 i.3 79-4 181 36.6 118.7 24. 181.9 58.i 2 oi.5 oi.3 62 46.8 4o. 7 22 92.1 80.0 82 37-4 119.4 42 182.6 58.8 3 02.3 02. o 63 47-5 4i.3 23 92.8 80.7 83 i38.i I 20. 1 43 i83.4 59.4 4 o3.o 02.6 64 48.3 42.0 24 9 3.6 81.4 84 38.9 I20. 7 44 184.1 60. 1 5 o3.8 o3.3 65 49.1 42.6 25 94.3 82.0 85 139.6 I2I.4 45 184.9 60.7 6 o4-5 o3. 9 66 49-8 43.3 26 9 5.i 82.7 86 1 4o.4 122.0 46 i85. 7 61.4 7 o5.3 o4-6 67 5o.6 44.o 2 7 9 5.8 83.3 8 7 i4i-i I22. 7 47 186.4 62.0 8 06.0 05.2 68 5i.3 44.6 28 96.6 84.0 88 141.9 123.3 48 .8 7 .2 62. 7 .9 06.8 05.9 69 52. I 45.3 29 97-4 84.6 89 142.6 124.0 49 187-9 63.4 10 o 7 .5 06.6 70 52.8 45. 9 3o 98.1 85.3 9 i43.4 124.7 5o 188.7 64.0 1 1 o8.3 07.2 7I 53.6 46.6 i3i 98-9 85.9 191 i44.i 125.3 25l 189.4 64- 7 .2 09.1 07 9 72 54.3 47-2 32 99.6 86.6 92 1 44 -9 126.0 52 190.2 65.3 i3 09.8 08 5 55.i 47-9 33 100.4 8 7 .3 9 3 i45.7 126.6 53 190.9 66.0 i4 10.6 09 2 74 55 8 48.5 34 IOI .1 07.9 94 i46.4 127-3 54 191.7 166.6 .5 n.3 09 8 75 56.6 49-2 35 loi .9 88.6 95 147-2 127-9 55 192.5 i6 7 .3 ,6 12. I 10 5 76 5 7 -4 49.9 36 102.6 89.2 96 147-9 128.6 56 193.2 1 68.0 17 .2.8 II 2 77 58.i 5o.5 3 7 io3.4 89.9 97 i48-7 129.2 5 7 194.0 1 68 .6 .8 i3.6 n 8 78 58. 9 5l.2 38 io4- 1 90.5 98 149.4 129.9 58 194.7 169.3 '9 i4-3 12 5 79 59.6 5..8 39 io4-9 91.2 99 I50.2 i3o.6 5 9 195.5 169.9 20 .5.1 i3 i 80 60.4 52.5 4o io5.7 91.8 200 150.9 l3l.2 60 196.2 i 7 o.6 21 .5.8 i3.8 8. 61.1 53.i i4i 106.4 92.5 201 ,5i. 7 i3i. 9 261 197.0 171.2 22 .6.6 i4.4 82 61 .9 53.8 42 107.2 9 3.2 O2 i52.5 i32.5 62 197-7 171.9 23 | 7 .4 83 62.6 54.5 43 107.9 9 3.8 o3 i53.2 i33.2 63 198.5 .72.5 24 18.1 i5. 7 84 63.4 55.i 44 108.7 94-5 04 1 54.0 i33.8 64 199.2 1732 25 18.9 16.4 85 64.2 55.8 109.4 9 5.i o5 1 54-7 i34.5 65 200.0 J 7 3. 9 76 19.6 .7 i 86 64-9 56.4 46 I 10.2 9 5.8 06 i55.5 i35.i 66 200.8 174.5 27 20.4 '7-7 87 65.7 5 7 .i 47 I 10.9 96.4 7 .56.2 i35.8 6 7 201.5 175.2 28 21.1 18.4 88 66.4 57.7 48 111-7 97.1 08 i5 7 .o 1 36.5 68 202.3 175.8 29 21.9 .9.0 89 67.2 58.4 49 112. 5 97-8 09 i5 7 . 7 i3 7 .i 69 2O3.O 176.5 3o 22 .6 19.7 90 67-9 59.0 5o II3.2 98.4 10 1 58.5 i3 7 .8 70 2o3.8 I77.I 3. 23.4 20.3 9' 68.7 59-7 i5i i i4.o 99.1 211 1 5 9 .2 1 38.4 271 2C4-5 177-8 3? 24.2 21 .0 92 69.4 60.4 52 1 14-7 99-7 12 1 60.0 139.1 72 2o5.3 178.4 33 24.9 21.6 93 70.2 61 .0 53 u5.5 100.4 l3 160.8 ^39.7 73 206.0 I79.I 34 75.7 22.3 94 70.9 61.7 54 116.2 101 .0 1^ i6i.5 1 4o-4 74 206.8 179.8 35 26.4 23.0 95 71 .7 67.3 55 .17.0 IOI . 7 i5 162.3 i4i.i 75 207.5 180.4 36 27.2 23.6 96 72.5 56 117.7 102.3 16 i63.o i4i-7 76 20&.3 181.1 38 2 7 .9 28.7 24.3 24.9 97 08 73.2 74.0 63.6 64.3 5 7 58 u8.5 1 19.2 io3.o io3. 7 17 18 i63.8 i64.5 142.4 i43.o 77 78 209.1 209.^ 181.7 182.4 39 4o 29.4 30.2 25.6 26.2 99 .00 74.7 7 5.5 64-9 65.6 S 120.0 120.8 io4-3 io5.o 19 20 i65.3 1 66.0 .43.7 i44-3 79 80 210.6 2 I 1. 3 .83.0 183.7 4i 30.9 26.9 IOI 76.2 66.3 161 121. 5 io5.6 221 1 66.8 i45.o 281 212. 1 184.4 42 3, 4 27 6 02 77.0 66.9 122.3 io6.3 22 167.5 i45 6 82 212.8 i85.o 43 32.5 2.8.2 o3 77-7 6 7 .6 63 123.0 106.9 2: i68.3 1 46.3 83 2 1 3.6 i85.7 44 45 46 47 48 4 9 5o 33.2 34.o 34-7 36^2 37.0 37.7 28.9 29.5 30.2 3o.8 3i.5 32.1 32.8 o4 o5 06 07 08 09 10 7 8.5 79-2 80.0 bo. 8 8i.5 82.3 83.o 68.2 68.9 6 9 .5 7 0.2 70.9 7 1.5 7 2.2 64 65 66 6 7 68 69 70 123.8 124.5 125.3 126.0 126.8 127.5 128.3 io 7 .6 108.2 108.9 109.6 I 10.2 I 10-9 ii i .5 2/ 2 5 26 2 7 28 29 3o 169.1 .69.8 i 7 o.6 I 7 2.I 172.8 173.6 1 47-o 1 47 -6 1 48. 3 148.9 149-6 i5o.2 i5o. 9 84 85 86 87 88 89 9 214.3 2I5.I 2i5.8 216.6 217.4 218. 1 218.9 i86.3 187.0 187.6 i88.3 188.9 1896 i 9 o.3 ~sT 38,5 33.5 1 1 1 83.8 72.8 1-71 129. i 112.2 23l 174-3 i5i.5 291 219.6 190.9 52 53 3 9 .2 4o.o 34.i 34.8 12 i3 84.5 85.3 7 3.5 74.1 72 7 3 129.8 i3o.6 112.8 ii3.5 32 33 I 7 5.i 175.8 152.2 152.0 93 220.4 221. 1 191.6 192.2 54 55 56 5 7 58 4o.8 4i.5 42.3 43.0 43.8 44.5 45.3 35.4 36.i 36.- 37.4 38 .7 38. 7 39.4 i4 i5 16 17 18 19 20 86.0 86.8 8 7 .5 88.3 89.1 89.8 90.6 74-8 75.4 76.1 7 6.8 77-4 7 8.i 78. 7 74 75 76 77 78 79 80 i3i.3 | I32.I i3 2 .8 i33.6 134.3 i35.i i35.8 114.2 n4.8 n5.5 116.1 116.8 u 7 .4 118.1 34 35 36 37 38 3 9 4o 176.6 177-4 178.1 178-9 179-6 i8o.4 181.1 i53.5 i54-2 1 54.8 i55.5 1 56. i 1 56.8 i5 7 .5 94 96 97 98 99 3oo 221.9 222.6 223.4 224. 224.9 226.4 194.2 194.8 196.6 Dist Dep. Lat. Dist Dep. Lat. Dist Dep. | Lat. Dis Dep. Lai. Dist Dep Lat. [For 49 Degrees. iv,-e58j TABLE II. Difference of Latitude and Departure for 42 Degrees. Dist. Lat. Dop. Dist. Lai. Dcp. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dop. I 00.7 00.7 6l 45.3 4o.8 121 89-9 81.0 181 i34-5 121 .1 241 179.1 161 3 2 oi.5 oi.3 62 46.1 4i.5 22 oo .7 81.6 82 i35.3 121.8 42 179-8 161.9 3 02. a 02.0 63 46.8 42.2 23 91 .4 82.3 83 1 36.o 122.5 43 1806' 162.6 4 o3.o 02.7 64 47-6 42.8 24 92.1 83.o 84 i36. 7 I23.I 44 181.3 i63.3 5 o3. 7 o3.3 65 48.3 43.5 25 92.9 83.6 85 i3 7 .5 123.8 45 182.1 1 63 .9 6 o4.5 o4.o 66 49.0 44-2 26 93.6 84.3 86 i38.2 124.5 46 182.8 1 64-6 7 05.2 o4-7 67 49.8 44.8 27 94.4 85.o 87 i3 9 .o 125. 1 47 i83.6 i65.3 8 o5.9 o5.4 68 5o.5 45.5 28 9 5.i 85.6 88 139.7 125.8 48 1 84.3 165.9 9 06.7 06.0 69 5i.3 46.2 29 9 5. 9 86.3 89 i4o.5 126.5 4 9 i85.o 1 66.6 10 07.4 06.7 ?o 52.0 46.8 3o 96.6 87.0 90 l4l-2 127.1 5o i85.8 167.3 1 1 08.2 07.4 7' 52. b 47.5 i3i 97-4 87.7 191 i4i. 9 127.8 "a5i i86.5 168.0 12 08.9 08.0 7 2 53.5 48.2 32 98.1 88.3 92 142.7 128.5 52 i8 7 .3 168.6 id 09.7 08.7 73 54.2 48.8 33 98.8 89.0 9 3 143.4 129.1 53 1 88.0 169.3 i4 io.4 09.4 74 55.o 49.5 34 99.6 89.7 94 i44.2 129.8 54 1 88. 8 170.0 i5 1 1 . 1 IO.O 75 55. 7 50.2 35 ioo.3 9 o.3 95 i44. 9 i3o.5 55 189.5 170.6 16 11.9 10.7 76 56.5 5o. 9 36 101 .1 91 .0 96 i45.7 i3i.i 56 190.2 i 7 i.3 17 12.6 n.4 77 5 7 .2 5i.5 3 7 101 .8 91.7 97 1 46 .4 i3i.8 57 191.0 172.0 18 i3.4 12.0 78 58.o 52.2 38 102.6 92.3 98 i4 7 .i i3a.5 58 191.7 172.6 *9 14.1 12.7 79 58. 7 52. 9 3 9 io3.3 9 3.o 99 i47-9 i33.2 5 9 192.5 i 7 3.3 20 14.9 i3.4 80 5 9 .5 53.5 4o 104.0 9 3.7 200 i48.6 1 33.8 60 193.2 i74.o 21 i5.6 14.1 81 60.2 54-2 i4i 104.8 9 4.3 201 149.4 i34.5 261 194.0 174-6 22 i6.3 14.7 82 60.9 54-9 42 io5.5 9 5.o 02 iSo.i i35.2 62 194.7 i 7 5.3 23 17.1 i5.4 83 61.7 55.5 43 io6.3 95.7 03 i5o-9 i35.8 63 195.4 176.0 24 17.8 16.1 84 62.4 56.2 44 107.0 0.4 04 i5i.6 i36.5 64 196.2 176.7 25 18.6 16.7 85 63.2 56.o 45 107.8 97.0 o5 i5a.3 l3 7 .2 65 196.9 177-3 26 i 9 .3 17-4 86 63. 9 5 7 .5 46 io8.5 97-7 06 i53.i i3 7 .8 66 I97-7 178.0 27 20.1 18. . 87 64.7 58.2 47 109.2 98.4 07 1 53.8 i38.5 67 198.4 178-7 28 20.8 18.7 88 65.4 58. 9 48 110. 99.0 08 1 54 .6 139.2 68 199.2 179.3 29 21.6 19.4 89 66.1 5 9 .6 49 1 10.7 99-7 9 i55.3 1 3 9 .8 69 199.9 1 80.0 3o 22.3 20. I 90 66.9 60.2 5o in. 5 100.4 10 1 56. i i4o.5 70 200 .6 180.7 3i 23.0 20.7 9 1 67.6 60.9 i5i I 12.2 101 .0 211 i56.8 141.2 271 20 1 .4 181.3 32 23.8 21.4 92 68.4 61.6 62 I l3.0 101 .7 12 i5 7 .5 i4i-9 72 202.1 182.0 33 24.5 22.1 93 69.1 62.2 53 il3. 7 102.4 33 1 58.3 i42.5 73 202-9 l82. 7 34 25.3 22.8 94 69.9 62.9 54 u4.4 io3.o i4 159.0 i43.2 74 203.6 i83.3 35 26.0 23.4 95 * 7O.O 63.6 55 I l5.2 i o3 . 7 i5 i5 9 .8 i43. 9 75 204.4 184.0 36 26.8 24.1 96 7 i.3 64.2 56 1 15.9 io4-4 16 i6o.5 i44.5 76 205.1 184.7 37 27.5 24.8 97 72.1 64.9 57 116.7 io5.i 17 i6i.3 i45.2 77 205.9 i85.3 38 28.2 25.4 98 72.8 65.6 58 117.4 io5. 7 18 162.0 145.9 78 206.6 186.0 3 9 29.0 26.1 99 7 3.6 66.2 5 9 118.2 106.4 J 9 162.7 i46.5 79 207.3 186.7 4o 29.7 26.8 100 74.3 66.9 60 118.9 107.1 20 i63,5 l4 7 .2 80 208.1 187.4 4i 3o.5 27.4 101 7 5.i 67.6 161 1 1 9 .6 107.7 221 164.2 i4 7 -9 281 208.8 188.0 42 3l.2 28.1 02 7 5.8 68.3 62 120.4 108.4 22 t65.o i48.5 82 209.6 188.7 43 3i.o 28.8 o3 7 6.5 68.9 63 121 .1 109.1 23 i65. 7 149-2 83 210.3 189.4 44 32.- 29.4 o4 77-3 69.6 64 121 .9 109.7 24 i66.5 1 49-9 84 21 I. I 190.0 45 33.4 3o.i o5 78.0 70.3 65 122.6 110.4 25 167.2 i5o.6 85 2II.8 190.7 46 34.2 3o.8 06 78.8 70.9 66 123.4 in. i 26 168.0 l5l.2 86 212.5 191.4 47 34-9 3. .4 07 79-5 71.6 67 124. I 111.7 27 168.7 1 5 1. 9 87 ai3.3 192.0 48 35.7 32.1 08 8o.3 72.3 68 124.8 1 12.4 28 169.4 1 52.6 88 2 I 4-0 192.7 4 9 36.4 32.8 09 81 .0 72.9 6 9 125.6 ii3.i 2 9 170.2 i53.2 89 214.8 193.4 So 3 7 .2 33.5 10 81.7 73.6 70 126.3 u3.8 3o 1-709 1 53. 9 9 2 1 5. 5 194.0 5i 3 7 . 9 34.1 1 1 1 82.5 74-3 171 127.1 ii4.4 23l I 7 J 7 1 54. 6 291 2i6.3 194.7 52 38.6 34.8 12 83.2 74-9 72 127.8 u5.i 32 172.4 i55.2 92 217.0 195.4 53 39.4 35.5 i.3 84.o 7 5.6 73 128.6 u5.8 33 I 7 3.2 i55.9 93 217.7 196.1 54 4o. i 36.i i4 84-7 7 6.3 74 129.3 116.4 34 173.9 1 56.6 94 2i8.5 196.7 5S 4o. 9 36.8 i5 85.5 77-0 75 i3o.i 117.1 35 174-6 l5 7 .2 95 219.2 197.4 56 4 1. 6 3 7 .5 16 86.2 77-6 76 i3o.8 117.8 36 175.4 i5 7 -9 96 22O.O 198.1 57 42.4 38.i 17 86.9 7 8.3 77 i3i.5 118.4 37 176.1 i58.6 97 22O.7 198.7 58 43.1 38.8 18 87.7 79.0 78 t.32.3 119.1 38 176.9 i59-3 98 221.5 99-4 59 43.8 3 9 .5 '9 88.4 79-6 79 i33.o 119.8 3 9 177.6 1 59.9 99 222.2 200. i 60 44-6 4o . i 20 89.2 8o.3 80 i33.8 1 20.4 4o 178.4 160.6 3oo 222.9 200.7 Di^u Dcp. | Lat. Dist. | Dep. Lat. Dist.| Dop. Lat. Dist. Dep. Lat. Dist Dep. Lat. I For 48 Degrees. TABLE II. Difference of Latitude and Departure for 43 Degrees. fPage 5'J Lat. | Dep. D si. Lai. Dep. )isl. Lai. Dep. 1st. Lai. Dep. )isl. Lai. Dep. )isl 00.7 00.7 61 44.6 4, .6 21 88.5 82.5 81 ,32.4 123.4 24, 176.3! n64-4 2 01.5 01 .4 62 45.3 42.3 22 89.2 83.2 82 ,33.i 124.1 42 ,77.0 165.0 3 O2 .2 02. o 63 46.i 43.o 23 90.0 83. 9 83 ,33.8 124.8 43 1777 165.7 4 02-9 02.7 64 46.8 43.6 24 90.7 84.6 84 ,34-6 ,25.5 44 178.5 1 60.4 5 03.7 o3.4 65 47-5 44.3 25 91.4 85.2 85 ,35.3 126.2 45 ,79.2 167.1 6 o4-4 o4-i 66 48.3 45.o 26 92.2 85. 9 86 ,36.o 126.9 46 '79-9 167.8 o5.i 04.8 6 7 49.0 45.7 2 7 92.9 86.6 87 i36.8 127.5 47 180.6 ,68.5 8 >5.9 o5.5 68 49.7 46.4 28 9 3.6 8 7 .3 88 ,3 7 .5 128.2 48 181.4 169.1 9 06.6 06. i 69 5o.5 47-1 29 94.3 88.0 89 ,38.2 128.9 49 182.1 169.8 I 10 07.3 06.8 70 5l.2 47-7 3o 9 5.i 88.7 90 139.0 ,29.6 5o 182.8 170.5 ii 08. o 07.5 71 5i. 9 48.4 i3i 9 5.8 8 9 .3 ,91 1 39.7 ,3o.3 25, ,83.6 171.2 12 08.8)08.2 72 52.7 49.1 32 90.5 90.0 92 ,4o.4 ,3o-9 52 i84.3 171.9 i3 09.5 08.9 73 53.4 49.8 33 97-3 90.7 93 ,41.2 ,3i.6 53 i85.o 172.5 ,4 ,0.2 09.5 74 54.i 5o.5 34 98.0 91 -4 94 ,41-9 ,32.3 54 ,85.8 1 7 3.2 i5 I ( .0 10.2 75 54-9 5i . i 35 98.7 92.1 95 ,42.6 ,33.o 55 ,86.5 173.9 16 II .7 10-9 76 55.6 5i.8 36 99.5 92.8 96 ,43.3| i33. 7 56 187.2 174.6 12.4 1 1 .6 77 56.3 52.5 37 100.2 93.4 97 ,44.t ,34-4 5 7 188.0 i 7 5.3 18 ,3.2 12.3 78 57.0 53.2 38 100-9 94.1 98 ,44-8 ,35.o 58 188.7 176.0 19 13.9 i3.o 79 5 7 .8 53.9 3 9 101.7 94.8 99 i45.5 ,35. 7 59 189.4 ,76.6 20 ,4-6 i3.6 80 58.5 54.6 4o 102.4 9 5.5 200 i46.3 1 36.4 bo 190.2 177-3 2 I i5. 4 i4.3 81 5o 2 55.2 i4, io3.i 90.2 20, ,47.0 i3 7 ., 261 190.9 178.0 22 16.1 i5.o 8? 60 . o 55.9 42 io3. 9 96.8 02 i47-7 i3 7 .8 62 191 .6 178.7 23 16.8 i5.7 83 60.7 56.6 43 104.6 97.5 03 ,48.5 1 38 .4 63 192.3 179.4 24 17,6 ,6.4 84 61 .4 5 7 .3 44 io5.3 98 2 o4 ,49.2 ,39.1 64 193.1 180.0 25 i8.3 ,7.0 85 62.2 58.o 45 106.0 9 <( 5 . 9 ob ,49.9 ,39.8 65 193.8 180.7 26 27 19.0 19.7 20. 5 17-7 l8.4 IQ. I 86 87 88 62.9 63.6 64.4 58.7 5 9 .3 60.0 46 47 48 106.8 107-5 108.2 99.6 IOG.O IOO-9 06 07 08 i5o.7 i5i.4 I52.I ,4o.5 i4>.a l4l.Q 66 67 68 194.5 i 9 5.3 196.0 ,81.4 182.1 182.8 20 21.2 19.8 89 65.i 60.7 49 109.0 09 l52. 9 i42.5 69 ,96.7 i83.5 3o 21 .9 20.5 9 65.8 6,.4 5o 109.7 102.3 10 ,53.6 i43.2 70 197.5 184. i 22 7 21 I o, 66.6 67.1 i5i 110.4 io3.o 2, I ,54-3 i43. 9 271 ,98.2 184.8 32 23 4 21 8 02 67.3 6?. 7 57 III .2 io3.7 '2 i55.o i44-6 72 ,98.9 i85.5 33 34 24-1 24.9 22.5 23.2 93 O/i 68.0 68 7 63.4 53 54 III .9 112. 6 io4.3 io5.o ,3 i4 ,55.8 ,565 i45.3 i45. 9 73 74 199.7 200-4 186.2 B6.o 35 36 25.6 26 3 23. 9 24.6 1 06 69.5 7O.2 64.8 65.5 55 5f n3.4 io5.7 106.4 i5 16 1 58.o i46.6 i4 7 .3 76 2O1 .1 | 201-9 187.5 188.2 37 38 3 9 4o 27.1 27.8 28.5 2 9 .3 2D.2 25.9 26.6 27.3 97 98 99 100 70.9 71-7 73!, 66.2 66.8 67.5 68.2 57 58 5 9 60 n4-8 ii5.6 ,i6.3 117.0 107. i 107.8 108.4 109.1 18 '9 20 1 58. 7 159.4 160.2 160.9 i48.o i48. 7 149.4 ,5o.o 77 78 79 80 2O2.6 203.3 2O4 .0 204.8 Iei8. 9 189.6 190.3 191.0 4i 42 43 44 45 46 47 48 i 9 5o 3o.o 3o.~ 3,.4 32.2 33^6 34.4 35.i 35.8 36.6 28.0 28.6 20.3 3o.o 3o. 7 3,. 4 32.1 32.7 33.4 34.i ,0' 02 o3 o4 o5 06 07 08 09 id -3. 9 74-6 7 5.3 76.1 76.8 77-5 7 8.3 79.0 79-7 8o.4 68.9 69.6 70.2 70.9 71.6 72.3 7 3.o 73.7 74.3 7 5.o 161 62 63 64 65 66 67 68 69 70 117-7 n8.5 i ,9.2 119.9 120.7 121 .4 122. I 122.9 ,23.6 124.3 109.8 no. 5 III .2 in. 8 112. 5 113.2 ,,3.9 1,4.6 n5: 9 221 22 23 24 25 2.6 27 28 g 3o 161.6 162.4 i63.i i63.8 164.6 ,65.3 1 66.0 166.7 ,67.5 168.2 i5o. 7 i5i.4 I52.I i52.8 i53.4 i54-i 1 54-8 i55.5 1 56.2 1 56.9 281 82 83 84 85 86 87 88 89 9 2o5.5 206.2 207.0 207.7 208.4 209.2 209.9 210.6 211.4 2,2.1 ,91.6 192.3 193.0 , 9 3. 7 194.4 , 9 5.i 195.7 196.4 197.1 197.8 ~57 52 53 54 55 56 57 58 3 7 .3 38.o 38.8 3 9 .5 40.2 4i.o 4i-7 42.4 43 ' 43-9 34.8 35.5 36.i 36.8 3 7 .5 138.2 38.9 3 9 .6 ! 4o . 2 40.9 , i , ,2 i3 i4 ,5 ,6 '7 ,8 '9 2C 8,. 2 81.9 82.6 83.4 84-1 84-8 85.6 86.3 87.0 87.8 75-7 76.4 77- 77-7 7 8.4 79- 81! 8,. 17 72 73 74 7 76 7 7 7 8 D- 125.1 125.8 126.5 127.3 128.0 128.7 129.4 ,3o.2 ,3o. 9 i3i.6 Dpri , 16.6 1,7-3 1,8.0 1,8.7 1,9.3 120. o ,20.7 ,21 .i I 2 2 . I 122.8 I al 23, 32 33 34 35 36 37 38 39 4o Dst 168.9 169.7 170.4 171.1 171.9 172.6 , 7 3.3 ,74-1 , 7 4-8 , 7 5.5 Deo. 158^2 1 58. 9 ,5,2 i6o.3 161.0 161.6 ,62.3 1 63.o 1 63. 7 Lat. 29, 93 94 96 97 98 99 3oo Dist 2,2.8 21 3.6 2,4.3 2,5.0 2i5-7 216.5 217.2 217.9 218.7 219.4 Dep. 198.5 199.1 199.8 200.5 201.2 201. 9 202.6 2O3.2 2o3. 9 2046 Lat. . I),-,) Lai. Dist Dep [For 47 Degrees. Page 60] TABLE II. Difference of Latitude and Departure for 44 Degrees. Dist. Lat. Dep. Dist. Lat. Dcp. Di.st. Lat. Dcp. Dist. Lat. Dep. Dist. Lat. De].. j 00.7 00.7 6l 43.9 42.4 121 87 o 84.1 181 130.2 125.7 241 173.4 167.4 2 01 .4 OI .4 62 44-6 43.i 22 8-. 8 84.7 82 i3o.9 126.4 42 174.1 1 68. i 3 O2 . 2 02. 1 63 45.3 43.8 23 88.5 85.4 83 i3i.6 127.1 43 174.8 1 68 .8 4 02.9 02.8 64 46.o 44-5 24 89.2 86.1 84 i3 2 .4 127.8 44 i 7 5.5 169.6 5 o3.6 o3.5 65 46.8 45.2 25 89.9 86.8 85 i33.i 128.5 45 176.2 170.2 6 o4.3 04.2 66 4 7 .5 45.8 26 90.6 8 7 .5 86 i33.8 129.2 46 177.0 170.9 7 o5.o 04.9 67. 48.2 46.5 27 91.4 88.2 87 i34.5 129.9 47 177-7 171.6 8 o5.8 o5.6 68 48.9 47-2 28 92.1 88.9 88 i35.2 i3o.6 48 178.4 172.3 9 o6.5 o6.3 69 49.6 47-9 29 92.8 89.6 89 i36.o i3i.3 49 179.1 173.0 10 07.2 06.9 70 5o.4 48.6 3o 9 3.5 90.3 90 1 36. 7 l32.0 5o 179.8 173.7 ii 07.9 07.6 7i 5i.i 49.3 i3i 94.2 91.0 191 i3 7 .4 i32. 7 261 180.6 174-4 12 08.6 c>8.3 72 5i.8 5o.o 32 95.0 91.7 92 i38.i i33.4 62 i8i.3 i 7 5.i i3 09.4 09.0 73 52.5 5o.7 33 95.7 92.4 9 3 i38.8 i34.i 53 182.0 175.7 i4 10. I 09.7 74 53.2 5i.4 34 96.4 93.1 94 139.6 1 34.8 54 182.7 176.4 i5 10.8 io.4 75 54.0 52.1 35 97.1 93.8 95 i4o.3 i35.5 55 i83.4 177.1 16 u. 5 u . i 76 54.7 52.8 36 97.8 94.5 96 i4i.o 1 36.a 56 184.2 177-8 i? 12.2 11. 8 77 55.4 53.5 37 98.5 9 5.2 97 141.7 1 36.8 57 184.9 i 7 8.5 18 12.9 12.5 78 56.i 54.2 38 99.3 95.9 98 142.4 i3 7 .5 58 186.6 179.2 19 i3.? 13.2 79 56.8 54-9 3 9 100. 96.6 99 i43.i i38.2 59 i86.3 179.9 20 i4.4 i3. 9 Bo 5 7 .5 55.6 4o 100.7 97-3 200 143.9 1 38 .9 60 187.0 180.6 21 i5.i i4.6 81 58.3 56.3 i4i 101 .4 97-9 201 1 44-6 139.6 261 187.7 i8i.3 22 i5.8 i5.3 82 59.0 5 7 .o 42 IO2 . I 98.6 O2 i45.3 i4o.3 62 188.6 182.0 23 i6.5 16.0 83 59.7 5 7 7 43 102.9 99 .3 o3 1 46.o i4i-o 63 189.2 182.7 24 i 7 .3 16.7 84 60.4 58.4 44 io3.6 IOO.O o4 146.7 141.7 64 189.9 i83.4 25 18.0 17.4 85 61.1 59.0 45 ip4.3 100.7 o5 i47-5 142.4 65 190.6 184.1 26 18.7 18.1 86 61.9 59-7 46 ibS.o ioi .4 00 i48.2 i43.i 66 191.3 184.8 27 19.4 18.8 87 62.6 60.4 47 io5.7 102. I 07 148.9 i43.8 67 192.1 i85.5 28 20.1 19.5 88 63.3 61.1 48 io6.5 102.8 08 149.6 i44.5 68 192.8 186.2 29 20.9 20.1 89 64.0 61.8 49 107.2 io3.5 09 i5o.3 i45.2 69 193.6 186.9 3o 21 .6 20 8 90 64-7 62.5 5o 107.9 104.2 10 iSi.i 145.9 70 194.2 187.6 "3i ~ 2 1T3~ 21.5 9 l 65.5 63.2 i5i 108.6 104.9 211 i5i.8 i46.6 271 194.9 i88.3 32 23.0 22.2 92 66.2 63.9 52 109.3 io5.6 12 i52.5 147-3 72 195.7 188.9 33 23.7 22.9 93 66.9 64.6 53 IIO. I io6.3 r3 i53.2 i48.o 73 196.4 189.6 34 24.5 23.6 94 67.6 65.3 54 110.8 107.0 i4 i53.o 148.7 74 197.1 190.3 35 2.5.2 24.3 95 68.3 66.0 55 in. 5 107.7 i5 r 54.7 149.4 75 197.8 191 .0 36 25.9 25.0 96 69.1 66.7 56 I 12.2 108.4 16 1 55.4 i5o.o 76 198.5 191.7 3 7 26.6 25.7 97 69.8 67.4 57 II2.9 109. i 17 1 56. i i5o.7 77 199.3 192.4 38 27.3 26.4 98 7 o.5 68.1 58 u3. 7 109.8 18 1 56.8 i5i.4 78 200.0 193.1 3 9 28.1 27.1 99 71.2 68.8 5c; ii4.4 uo.5 1 9 157.5 1 62.1 79 200.7 193.8 4o 28.8 27.8 100 71-9 69.5 60 ii5.i in . i 20 i58.3 162.8 80 201-4 194.5 4i 29.5 "2875" 101 72.7 70.2 161 u5.8 11 1 .8 221 139.0 i53.5 281 202.1 195.2 42 30.2 29.2 02 73.4 70.9 62 ii6.5 112. 5 22 159.7 164.2 82 202-9 195.9 43 30.9 29.9 o3 74-1 71 .5 63 ii 7 .3 II3.2 23 160.4 164.9 83 2o3.6 196.6 44 3i. 7 36.6 o4 74.8 72.2 64 118.0 1 13.9 24 161.1 i55.6 84 2o4-3 197.3 45 32.4 3.. 3 o5 7 5.5 72.9 65 118.7 u4-6 25 161.9 1 56.3 85 205.0 ,98.0 46 33.i 32.0 06 7 6.3 7 3.6 66 119.4 n5.3 26 162.6 167.0 66 206.7 198-7 47 33.8 32.6 07 77.0 74.3 67 1 20. i 116.0 2 7 i63.3 i5 7 -7 87 206.5 199.4 48 34.5 33.3 08 77-7 7 5.o 68 120.8 116.7 28 164.0 168.4 88 207.2 200.1 49 35.2 34.o 09 78.4 75-7 69 121 .6 117.4 29 164.7 159.1 89 207.9 2OO.8 5o 36.o 34-7 10 79.1 76.4 70 122.3 118.1 3o i65.4 169.8 90 208.6 2O1.5 5i 36. 7 35.4 n i 79.8 77.1 171 123. 118.8 a3i 166.2 i6o.5 291 209.3 2O2. [ 52 3 7 -4 36.i 12 80.6 77.8 72 123.7 119.5 32 166.9 161.2 92 210.0 202.8 53 38.i 36.8 i3 8i.3 7 8.5 73 124.4 120.2 33 167.6 161.9 93 210.8 2o3.5 54 38.8 3 7 .5 1 4 82.0 79.2 74 125.2 120.9 34 1 68. 3 162.6 94 241.5 204 2 C ^^ 39.6(38.2 i5|3 2 . 7 79-9 7 5 125-9 121 .6 35 169.0 i63.2 9 5 212.2 204.9 56 4c.3 38. 9 i6|83.4 80.6 76 126.6 122.3 36 169.8 163.9 96 212-9 2o5.6 5 7 4i .0 39 6 17 84.2 8i.3 77 127.3 123. 3 7 170.5 164.6 97 2i3.6 206.3 58 41.7 4o.3 18 84. Q 82.0 78 I28.O 123.6 38 171.2 i65.3 98 214.4 20- .0 59 42.4 4i .0 19 85.6 82.7 79 128.8 124 3 3 9 i"i 9 166.0 99 2l5.I 207.7 ()0 ,43.2 4l. 7 20 86.3 83.4 80 129.5 125. O 4o 172.6 166.7 3oo 2 1 5.8 208.4 Dist. Dep. Lat. ;Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. "TaT [For 4C Degrees. TABLE II. fl > age61 Difference of Latitude and Departure for 45 Degrees. Dist Lat. Dep Dist Lat. Dep Dis Lat. Dep. Dist Lat. Dep. Dist Lat. Dep. 2 3 4 5 6 7 8 9 10 00.7 01 .4 02. i 02.8 o3.5 04.2 04.9 o5. 7 06.4 07.1 00.7 01 .4 02.1 02.8 o3.5 04.2 04.9 o5. 7 06.4 07.1 61 62 63 64 65 66 67 68 69 70 43.i 43.8 44-5 45.3 46.o 46.7 47-4 48.i 48.8 4 9 .5 43.i 43.8 44-5 45.3 46.o 46. 7 47-4 48.i 48.8 49-5 121 22 2c 2t 25 26 2 7 28 29 3o 85.6 86.3 8 7 .o 87-7 88.4 89.1 85.8 90.5 91.2 91.9 85.6 86.3 8 7 .o 87-7 88.4 89.1 89.8 90.5 91.2 91.9 181 82 83 84 85 86 87 88 89 9 128.0 128.7 129.4 i3o.i i3o.8 i3i.5 132.2 132.9 i33.6 i34.4 128.0 128.7 129.4 i3o.i i3o.8 i3i.5 132.2 132.0 i33.6 1 34.4 24 1 42 43 44 45 46 47 48 i 9 5o 170.4 171.1 171.8 172.5 I 7 3.2 173.9 174-7 175.4 i 7 6.i p i 7 6.8 170.4 171.1 171.8 172.5 I 7 3.2 173.9 174.7 175.4 176.1 176.8 ii 12 i3 i4 i5 16 17 18 1 9 20 07.8 o8.5 09.2 09.9 10.6 ii.3 12.0 12.7 i3.4 14.1 07.8 o8.5 09.2 09.9 10. b ii. 3 12.0 I2. 7 i3.4 14.1 7i 72 73 74 75 76 77 78 79 80 50.2 5o. 9 5i.6 52.3 53.o 53,7 54-4 55.2 55.9 56.6 5o.2 5o. 9 5i.6 52.3 53.o 53. 7 54-4 55.2 55. 9 56.6 i3i 32 33 34 35 36 37 38 I 9 92.6 9 3.3 9 4-o 9 4.8 9 5.5 9 6.2 96-9 97-6 9 8.3 99- 92.6 9 3.3 94.0 94.8 9 5.5 96.2 96-9 97-6 9 8.3 99.0 191 92 9 3 94 9 5 96 97 98 99 200 i35.i i35.8 i36.5 I3 7 .2 i3 7 -9 i38.6 i3 9 .3 i4o.o i4o. 7 i4i.4 i35.i i35.8 i36.5 I3 7 .2 i3 7 . 9 1 38. 6 i3 9 .3 r4o.o 1 40.7 i4i-4 25l 52 53 54 55 56 57 58 59 60 177.5 I 7 8.2 178.9 179-6 i8o.3 181.0 181.7 182.4 i83.i i83.8 177.5 178.2 178.9 179.6 180.3 181.0 181.7 182.4 i83.i i83.8 21 22 i4.8 i5.6 i4.8 i5.6 81 82 5 7 .3 58.o 5 7 .3 58.o i4i 42 99-7 100.4 99-7 100.4 201 02 i4?..i 142.8 142.1 142.8 26l 62 184.6 i85 3 . 184.6 i85 3 23 ib.3 i6.3 83 58. 7 58. 7 43 IOI .1 101. 1 o3 i43.5 i43.5 63 186.0 1 86.0 24 17.0 17.0 84 5 9 .4 5 9 .4 44 101. 8 101.8 04 144.2 i44-2 64 186. 7 186.7 25 26 17-7 18.4 17.7 18.4 85 86 60. i 60.8 60. i 60.8 45 46 IO2.5 103.2 102.5 103.2 o5 06 i45.o i45. 7 i45.o i45. 7 65 66 i8 7 .4 188.1 187-4 188.1 2 7 19.1 19.1 87 6i.5 6i.5 47 io3. 9 io3. 9 07 i46.4 146.4 67 188.8 1 88 .8 28 19.8 19.8 88 62.2 62.2 48 104.7 104.7 08 147. i 147-1 68 189.5 i8o.5 3o 9 20.5 21 .2 20.5 21 .2 89 9 62. o 63.6 62.9 63.6 P 5o io5.4 1 06. i io5.4 1 06. i 09 10 147.8 M8.5 147-8 i48.5 69 70 190.2 190.9 I9O.2 190.9 3i 21. 9 21 .9 9 1 64.3 64-3 i5i 106.8 106.8 211 149.2 149-2 271 191 .6 1 9 1 .6 32 33 22.6 23.3 22.6 23.3 9 ? 9 3 65.i 65.8 65.i 65.8 52 53 io 7 .5 108.2 io 7 .5 108.2 12 13 i4 9 . 9 i5o.6 1 49-9 i5o.6 72 73 192.3 193.0 192.3 193.0 34 35 24.0 24.7 24.<"> 24.7 94 9 5 66.5 6 7 .2 66.5 67.2 54 55 io8. 9 100.6 108.9 109.6 i4 i5 i5i.3 l52.0 i5i.3 l52.0 74 75 193. 7 194.5 193-7 i 9 4.5 36 25.5 25.5 96 67-9 67.9 56 110.3 i io.3 16 l52 . 7 l52. 7 76 195.2 195.2 37 26.2 26.2 97 68.6 68.6 5 7 in .0 I I I.O 17 i53.4 1 53. 4 77 195.9 I 9 5.9 38 26.9 26.9 98 6 9 .3 6 9 .3 58 111.7 111.7 18 i54.i i54.i 78 196.6 ,96.6 3 9 27.6 27.6 99 7 o.o 70.0 5 9 112.4 1 12.4 19 i54. 9 1 54.g 79 19-7.3 197.3 4o 28.3 28.3 JOO 70.7 70-7 60 ii3.i u3.i 20 .55.6 1 55.6 80 198.0 198.0 4i 29.0 29.0 IOI 71-4 71-4 161 n3.8 ii3.8 221 i56.3 1 56.3 281 198.7 198.7 42 29.7 29.7 02 72. i 72.1 62 ii4-6 ii4-6 22 i5 7 .o i5 7 .o 82 199.4 199.4 43 3o.4 3o.4 o3 72.8 72.8 63 n5.3 ii5.3 23 167.7 l5 7 -7 83 200. i 200.1 44 3i.i 3i.i 04 7 3.5 7 3.5 64 116.0 116.0 24 i58.4 1 58.4 84 200.8 200.8 45 3i.8 3i.8 o5 74-2 74-2 65 n6. 7 u6. 7 25 159. i i5 9 .i 85 201 5 2OI.5 46 32.5 32.5 06 7 5.o 7 5.o 66 H7.4 1 17-4 26 i5 9 .8 169.8 86 202.2 202.2 47 33.2 33.2 07 75.7 75.7 67 118.1 118.1 27 i6o.5 160.5 87 2O2 . 9 202-9 48 33.9 33.Q 08 76.4 76.4 68 118.8 118.8 28 161 .2 161 2 88 2O3.6 2O3.6 49 34.6 34.6 09 77-1 77-1 69 ii 9 .5 119.5 29 161 .9 161.9 89 204-4 204.4 bo 35.4 35.4 IO 77-8 77-8 70 120.2 120.2 3o 162.6 162.6 9 205.1 205.1 5i 36.i 36.i II I 7 8.5 7 8.5 171 I20. 9 120.9 23l i63.3 i63.3 291 205.8 2o5.8 52 36.8 36.8 12 79.2 79.2 72 121. 6 I 2 1. 6 32 164.0 164.0 92 206.5 206 5 53 3 7 .5 3 7 .5 i3 79.9 73 122.3 122.3 33 164.8 164.8 93 207.2 207 2 54 38.2 38.2 i4 80.6 3o.6 74 123.0 123.0 34 i65.5 i65.5 94 207.9 207.9 55 38.Q 38.9 i5 8i.3 8i.3 75 123.7 I23. 7 35 166.2 166.2 95 208.6 208.6 56 1 9 .6 3 9 .6 16 82.0 82.0 76 124.5 124.5 36 166.9 i66. 9 9^ 209.3 209.3 57 4o.3 4o.3 17 82. 7 82. 7 77 125.2 125.2 37 167.6 167.6 97 210.0 2-IC.O 58 4: .0 4i.o 18 83.4 83.4 78 125.9 125-9 38 i68.3 i68.3 98' 210.7 2:0.7 5 9 4i.? 4l-7 Z 9 84.i 84.1 79 26.6 126.6 39 169.0 i6 9 .o 99 21 1 .4 21 1.4 60 42.4 42.4 20 84.9 84-9 80 I2 7 .3 I2 7 .3 4o 169.7 i6 9 .7 3oo 2 I 2 . I 212.1 Dis. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. D,-,>. Lai [For 45 Degrees. Pa*e62] TABLE III. Meridional Parts. M OP 1 2 3 4 5 6 7 8 9 10 11 12 13 M. /. 3 4 5 G -7 b V o 2 3 4 60 61 62 63 64 1 20 121 122 123 124 1 80 181 182 i83 1 84 i85 186 187 1 88 1 80 240 241 242 243 244 3oo 3oi 302 3o3 3o4 36 1 362 363 364 365 421 422 423 424 425 482 483 484 485 486 542 543 544 545 546 6o3 6o4 6o5 606 6o 7 "664 665 666 667 668 725 726 / 2 7 7 28 729 7 3o 7 3. ?32 7 34 7 35 7 8 7 7 88 789 79 o 791 i 2 3 4 5 6 8 9 65 66 67 66 69 125 126 127 128 129 245 246 247 248 249 3o5 3o6 3o 7 3o8 3o 9 366 36 7 368 369 370 426 427 428 429 43o 48 7 488 48 9 4 9 o 4 9 ' 547 548 54 9 55o 55i 608 609 610 611 012 669 670 671 6?a 6/3 792 79 3 7 94 79 5 79 6 5 6 8 9 1C' 1 1 12 i3 4 10 1 1 12 i3 i4 73 ?r 74 i3o i3i 132 i33 1 34 190 191 ,92 i 9 3 194 250 25l 252 253 254 3io 3ii 3l2 3i3 3i4 3Jl 3 7 2 3 7 3 3 7 4 3 7 5 43. 432 433 434 435 436 43 7 438 43 9 44o 4Q2 4 9 3 4 9 4 495 4 9 6 55 2 553 554 555 556 6i3 6i4 6i5 616 6. 7 674 6/5 676 677 6 7 8 7 36 7 3 7 7 38 7 3 9 7 4o 797 798 799 800 80 1 10 ;i 12 i3 i4 i5 16 ' 1 18 '9 i5 16 17 18 '9 75 76 79 i35 1 36 i3 7 1 38 i3g 'S 196 197 i 9 8 199 255 256 25 7 258 25 9 3i5 3i6 3i7 3i8 3 19 320 321 322 323 324 3 7 6 3 77 3 7 8 3 79 38o 497 4 9 8 4 99 5oo 5oi 55 7 558 55 9 56o 56 1 618 619 620 621 622 6 7S> 680 68 1 682 683 74i 7 42 7 43 7 44 7 45 7 46 7 4 7 748 749 7 5o 802 8o3 8o4 8o5 806 i5 16 '7 18 12 20 21 22 23 24 25 26 2 7 28 2 9 20 21 22 23 24 20 21 22 23 24 80 81 8?. 83 84 i4o i4i i4 i43 1 44 200 201 202 203 204 260 261 262 263 264 38 1 382 383 384 385 386 38 7 388 38 9 3 9 o 44 1 442 443 444 445 446 44 7 448 449 45o 502 5o3 5o4 5o5 5o6 562 564 565 566 56 7 623 624 625 626 627 628 629 63i 632 633 684 685 687 688 68 9 807 808 809 810 8t! 812 8i3 8i5 816 817 818 819 820 821 822 2D 26 2 7 28 2 9 25 26 27 28 29 85 86 87 88 _8o_ 9 9 1 9 ? 9 3 94 ~95 9 6 97 9 8 99 i45 1 46 i47 1 48 149 i5o i5i l52 1 53 1 54 205 206 207 208 20 9 210 211 212 2l3 2t4 265 266 267 268 269 3 2 5 3 2 6 32 7 328 33o 33 1 332 333 334 335 5o 7 5o8 5o 9 5io 5ii 568 56 9 5 7 o 5 7 i 5 7 2 690 691 692 6o3 6 9 4 7 5i 7 52 7 53 7 54 7 55 3o 3i 3^ 33 34 35 36 3 7 38 39 3o 3i 32 33 34 "35 36 3? 38 3 9 4o 4i 42 43 44 270 271 372 2 7 3 274 3or 392 3 9 3 3 9 4 3 9 5 45i 452 453 454 455 5l2 5i3 5i4 5i5 5i6 5 7 3 5 7 4 5 7 5 5 7 6 5 7 7 634 635 636 63 7 638 6 9 5 696 6 97 6 9 8 699 7 56 7 5 7 7 58 7 5 9 760 3o 3i 32 33 34 i55 1 56 1 5 7 1 58 i5 9 2l5 216 217 218 219 2 7 5 276 277 278 _279_ 280 281 282 283 284 336 33 7 338 33 9 34o 3 9 6 3 97 3 9 8 3 99 4oo 456 45 7 458 459 46o 5i 7 5i8 5, 9 520 521 5 7 8 5 79 58o 58 1 582 639 64o 64 1 642 643 700 7 OI 7 02 7 o3 704 761 7 62 7 63 764 7 65 8 2 3 824 8 2 5 826 827 35 36 37 38 3 9 4o 4i 42 43 44 45 46 47 48 49 100 101 102 io3 io4 1 60 161 162 i63 1 64 220 221 222 223 224 34 1 342 343 344 345 4oi 402 4o3 4o4 4o5 46 1 462 463 464 465 522 5 2 3 524 525 526 583 584 585 586 58 7 644 645 646 64 7 648 "OD 7 o6 7 7 708 709 710 711 712 7 i3 7 i4 7 66 7 6 7 768 7 6 9 77 o 771 772 77 3 774 775 828 829 83o 83 1 83 2 4o 4i 42 43 44 45 46 47 48 49 io5 1 06 107 1 08 109 1 65 1 66 167 1 68 169 225 226 227 228 22 9 285 286 287 288 289 346 34? 348 34 9 35o 4o6 4o 7 4o8 4o 9 4io 466 467 468 469 4 7 o 52 7 528 529 53o 53 1 588 58 9 5 9 o 5 9 i 592 64 9 65o 65i 652 653 833 834 835 836 83 7 45 46 47 48 4 9 5o 5i 52 53 54 5o 5i 52 53 54 55 56 5? 58 r >9 no III 112 n3 _u4_ ii5 116 "7 118 n 9 170 171 172 i 7 3 174 230 23l 232 233 2 34 290 291 292 2 9 3 2 9 4 35i 352 353 354 355 4n 412 4i3 4i4 4i5 471 4 7 2 4 7 3 4 7 4 4 7 6 532 533 534 535 536 5 9 3 5 9 4 5 9 5 596 5 97 654 655 656 65 7 658 ~65o~ 660 66 1 662 663 7 i5 716 717 718 719 777 778 77 9 780 7 8i 838 839 84o 84 1 842 5o 5i 52 53 54 55 56 5- 58 5 9 i75 176 177 178 179 235 236 23 7 238 23 9 2 9 5 296 2 97 298 2 99 356 35 7 358 35 9 36o 4i6 4i 7 4i8 4i 9 420 4 77 4 7 8 4 7 9 48o 48 1 53 7 538 53 9 54o 54 1 598 .5 99 600 60 1 602 720 721 722 7 23 724 782 7 83 7 84 7 85 786 843 844 845 846 84 7 55 56 5 7 58 ^9 ft! 1 2 3 V 5 6 7 8 9 10 11 12 13 M. TABLE III. [Page Go Meridional Parts. M. 14 15 16 17 18 19 1 161 63 64 65 66 20 21 22 23 24 25 26 27 M. o i 2 3 4 5 6 7 8 9 848 85o 85 1 85a 853 910 91 i 9 i3 914 9 i5 973 974 975 976 977 io35 36 37 38 3 9 1098 99 I 1 00 OI 02 1225 2.6 27 28 2 9 1289 9 9 1 9 l 9 3 1 354 55 56 5 7 58 1419 20 21 22 23 i484 85 '86 87 88 i55o 5i 52 53 54 1616 18 9 20 21 l622 23 24 25 26 1684 85 86 87 88 o i 2 3 4 854 855 856 85 7 858 916 917 918 919 920 978 979 980 981 982 1041 42 43 44 45 Iio3 o5 06 07 08 1167 68 69 70 7i ia3o 32 33 34 35 I2 9 5 9 6 97 9 8 99 i35 9 60 61 62 63 1424 25 26 *7 28 1490 9 1 9 ? 9 3 94 1 556 5 7 58 5 9 60 1689 9 9 l 9 3 94' 5 6 1 8 9 10 1 1 12 i3 i4 85 9 860 86 1 862 863 921 922 923 924 925 9 83 9 84 985 986 9*7 1046 47 48 5o 1 109 10 II 12 i3 ti i4 i5 16 17 18 II 7 2 73 74 75 76 1236 3 7 38 3 9 4o i3oo 01 02 o3 o4 1 364 66 67 68 69 i43o 3i 32 33 34 i435 36 37 38 3 9 i4 9 5 96 97 9 8 99 i56i 62 63 64 65 1628 |9 3o 3i 32 i6 9 5 96 97 9 8 99 10 1 1 12 i3 i4 i5 16 17 18 !9 i5 16 "7 18 '9 864 865 866 867 868 926 927 928 929 93o 988 989 990 991 99 3 io5i 52 53 54 55 "77 78 79 81 82 1241 42 43 44 45 i3o5 c>6 7 08 10 i3 7 o 7i 72 73 74 i5oo 02 o3 o4 o5 i56 7 68 69 70 7i i633 34 35 3 7 38 1700 OI o3 o4 o5 20 21 22 7.3 24 869 870 87. 872 8 7 3 9|i 9 32 9 33 934 9 35 994 99 5 996 997 99 8 io56 57 58 I 9 ii 19 20 21 22 23 ii83 84 85 86 87 1246 48 * 5i i3ii 12 i3 i4 i5 i3 7 5 76 77 79 80 i44o 4i 43 44 45 i5o6 07 08 9 10 l5 7 2 73 74 75 77 i63 9 4o 4i 42 43 1706 07 08 9 ii 20 21 22 23 24 25 26 7 28 119 8 7 4 8 7 5 876 877 878 9 36 9 3 7 933 9 3 9 9 4 999 1000 01 02 o3 1061 63 64 65 66 1125 26 27 28 2 9 1188 8 9 9 9i 9 2 1252 53 54 55 56 i3i6 17 18 19 20 i38i 82 83 84 85 1 446 47 48 i 9 5o i5u i3 i4 i5 16 i5 7 8 79 80 81 82 i644 45 4 7 48 49 1712 i3 i4 i5 16 25 26 27 28 29 ;!o :ii la 33 34 879 880 882 883 884 942 943 944 945 946 1004 o5 06 07 08 1067 68 69 70 7' i i3o 3i 32 33 34 1 1 9 3 94 95 9 6 98 I25 7 58 59 60 61 1321 22 24 25 26 1 386 87 88 8 9 9 i45i 52 53 55 56 i5i 7 18 *9 20 21 1 583 84 85 86 88 i65o 5i 52 53 54 1717 18 20 21 22 3o 3i 32 33 34 35 36 3 7 38 3 9 35 36 37 38 3 9 885 886 887 888 889 947 948 949 9 5o 9 5i I OO 9 10 [ I 12 i3 1014 i5 16 18 W 1072 73 74 75 76 ii35 36 37 38 _J9 1 140 4i 42 44 45 1199 1 200 01 02 o3 1262 64 65 66 67 I32 7 28 y 3o 3i iT3T 33 34 35 36 l3 9 2 93 94 9 5 __96 139-7 98 99 i4oo 01 i45 7 58 5 9 60 61 1522 24 25 26 2 7 "7528" 3o 9 3i 32 1 589 90 9 1 9 ? 9 3 i656 5 7 58 5 9 60 1723 24 25 26 27 4o 4 42 43 44 890 891 892 893 894 9^ 9 53 954 9 55 9 56 I0 77 78 79 80 81 1204 o5 06 7 08 1268 69 70 7i 72 1462 63 64 65 67 i5 9 4 9 ^ 96 98 99 1661 62 63 64 66 1729 3o 3i 32 33 4o 4i 4:> 43 44 45 46 47 48 49 5o 5i 52 53 54 8y5 896 897 898 899 9 5 7 9 58 9 5 9 960 96. 1020 21 22 23 24 1025 26 27 28 2 9 1082 84 85 86 8 7 1146 47 48 4 9 5o 1209 10 II 12 i3 I2 7 3 74 75 76 77 1 338 39 4o 4i 42 1402 o3 o5 06 7 1 468 69 70 7 1 7 2 i533 35 36 3 7 38 i53 9 4o 4i 42 43 1600 01 02 o3 o4 i66 7 68 69 70 71 1734 35 36 38 39 i74o 4i 42 43 44 45 46 47 48 49 900 901 902 9 o3 904 9o5 906 907 908 909 962 o63 9 ^ 965 966 968 969 970 971 972 1088 89 90 9 1 92 n5i 52 53 54 55 I2l5 16 17 18 T 9 1278 80 81 82 83 1 343 44 45 46 47 1408 09 10 II 12 i473 74 75 76 77 i6o5 06 08 9 10 1672 73 75 76 77 bo 5i 52 53 54 55 56 57 58 5? M io3o 3i 32 33 34 1093 9 4 9 A 96 97 u56 57 58 g 60 1220 21 22 23 24 1284 85 86 87 88 1 348 i 9 5o 52 53 i4i3 i4 i5 16 18 1 479 80 81 82 83 23^ 1 544 46 4 7 48 49 1611 12 i3 i4 i5 1678 79 80 81 82 i 7 46 4 7 48 4 9 5o 27^ 55 56 5 7 58 ^? M 14 15 16 17* 18 19 20 21 22 24 25 26 to* 64] TABLE III Meridional Parts. M. 28 7^5? 52 53 55 56 29 30 31 32 33 34 35 "2244 46 47 48 49 36 37 38 39 40 41 2702 o3 o4 06 07 "2708 10 1 1 12 i.4 M. o i 2 3 4 5 6 8 9 1819 21 22 23 24 1888 90 9 r 9 ? 9 3 i 9 58 5 9 60 62 63 2028 3o 3i 32 33 2IOO 01 O2 o3 o4 2171 73 74 75 76 23i8 9 20 22 23 2 3 9 3 94 95 96 98 2468 70 7i 72 73 2545 46 48 n 2623 24 25 27 28 o i 2 3 4 1757 58 59 60 61 1825 26 27 ? 3o 1894 9j> 96 98 99 1964 65 66 67 69 2o34 35 37 38 '39 2040 4i 43 44 45 2105 07 08 9 10 2178 79 80 81 82 2250 52 53 54 55 2324 25 27 28 29 2 3 99 2400 01 o3 o4 2475 76 77 78 80 255 1 53 54 55 57 2629 3i 32 33 34 5 6 7 8 9 10 ii 12 i3 i4 1762 64 65 6 67 i83i 32 33 34 35 1900 01 02 o3 o5 1970 7i 72 73 74 2III i3 i4 1 5 16 2184 85 86 87 88 2257 58 : s 61 233o 32 33 34 35 24o5 06 08 9 IO 2481 82 84 85 86 2487" 89 9 9 l 9 2 2558 59 60 62 63 2636 37 38 4o 4i 27,5 16 18 9 20 10 1 1 12 1 3 M i5 :6 i? 18 '9 1768 69 70 72 7 3 1774 75 76 77 78 :83 7 38 3 9 4o 4i 1906 07 08 09 10 1976 77 78 79 80 2046 47 48 5o 5i 2117 '9 20 21 22 2I 9 9 1 9 l 9 3 94 2263 64 65 66 68 233 7 38 39 4o 42 24 1 1 i3 i4 i5 16 2564 06 6 7 68 69 2642 44 45 46 48 2649 5o 5i 53 54 2/22 23 24 26 27 i5 16 17 18 '9 20 21 22 23 24 1842 43 45 46 47 1912 i3 i4 i5 16 1981 83 84 85 86 2052 53 54 56 5 7 2123 25 26 27 28 21^ 97 98 99 2200 226 9 70 71 72 74 a343 44 45 46 48 2418 *9 20 22 23 24 9 4 95 96 98 99 2571 is 75 76 2728 3? 32 33 20 21 22 23 24 25 26 27 28 2 9 25 26 2 7 28 2 9 1780 61 82 83 84 1 848 P 5o 52 53 1917 18 20 21 22 1987 88 9 9 1 92 2o58 59 60 61 63 2I2 9 3l 32 33 34 2202 03 o4 05 07 2275 76 77 79 80 2349 5o 5i 53 54 2424 25 27 28 2 9 2500 01 o3 o4 o5 2577 78 80 81 82 2655 57 58 e? 2 7 35 36 37 3 9 4o 3o 3i 32 33 34 1785 86 87 89 9 1854 55 56 57 58 1923 24 25 27 28 1-993 9 4 9 5 97 98 2064 65 66 67 69 2 1 35. 37 38 3 9 4o 2208 9 10 1 1 i3 2281 82 83 85 86 2355 56 58 59 60 243o 32 33 34 35 25o6 08 OQ 10 12 2584 85 86 88 89 2662 63 65 66 67 2742 43 44 46 47 3o 3i 32 33 34 35 36 3? 33 3 9 1791 2 1860 61 62 63 64 1929 3o 3i 32 34 1999 2OOO OI O2 o4 2070 7i 72 73 75 2l4l 43 44 45 46 22l4 i5 16 17 '9 2287 88 90 9 1 92 236i 63 64 65 66 ~2~368~ 69 70 71 73 2374 75 76 78 79 243 7 38 3 9 4o 42 2443 44 45 47 48 25i3 i4 i5 17 18 2 5 9 o 9 9 3 94 95 2669 70 71 73 74 2748 5o 5i 52 54 35 36 3? 38 39 4o 4i 42 43 44 1797 9 8 99 1800 01 1 865 66 68 69 70 1935 36 3 7 38 3g 2005 06 07 08 10 2076 77 78 79 80 2 1 47 P 5o 5i 52 2220 21 22 24 25 2293 95 96 97 98 25l 9 21 22 23 24 2597 98 99 2601 02 26 7 5 76 78 79 80 2 7 55 56 58 59 60 2762 63 64 66 67 4o 4i 4a 43 44 45 46 47 48 49 45 46 47 48 4 9 1802 o3 o5 06 07 1871 72 73 75 76 1941 42 43 44 45 201 I 12 13 i4 i5 2082 83 84 85 86 2088" 89 90 9 1 92 2i53 55 56 5 7 58 2226 27 28 3o 3i 2299 a3oi 02 o3 o4 244 9 5i 52 53 54 2526 27 28 3o 3i 26o3 o4 06 07 08 2682 83 84 86 87 5o 5i 52 53 54 55 56 57 58 5 9 1808 9 10 1 1 i3 1877 78 79 80 81 1946 48 i 9 5o 5i 2017 18 '9 20 21 2l5 9 61 62 63 64 2232 33 35 36 37 23o'o 07 08 09 1 1 238o 81 83 84 85 2 386 88 89 90 9' 2456 5- 58 r 9 61 "2762" 63 64 66 67 2532 33 35 36 37 2538 4o 4i 42 44 2610 1 1 12 i4 i5 2688 9 9 1 9 2 94 2768 70 71 -]> 74 5o 5i 52 53 54 1814 i5 16 17 18 j883 84 85 86 87 1952 53 55 56 5 7 2022 24 25 26 27 2094 $ 1 2i65 67 68 69 70 2238 3 9 4i 42 43 23.2 i3 i4 16 17 2616 17 *9 20 21 39 26 9 5 96 98 99 2700 2775 76 78 79 80 55 56 57 58 5c; M. 28 29 30 31 32 33 34 35 3<> 37 38 40 | 41 M. TABLE III. [P^e 65 Meridional Parts. M. 42^ 43 44 45 46 3n6 17 18 20 21 47 48 49 50 51 52 53 54 55 M 2 3 4 ~5 6 7 8 -? IO 1 1 12 1 3 M o i 2 3 4 2782 83 84 86 87 2863 64 66 67 69 2946 47 & 5i 3o3o 3i 33 34 36 3ol7 38 4o 4i 43 3ao3 o4 06 07 09 3292 93 95 96 98 3382 84 85 87 88 3474 76 78 79 81 56 9 70 72 74 75 3665 67 68 70 72 3 7 64 65 6 7 69 70 3865 66 68 70 7i 38 7 3 " 75 77 78 80 3 9 68 70 71 73 7 5 3977 78 80 82 84 5 6 i 8 9 10 1 1 1 2 i3 i4 ->788 9 9 1 92 94 2870 71 73 74 7^ 2877 78 80 81 82 2 9 53 54 56 5 7 58 3i23 24 76 27 29 32 I O 12 i3 i4 16 |?99 33oi 02 o3 o5 3390 9' 93 9 i 9 6 33 97 99 34oo 02 o3 3482 84 85 87 88 35 77 78 80 82 83 36 7 3 75 77 78 80 3772 74 <75 77 79 3 7 8o 82 84 85 87 2795 97 98 99 2801 2802 o3 o5 06 07 2960 61 63 64 65 2967" ) 70 7i 72 3o44 46 47 48 5o 3^5T 53 54 55 57 3i3o 3i 33 34 36 3737 3 9 4o 42 43 32i 7 1 9 20 23 33o6| 08 09 ii 12 3490 92 9 3 9 5 96 3585 86 88 90 9' 35 9 3 9 r 4 96 98 99 368 1 83 85 86 88 31^7 91 9 3 9 ? 96 3882 83 85 87 89 3 9 85 87 89 9' 92 i5 16 17 18 19 2(1 21 22 23 24 288/1 85 86 88 89 3225 26 28 y 3i 33i4 16 17 '9 20 "3322" 23 25 26 28 34o5 07 08 10 1 1 3498 _ 99 35oi o3 o4 3 7 3 9 9 92 9 i 9 5 3890 92 9 i 9 5 97 3 99 4 9 98 99 4ooi 4oo3 o5 06 08 IO i5 16 17 18 19 2.809 10 1 1 i3 i4 289, 92 9 3 9* 96 2974 75 76 78 79 3o58 60 6 1 63 64 3i44 46 47 49 5o 3232 34 35 3 7 38 34i3 i4 16 17 '9 35o6 07 9 10 12 36oi 02 o4 06 07 36 9 8 , 99 3701 o3 o4 3797 02 o4 3b 99 3 9 oi 02 o4 06 20 21 2?. 23 2^ 25 26 27 28 29 2 8i5 17 18 20 2 I 2897 99 2900 02 o3 2981 82 83 85 86 3o65 67 66 70 71 3i5 2 53 55 56 57 324o 4i 42 44 45 3329 3i 32 34 35 3420 22 23 25 27 ~3"4^8~ 3o 3i 33 34 35i4 i5 '7 18 20 3609 10 12 i4 i5 3 7 o6 08 09 ii i3 38ob 07 09 ii 12 ~3~8~74~ 16 17 *9 21 ~3"822~ 24 26 27 29 383 1 32 34 36 38 3907 09 ii i3 i4 4012 i4 i5 17 i9 25 20 27 28 29 33 3i 32 33 34 35 36 3? 38 3o 3i 32 33 34 2822 24 25 26 28 2904 06 07 08 IO 2988 89 9 1 3o 7 3 74 75 i 3i5 9 60 62 63 65 3247 48 5o 5i 53 333 7 38 4o 4i 43 352i 23 25 26 28 36i7 18 20 22 23 37i4 16 17 19 21 T^T 24 26 2 7 2 9 3916 18 19 21 23 "925~ 26 28 3o 32 ~3^33 35 3 7 38 4o 3942 44 45 4 7 49 4021 22 24 26 28 4029 3i 33 35 37 35 36 3 7 38 39 2829 3o 32 33 34 2836 3 7 3 9 4o 4t 291 1 i3 i4 i5 17 2 99 5 96 98 , 99 3oou 3002 o3 o5 06 07 3o8o 81 83 84 85 1^87 88 9 91 9 3 3i66 68 69 71 72 3254 56 5 7 59 60 3344 46 47 | 3436 37 39 4o 42 35 3? 32 34 36 3625 26 28 3o Ji 4o 4i 4 a 43 44 45 46 47 48 49 5o 5i 52 53 54 55 50 57 58 5 9 |M 2918 19 21 22 24 2925 26 28 3? 3i 7 3 75 76 78 79 3262 63 65 66 68 "3^69" 7i 72 74 75 3352 53 55 56 58 3443 45 47 48 5o 353 7 3 9 4o 4? 43 3633 34 36 38 3 9 3 7 3, 32 34 36 3 7 4o38 4o 42 44 45 40 4i 42 43 44 45 4b 4: 48 49 2843 44 45 47 48 "2849 5* 52 54 55 I 3009 10 12 i3 i4 3094 9 5 97 98 3ioo 3i8i 82 84 85 87 335 9 61 62 64 65 345 1 53 54 56 57 3b4b 47 48 5o 5i 364 1 43 44 46 47 3 7 3 9 4i 42 44 46 3839 4i 43 44 46 4o4 7 $ 52 54 2032 33 35 36 3 7 3oi6 17 i9 20 21 3ioi o3 o4 o5 07 3i88 9 9 r 92 94 3277 78 80 81 .83 3367 68 70 71 73 J l 9 62 64 65 3553 55 56 58 5 9 364 9 5i 52 54 55 ~365 7 5 9 60 62 64 3 7 47 4 9 5o 52 54 3848 4 5? 53 54 ^ 54 56 58 4o56 58 DO 6l 63 4o65 67 69 TO 72 55 5o 5i 52 53 54 CK 1 a856 58 59 60 62 '42^ 2939 4o 42 43 44 "43 3o23 24 26 27 9 ? 44 3 1 08 10 K i4 " "45 3i 9 5 ,1 OI "~4 57 58 59 60 61 62 63 64 05 66 f>7 63 ~ S6 36 3 9 42 6& M c i 4 4oy4 76 77 79 81 4i83 84 86 88 90 4294 96 98 43oo 02 4409 u i3 iS 17 4527 3? 33 35 4649 5i 53 55 5 7 4775 77 8? 84 4905 7 09 12 *4 5o3 9 42 44 46 49 5179 81 84 86 88 5324 26 26 3i 33 5474 79 82 84 5795 97 58oo c3 06 i 2 3 4 6 8 _9 10 1 1 13 i3 i4 4o83 85 86 88 90 4192 9 4 9 5 97 99 4jo4 06 08 09 ii 4419 21 23 25 2 ~ 7 4537 3? 43 45 466o 62 64 66 68 4786 88 90 92 94 4916 18 20 23 25 5o5i 53 55 58 60 5191 9 3 95 9 5200 5336 38 4i 43 46 548 7 89 92 90 97 5644 $ 5o 52 55 58o 9 1 1 i4 17 20 5 6 8 9 4092 9 < 9 5 9" 99 4201 o3 o5 07 08 43i3 i5 17 9 21 4429 3i 33 34 36 4547 53 55 4670 72 74 76 78 4796 98 48ox o3 o5 4 9 27 3? 34 36 5o6 2 65 67 69 7' 52o3 o5 07 JO 12 5348 5i 53 56 58 55oo 02 o5 07 10 5658 60 63 66 60 5823 25 28 3i 34 lo 1 1 1 2 i3 M ;5 1 6 '7 18 19 i5 16 17 18 ; 9 4ioi o3 04 06 08 4210 12 i4 16 18 4323 25 27 28 3o 4438 4o 42 44 46 455 7 9 62 64 66 468o 82 84 87 89 4807 09 u i4 16 4 9 38 4o 43 45 47 5o 7 4 76 78 8 1 83 5214 17 9 22 24 536 1 63 66 68 7i 55 i 3 i5 18 20 23 5671 74 76 79 82 5837 39 42 45 48 20 21 22 23 24 25 26 2? a8 a 9 3o 3i 3^ 33 34 4i 10 I 2 i3 i5 17 4220 21 23 25 27 4332 34 36 38 4o 4342 44 46 47 49 4448 5o 52 54 56 4568 70 72 74 76 46 9 . 93 95 97 99 48i8 20 22 24 26 4949 5i 54 56 58 4960 63 65 67 69 5o85 88 90 92 9 5 5226 3? 34 36 53 7 3 76 78 80 83 5526 28 3i 33 36 "5537 4i 44 46 49 5685 87 90 93 9 5 56 9 8 6701 o4 06 09 585 1 54 56 59 62 20 21 22 a 3 24 25 26 27 28 29 4119 21 22 24 26 4728~ 3o 32 33 35 4229 Si 32 34 36 "4T38" 4<> 42 44 46 4458 60 62 64 66 45 7 8 80 82 84 86 4701 o3 o5 07 10 4829 3i 33 35 3 7 5o 97 - 99 DIO2 o4 06 5io8 ii i3 i5 18 5238 4i 43 46 48 5385 88 9 ? 9 3 95 53 9 8 54oi o3 06 08 5865 68 7i 74 76 435 1 53 55 57 59 4468 70 72 74 76 4588 90 92 g 4712 i4 16 18 20 483 9 42 44 46 48 4972 74 76 78 81 525o 53 55 58 60 5552 54 I 5 7 I2 i5 17 20 23 58 7 9 82 85 88 9' 3o 3i 32 33 34 35 30 38 '9 4i3 7 3 9 4i 42 44 4i46 48 5o 52 53 4247 53 55 436 1 63 65 67 69 4478 80 82 84 86 45 9 8 46oo 02 o4 06 4722 24 26 28 3i 485o 52 55 5 7 5 9 4983 85 87 9 92 5l2O 22 25 27 2 9 5263 65 67 70 72 TayB" 77 80 82 84 54u i3 16 18 21 ~5423~ 26 28 3i 33 5565 67 70 73 75 55 7 8 80 83 86 88 5 7 25 28 3i 34 36 ~^9 42 45 47 5o 58 9 4 96 , 99 5902 o5 35 36 37 38 39 4t> 4i 42 43 44 4a5 7 5 9 60 62 64 4370 72 74 76 78 4488 90 9 2 9 4 9 5 46o8 10 12 i4 1.6 4733 35 3 7 3 9 4i 486 1 63 65 68 70 4994 96 . 99 5ooi o3 5oo5 08 10 12 14 5i32 34 36 3 9 4i 5908 u i4 17 '9 4o 4i 42 43 44 40 46 4? 48 49 )O 5i 52 53 54 4i55 57 ? 61 62 4266 68 70 72 74 42 7 5" 77 79 81 83 4285" 7 89 9 1 92 438o 82 84 86 88 4497 99 45oi o3 o5 4618 20 23 25 27 4743 45 47 5o 52 4872 74 76 79 81 4"88T 85 87 9 92 5i43 46 48 5i 53 5287 89 92 94 97 5436 38 4i 43 46 5591 94 96 99 56o2 5 7 53 56 >8 61 64 5922 25 28 3i 34 45 46 47 48 49 464 66 68 70 72 4i73 75 77 79 81 43 9 o 92 94 96 98 45o 7 09 ii i3 1.5 4629 3i 33 35 3 7 4754 56 58 60 62 5oi7 19 21 23 26 5i55 58 60 62 65 52 99 53oi o4 06 09 5448 5i 54 56 5 9 56o4 07 10 12 i5 5-6 7 70 72 78 5 9 37 4o 43 46 48 5o 5i 52 53 54 55 56 57 58 59 M, >5 56 5? 58 5 9 43 99 44ui o3 o5 07 45i7 '9 21 23 25 "59 4639 4i 43 45 47 CO 4764 66 69 71 73 48 9 4 96 98 4901 o3 5028 3o 33 35 3 7 5i6 7 69 72 74 76 53ii i4 16 T 9 21 546 1 64 66 69 7i 5617 20 23 25 28 "67 5 7 8i 83 86 89 92 11 63 "GSP M. 56 57 i 58 61 62 63 64 65 66 68 TABLE III. FPa g r,< Meridional Farts. ;T 11 I 2 3 4 M o I a 3 4 70 71 W ~6i 46 55 58 7!! jo 73 74 6746 49 53 60 75 | 76 77 78 79 80 375" 81 87 93 98 81 52 58 65' 91 53 60 74 83 "9600 -4 22 3i 3 9 5966 69 72 75 78 6335 38 4i 45 48 6534 38 4i 45 48 6970 74 78 82 86 7210 i4 18 22 2 7 7 46 7 76 81 85 7745 54 59 64 8046 5i 56 61 6~ 5 6 8 9 6981 84 86 89 92 6161 64 67 70 73 ' 635 1 54 58 61 64 6552 55 58 62 65 6764 68 7* 75 79 0990 94 97 7001 o5 723l 35 3 9 43 4 7 7490 94 98 7 5o3 0-7 7769 74 78 83 88 8072 77 83 88 93 84o4 10 1 6 22 27 877. 78 84 9' 97 9182 89 9 () 9 2(>3 1 I 9 64 7 55 64 72 80 5 6 7 8 1 ; i i ) i3 i 7 ) 16 '7 18 '9 5995 98 OOOl o4 07 6i 77 80 83 86 89 63b 7 74 77 80 6569 72 76 8 6586 90 9 3 97 6600 6782 86 9 9 3 97 7009 1 3 17 21 25 56 60 64 68 7 DI2 16 21 25 3o 7793 98 7 8o3 08 i3 8099 8104 20 8433 3 9 45 5i 57 8804 1C) 17 23 3o 9218 25 33 4o 48 9689 97 9706 M 23 1 1 12 i3 6010 i3 16 22 6192 9 5 98 6201 o5 6208" 1 1 i4 '7 20 6384 87 90 94 97 6801 o4 08 12 16 7029 33 3 7 4i 45 7273 77 81 85 89 7 535 3 9 44 48 53 755 7 62 66 76 7 8. 7 22 2 7 32 3 7 8l25 3i 36 4i 47 8463 69 74 80 86 8836 43 49 56 63 9255 62 7 77 85 973. 4o 48 65 i5 16 .8 '9 20 :> ! 32 23 -4 a 5 26 a? 28 3n 33 .1; 6O25 28 3i 34 37 6o4o 43 46 6400 o3 7 10 i3 64 1 7 20 23 2 7 3o 66o3 07 10 i4 68i 9 23 26 3o 34 7048 52 56 60 64 7068 72 76 80 84 7 2 94 302 06 II -7842 4 7 52 5 7 62 7867 72 77 82 87 8i52 58 63 68 74 8492 98 85o4 JO 16 886 9 76 83 89 96 9 3oo 07 i5 22 9774 83 9' 9800 o? 35 44 52 20 21 2,3 M 6223 26 3o 33 36 6621 24 28 3r 35 6838 4i 45 7 3i5 3 28 32 7680 85 99 0179 85 90 96 8201 8522 28 34 4o 46 8903 1 6 23 3o 9 33o 3.7 45 53 60 ~9~368~ 76 83 9 1 99 25 26 28 39 3o 3i 32 33 34 6o55 58 6 1 64 67 6070 73 76 79 82 42 45 6433 37 4o 43 47 663 9 42 46 3 6856 60 64 68 7' 7088 92 96 7100 04 7 336 4i 45 3 7 6o3 08 12 17 22 7892 97 7902 07 12 8207 12 18 23 29 8234 4o 45 5i 56 "8262" 67 73 79 84 8552 58 65 77 8 9 36 43 5o 5 7 63 9861 70 IS 9_7 9906 i5 24 33 42 36 38 4i 43 44 45 40 47 48 49 5o 5 1 53 54 6255 58 61 64 68 645.) 53 5 7 60 63 6656 60 63 67 70 68 7 5 79 83 86 9 68 9 4 if 690, o5 09 7108 12 16 20 24 7 358 62 66 71 75 7626 3s 36 4o 45 7917 22 27 32 37 8583 89 8601 07 8970 77 84 9 1 98 9 4c>7 i4 22 3o 38 35 30 3- 38 608 5 88 9' 94 97 6271 74 77 80 83 646 7 70 73 77 80 66 7 4 77 81 85 88 7128 32 36 4o 45 7379 84 88 02 97 7 65o 54 5 9 64 68 7942 48 53 58 63 86i4 20 26 32 38 9005 I 2 18 25 32 61 69 77 99 5 ' go 69 78 87 4o 4i 42 43 44 45 46 47 48 49 6100 o3 06 09 12 628 7 9? 93 96 V9 6483 87 90 94 97 6692 9 5 6702 06 69 1 3 17 20 24 28 7149 53 57 61 65 7 4oi 06 10 i4 '9 7673 78 83 87 9 2 7968 73 78 83 89 8290 9 5 83oi 07 12 8644 5i 57 63 69 9039 46 53 60 67 9485 9 3 9 17 9996 10000 i oo 1 5 10024 ioo33 7oo43 10052 10061 10071 10080 6u5 18 21 " 63o3 06 I 63i 9 22 25 28 32 6boo o4 07 i4 6517 21 24 28 3i 6710 i3 17 20 24 6932 36 4o 43 47 7169 73 77 8. 85 74 2 3 27 32 36 4i 76 97 770?. 06 1 1 16 7994 99 8004 09 i4 83.8 24 29 35 4j 8670 82 88 9 5 8701 9074 81 88 96 9io3 91 10 17 24 3i 38 33 4i 49 5 7 5i 52 53 54 55 5t> 5 7 58 % M. 6i3o 33 36 4o 43 ~70 6728 3i 35 38 42 6 9 5i 55 5 9 63 66 7189 94 98 7202 06 7445 49 54 58 63 7721 9.5 3o 35 4o 8020 25 3o 35 834 7 52 58 64 69 8707 i4 20 20 33 81 ~82~ 10089 10099 10108 10118 101 2 7 ' 55 56 58 ^ 71 ,72 73 74 75 7f> 77 78 79 80 i'age78J TABLE VII. Amplitudes. DECLINATION. Lat. o cs rn xrtn co t^OO ON O - cs oo xr >n co t^-co ONC oi oo XT to xr m OO es r- es ro CO CO CO CO OO OO OO CO CO CO OO CO CO CC CO CO OO CO ON ON ON ON ON ON ONO C d o - -ooxrco CO O ro CO C xr ico 01 r- 01 co xr oi ro ro XT XT in - CO to OO C - oi ro xr 1 ON ON ON O n XT xrtn 01 ro xr r-- o xr in es r-r-r-r- t- r- r- r-r- r- t-r^ r- t- r- r- r- t- CO CO OO OO OO OO CO OO ON ON ON ON ONO 1 e\ r< S d o M _i 01 xrm r^ o cs to co o; ~ Oi O C to C to 01 oo oo XT XT tn t^oo c co to XT ) 01 es oj XT to 01 ro ixrtn >- es ro m oo - xrm - co cO cO CO cO co co co O CO CO O co r-r- t- i- t r^ t^oo co oo co OO OO ON a d o 1-1 *~ cs xrm >-c CN es es ro ro XT XT ro ONCO oo O r- to to Oi Oi CO XT ro ro ro ro oo xr m i o) co co co r- o r- XI AO ON oo xrm r^ r^ t^ tn tn in m m to to to to tn to to tn in to to to m tn m co co O ro ro ro ro ro oo ro oo i < 1 O O O C O O | CS Oi Oi 0) OO OO o xr xrm m co o r^ r^-co ON ON C - es Lat. cs ro xrn co r~-co ON c oi no xrm co r^co ON C - 01 ro xr 1 n co r-oc ON c - ro ! -0 oo ro TABLE VII l p *& Amplitudes. Lat. sss. r-00 ONO - es r. o ro ro XTXTXT ^ ~> XT m to r-oo 3-xTXrxrxrxT -. > O cs ro XT u g-m in in in 10 u ~) to r-oo ON o > in in in m to y 55SSSS QO 1 _S 'v S S a CS m ON u xr cs u - ON ON - XT -) cs XT -m es u ^^m^xTC^ N l>in 00 O ON|O -q M CN ro U o xr ONCO oo r- r o es m xrro xr ooo r-to m CO ON ON "S ro ro ro ro ro r s ro xr xr m to O ro ro ro ro ro |r r co ON o cs o o ro ro xrxr xr - o in to oo O es u sTxrxrxrinm u o oo m o oo o m to to r- r- 15 * cs in CO OO OO cs cs cs xr c ro o - XT - xr - XT o xr ro XT t^xr c - m ro m xr r O ro XT ONO t. O cs es es cs xr >. o o o c - xr n cs m ro cs cs v N o ro cs to cs q- cs es ro m -s cs ro ro ro ro Ir N cs ro xr xrm t. O ro ro ro ro ro c D r-oo ON o - O ro ro ro xr XT r cs xrin r- ON- r CO OO ON ON O O es ro xr I xr m o r-co ON o esroxrtoco orororororoirorororororolxrxrxrxTxrxr i O es m oo cs r- n m m m to to DECLINATION. 1 m 55 o r- t^co ro in - C ro CO XT - O ~vT cs in cs m O ro r-ro cs co cs m cs XT cs t^-ro ro to ro xr n XT ro eo ro O ONOO O t >q-m ro xr c to oo o ONn in to t o t-- r- r-co co ON ON O " es cs CN ro ro ro ro I o ro xrm to r- O ro ro ro ro ro xj ON cs xrm r> ro xr XT xr xr r- ON cs XT r- ^r XT in in in to s * esxr " - ro r- - r-xr cs XT ro m cs r> ro to O tO XT 1 n cs m ro XT n ONU-) m oo m cs in xrro ro o CN XT es r- o -o xr in ro cs to ro r- cs xr n xrm - - XT XT m n m to o o t- r-co oo ON o o - es es ro xrm T) ro ro ro ro ro O r-oo o ro o ro ro XT xr XT i xro oo - xr r- xr xr XT m m m 05 S 7^5 o xro ONTO ON es xr ro m cs m es m ro xr cs m xrro in to ro xj es oo ro ro xrm - ro m xrm es ro ro ro cs es es xr XT XT m m in CN cs es cs cs cs CN CS CS CS CS CS QS O >-i es ro xrm to r- ON o ro ro ro ro ro xr es ro in r- O ro XT xr XT xrm m 00 ^ *"* c ro O t- in - cs O m to t-- O XT xr cs XT ro O a m cs in ro " XT Is"* 3 m XT to ro XT O CN O ro ro ro xrm tO O XT ON ON r- ro - m xrm cs - cs cs CS CN CS cs ro ro ro xr XT cs cs es es es es m mm to O t^ ^,0^ CN ro XT in to oo ON- CS XTtO ON ro xr XT xr XT XT ^ r oo r-o to co o es xr CN XT - xr ONin ro ro m ro m es in es m co ro i- " XT O cs xr es in ro ro cs cs ro XT ^c^mxrin S S S S es es cs ro ro ro XT XT in m t6 l> l>00 ON ON O - es ro xrm ro ro ro ro ro ro r co O ( ^o in ro ro XT XT XT x- g ; m o m es xrm - oo to m m to - es xr es XT 6 o O - cs cs cs es cs es OO cs r-ro O O ro in cs in es cs' cs' cs' ro' ro xr cs CN cs cs es es XT ON^O to co m es m ro in xrin m to t r ro es xr >- t- XT ro es es es cs CO ON O es ro SN cs ro ro ro ro ON r-ro OO ro O ro m es m xrxr xfin r--cd O r 10 ^ s* : -^^ in o r-in ro ro m >- es XT cs XT cs m XT xrin t> es oo f- - xr m cs xrro es es xr xrro oo co co OO ON ON ON O Q _ M CS CS es CN es cs cs es ro ro xr XT m to es es es es cs es tO t^OO ONO - es es rs cs ro ro cs ro xr to r-: ON ^ ^ i 8 -^ oo ro oo to es o ro in e% XT r- r-cc oo co ON snssisii in ro es * in xrm to r-oo co es cs es es es cs m i- ro m ro ON cs ro XT to es ro ro ro ro ro I) o 2 * c ^ m o ON s; xrm . m m to cs \n o in o r- es ro m es ro in ro ro XT cs m cs m ro 6 6 O ~ es ""'xr'es' ^mxr ro ro xrin m to es cs es cs cs cs ro ro xj in - ro Ir-oo ONO es ro es es es ro ro ro ^ c S ro xrm XTXTXT m co m ONin ro XT m in m m m in to ro xr cs XT o to r- r- r-oo cs m - XT - XT 00 OO ON ON O O m es xrro - - es' ro' ro XT cs cs es CN cs es m o r--co ON c es es es cs es ro ^ c ^ 1 ro ro ro ON ro m o\ro XT es ro in r-ro ON t-m xr cs ro m ro in m m in to to O ro es in es in ro XT cs ON O^O - -* m m xrm m ro ro xr m to r- 3 es ro xrm to oo ro xrm ro XT co ro ONm cs xr m >- es XT ro ro xr xr xr m O - ro O es XT es XT u") in tO tO tO l> r-CO 00 ON ONO ONCS ONO tO tO in XT es es 6 - es ro xrm CS CS CS CS CN CV o 05 ' gS-* oo r- r- r-oo ON - cs ro xrm cs ro XT ro cs es es ro ro ro XT es XT cs ro' xf xr XT >n m m XT XT m to O r- r-co xr es m xrro CO O^O O - - - es cs es cs * QO ' 511* es 0>co co co 660600 CO ON ro to O in es ro xr Q I M M M (1 *C ro XT es xr es XT - XT - XT xr XT m m o xr - m ro - to r^ r-oo ON c O J^ _; t--ro O *5 CN ro XT ; oo oo oo 00 00 ON ON ON ON ON ON ON 6 6 6 xrm *. es xrm 6 6 - ro m xr cs cs es ro ro XT xrro XTOO to to ro ro XT es xf m* m' to to r- o to s "2" " ro ro xrin in t>- r- r- .> r-cc ~ es ro ro xrm CO 00 CO 00 CO 00 cs ro XT - ro xr cs XT Q 6 ' - - es cs m - xr - m es es ro ro XT x O lO s cl .'. ^ to too -J OPO r- "tO - to es oo xr CN cs ro ro XT in m P- cs cs ro xrm es m r- r- r-oo oo oo ixrco ro oo m es xrm - es xr 00 OO ON ON ON O m es ro XT es xr es m cs 6 6 - - o ^ o CO g m mm S XTXTXT in in m in m m " in oo N rn ON cs XT XT in *n in tO O m ON xr O 1 XT xr XT xr xr N T to' to' Q to to m O to ro ON C- ro xrxrinm xf xf xf xf XT m " xr cs O O O CN ro xrm m in m m m o 00 CO CO O ON ON - es ro m es tO O tO ro r- - in ONXT ro ro ro ro ro ro ro ro ro ro ro XT XT xrm m in es ro xr in xf xrxr xr N T xr "^co es r- (s co i 1 Lc t xrm to It- ro ro ro |*2 ro xrin to t cc xr xr xr XT XT xj ON o " es ro xr xrm in m in in ** to too to o o Pa g' 84 ] TABLE IX. a DECLINATION. Lat. -i cs ro XT in o i--co ox o - CN ro xrin o r-oo ox o - CN ro xj-m o r^ eft Qx C rd 05 1 i i 2 t. 1 'S Q cd "2 r* 3 .2 '** 0) rt -c c 3 '.:: J-l J i C QJ '5 "5 CO qj> 03 '< -^ ' *- C5 ^ M '5 t3 4 g eq i -a s si E N co m 000 r^ ox o cs xj- ^c - - - - co Ox- ro in f- CN CN XT in in in odd ood oooooo o_o o o o o :C CO z" - ro in OOOOOO 1 0*0 *0 o o - - 2 f2 r-co c cs xro cs cs co ro ro ro co CN co in CO C CS X7 in in in odd oooooo o o o. o o o OOOOOO O O O O O O 000 cS 1 coo O oo CN cs XT 000 o r- CN c cs XT n t-^ CN o cs XT ID oo Os ro in ro ro ro XT XT XT Xj XT *T! o o o oooooo oooooo oooooo OOOOOO O O O XT XT XT i o o o * o o"2 2*2 m o co CN > XT o r- CN c CN xro r^ CN ro ro ro ro ro XT XT d d o d d d oooooo oooooo OOOOOO o o o 2 = o o o r-oo -ro XT m r^co C. ro ^^T O r^ CN C 1 cs XT in r^ CN O cs XT o XT XT XT oooooo ododdd do'ddddldddddd 000 * S a cs ro O O O "0*0 "8 oo o* o CN ro xrm o r- CNO - CN ro XT in r^ co CN ro ro co. oooooo oooooo oooooo o d o o o o d_d_ Is-cVrc 2 3 cs ro 000 odd c*~> XT u~> O i^ cO oooooo d d d d d d o'o'S - 2^ xr'n ^ |j q q q odd ro XT n ir> o r- OOOOOO o'S'S ~ 2 ro XT XT mO r^tco CN CN ro OOOOOO oooooo oooooo lodoooo o 2 j o o o ro XT v - in o o C 000 [---CO CN CN C C n C C OXC C CN o ro XT XT in o O ~cs >71o~ro~xr^T -d d o o o o o o -rood o' d vo (>. 8;qq o o o m m o o (^ oo C C C C oo Ox Ox C C - - cs r^ ro XT XT oooooo d o' d d d d OOOOOO. do >o O & a Boo CN cs ro co co XT > ?'3'3<8 t <8 r^ [^ CO CC s CN 2 - 2! 2 ro ro X r OO OOOOOO oooooo OOOOOO o o o o o o O O O o io 3 000 CN CN cs ro ro 000000 XT xr XT in m ~> in o m c > ^rm m o o 1-1 O M t^-OO O CO '-J CN CN OO XT XT I- R c^e 1 r- i> o t> o r^ i - r^ i> r- r- t- i> r- r- r^ r- r^co co oo c O CO 00 CO CO CO C o o oj ^ 1 ir c rs^ *~^. ^ r ^ CN oo oo oo XT s oo XT og a oo m in m m K-^5 o"'^ ri-^IT^S'S o cs in ooo r^- 1 CN OO OO oo XT XT - o cm - o i o! o<."6 o m o O K j i csroj O '^j ** CO C CN xr m m OOO XT O CO O cs m m in m o c o r- c cs m co o CN XT r-. o oo r- - CN CS OO OO OO XT in ooo co oo co xr xr m m o o CO CO CO I Q ^0 ^ XT xr XT oo in r-o irooco ooo uomminm c|C 3 o O CN m co m CN CN cs oo ro co CN o m o oo XT XTUO m o ^ - - o ^ CN XTO i XT XT XT d d o* co o oo m r- 1 XT XT m uo m m o o o o o o 1 o r- r- r^ r- r- t-- r- r^ r- r- r- t^ r^ r- r^ r- r-co co OXT O xrm m DECLINATION. H ^ XT XT "XT in O CO C cs XT XT XT XT in n m o co o cs XT r- m m c C O O o CN XT r^ o oo O -, _ CS CN o oro t-- m CN CN OO OO XT XT o J2 ? (^ O C ro oo XT odd cs oo in r^co o xr XT XT XT xr m CN xr o co o cs m m m in c O XT r^ O cs xr r^ ooo o oo c^ o XT r~- CN CN CN OO OO OO XT XTUO o o o d o d O O O O r- r- r- r^ r- r- i~- r- r- r- t^ r- r-~ r- r- r- r-- SI J 3 "^ QJ 11 1 a 2 : ; XT O r^ioo csoom r- , ro oo oo OOXTXTXTXTXT co o CN XT o co XT m in m in uo 8cs XT r-- o o: C C - XT r^- o oo r^ o - CN CN CN 00 XT co o) oo oo XT j o 22 f o o o ; rs ro XT " ro oo oo i odd O r^oc csoo|inocxD c csoo ooooooxTXTXTXT'-srxTinmin o o o o o o 'o o o o o o m r- o CN XT o m in m o o o O O o r^ t^ r^ o XT t- c oo - - CN CN r$ r- r- r^ 2 ^ oo XTO r-co c oo oo oo oo oo XT ro XT O t^ O xr XT XT xr XT XT oo m r~ o in in in in in c oo O OO oo O O O O - - - o - I r-co o CN CN CN : do d c - CN XT m o ro ro ro oo oo ro d d d d d d oo oo XT XT XT XT d d o o o o ooo c TSXTOJCO o csxrr-o XTxrinminmin o O C C d d o o o o ! o r^ r^ r^ r- r^ r- r- r- o ? xTin o CN CN CS : do d r-~co o ^ oo CN CN CN ro oo oo d d d d d d XTUO r-oo o oo oo oo oo oo XT d o o o o o CN xr m K XT XT XT XT XT m d o o o o o CN XT o co oo m m m m o o o o o o r- r- r^ r- r- 00 cu 5 1' ^) 7} a 5 '3 2 s ^o J2 3 M W CQ o^ : \ ." in n o ."^co l^ CN CN CS CN CS CS OO OO OO OO OO OO oo o CN XT m oo oo XT XT XT XT XT XT m m in in mCO O t^ (^ GO * -OOO CN ro ro XT m O CM CN CN CN CS <% o o o o o o r-~co o o CN CN CN CS OO OO OO d d d d o d oo in o r- o c oo oo oo oo oo XT dddddd XTXTXTXTxrin m in m lo ooooo ooo. O f^ ' - ooo o o o o o o xrm m o r^oo CN CN CN CS CS Ol d d d o o o O i ^ x- m cs oo oo OO OO OO d o' o o o o ooroc-OXTXTXT XT XT xj 'odd odd o'oo o ~O _; xrn O 2 OOO o r--co co o o __-__ CS d d d d d d O cs cs ro XT CS CN CS CN CS CN d d d d d o rN CN CN CN r\ OO oo oo oo oo oo ro !od dodo oo XTXT o 10 ^ M ^3 -- 2 d d XT xr m m o o o o o o o o d o o o o o CN CN CS 0. CS CN o o o o o o CS CN CS CS 00 00 o o o o o o -, oj ro xrm oo oo oo d d o o r^cc O ^ _ O O O d d d d o '.c o o o o o o _ o' o o o o o o o o o CO ^-CO CO 5 cTp o d ddd CO CO O O O O o o o c o - o o o o o o d o o o o o d d d d d o ooo OO oo XT o oi ?i 'o'o'q ""OOO o d d o o o o c o'o'? kod do d o O C * d o o -d o o o o o o o o OOO ""o o c ooo 1888 c = odd ?"8S 8 o o o o o c d d d d d o o o o c o >_ o c o o o c ^ O 1 G^C^C o o o o o o 8 8 8 c d o o o do 8 c o o o c d d d o o o 8 C o O Lr .t. ir> oo o- ooooo^: ^ O CN oo XTK" XTXTXTXTXTX o o o o o 0 II 21 // 22 n 23 II 24 // 25 It 2(5 // 27 // 28 II 30 // 35 Alt. D. o 2 3 L 5 6 7 8 9 10 II 12 i3 i4 i5 16 17 18 19 JO 21 22 23 24 25 26 27 28 3o 35 10 . 2 3 L ' 5 6 7 8 10 1 1 12 i3 i4 i5 16 17 18 J 9 JO 21 22 23 24 2.5 26 27 v.8 3o 35 10 20 2 3 / f 5 6 7 8 8 9 10 II 12 i3 1 4 i5 16 17 18 9 2O 21 22 23 23 24 >5 26 28 33 20 3o 2 3 4 5 6 7 8 9 10 10 II 12 i3 i4 i5 16 16 7 18 19 2O 21 22 23 >.3 24 26 3o 3o 35 2 2 C ! 4 5 6 7 7 8 9 10 II II 12 i3 i4 i5 16 6 17 18 19 2O 20 21 1-2. 2,3 2.5 29 35 4o 2 2 ^ i 4 5 5 6 7 8 8 9 10 II I I 12 i3 i4 i5 t5 16 17 18 18 ] 9 2.0 21 21 23 27 4o 43 5 4 4 5 6 7 7 8 9 1C 10 II 12 i a i3 i4 i5 i5 16 17 18 18 19 2O 2O 22 2,6 43 46 \ 3 4 5 6 6 7 8 8 9 10 10 I I 12 i3 i3 i4 i5 i5 16 17 17 18 '9 IO 21 24 46 49 5 3 4 5 5 6 7 7 8 9 10 10 II 12 12 t3 i4 i4 i5 16 16 17 .8 18 20 23 4 9 52 s 3 4 4 5 6 6 7 7 9 9 10 10 I I 12 12 id i4 i4 i5 i5 16 17 17 18 22 52 55 i 3 3 4 5 5 6 6 7 7 8 o 10 10 I I I I 12 i3 i3 i4 i4 i5 1 5 16 17 20 55 58 8 3 3 4 4 5 5 6 6 7 7 8 8 o 10 10 I I II 12 12 i3 i3 i4 i4 i5 16 J 9 58 61 I 2 3 3 4 4 5 5 6 6 7 7 8 g 9 ro 10 II II 12 12 i3 i3 i4 i5 17 61 64 ) 2 3 3 4 4 4 5 5 6 6 7 7 7 8 8 9 9 10 10 I I 11 u 12 12 i3 i5 64 67 J 2 2 3 3 4 4 4 5 5 5 6 6 7 7 7 8 8 9 9 9 10 10 I I II 12 i4 67 70 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 8 8 8 9 9 9 10 10 12 70 72 I 2 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 6 7 7 7 8 8 8 n 9 II 77 74 I 2 2 2 2 3 2 3 4 4 4 4 5 5 5 6 6 6 6 7 7 7 7 8 8 10 74 76 I 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 8 76 78 I I 2 2 2 2 2 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6 6 6 7 78 80 1 I I 2 2 2 2 a 2 3 3 3 3 3 3 4 4 4 4 4 5 5 5 5 6 80 82 I I I I I 2 2 9 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 5 82 84 t) ( 3 I I I I j I I I I 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 4 84 86 < ) O I I I I I I I I I I j I I I 2 2 2 2 2 2 2 2 2 86 88 < ) O O O I I I I I I I I I I I I I I I I 88 90 ( 3 O O c O O O 90 Fagebaj TABLES XII, XIII, XIV, XV, AND XVI. TABLE Xll. The Refraction of the Heavenly Bodies in Altitude. TABLE XIII. pressiou or Dip of the Horizon of the Sea. TABLE XIV. The Sun's Parallax in Altitude. App. Alt. Ref. App. Alt. Ref. pp. It. ). Ref. leight of the Eye. Dip of the Horizon. Sun's AH. Sun's Parallax. D. M. VI. S. D. M. M. S. M. S. Feet. M. S. D. S. o. o o. 5 O.IO o.i5 0.20 0.25 o.3o o.35 o.4o o.45 53. o iu.ii 3l .22 3o.36 , 9 .5o 29. 6 28.23 27.41 27. o 26.20 6.3o 6.40 6.5o 7- o 7.10 7.20 7 .3o 7 .4o 7 .5o 8. o -7.52 7-41 7 .3i 7.21 7.12 7. 3 6.54 6.46 6.38 6.3o o i ' 2 33 34 35 36 3 7 38 39 i.38 .35 .3i .28 .24 .21 .18 .16 .i3 .10 Q Q 10 0.59 1.24 1.42 i.58 2.12 2.25 a.36 2.47 2.5 7 3. 7 10 20 3o 4o 5o 55 9 8 6 5 60 65 70 4 4 3 2 2 o.5o o.55 I . i. 5 I .10 i.i5 I .20 1.25 1 .3o i.35 25.42 2 5. 5 24 . 29 23.54 23.20 22.47 22. 15 i.44 :.i5 0.46 8.10 8.20 8.3o 8.4o 8.5o 9. o 9. 10 9.20 9-3o 9.40 6.22 6.i5 6. 8 6. i 5.55 5.49 5.43 5.3 7 5.3i 5.26 4o 4i 42 43 44 45 46 4 7 48 49 . 8 . 5 i. 3 i . i 0.59 0.57 o.55 o.53 o.5i o.5o 1 1 12 i3 i4 i5 16 i 7 18 1 9 20 3.16 3.25 3.33 3.4i 3.49 3.56 4. 3 4. ii 4.17 4.24 75 80 85 90 TABLE XV. Augmentation of the Moon's Semi-diameter. Moon's Alt Augment. D. S. i .4o 1.45 i.5o i.55 a. o a 5 2.10 2.l5 2.20 2.25 20.18 9 .5i 9 .25 i8.5o i8.35 18.11 i 7 .48 17.26 17- 4 i6.44 9.5o 10. o 10. i5 io.3o 10.45 II . 11. i5 ii .3o ii.45 12. 5.20 5.i5 5. 8 5. o 4.54 4-4 7 4-4i 4-35 4.29 4.20 !DO 5i 52 53 54 55 56 5 7 58 59 0.48 o.46 o.45 o.43 o.4i o.4o o.38 o.3 7 o.36 o.34 21 22 23 24 26 28 3o 35 4o 45 4.3i ' 4.3 7 4-43 4-49 5. i 5.i3 5.23 5.49 6.i4 6.36 5 10 il 20 25 3o 35 i 3 4 5 1 8 9 4o 45 5o 55 60 70 80 9 IO ii 12 i3 i4 i5 iS 16 2.30 2.35 2 ,4O 2.45 2 50 2.55 3. o 3. 5 3.io 3.i5 16.23 16 4 i5.45 15.27 i5. 9 i4-52 i4.35 14.19 i4. 3 i3.48 12.20 12.40 i3. o 13.20 i3.4o i4. o l4-20 i4.4o i5. o i5.3o 4.16 4. 9 4. 3 3.5 7 3.5i 3.46 3.4o 3.35 3.3o 3.23 60 61 62 63 64 65 66 6 7 68 69 o.33 O.32 o.3o 0.29 0.28 0.2 7 O.25 0.24 0.23 O.22 5o 60 70 80 9 100 6.58 7 .3 7 8.i4 8.48 9.20 9 .5i TABLE XVI. Dip of the Sea at different Distances from the Observer. 3.20 3.25 3.3o 3.4o 3.5o 4. o 4.10 4.20 4.3o 4.4o i3.33 13.19 i3. 5 12.39 12. I/ ii .5o 11.28 II. - 10.4? 10.28 16. o i6.3o 17. o 17. 3o 18. o i8.3o 19. o 19.30 20. 20. 30 3.i 7 3. 1 1 3. 5 2.59 2.54 2.49 2.44 2.40 2.36 2.32 70 7i 7 2 ?' 74 7 5 7 6 78 79 O.2 O.2O 0.19 O.I O.I O.I 0.1^ O.K O.I O.I 2 2 Height of the Eye above the Sea iu b cet. -W . far dis 2.28 2.2/ 2.20 2.1^ 2. 2. i.5 i .5 i.4 i.4 XVI.' n Table tanl as 80 8 82 83 84 8 86 8 8 8 Fhe i XII ,he la O.I o. o. 0. o. o. t O. i o. * o o. lumber I, the i nd :! 2 4 3 3 2 9 5 4 4 IO 8 6 12 10 8 7 14 10 12 l4 2 " 8 9 3 3J 4 5 2 2 2 2 3 3 3 MMB 3 4 4 \ 5 5 5 4 4 6 6 5 5 7 8 6 7 6 7 6 6 = ;r~ I 7 7 1 6 2 3 4 | 5 b o . of this~Tahle below the black lines, are the risible horizon, corresponding to. those heiffhts, * ' TABLE XXI. (Page 131 For turning Degrees and Minutes into Time, and the contrary. D. H. M. D. H. M. D. H. M. D. H. M. D. H. M D. H. M. M. M. S. M. M.S. M. M.S. M. M. S. M. M. S. M. M. S. i o. 4 61 4. 4 121 8. 4 181 12. 4 24 1 16. 4 3oi ac. 4 2 o. 8 62 4. 8 122 8. 8 182 12. 8 242 16. 8 302 2C. 8 3 0.12 63 4.12 123 8.12 i83 12.12 243 16. 12 3o3 20.12 4 o. 16 64 4.16 124 8.16 1 84 12. 16 244 16.16 3o4 20. l6 5 0.20 65 4.20 125 8.20 i85 12.20 245 16.20 3o5 20.2O 6 0.24 66 4.24 126 8.24 1 86 12.24 246 16.24 3o6 20.24 7 0.28 67 4.28 I2 7 8.28 187 12.28 24 7 16.28 3o 7 20.28 8 0.32 68 4.32 128 8.32 1 88 12.32 248 16. 32 3o8 20.32 9 c.36 69 4-36 I2 9 8.36 189 12.36 249 i6.36 3o 9 20.36 10 o,4o 70 4-4o r3o 8.4o 190 12.40 250 16.40 3io 20.40 1 1 o.44 7i 4-44 i3i 8.44 191 '12.44 25l 16.44 3ii 20.44 12 0.48 72 4-48 132 8.48 192 12.48 252 16.48 3l2 20.48 1 3 0.52 73 4.52 1 33 8.52 i 9 3 12.52 253 i6.5 2 3i3 20.52 i4 o.56 74 4.56 x34 8.56 194 12.56 254 i6.56 3r4 20.56 i5 . o 75 5. o 1 35 9. o i 9 5 i3. o 255 17. o 3i5 21. 16 . 4 76 5. 4 1 36 9. 4 .96 i3. 4 256 17. 4 3i6 21. 4 17 . 8 77 5. 8 i3 7 9. 8 197 i3. 8 25 7 17- 8 3i 7 21. 8 18 . 12 78 5.12 1 38 9.12 198 l3. 12 258 17.12 3i8 21 . 12 J 9 .16 79 5.i6 i3 9 9.16 199 i3.i6 25 9 17.16 3i 9 21. 16 20 .20 80 5.20 i4o 9.20 200 13.20 260 17.20 32O 21 .20 21 .24 81 5.24 i4i 9.24 201 i3.24 261 17.24 321 21 .24 72 .28 82 5.28 i4a 9.28 2O2 i3.28 262 17.28 322 21.28 23 .32 83 5.32 i43 9 .3 2 2O3 i3.32 263 17.32 323 21 .32 24 .36 84 5.36 1 44 9.36 204 i3.36 264 17.36 324 21.36 25 .4o 85 5.4o i45 9.40 205 i3.4o 265 17.40 325 21 .40 26 .44 86 5.44 1 46 9-44 206 i3.44 266 17.44 3 2 6 21.44 27 .48 87 5.48 1 4 7 9-48 207 i3.48 267 17.48 32 7 21.48 28 .52 88 5.52 1 48 9 .5 2 208 i3.5a 268 17-52 3 2 8 21.52 29 .56 89 5.56 1 49 9.56 209 i3.56 269 17-56 32 9 21.56 3o 2. 90 6. o i5o 10. o 2IO 14. o 270 18. o 33o 22. 3i 2. 4 9< 6. 4 i5r 10. 4 21 I ~i47~T 271 18. 4 33i 22. 4 32 2. 8 92 6. 8 152 10. 8 212 14. 8 272 18. 8 332 22. 8 33 2. 12 9 3 6.12 1 53 IO.I2 2l3 14.12 2 7 3 18.12 3J3 22. 12 34 2.16 94 6.16 1 54 10. l6 2r4 14.16 274 18.16 334 22.16 35 2.20 9 5 6.20 1 55 IO . 20 2l5 14.20 2 7 5 18.20 335 22.2O 3G 2.24 96 6 24 1 56 IO.24 216 14.24 276 18.24 336 22.24 37 2.28 97 6.28 i5 7 10.28 2I 7 14.28 277 18.28 33 7 22.28 38 2.32 V 8 6.3 2 1 58 IO.32 218 i4.32 278 18.32 338 22.32 3 9 2.36 99 6.36 i5 9 io.36 2I 9 i4.36 279 i8.36 33 9 22.36 4o 2.4o 100 6.40 1 60 10. 4o 220 i4-4c> 280 18.40 34o 22.4O 4i 2.44 101 6.44 161 10.44 221 14-44 281 i8.44 34i 22.44 42 2.48 102 6.48 162 10.48 222 14.48 282 18.48 342 22.48 43 2.52 io3 6.52 1 63 10.52 223 i4.52 2&3 18.52 343 22.52 44 2.56 104 6.56 1 64 io.56 224 i4.56 284 18. 56 344 22.56 45 3. o io5 7. o i65 II . O 225 i5. o 285 19. o 345 23. 46 3. 4 106 7- 4 166 ii. 4 226 i5. 4 286 19. 4 346 23. 4 47 3. 8 107 7. 8 167 ii. 8 227 i5. 8 287 19. 8 347 23. 8 48 3.12 :o8 7.12 1 68 II .12 228 l5. 12 288 19. 12 348 23.12 4 9 3.i6 109 7.16 169 ii. 16 22 9 i5.i6 289 19.16 34 9 23.16 5o 3.20 no 7.20 170 ii .20 230 1 5. 20 290 I9.2O 35o 23.20 ~irr 3.24 in 7-24 171 ii .24 23l i5.a4 291 19.24 35i 23.24 52 3.28 112 7.28 172 11.28 232 i5.28 292 19.28 352 23.28 53 3.3 2 :;3 7 .32 i 7 3 11.32 2 33 i5.32 293 19.32 353 23.32 54 3.36 u4 7.36 174 n.36 234 i5.36 294 19. 36 354 23.36 55 3.4o ii5 7-4o i 7 5 n.4o 2 35 i5.4o 296 19.40 355 23. JO 56 3.44 116 7-44 176 n.44 236 r5.44 2$6 19.44 356 23.44 57 3.48 117 7.48 177 n.48 23 7 1 5. 48 297 19.48 35 7 2 3 48 b8 3.52 118 7 .52 178 11.52 238 i5.52 298 19.52 358 23. 5a 59 3.56 119 7 .56 179 u.56 23 9 i5.56 299 19. 56 35 9 23.56 60 4. o 120 8. o r8o 12. 2.40 16. o 3oo 20. o 36o 24. o Page 132] TABLE XXII. s. h m (X h, m 1' h m W h m 3' h m 4' h m 5' h m 6! h m 7' h m 8 S o i 2 3 4 4.o334 3 7 324 5563 43i4 2.2553 2481 2410 234 1 2272 :. 9 542 9 5o6 9471 9 435 9400 1.7782 77^7 77 34 7710 7686 .6532 65i4 64 9 6 6478 646o 1.5563 5549 5534 5520 55o6 1.4771 4769 4747 4735 4723 i .4102 4091 4081 4071 4061 1.3522 35i3 35o4 3496 3486 o 2 3 4 5 , 6 8 9 3.3345 2553 1 883 i3o3 0792 2.22O5 2l39 2073 2009 1946 i . 9365 9 33 1 9296 9262 9228 1.7663 7 63 9 7616 7 5 9 3 7670 i .6443 6425 6407 63 9 o 63 7 2 1.5491 54 77 5463 5449 5435 1.4711 46 99 4688 46 7 6 4664 i .4060 4o4o 4o3o 4020 4o i o 1.3477 3468 345 9 34 5o 344 1 5 6 7 8 9 10 1 1 I 2 1 3 i4 3.o334 2.9920 9542 9195 fe8 7 3 2.i883 1822 1761 17.01 1642 1.9195 9162 912.8 996 9063 1.7547 7524 7601 7479 7456 1.6355 6338 6320 63o3 62.86 1.5421 54o 7 5393 5379 5365 1.4652 464o 4629 46i 7 46o6 i . 4ooo 3 9 8 9 3 979 3 9 6 9 3 9 5 9 1.3432 3423 34i5 34o6 33 97 10 ii 12 i3 i4 i5 16 17 18 '9 a.8573 8ao3 BoSo 7782 7547 2.i584 1 5 26 1469 Ui3 i358 i .903 1 8999 8967 8 9 35 8904 1.7434 74 12 73 9 o 7368 7346 i .626 9 6262 6235 6218 6201 i.535i 533 7 5324 53.o 5296 i .45 9 4 4582 457i 455 9 4548 i .3 9 4 9 3 9 3 9 3 9 2 9 3 9'9 3 9 io 1.3388 3379 33 7 i 3362 3353 i5 16 17 18 19 2O 21 22 23 a4 2.7324 71 12 69 1 o 6717 6532 2 . 1 3o3 1249 1 1 96 ii43 1091 i.88 7 3 8842 8811 8781 8 7 5. i .732.4 7 302 7281 7259 7238 i.6i85 6168 6i5i 6i35 6118 1.5283 5269 5256 5242 5229 i .4536 4525 45i4 45o2 4491 388o 38 7 o 386o 1.3345 3336 332 7 33i 9 33io 2G 21 22 23 24 a 5 26 7 28 29 2.6355 6i85 6021 5863 5710 2 . I 040 0989 O 9 3c; 0889 o84o i .8721 8632 8602 1.7217 7196 7 i 7 5 7 ' 54 7 i33 i .6102 6o85 6o6 9 6o53 6o3 7 i.5vi5 5202 5i8 9 5. 7 5 5 1 62 i.448o 4468 445 7 4446 4435 i.385i 384 1 383i 382i 38i2 j.33oi 32 9 3 32^4 3a 7 6 3267 25 2.6 27 28 29 3o 3i 32 33 34 2.5563 5421 5283 5i49 5019 2.0792 o 7 44 0696 0649 o6o3 1.8673 8544 85i6 848? 845 9 I .71 12 7091 7071 7060 7o3o i .6021 6oo5 5989 5 97 3 5 9 5 7 1.6149 5 1 36 5ia3 5no 6097 r.4424 44 12 44oi 4390 4379 i.38o2 37 9 2 3 7 83 3773 3 7 64 1.3269 32.5o 3242 32.33 3225 3c 3i 32 33 34 35 36 3 7 38 39 2.4894 477' 4652 4536 4424 2.o557 O5l2 0467 0422 0378 1.843! 84o3 8376 8348 8320 i . 70 1 o 6900 6970 6950 6 9 3o 1.6941 5 9 25 6909 58 9 4 58 7 8 i.5o84 5o 7 i 5o58 5o45 5o3 2 1.4368 435 7 4346 4335 4325 1.3754 3 7 45 3 7 35 3726 3 7 i6 i. 32i6 32.08 3 '99 3191 3i83 35 36 3 7 38 39 4o 4i 4a 43 44 2.43i4 4206 4l02 4ooo 3900 2.o334 0291 0248 0206 01 64 1.8293 8266 8239 8212 8i8f i . 69 1 o 6890 6871 685 1 6832 1.5863 5847 5832 58i6 58oi i .6019 5oo7 4994 4 9 8i 4 9 6 9 i.43i4 43o3 4202 4281 4270 i .3707 36 97 3688 3678 3669 i.3i 7 4 3 1 66 3.58 3i49 3i4i 4o 4i 42 43 44 4 r > 46 47 48 49 2.3802 3707 36i3 3522 3432 2.0122 Ou8l o<>4o oooo 1.9960 1.8169 8i33 8107 8081 8o55 1.6812 6793 6774 6 7 55 6 7 36 1.6786 5 7 7i 5 7 55 5 7 4o 5 7 25 i .4956 4943 4 9 3i 4918 4906 1.4260 4249 4238 4228 4217 i.366o 365o 364 1 3632 3623 i.3:33 3 1 2.4 3 1 16 3io8 3 1 oo 45 46 47 48 4 9 5o 5i 52 53 54 2.3345 3259 3i 7 4 8091 3oio I .9920 9881 9842 9 8o3 9?65 i.8o3o 8oo4 7979 7954 7929 i .6717 6698 6679 666, 664 2 I .5710 56 9 5 568o 5666 565 1 1.4894 488 1 4869 4856 4844 i .4206 4196 4i85 4i75 4i64 i .36i3 3*o4 3576 i 3091 3o3 3o 7 5 3o6? 3o5 9 f)<> 5i 52 53 54 re 55 56 5 7 58 K 2 293l 2852 2-775 2700 2626 1.9727 9600 9652 9615 9579 1.7904 7879 7 85$ 7 83o 7806 1.6624 66o5 658 7 6568 655o 1.5636 562i 56o 7 55 9 2 55 7 8 1.4832 4820 48o8 4 7 95 4783 i.4i54 4i43 4i33 4l22 4l 12 i .3567 3558 3549 354o 353i ! .OODI 3o43 : 3o34 '< 3o?.6 3oifi 56 57 58 59 S 0' 1' 2' 3 4' 5' & 7' H' S. TABLE XXII. [Pa,- 133 Proportional Logarithms. S. h m 9> h m 10' h m 11 h m 12' h m 13' h m 14' /* TO 15' h m 16' k m 17' 3. i 2 3 4 5" 6 6 9 10 ii 12 i3 i4 i ,3oio 3OO2 2994 2986 2978 1.2553 2545 2538 253 1 2524 i .2139 2l32 2126 2119 2Il3 1.1761 i 7 55 1749 1743 i 7 3 7 'i4o8 1402 i3 97 1391 i. 1091 1086 1081 1076 1071 1.0792 0787 0782 0777 o 77 3 I .O5l2 0507 0502 0498 0493 i .0248 0244 0240 0235 023l I .0297 0223 0219 0214 02IO I 2 3 4 1.2970 2962 2 9 54 2946 2 9 3 9 i.25i 7 25lO 2502 24 9 5 2488 I .2106 2080 i.i 7 3i I 7 25 1710 I 7 i3 1707 i.i386 i38o i3 7 4 1 369 1 363 i .1066 1061 io55 io5o io45 1.0768 o 7 63 o 7 58 o 7 53 0749 i .0489 0484 0480 0471 5 6 8 9 1.2931 2923 2915 2907 2899 i. 2481 2474 2467 2460 2453 I .2073 2067 2061 2o54 2048 l.I 7 OI 1695 1 683 i6 77 i.i358 i352 i34 7 1 342 1 336 i . io4o io35 io3o IO25 IO20 1.0744 o 7 3 9 o 7 34 0730 0725 1.0467 0^62 o458 o453 0449 I .0206 02O2 0193 0189 10- ii 12 i3 i4 i5 16 17 18 19 i5 16 18 1 9 1.2891 2 883 2876 2868 2860 r.2445 2438 243 1 2424 2417 i .2041 2o35 2028 2022 20l6 i.i6 7 i 1 665 1660 i654 1 648 '"iSaS l320 i3i4 1 309 i ,ioi5 1009 ioo4 0999 0994 i .0720 0715 0711 0706 0701 i.o444 o44o o435 o43 1 0426 I.OI85 0181 oi 7 6 OI 7 2 0168 20 21 22 23 24 1.2852 2845 283 7 2829 2821 i .2410 2 3o6 2389 2382 I . 2009 2003 1996 1990 1984 i .1642 1 636 i63o 1624 1619 i.i3o3 1298 1292 128-7 1282 1.0989 0984 0979 0974 0969 i .0696 0692 0687 0682 0678 i .0422 o4i8 o4i3 0409 o4o4 I .0164 0160 oi56 oi5i oi4 7 20 21 22 23 24 25 26 27 28 1.2814 2806 2798 2-791 2 7 83 i.23 7 5 2368 2362 2355 2348 1.1977 1971 i 9 65 i 9 58 1952 i6o 7 1 60 1 i5 9 5 i58 9 I .I2 7 6 I2 7 1 1266 I2OO 1255 1.0964 o 9 5 9 0954 0949 0944 1.0673 0668 o663 o65 9 o654 i .o4oo o3 9 5 0391 0387 o382 i.oi43 01 .3 9 oi35 oi3i 0126 25 26 27 28 29 CO CO CO CO CO 4X Co to O 1.2775 2768 2760 2 7 53 2 7 45 i.234i 2334 232 7 2320 2 3i3 1.1946 1939 i 9 33 1927 1921 r.i584 i5 7 8 l5 7 2 1 566 i56i i . 1 249 1244 1239 1233 1228 1.0939 0934 0929 0924 0919 i .0649 o645 o64o o635 o63i 1.0378 o3 7 4 o36 9 o365 o36o i .0122 0118 01 14 01 10 0106 3o 3i 32 33 34 35 36 3 7 38 39 1.2738 2700 2722 2 7 l5 2707 i .2307 23oo 2293 2286 2279 1.1914 1908 1902 i.i555 1 549 1 543 1 538 i532 I. 1223 I2I 7 1212 1207 I2OI 1.0914 0909 0904 0899 0894 i .0626 0621 0617 0612 0608 i.o356 o352 o347 o343 0339 i .0102 0098 0093 0089 0085 35 36 38 39 4o 4i 42 43 44 4o 4i 42 43 44 45 46 47 48 49 I .2700 2692 2685 2678 2670 I .2272 2266 2259 2252 2245 i.i883 i8 77 1871 1 865 i85 9 1.1626 l520 i5i5 i5o 9 i5o3 I .1196 II9I 1186 1180 n 7 5 i .0889 0884 0880 o8 7 5 0870 i.o6o3 o5 9 8 o5o4 o58 9 o585 i.o334 o33o o326 O32I o3i7 1.0081 00 77 oo 7 3 0069 oo65 1.2663 2655 2648 2640 2633 I .2239 2232 2225 22l8 2212 i.i85a 1 846 i84o i834 1828 1.1498 1492 i486 i48i i4 7 5 I . 1 1 7 1164 1 1 59 ii54 1149 i.o865 0860 o855 o85o o845 i .o58o o5 7 5 0571 o566 o562 i.o3i3 o3o8 o3o4 o3oo 0295 i .0061 0057 oo53 0049 oo44 45 46 47 48 49 So 5i 52 53 54 i . 2626 2618 2611 2604 2596 I .2205 2108 2192 2i85 2178 1.1822 1816 1809 T8o3 1797 1.1469 i464 i458 1 447 i.n43 n38 ii33 1128 1123 i .0840 o835 o83i 0826 0821 i .o55 7 o552 o548 o543 o53 9 I. 0201 0287 0282 0278 0274 i .0040 oo36 0032 0028 0024 bo 5i 52 53 54 55 56 57 58 5 9 1.2589 2582 2 5 7 4 256 7 256o i .2172 2i65 2 I 59 2l52 2i45 1.1791 i 7 85 1779 i 77 3 1767 'i436 i43o 1424 1419 i .1117 III2 1107 1 102 1097 i. 0816 0811 0806 0801 0797 i ,o534 o53o o525 O52I o5i6 1.0270 0265 0261 O25 7 O252 I .0020 0016 OOI2 0008 ooo4 55 56 57 58 5 9 S. 9* 10' 11' 12' 13' 14' 1.7 16' 17' S. Page 134] TABLE XXII. Proportional Logarithms. S. o i 2 3 4 5 6 8 9 m 18' m 19' h m 20' m h m )22' m m 24' h m 25' k m 26 / m h m 28' h m 29' S. o i 2 3 _4_ 6 8 10 ii 12 i3 i4 0000 9996 9992 Q9 88 99 84 7 65 7 6i 7 58 7 54 7 5o 9 542 9 53 9 9 535 9 53 2 933 1 9 32 7 9 320 9 3i 7 9 I28 9 I25 9 I22 9 II 9 9 n5 9 35 9^2 929 926 8923 8 7 5i 8 7 48 8 7 45 8 7 42 8 7 3 9 85 7 3 85 7 o 8568 8565 8562 84o3 84oo 83 97 83 9 5 8892 a3 9 234 23l 8228 808 1 8076 8073 8071 7929 7926 7924 7921 7916 7911 799 7906 9980 99-76 9972 9968 99 64 7 46 7 42 7 3i *& 9 bi 7 9 5i4 93i3 93io 9 3o6 9 3o3 9112 9109 9106 9102 9099 920 8917 8 9 i3 910 8907 8 7 36 8 7 33 8 7 3o 872-7 8-724 8559 8556 8553 855o 8547 838 9 8386 8384 838 1 83 7 8 8226 8223 8220 8218 8215 8068 8c66 8o63 8061 8o58 10 ii 12 i3 i4 9960 99 56 99 52 9948 9944 7 2 7 7 23 720 7 l6 7 I2 9 5o6 9 5o3 9 499 9496 9492 9296 9 2 9 3 9289 9286 9283 9096 9092 9 o83 8 9 o4 8 9 oi 88 9 8 88 9 5 889.2 8 7 2I 8 7 i8 8 7 i5 8 7 I2 8 7 o 9 8544 8542 8539 8536 8533 83 7 5 83 7 2 83 7 o 836 7 8364 8212 8210 $204 8o55 8o53 8o5o 8o48 8o45 -7904 79 o: 7899 7896 7894 i5 16 18 20 21 22 23 24 994 99 36 99 32 9928 9924 7 08 7 o5 701 9 6 97 9693 9488 9 485 948i 94 7 8 9 4 7 4 9279 9276 9272 9 26 9 9266 9079 9073 9070 9066 8888 8885 8882 88 79 88-76 8 7 o6 8 7 o3 3 7 oo 86 97 86 9 4 853o 852 7 8524 8522 8519 836i 835 9 8356 8353 835o 8i 99 8196 8194 3191 8188 8o43 8o4o 8o3 7 8o35 8o32 7891 7889 7884 7 882 i5 16 17 18 '9 0920 9916 9912 9908 99 o5 9686 9682 9678 9 6 7 5 9471 946 7 9464 9460 9 456 9262 9259 9,55 9252 92.49 9063 9060 9057 9 o53 9 o5o 88 7 3 88 7 o 886 7 8864 8861 86 9 i 8688 8685 8682 86 79 85i6 85i3 85io 85o 7 85o4 8348 8345 8342 8339 8337 8186 8i83 8181 8178 8175 8o3o 8027 8o25 8022 8020 7879 7 8 77 7874 7 8 7 2 7 86 9 20 21 22 23 24 25 26 27 28 2 9 25 26 27 28 29 9901 9897 9 8 9 3 9889 9885 9671 9667 9664 9660 9 656 9 453 9449 9 446 9 442 9439 9245 9242 9238 9235 9232 9 o47 9 o44 9 o4i 9037 9 o34 885 7 8854 885i 8848 8845 86 7 6 86 7 3 86 7 o 866 7 8664 85o2 84 9 9 8496 84 9 3 8490 8334 833 1 8328 8326 8323 8173 8i 7 o 8167 8i65 8162 8017 80 1 4 8012 8009 8007 7864 7862 7 85 9 7 85 7 3o 3i 32 33 34 35 36 3? 38 3 9 9881 9877 9 8 7 3 9869 9865 9652 964? 9645 9641 9 638 9435 9425 9421 9228 9225 9222 9218 9215 903 1 9028 9024 9021 9018 8842 883 9 8836 8833 883o 8661 8658 8655 8652 8649 848 7 8484 8482 84 7 9 84 7 6 8320 83i8 83i5 83i2 83o 9 8i5 9 8i54 8i52 8149 8oo4 8002 7999 7997 7994 7 852 7 85o 7 84 7 7845 3o 3i 32 33 34 9861 9 858 9 854 9 85o 9 846 9 634 963o 9626 9623 9619 9 4i8 9 4i4 9 4n 9 4o 7 9 4o4 9212 9208 9205 9201 9198 901 5 9012 9ooc 9005 9002 882 7 8824 8821 88i 7 8814 8646 8643 864o 863 7 8635 84?3 84 7 o 846 7 8465 8462 83o4 83oi 829.8 829.6 8i46 8i44 8i4i 8. 1 38 8 1 36 7992 7989 79.87 7 9 84 _798_i_ 7979 7976 79/4 79 6 9 7 84o 7 83 7 7 835 7 832 35 36 3 7 38 3 9 4o 4a 43 44 4o 4i 42 43 44 45 46 47 48 49 9 842 9 838 9 834 983o 9827 9615 9612 9608 9604 9601 9 4oo 9 3 97 9393 9390 9 386 9 i 9 5 9 i 9 i 9 i88 9 i85 9 i8i 8999 8996 8992 8989 8986 88n 8808 88o5 8802 8 799 8 79 6 8 79 3 8-^90 8 7 8 7 8 7 84 8632 8629. 8626 8623 8620 8459 8456 8453 845i 8448 82 9 3 829.0 8288 8285 8282 8i33 8i3i 8128 8125 9571 9 568 9 365 9 362 9 358 9 355 9 35 9 l62 9 i58 9 i55 9 l52 9 i48 8967 8 9 64 896 8 9 58 8 9 5 8 7 8i 8 77 8 8 77 5 8 77 2 8 7 6 9 8602 85 99 85 97 85 9 4 85 9 i 843 1 8428 8425 8423 8420 8266 8263 8261 8258 82.55 8107 8io4 8102 8099 8097 79 5 4 79 5: 794.9 7 9 46 79 44 7 8o3 7 8oi 7798 7796 97 8/ 9780 9777 977- 0700 9557 9 553 9 55o 9 546 9 348 9 344 9 34 933 o33 9 i45 9142 9 i38 9i35 8 9 5 8 9 4 8 9 45 8942 8 9 3 9 8 7 66 8 7 63 8 7 6o 8 7 5 7 8 7 54 8588 8585 8582 85 79 85 7 6 84i 7 84i4 84n 8409 84o6 8253 825o 8244 824 8094 8091 8089 8086 8o84 7941 7939 79 36 7934 79 3i 7794 779 77 8 9 7786 77 84 '029 S 1 19' 2 02 '02, 024 '025 . 02 027 028 S. TABLE XXIL l 1 '^ us Proportional Logarithms. S. A m o3(y A m 031' h m 32' h m h m 33 / | 34'' A m 035' A m 036 / A m 037' A m 38' A m 39' |A m 040' A m 41' S. c i 2 3 4 5 6 8 9 o 2 3 4 7782 7779 7777 7774 7772 7639 7 63 7 7634 7 63 2 7 63o 7 5oi 74 99 74 9 7 74 9 4 7492 7 368 7 365 7 363 7 36i 7 35 9 7238 7236 7234 7232 7112 7110 7108 7106 7104 6990 6988 6986 6984 6982 68 7 i 6869 686 7 6865 6863 6 7 55 6 7 53 6 7 5i 674 9 6 7 4 7 6642 66'4o 6638 663 7 6635 663T 663 1 6629 662-7 6625 6532 653o 6629 6527 6525 6425 6423 6421 6420 6418 5 6 7 8 9 7769 776 7 77 65 7762 7760 7627 7625 7623 7620 7618 7490 7488 7485 7483 748 1 7 35 7 7354 7 352 735o 7348 7227 7225 7223 7221 7219 7102 7100 7098 7096 7093 6980 6978 6976 6974 6972 6861 685 9 685 7 6855 6853 6 7 45 6 7 43 6742 6740 6 7 38 6523 652i 65i9 65i8 65i6 64 16 64 14 64i3 64ii 6409 10 ii 12 i3 i4 775 7 7755 7753 775o 7748 7616 76i3 7611 7609 7607 7479 7476 74 7 4 7 4 7 o 7346 7344 7339 7 33 7 7 335 7 333 7 33o 7 3 2 8 7 3 2 6 7217 7 2i5 7212 7210 7208 7089 7087 7o85 7 o83 6970 6968 6966 6964 6962 685 1 6849 684 7 6845 6843 6736 6734 6 7 32 6 7 3o 6728 6624 6622 6620 6618 6616 65i4 65i2 65 10 6509 65o 7 6407 G4o6 04o4 6402 64oo 10 ii 12 i3 i4 i5 16 18 20 21 22 23 24 7745 7743 774 1 77 38 77 36 7604 7602 7600 7597 7 5 9 5 746 7 7465 7463 746 1 7458 7206 7204 7202 7200 7198 7081 7079 7077 7075 7073 6960 6 9 58 6956 6 9 54 6 9 5 2 684 1 684o 6838 6836 6834 6726 6725 6723 6721 6719 6614 6612 6611 6609 66o 7 65o5 65o3 65oi 65oo 6498 63 9 8 63 97 63 9 5 63 9 3 63 9 r i5 16 17 18 19 7734 77 3i 7729 7726 7724 7 5 9 3 75 9 o 7 588 7586 7.583 7456 7454 7452 745o 7447 7 322 7 320 7 3i 7 7 3i5 7196 7i 9 3 7191 7189 7187 7071 7069 7067 7065 7063 6 9 5o 6 9 48 6 9 46 6944 6942 6832 683o 6828 6826 6824 6717 6 7 i5 6 7 i3 6711 6709 66o5 66o3 6601 6600 6598 6496 64 9 4 64 9 2 64 9 i 6489 63 9 o 6388 6386 6384 6383 20 21 22 23 24 25 26 27 28 7722 7719 7 7 i 7 7714 7712 7 58i 7579 7 5 77 7 5 7 4 7 5 7 2 7445 7443 744 1 7438 7436 7 3i3 7 3n 7 3oo 7 3oo 7298 7296 7294 7i85 7 i83 7181 7179 7177 7061 7059 7057 7 o55 7o52 6940 6938 6 9 36 6 9 34 6 9 32 6822 6820 6818 6816 6814 6708 6706 6704 6702 6 7 oo 65 9 6 65 9 4 65 9 2 6590 658 9 648 7 6485 6484 6482 648o 638 1 63 79 63 7 6 63 7 4 25 26 27 28 29 Co Co Co Co Co 4X Co (0 t-t CD 7710 7707 7706 77 o3 7700 7570 7 56 7 7 565 7 563 7 56o 7434 7 43 2 7429 7427 7425 7172 7170 7168 7166 7o5o 7 o48 7046 7044 7042 6 9 3o 6928 6926 6924 6922 6812 6810 6809 68o 7 68o5 6698 6696 66 9 4 6692 6691 "6689" 668 7 6685 6683 6681 658 7 6585. 6583 658 1 65 79 0478 64-6 64 7 5 64 7 3 64 7 i 63 7 2 63 7 i 6369 636 7 6365 "6364" 6362 636o 6358 635 7 3o 3r 32 33 34 35 36 11 3 9 7698 7696 76 9 3 7691 7688 7 558 7 556 7 554 7 55i 7423 74i8 74i6 74i4 7291 7289 7287 7 285 7283 7164 7162 7160 7i58 7 1 56 7040 7o38 7036 7034 7o32 6920 6918 6916 6914 6912 68o3 6801 6 799 6797 6 79 5 6578 65 7 6 65 7 4 65 7 2 6570 6568 656- 6565 6563 656 1 646 9 646 7 6466 6464 6462 35 36 38 4o 4i 42 43 44 "45" 46 47 48 49 4o 4i 42 43 44 7686 7 684 7681 7679 7677 7544 7 542 7 54o 7 538 7412 7409 7407 74o5 74o3 7281 7279 7276 7274 7272 7 !52 7149 7 i47 7 i45 7o3o 7028 7026 7024 7022 6910 6908 6906 6004 6 9 O2 6793 6 7 9i 6 7 8 9 6 7 8 7 6 7 85 66 79 66 77 66 7 6 66 7 4 66 7 2 646o 64 5 9 645 7 6455 6453 6355 6353 635i 635o 6348 45 46 47 48 49 7b74 7672 7670 7667 7665 7 535 7 533 7 53i 7 528 7 526 74oi 7 3 9 8 7 3 9 6 7 3 9 4 7392 7270 7268 7266 7264 7261 7i43 7 i4i 7139 7 i3 7 7 i35 7020 7018 7016 7014 7012 6 9 oo 6898 6896 68 9 4 6892 6 7 84 6782 6780 6778 6776 6670 6668 6666 6664 6663 6559 6558 6556 6554 6552 645 1 645o 6448 6446 6444 6346 6344 6343 634 1 6339 5o 5i 52 53 54 55 56 5 9 7 663 7660 7 658 7 655 7653 ?522 75i 9 7 5i 7 75i5 7390 738 7 7 385 7 383 7 38i 7259 7255 7253 7 25l 7 i33 7 i3i 7129 7127 7124 7010 7008 7006 7004 7002 6890 6888 6886 6884 6882 6 77 4 6772 6770 6768 6766 6661 665 9 665 7 6655 6653 655o 6548 654 7 6545 6543 6443 644 1 643 9 643 7 6435 6338 6336 6334 6332 633 1 5o 5i 52 53 54 IT" 56 57 58 S. 765 1 7 648 7 646 7 644 7 5i3 7 5io 7 5o8 7 5o6 7 5o3 7 3 79 7376 7374 7 3 7 2 7 3 7 o 7249 72.46 7244 7242 7240 033' 7122 7120 7118 7116 7114 7000 6998 6996 6 99 4 6992 6881 6879 6877 68 7 5 68 7 3 6764 6 7 63 6761 6 7 5 9 6757 665 1 665o 6648 6646 6644 654 1 6539 6538 6536 6534 6~39' 6434 6432 643o 6428 6427 632 9 6327 6325 6324 6322 S 0?W 31' 32' 34'iO 35'' 36'jO 37' 38' 40'JO 41' ^ 13UJ TABLE XXII. Proportional Logarithms. S. i 2 3 4 5" 6 j 8 9 10 n 12 i3 i4 "i5 16 17 18 ]9 h m h in 42' 43' h m 044' h m 045' k m 046' h m 047' h m 48' h m Q49' h m Q50 h m 051 h m 052' h m 053' S. o 2 3 4 ~r 6 8 9 63 20 63 r 9 63i 7 63 1 5 63 1 3 6218 6216 62i5 6213 621 1 6118 61 17 6n5 6u3 6112 61 10 6108 6107 6io5 6io3 6021 6019 6017 6016 6014 5925 5924 5922 5920 5 9 i 9 583a 583o 582 9 5827 5826 5 7 4o 5 7 3 9 5 7 3 7 5 7 36 5 7 34 565 1 564 9 5648 5646 5645 5563 5562 556o 555 9 555 7 5477 5476 5474 5473 5471 53 9 3 53 9 i 53 9 o 538 9 538 7 53io 5309 53o 7 53o6 53o5 63 1 2 63io 63o8 63o6 63o5 6210 6208 6206 6205 6203 6oi3 6011 6009 6008 6006 5917 5 9 i6 5 9 i4 5913 591 1 5824 5823 582i 58i 9 58i8 5 7 33 5 7 3i 5 7 3o 5 7 28 5727 5643 5642 564o 563 9 563 7 5556 5554 5553 555i 555o 5470 5469 546 7 5466 5464 5386 5384 5383 5382 538o 53o3 53o2 53oo 52 99 5298 63o3 63oi 63oo 6298 6296 6201 6200 6198 6196 6195 6102 6100 6099 6097 6o 9 5 6oo5 6oo3 6001 6000 5 99 8 5909 5 9 o8 5 9 o6 5 9 o5 5903 58i6 58i5 58i3 58i2 58io b 7 2b 5 7 24 5 7 22 5 7 2I 5719 5636 5635 5633 5632 563o 554 9 554 7 5546 5544 5543 5463 546 1 546o 545 9 545 7 63 79 53 77 53/6 53 7 5 53 7 3 5296 52 9 5 52 9 4 52 9 2 52 9 1 52 9 5288 528 7 5a85 5s84 10 1 1 12 i3 i4 6294 6293 6291 6289 6288 6193 6191 6190 6188 6186 6094 6092 6090 6089 6087 ^997 *"l 5 99 3 5 99 2 D 99 o 5902 5900 58o8 58 97 58 9 5 58o 9 58o 7 58o6 58o4 58o3 5718 5 7 i6 5 7 i5 5 7 i3 5 7 I2 562 9 562 7 5626 5624 5623 554 1 554o 5538 553 7 5536 5456 5454 5453 5452 545o 53 7 2 53 7 o 536 9 5368 5366 "5365" 5364 5362 536 1 535 9 ~5358~ 535 7 5355 5354 5353 i5 16 *7 18 _L?__ 20 21 22 23 24 20 21 22 23 24 6286 6284 6282 6281 6279 6 2 ~77 6276 6274 6272 6271 6i85 6.83 6181 6179 6178 6o85 6084 6082 6081 6079 5 9 8 9 5 9 8 7 5 9 85 5 9 84 5982 58 9 4 5892 58 9 i 5889 5888 1)886" 5884 5883 588 1 588o 58oi 58oo 5798 5796 5 79 5 5 7 io 5 7 o 9 5 7 o 7 5 7 o6 5 7 o4 562i 5620 56i8 56i 7 56i5 5534 5533 553i 553o 5528 5449 5447 5446 5445 5443 5283 5281 5280 52 79 52-77 25 26 27 28 2 9 3o 3i 32 33 34 6176 6174 6; 7 3 6171 6169 6077 6076 6074 6072 6071 5 9 8i 5 979 5977 5 97 6 5 97 4 5 79 3 5 79 2 5 79 o 5 7 8 9 5787 5 7 o3 5 7 oi 5 7 oo 56 9 8 56 97 56i4 56i3 56n 56io 56o8 552 7 55 2 6 5524 5523 552i 5442 544o 543 9 543 7 5436 52-76 52 7 5 5 2? 3 52"'2 52 7 I 25 26 7 28 29 6269 6267 6265 6264 6262 6168 6166 61 65 6i63 6161 6069 6067 6066 6064 6o63 5 97 3 5 9 7i 5 9 6 9 5 9 68 5 9 66 58 7 8 58 77 5875 58 7 4 58 7 2 5 7 86 5 7 84 5 7 83 5-8 1 5 7 8o 56 9 5 56 9 4 56 9 2 56 9 i 568 9 5607 56o5 56o4 56o2 56oi 5520 55i8 55i 7 55i6 55 1 4 5435 5433 543 2 543o 5429 535i 535o 5348 534 7 5346 520 9 5268 52.66 5265 5264 3o 3i 32 33 34 35 36 37 38 39 6260 6259 6257 6255 6?54 6160 61 58 6i56 6i55 6i53 6061 6o5 9 6o58 6o56 6o55 5 9 65 5^3 5 9 6i 5 9 6o 5 9 58 58 7 o 586 9 586 7 5866 5864 5778 5777 5775 5774 5 77 2 5688 5686 5685 5683 5682 55 99 55 9 8 55 9 6 55 9 5 55 9 4 55i3 55ii 55io 55o8 55o 7 5428 5426 5425 5423 Szfea 5344 5343 534 1 534o 533 9 5262 5261 5260 5258 525 7 5256' 5254 5253 5252 5u5o 35 36 II 3 9 4o 4i 42 43 44 45 46 47 48 49 6252 6 2 5o 6248 62.47 6245 6i5i 6i5o 6i48 6i46 6i45 6o53 6o5i 6o5o 6t>48 6046 5 9 5 7 5 9 55 5 9 54 5932 5950 5863 586 1 586o 5858 5856 5 77 i 5 7 6 9 5 7 68 5 7 66 5 7 65 568o 56 79 56 77 56 7 6 56 7 4 55 9 2 5589 5588 5586 55o6 55o4 55o3 55oi 55oo 5421 54i 9 54i8 54i6 54i5 533 7 5336 5335 5333 5332 4o 4i 42 43 44 62.43 62.42 6240 6238 6237 6:43 6i4i 6i4<> 6i38 6i36 6o45 6o43 6042 6o4o 6o38 ^949 5947 5 9 46 5 9 44 5 9 42 5855 5853 5852 585o 584 9 5 7 63 5 7 6i 5 7 6o 5 7 58 5 7 5 7 56 7 3 56 7 i 56 7 o 566 9 566 7 5585 5583 5582 558o 55 7 9 5498 5497 5496 5494 5493 54i4 54i2 54n 54o 9 54o8 533 1 532 9 5328 532-6 5325 524 9 5248 5246 5245 5244 45 46 47 48 49 5o 5i 52 53 54 6235 6233 6232 62 3o 6228 6i35 6i33 6i3i 6i3o 6128 6037 6o35 6o33 6o32 6o3o 5941 5 9 3 9 5o38 5 9 36 5935 584 7 5846 5844 5843 584 1 5 7 55 5 7 54 5 7 5 2 5 7 5i 5 7 4 9 5666 5664 5663 566 1 566o 55 7 8 55 7 6 55 7 5 55 7 3 55 7 2 5491 5490 5488 548 7 5486 54o 7 54o5 54o4 5402 54oi ~54oo~ 53 9 8 53 97 53 9 5 53 9 4 5324 5322 532i 5320 53i8 5242 5241 524o 5238 523 7 5o 5i 52 53 C4 55 56 57 58 _. 5 ?_ S. 55 56 5? 58 _rL s. 6226 6225 6223 6221 6220 6126 6 iv. 5 6123 6121 6120 6029 6027 6025 6024 6022 5 9 33 5 9 3i 5 9 2o 5 9 a8 5927 583 9 5838 5836 5835 5833 5 7 48 5 7 46 5 7 45 5/43 5 7 42 5658 565 7 5655 5654 5652 55/0 556 9 556 7 5566 5564 5484 5483 548 1 548o 5478 Wi 7 53i5 53i4 53i3 53ii 5235 5 2 34 5233 523i 523o 42' 43'|0 44' 45' 46'iC 47' 48'|0 4v' 50' 51 'JO 52 / iO 53' TABLE XXII. [Page 137 Proportional Logarithms. 8. h m 054' h m tt h in 05& h m 057 / k m 058' k m 59' h m i7' 48 5o 4849 4848 484 7 4845 4 777 4 77 6 4 77 5 4 77 4 4 77 2 4705 4 7 o4 4 7 o3 4 7 02 4 7 oi 4635 4633 4632 463 1 463o 4565 4564 4563 4562 456o 449-7 44 9 5 4494 4493 4492 442 9 44?8 442 7 4426 4425 4363 4362 436 1 435 9 4358 55 56 57 58 59 S. 54' 55' 58' 10 50' ]0' 1 1' 12- 13' 14' i5' rage 138] TABLE XXII. Proportional Logarithms. S. h m 435 7 4356 4355 4354 4353 h m h m h m 1 9' h m 1 Q 10' h m 1 11' h m 1 12' h m 1 13' h m L 14' h m 10 1 r/ h m P16' h m S. o i 2 3 4 4292 4291 4290 4289 4288 4228 422-7 4226 4224 4223 4i64 4i63 4162 4i6i 4 160 4lO2 4101 4ioo 4099 4098 4o3 9 4o3ti 4o3 7 4o36 ^979 3978 397-7 3976 3 97 5 3 9 i 9 3 9 i 9 3 9 i8 3 9 i 7 3916 386o 385 9 3858 385 7 3856 38o2 3801 7800 3799 3798 3 7 45 3744 3 7 43 3 7 42 3 7 4i 3688 368 7 3686 3685 3684 i a 3 4 5 6 8 5 6 7 8 9 4352 435i 435o 4349 434 7 428 7 4285 4'->84 4283 4282 4222 4221 4220 4219 4218 4i5 9 4i58 4i5 7 4i56 4i55 409-7 4096 4093 4092 4o35 4o34 4o33 4o32. 4o3i 3974 3 97 3 3971 3970 3915 3 9 i4 3 9 i3 3 9 I2 3 9 i i 3856 3855 3854 3853 3852 3797 3796 3-794 3-793 3 7 4o 3 7 3 9 3738 3 7 3 7 3 7 36 3683 3682 368 i 368o 36 79 10 1 1 12 i3 i4 4346 4345 4344 4343 4342 4281 4280 42-78 4277 42I 7 4216 4214 4i54 4i53 4i52 4i5i 4i5o 4091 fooo 4089 4o88 4o8 7 4o3o 4029 4028 4027 4026 3 9 6 9 3 9 68 3 9 6 7 3 9 66 3 9 65 3 9 io 3 99 3 9 o8 3 9 o6 385 1 385o 384 9 3848 384 7 3 7 92 3 7 92 3-791 3-790 3 7 8 9 3 7 35 3 7 34 3 7 33 3 7 3a 3 7 3i 36 7 8 36 77 36 7 7 3676 36 7 5 10 H 12 i3 i4 ib 19 20 21 22 23 24 1 5 16 18 1 9 434i 434o 433o 4338 4336 4276 4275 4274 4273 4271 4212 4211 4210 4209 4207 4149 4i47 4i46 4i45 4i44 4o86 4o85 4o84 4o83 4082 4025 4024 4023 4022 4021 3 9 64 3o63 3962 3o6r 3960 3 9 o5 3 9 o4 3 9 o3 3 9 02 3 9 oi 3846 3845 3844 3843 3842 3 7 88 3 7 8 7 3 7 86 3 7 85 3 7 84 3 7 3o 3 7 2 9 3 7 28 3 7 2 7 3 7 2 7 36 7 4 36 7 3 36 7 2 36 7 i 36 7 o 20 21 22 23 24 25 26 2 7 28 2 9 3o 3i 32 33 34 " 35 36 3 7 38 39 4o 4i 42 43 44 4335 4334 4333 4332 433 1 4270 4269 4268 4267 4266 4206 4205 4204 4203 4202 4i43 4142 4i4o 4i3 9 4i38 4i3 7 4i36 4i35 4i34 4081 4o8o 40-79 4o 7 8 4o 77 4020 4oio 4oi8 4017 4oi6 3958 395 7 3 9 56 3 9 55 3 900 38 99 38 9 8 38 97 38 9 6 384 1 384o 383 9 3838 383 7 3 7 83 3 7 8 2 3 7 8i 3 7 8o 3 77 9 3-726 3 7 25 3 7 23 3 7 22 366 7 3666 3665 433o 432 9 432 7 4326 42.65 4264 4263 4262 4261 ^260 4259 4258 4 2") 6 42.55 4201 4200 4'99 4198 4197 4o 7 6 4o 7 5 4o 7 4 4o 7 3 4o 7 2 4oi5 4oi4 4oi3 4012 4oi i 3 9 54 3 9 53 3952 3 9 5i 3950 3895 38 9 4 3893 38 9 2 38 9 i 3836 3835 3834 3833 3832 3 77 8 3-777 3776 3775 3774 3 7 2I 3 7 2O 3 7 i 9 3 7 i8 3 7 i 7 3664 3663 3663 3662 366 1 25 2.6 2 7 28 4325 4323 4322 432i 4320 4196 4190 4194 4192 4i33 4 1 32. 4i3i 4i3o 4129 4o 7 i 4o 7 o 4069 4068 4o6 7 4oio 4009 4oo8 4007 4oo6 3949 3 9 48 3 9 4 7 3 9 46 3 9 45 38oo 3889 388 7 3886 383 1 383o 382 9 38 2 8 382 7 3 77 3 3772 3 77 i 3 7 7o 3 7 6 9 3716 3 7 i5 3 7 i4 3 7 i3 3 7 I2 366o 365 9 3658 365 7 3656 3o 3i 32 33 34 43i8 43i 7 43i6 43i5 4254 4253 42.5a 425i 4191 4i8 9 4i88 4i8 7 4i86 4128 4127 4126 4 1 2.5 4124 4o66 4o65 4o64 4o63 4062 4oo5 4oo4 4oo3 4OO2 4ooi 4ooo 3999 3 99 8 3997 3 99 6 3 9 44 3 9 43 3 9 4i 3940 3885 3884 3883 3882 388 1 3826 3825 3824 3823 3822 382i 3820 3820 38i 9 38i8 3768 3 7 68 3 7 6 7 3-66 3 7 65 3 7 u 3 7 io 3 7 o 9 3 7 o8 3655 3654 3653 3652 365i 35 36 38 39 43i4 43i3 43 ii 43io 4309 4249 4248 4'M7 4246 4245 4r85 4i84 4i83 4182 4i8i 4l22 4l2I 4 1 20 4119 4118 4061 4<>6o 4o5 9 4o58 4o56 3 9 3 9 3 9 38 3 9 3 7 3 9 36 3 9 35 388o 38 7 9 38 7 8 38 7 7 38/6 3 7 64 3 7 63 3 7 62 3-6i 3 7 6o 3 7 o 7 3 7 o6 3 7 o5 3 7 o4 3 7 o3 365o 364 9 3649 3648 364 7 4o 4i 42 43 44 45 46 4 7 48 49 5o 5i 53 54 43o8 43o 7 43o6 43o5 43o4 4244 4243 42.3 9 4 1 80 4178 4177 4176 4117 4u6 4u3 4o55 4o54 4o53 4o5i ^995 3 99 3 3 99 2 3 99 i 3990 3 9 34 3 9 33 3 9 3a 3o3i 3930 38 7 5 38 7 4 38 7 3 38 7 2 38 7 i 38i 7 38i6 38i5 38i4 38i3 3 7 5 9 3 7 58 3 7 5 7 3 7 56 3 7 55 3 7 o? 3 7 oi 3 7 oo :i6 99 35 9 8 3646 3645 3644 3643 364 2 45 46 4 7 48 4 9 5o 5i 52 53 54. 43o3 43oi 43oc 429-7 4296 4294 4293 42.38 4^35 j 4234 4.75 4i 7 4 4172 4171 4i 12 4iio 4109 4io8 4o5o 4049 4o48 4o4 7 4o46 3 9 8 7 3 9 86 3 9 85 3929 3928 3 9 26 3 9 25 38-70 386 7 3866 38i2 38n 38io 38o 9 38o8 3 7 54 3 7 53 3 7 52 3 7 5i 3 7 5o 36 97 3fio6 36 9 5 36 9 4 36 9 3 364 1 364o 3639 3638 363 7 55 56 5 7 58 59 S. ]4233 4232 42.3 1 423o 4220 4169 4168 4167 4 1 66 4i65 4107 4io6 4io5 4104 4io3 1 9' 4o45 4o44 4o43 4o4i JMO" 3 9 84 3 9 83 3982 3 9 8i 3 9 8o 3 9 24 3 9 2.3 3 9 22 3 9 2I 3 9 20 3865 3864 3863 386?. 386 1 38o 7 38o6 38o5 38o4 38o3 3 7 49 3 7 48 3 7 4 7 3 7 46 36 9 3 36 9 i 36oo 368 9 3636 3635 3635 3634 3633 55 56 5 7 58 "h. 1()' I7' 18' 1 11' 1 12 jo 13/1 o 14 / 1 15' 1 16' 1 17' TABLE XXII. ii'ageisg Proportional Logarithms. S. h m 3 18' h m 1 C 19' ;* m i2 9 3 3o 9 2 3o4 7 3o46 3o45 3o44 3o43 i5 16 17 18 ]9 20 21 22 23 24 36 1 3 36i2 36n 36 10 36io 3558 355 7 3556 3555 3555 35o4 35o3 3502 35oi 35oo 345o 344 9 3448 344 7 3446 33 97 3396 33 9 5 33 9 4 33 9 3 3345 3344 3343 3342 334i 32 9 3 32 9 2 32 9 I 32 9 328 9 3242 3241 3 240 323 9 3238 3i 9 i 3i 9 o 3iSa 3i88 3i88 3i4i 3i4o 3i3 9 3:38 3i38 3i37 3i36 3i35 3i34 3i33 3o 9 i 3o 9 i 3o 9 o 3o8 9 3o88 3o43 3042 3o4i 3o4o 3o3 9 20 21 22 23 24 25 26 7 2 9 36oo 36o8 3607 36o6 36i,5 3554 3553 3552 355i 355o 34 9 9 3498 3497 34 97 34o6 3446 3445 3444 3443 3442 33 9 3 33 9 2 33 9 i 33 9 o 338 9 334o 333 9 3338 3338 333-7 3288 3288 3 3 8 7 3286 32.85 3237 3236 3236 3235 3234 3i8 7 3i86 3i85 3.84 3i83 3087 3o8 7 3c86 3o85 3o84 3o3 9 3o38 3o3 7 3o36 3o35 2.5 26 27 28 2 9 3o 3i 32 33 34 3o 3 1 32 33 34 36o4 36o3 36o2 36or 36oo 354 9 3548 354 7 3546 3545 34 9 5 34 9 4 34 9 3 34 9 2 34 9 i 344 1 344o 343 9 3438 3438 3388 3387 3386 3386 3385 3336 3335 3334 3333 3332 3284 3283 3282 3282 3281 3233 3232 323i 323i 323o 3i83 3i82 3i8i 3i8o 3 1 79 3i33 3i32 3i3i 3i3o 3l2 9 3o83 3o8a 3o82 3o8i 3o8o 3o34 3o34 3o33 3o3 2 3o3i 35 36 3 7 38 39 35 99 35 9 8 3598 35 97 3596 3545 3544 3543 3542 354i 3490 348 9 3488 3488" 348 7 343 7 3436 3435 3434 3433 3384 3383 3382 338. 338o 3332 333i 333o 332 9 3328 3280 32 79 3278 3277 32 7 6 322 9 3228 322 7 8226 3225 3i 7 8 3 1 78 3i77 3i 7 6 3i 7 5 3 1 2 9 3i28 3l2 7 3i26 3i25 1724 3ia4 3i23 3l22 3l2I 3o 79 3o 7 8 3o 7 8 3o 77 3o 7 6 lo^S 3o-4 3o 7 3 3o 7 3 3o 7 2 3o3o 3o3o 3o2 9 3028 302 7 Iol6~ 3o26 3o2.5 3024 3o23 35 36 37 38 3 9 4o 4i 42 43 44 35 9 5 35 9 4 35 9 3 3592 3591 3590 358 9 3588 358 7 3587 "3586" 3585 3584 3583 3582 354o 3539 3538 353 7 3536 3486 3485 3484 3483 3482 3432 343 1 343 1 343o 34 2 9 33 79 33 79 33 7 8 33 77 33 7 6 332 7 33 ?6 3325 3325 3324 32 7 6 32 7 5 32 7 4 32 7 3 3272 322.5 32.24 322.3 3222 3221 3 1 74 3i 7 3 3i 7 3 3172 3i 7 i 4o 4i 42 43 M 45 46 47 48 49 45 46 47 48 4 9 3535 3535 3534 3533 3532 348i 348o 348o 34~ 9 3478 3428 3427 3426 3425 3424 33 7 5 33 7 4 33 7 3 33 7 2 33 7 2 332.3 3322 332i 3320 33r 9 32 7 I 32 7 32 7 326 9 3268 3220 3220 32I 9 32 1 8 32i 7 3i 7 o 3i6 9 3 1 68 3i68 3i6 7 3 1 20 3i i 9 3i i 9 3n8 3.i 7 3u6 3n5 3n4 3n4 3ii3 3o 7 i 3o 7 o 3o6o 3o6 9 3o68 3(22 3022 3O2 I 3020 3o 1 9 5o 5i 52 53 J* 353i 353o 35 29 3528 35s 7 3477 3476 34 7 5 34 7 4 34 7 3 342.3 3423 3422 3421 34ao 33 7I 33 7 o 336 9 3368 336 7 33i 9 33i8 33 17 33i6 33i5 326 7 3266 3 2 65 3265 3264 "3163" 3262 3261 3260 3s5 9 3216 32 1 5 32i4 32i4 32 1 3 3i66 3i65. 3 1 64 3 1 63 3.63 3o6 7 3o66 3o65 3o65 3o64 3oi8 3oi8 3o, 7 3oi6 3oi5 5o 5i <;., 53 54 55 56 57 58 r >9 S. 358 1 358o 3579 35 7 8 35 77 3526 3525 3525 3 5 24 35a3 34 7 2 34-i 34 7 i 34 7 o 3469 34 1 9 34i8 34 1 7 34 1 6 34i5 3366 3365 3365 3364 3363 33 r 4 33i3 33i3 33i2 33u 3212 3211 3210 32.0 9 32U 9 3 1 62 3i6i 3i6o 3.59 3i58 3lI2 3ni 3i 10 3i 10 3io 9 3o63 3o62 3o6i 3o6o 3ooo 3oi4 3oi4' 3oi3 3012 3oii 5 r . So 5? 58 5 9 1 IR' i I})' 120' i21' 1 22' r '3 i24' 1 25' 1 26' 1 27' ! r 28'! 1 29' S. Page 14 1 TABLE XXII. Proportional Logarithms. S. h m 130 h m 1 31' h m 1 32' h m k m 1 33': 1 34' h m 1 35' h m 136' h m 137' h in k m 1 38' J 39' li m 140' h m 1 41 S. o i 2 3 4 o i 2 3 4 3oio 3009 3 009 3oo8 3007 2962 2962 2961 2960 2 9 5 9 2915 2914 2913 2912 2912 2868 2867 2866 2866 2865 2821 2821 2820 2819 28(8 2775 2775 2774 2773 2772 2 7 3o 2729 2-729 2 7 28 2 7 2 7 2685 2684 2684 2683 2682 2640 2640 263 o 2638 2638 25 9 6 2596 25 9 5 2 5 9 4 2593 2553 2552 255i 255i 255o 7549 2548 2.548 254 7 2546 25lO 2509 2 5o8 250 7 25o 7 5 6 7 8 9 3oo6 3oo5 3oo5 3oo4 3oo3 2958 2 9 58 2957 2 9 56 2955 2911 2910 2909 2909 2908 2864 2863 2862 2862 2861 2818 2817 2816 2815 2815 2772 2771 2770 2769 2769 2 7 26 2 7 25 2 7 25 ?.72.4 272.3 2681 2681 2680 2679 2678 263 7 2636 2635 2635 2634 2593 2692 2591 2591 2500 25o6 25o5 25o4 25o4 25o3 5 6 8 9 10 ii 12 i3 i4 3002 3ooi 3 oo i 3ooo 2999 2954 2954 2 9 53 2952 2951 2907 2906 2905 2905 2904 2860 2859 2859 2858 285 7 2814 2813 2812 2811 2811 2768 2767 2766 2766 2 7 65 2 7 22 2 7 22 2721 2 7 2O 2719 2678 26 77 26-6 2675 26-7 5 2633 2632 2632 263 1 263o 2589 2.588 2588 258 7 2586 2545 2.545 2544 2543 2543 "254-T 2541 2540 2640 2539 2502 2502 2501 2500 2499 10 11 12 i3 i4 i5 16 17 18 1 9 2998 2997 2997 2996 2 99 5 2950 2950 2949 2948 2947 2903 2902 2901 2901 2900 2856 2855 2855 2854 2.853 2810 2809 2808 2808 2807 2764 2 7 63 2 7 63 2762 2761 2719 2 7 l8 27I 7 2 7 l6 2 7 l6 2674 26 7 3 26-72 2672 2671 262 9 262 9 2628 262 7 2626 2585 2.585 2584 2583 2583 2499 2498 249 7 2497 2496 16 16 17 18 1 9 20 21 22 23 24 2 9V 4 ?y93 2993 2992 2.991 2946 2946 2945 2944 2 9 43 2899 2898 2898 2897 2896 2852 2852 285 1 285o 2849 2806 2.8o5 2.8o5 2804 28o3 2760 2760 2 7 5o 2 7 58 2 7 5 7 2 7 l5 2 7 l4 2 7 l3 2 7 l3 2 7 I2 26-70 2669 2669 2668 266-7 2.626 2.625 2624 262.4 2623 2582 2 58 1 258o 258o 2579 2538 2538 2 53 7 2536 2535 2495 2494 2494 2493 2492 20 21 22 23 24 25 26 2 7 28 29 3o 3i 32 33 34 2990 2989 2989 2988 2987 2942 2942 2941 2940 29.39 2.8 9 5 2894 2894 2893 2892 789T 2891 2890 2,889 2888 2848 2848 2847 2846 2845 2802 2801 2801 2800 2799 2 7 56 2 7 56 2 7 55 2 7 54 2 7 53 2711 2 7 IO 2 7 IO 2 7 09 2 7 C>8 2666 2666 2665 2664 2663 2622 2621 2621 2,6?C 2619 ~26l8~ 2618 2617 2616 2.6 1 5 2578 2577 25 77 25 7 6 ;5 7 5 25 7 4~ 25 7 4 25 7 3 2672 25 7 2 2535 2534 2533 2533 2532 *253f 2.53o 2 53o 252.9 2528 2492 2491 2490 ^48 9 2489 2488 2487 2487 2486 2485 25 26 27 ^8 29 3o 3i 32 33 34 2986 2 08 5 2 9 85 2984 298 3 2 9 3 9 2 9 38 293-7 29.% 2935 2845 2.844 2843 2842 2842 2798 2798 2797 2796 2 795 2795 2794 2793 2792 2792 2 7 53 2 7 52 2 7 5l 2 7 5o 2 7 5C 2 7 7 2 7 7 2706 2 7 05 2 7 o4 2663 2662 2661 2660 2660 35 36 37 38 3 9 4o 4i 42 43 44 45 46 47 48 49 2982 2981 298, 2980 2979 2.935 2934 2 9 33 2932 2 9 3i 2887 2.887 2886 2885 2884 2841 2840 283 9 2838 2838 2 7 4 9 2 7 48 2 7 4 7 2 7 4 7 2 7 46 2-704 2 7 o3 2 7 02 2 7 OI 2 7 OI 2659 2658 2657 2657 2.656 261 5 2614 2 6i3 2612 2612 25 7 I 25 7 256 9 2 56 9 2568 252 7 2 5 2 7 2526 2525 2.52.5 2485 2484 2483 2482 2482 35 36 3? 38 3 9 4o 4i 42 43 44 2978 3 977 2977 2976 2975 2931 2930 2929 2928 2927 2883 2.883 2882 2881 2880 2837 2836 2.835 2835 2834 2791 2790 2789 2788 2788 2745 2744 2744 2 7 43 2742 2 7 00 2.698 2697 2655 2655 2654 2653 2.652 2611 2610 2.610 2609 2608 *56 7 2566 2.566 2565 2564 2.524 2523 2522 2522 2.021 2520 2520 2519 25ib 25_i7 2.481 2480 2480 2479 2478 2.477 2477 2476 24"5 2475 2974 2 97 3 2973 2972 2 97t 2970 2969 2969 2968 2967 2927 2926 292.5 2924 2924 2880 9879 2878 '877 2876 2833 2832 283 1 2 83i 283o 2787 2786 2 7 85 27 85 2784 2 7 4l 2741 2740 2 7 3 9 2 7 38 2696 2.6 9 5 26 9 5 2694 26 9 3 2652 265 1 265o 2649 2.64 9 260-7 260-7 2606 2.6o5 2.604 2564 2563 2562 2 56i 2 56 1 45 46 4 7 48 49 5o 5i 52 53 54 292.3 2922 2921 2920 2920 2876 2875 2874 2 8 7 3 28 7 3 2829 2828 2828 2827 2.826 2 7 83 2782 2782 2781 2780 2 7 38 2 7 3 7 2 7 36 2 7 35 2 7 35 2692 2692 2691 2690 2689 2648 2647 2646 2.646 2645 2604 26o3 2602 260 r 2601 256o 2559 2559 2558 255 7 2bl 7 25io 25.5 2 5 1 5 25 1 4 2474 24 7 3 2,4 7 2 24 7 2 24 7 I 5o Gi 5a 53 54 55 56 57 58 5 9 S. 2966 2965 2965 2964 2963 2919 2918 2917 2916 2916 2872 2871 2870 2869 2869 2825 2825 2824 2823 2822 2779 2779 2778 2777 2.776 2 7 34 27 33 2 7 32 2 7 32 2 7 3l 2689 2688 2.68 7 2687 2686 2.644 2643 9643 2642 2641 2600 2599 2599 2598 2597 2556 2556 2555 2554 2553 25 1 3 25l2 2.5 I 2 25lJ a5io 24 7 34 7 2469 2468 2467 55 56 5 7 58 5 9 1 30' i3r 1 39 1 33' 134' 1 35' 1 36' 1 37' ]38' 39'|l 40'i]4r S. TABLE XXII. U*fc-i Proportional Logarithms. S. h m 142 k m \ h m 1 43'!l 44 h m 145 146^ 147 148 149 150' h in 151 h m 152 2061 2060 2059 2059 2o58 h m 153 s, o 2 3 4 5 6 7 8 9 i 2 3 4 2467 2466 2465 2465 2464 2424 2424 2423 2422 2422 2382 2382 1 238i 238o 238o 234 1 234o 2 33 9 233 9 2338 2300 2299 2298 2298 229-7 2259 2258 2258 225 7 2256 2218 2218 2217 2216 2216 2I 7 8 2I 7 8 2177 2176 2176 2l3 9 2i38 2l3 7 2l3 7 2136 2099 2099 2098 2098 2097 2022 2021 2O2I 2020 2019 5 6 8 9 2463 2462 2462 2461 2460 2421 2420 2419 9.419 2418 23 7 9 23 7 8 23 7 8 2-377 23 7 6 233 7 233 7 2336 2335 2335 2296 2296 2295 2294 2294 2256 2255 2254 2253 2253 22l5 22l4 22l4 2213 2212 2I 7 5 2174 2174 2I 7 3 2172 2i36 2i35 2i34 2 1 34 2i33 2096 2096 2095 2094 2094 2057 2057 2o56 2o55 ao55 2019 2018 2017 2017 2016 10 ii 12 i3 i4 2460 2459 2458 2458 245 7 3417 2417 2416 24i5 24r5 23 7 5 23 7 5 23 7 4 2 3 7 3 2 3 7 3 2334 2.333 2333 2332 2 33i 2293 2292 2291 2291 2290 2252 225l 225l 2250 2249 2212 2211 2210 2210 5209 2172 2I 7 I 2I 7 2I 7 2169 2l32 2132 2l3l 2i3o 2i3o 2093 2092 2092 2091 2090 2054 2o53 2o53 2O52 2052 2016 201 5 aot'4 2014 20l3 10 ii 12 i3 i4 i5 16 [? 18 '9 2456 2455 2455 2454 2453 2414 24i3 24 1 2 24l2 24ll 2372 2371 23 7 I 2370 2.36 9 233i 2 33o 2329 2328 2328 2289 2289 2288 228 7 2287 2249 2248 224 7 224 7 2246 23C8 2208 220 7 2206 2206 2169 2l68 2l6 7 2l6 7 2166 2129 2128 2128 2127 2126 2090 9.089 2088 2088 2087 2o5l 2o5o 2o5o 2049 2o48 2012 2012 201 I 2010 2010 i5 16 17 18 r 9 20 21 22 23 24 2453 2452 245i 245c 245o 24lO 2410 2409 2408 2408 2368 2368 2367 2366 2366 232 7 2326 2326 2325 2324 2286 2285 2285 2284 2.283 2^8T 2282 2281 2281 2280 2245 2245 29.44 2243 2243 2205 2204 2204 2203 2202 2i65 2i65 2164 2i63 2i63 21 26 2125 2124 2124 2123 2086 2086 2o85 2o85 2084 2048 2047 2046 2046 2045 2009 2009 2008 2OO 7 2OO 7 20 21 22 23 24 25 26 27 28 29 3o 3i 32 33 34 25 26 2? 28 2 9 2449 2448 2448 2447 2446 2407 2406 24o5 24o5 2404 2365 2364 2364 2363 2362 239.4 2323 2322 2322 2321 2242 224l 2 24 1 2940 2239 2202 2201 2200 2200 2199 2162 2161 2161 2160 2 I 59 2J9.2 2122 2121 2120 2120 21 19 21(8 2118 21 17 2116 2o83 208 3 2089 2081 2081 2044 9044 2043 2042 20-49. 2006 2OO5 20O5 9004 2OO3 3o 3i 32 33 34 2445 2445 2444 2443 2443 2403 24o3 2402 2401 2401 2362 2 36i 236o 2 35 9 2 35 9 2320 2320 2319 2 3i8 23l 7 23l 7 2 3i6 23i5 2 3i5 23r4 2279 2279 2278 2277 2277 2239 2238 2237 223 7 2236 2198 2198 2 '97 2196 2196 2 I 59 2 1 58 2l5 7 2I 5 7 2i56 2080 2079 2079 2078 2077 2041 2041 2040 9.039 2039 2CK)3 2002 2001 2001 2OOO 35 36 3? 38 3 9 2442 244 1 2441 2440 243 9 2400 2 3 99 2398 2398 23 97 2358 235 7 235 7 2356 2355 2276 2275 2274 22"?4 22 7 3 2235 2235 2234 2233 2233 2195 2194 2194 2I 9 3 2192 2192 2191 2 I 90 2190 2189 21 55 2 1 55 2i54 2 1 53 2 1 53 21 l6 21 r5 2.1 J 5 2114 21 I 3 20-7? 2076 2O75 2075 2074 2o38 2()37 2C)3 7 2o36 2o35 2OOO ! 998 '997 35 36 3 7 38 3 9 4o 4i 42 43 44 4o 4i 42 43 44 2438 2438 243 7 2436 2436 2 3 9 6 2 3 9 6 2395 2.3?4 23v;4 a 355 2354 2353 2353 2352 23i3 23i3 23l2 23ll 23ll 22 7 2 22 7 2 22 7 I 22 7 22 7 2232 223l 223l 2230 2229 11 59 2l5l 2l5l 2l5o 2149 21 I 3 21 12 2111 21 I I 21 10 9(>73 2073 2072 2O72 2071 2o35 9o34 2o33 2o33 2032 1996 1996 i 99 5 1994 1994 45 46 4? 48 49 2435 2434 2433 2433 2432 2393 2392 2391 2391 2390 235 1 235o 2 35o 2349 2348 23lO 2309 9.30Q 23o8 230 7 2269 2968 2268 226 7 2266 2229 2228 222 7 2227 2226 2)88 2188 2l8 7 2186 2186 2149 2 1 48 2l4 7 21 47 2146 2109 2109 2108 2I0 7 2107 2070 2O7O 2069 2()68 2068 ^o3a 2o3l 2o3o 2o3o 2029 i 99 3 t 99 3 1992 1991 1991 45 46 47 48 49 5o 5i 52 53 54 243 1 243i 2.43o 2429 2429 2389 2389 2388 238 7 2 38 7 9.348 2 34 7 9.346 2346 2345 23o 7 2 3o6 23o5 23o4 23o4 l3oT a3o2 2302 2301 2300 2266 2265 2264 2264 2263 2225 2225 2224 2223 2223 2 1 85 2184 2 1 84 2i83 2:82 2)45 2145 2144 2i43 2i43 2106 2io5 2105 2104 2103 9.067 2066 0066 ?o65 2064 2028 209.8 2027 202.6 2026 1989 1988 198-7 5o 5i 52 53 54 15" 56 57 58 _L s. 55 56 5? 58 59 2428 2427 2426 2426 2425 2386 2385 2384 2384 2383 2344 2344 2343 2.342 2342 2262 2262 226l 2260 226O 2292 2221 2220 222O 2219 2:82 2181 2180 2180 2179 2t42 2141 2141 2140 2l3 9/ 2 1C>3 21C2 2101 2101 2100 20f>4 9.o63 2oC>2 2062 2061 2025 2025 2024 2023 2O23 ,987 ,986 1986 1985 1984 S. 1=42' 1 43'|1 44' 1 45' ]46'|147' J -J8''jr 49' r so' 1 51' 1 52' 1 53' Page 142] TABLE XXII. Proportional Logarithms. S. h m 154' k m 155' h m 156' h m 157' k in 158' k m 159' h m 2 0' h m 2 1' k m 2 2' T68 9 1689 1688 1687 1687 k m 2 3' h m 2 4' S. i 2 3 4 I 2 3 4 5 6 8 9 1984 i 9 83 1982 1982 1981 1946 1945 1944 1944 1943 1908 1908 1907 1906 1906 1871 1870 1870 1869 1868 1 834 r833 i833 i83 2 i83i 1797 1797 1796 1795 1795 1761 1760 1760 i 7 5 9 i 7 5 9 1725 1724 1724 1723 1722 i654 i653 1 652 1 652 i65i 1619 1618 1617 1617 1616 1981 1980 1979 1979 1978 1943 1942 1941 i94i 1940 1905 1904 1904 1903 1903 1868 1867 1867 1866 1 865 i83i i83o i83o 1829 1828 1794 1794 1793 1792 1792 1758 I75 7 i 7 5 7 i 7 56 i 7 55 1722 1721 1721 1720 1719 1686 1686 1 685 1684 1684 "T683~ 1 683 1682 1681 1681 i65i i65o i65o 1649 1 648 1616 i6i5 1614 ioi4 i6i3 5 6 8 9 10 ii 12 i3 i4 1 5" 16 17 18 1 9 20 21 22 23 24 IO 1 1 I 2 i3 14 i5 16 17 18 1 9 20 21 22 23 24 1977 1977 1976 1975 1975 i 9 3 9 1939 1938 i 9 38 1937 1902 1901 1901 1900 1899 1 865 1 864 1 863 1 863 1862 1828 1827 182-7 1826 1825 1791 1791' 1790 1789 1789 i 7 55 i 7 54 i 7 54 i 7 53 I 7 52 1719 1718 1718 1717 1717 1716 I 7 i5 I 7 i5 i 7 i4 i 7 i4 T-rlT 1712 1712 1711 1711 1648 1 647 1647 1 646 i645 i6i3 1612 1612 1611 1610 1974 1974 1973 1972 1972 1936 i 9 36 r 9 35 1934 1934 !8 9 8 1897 1896 1862 1861 1860 1860 i85 9 1825 1824 1823 1823 1822 1788 1788 1787 1786 1786 1-752 i 7 5i i 7 5i i 7 5o 1749 1680 1680 1679 1678 1678 i645 1 644 1 644 i643 i643 1610 1609 1609 1608 1607 1971 1970 1970 jo68 1933 i 9 33 1932 1931 1931 1896 i8 9 5 1894 1894 i8 9 3 1859 1 858 1857 i85 7 1 856 1822 1821 1820 1820 1819 1785 1785 1784 1783 1783 1749 1 7 48 1748 1747 1746 1677 1677 1676 1676 i6 7 5 1642 i64i i64i i64o i64o 1607 1606 1606 i6o5 i6o5 25 26 27 28 29 1968 1967 1967 1966 1965 ~ 45 44 1927 1926 1926 1925 1 924 1889 1889 1888 1888 1887 i852 i852 i85i i85o i85o 1816 i8i5 1814 1814 i8i3 1779 1778 1778 1777 1777 1743 1742 1742 i 7 4i ' 1740 1707 1706 1706 I7o5 1705 1671 1671 1670 1670 1669 1 636 1 635 1 635 1 634 1 634 1601 1600 1600 i5 99 1 5 99 3o 3i 32 33 34 1962 ,961 1960 1960 1959 1924 1923 192.3 1922 1921 1921 1920 191 j) 1919 1918 1886 1886 1 885 1 884 1 884 1849 1849 1848 1 847 1847 1812 1812 1811 1811 1810 1776 1775 1775 1774 1774 i?4o i 7 39 1739 i 7 38 1737 17^4 I7o3 I7o3 1702 1702 1668 1668 1667 1667 1666 1 633 1 633 i63 2 i63i i63i i5 9 8 i5 9 8 1597 i5 9 6 1596 35 36 3 7 38 3 9 4o 4i 42 43 44 1958 i 9 58 1957 1936 i 9 56 1 883 1883 1882 1881 1881 1846 1646 i845 1 844 1844 1809 1809 1808 1808 1807 i 77 3 1772 1772 1771 1771 i 7 3 7 i 7 36 i 7 36 i 7 35 i 7 34 1701 1700 1700 1699 1699 1 665 1 665 1 664 1 664 1 663 i63o i63o 1629 1628 1628 i5 9 5 i5 9 5 i5 9 4 i5 9 3 i5 9 3 45 46 47 48 4 9 5o 5i 52 53 54 ~55~ 56 5? 58 5 9 S. 1955 K;55 1954 1953 i 9 53 1918 1917 1916 1916 19/5 1914 1914 1913 1913 1912 1880 1880 1879 1878 1878 1 843 i843 1842 i84i i84i 1806 1806 i8o5 i8o5 1804 1770 1769 1769 1766 1768 1767 1766 1766 i 7 65 1765 i-34 x 7 33 1733 I 7 32 i 7 3i 1698 1697 1697 1696 1696 1 663 1662 1661 1661 1660 1627 1627 1626 1626 1625 1592 1592 i5 9 i i5 9 i 1590 45 46 4 7 48 49 5o 5i 52 53 54 1952 1951 1951 1950 1 9 jo 1877 1876 1876 :8 7 5 i8 7 5 1840 1839 1839 1 838 1 838 i8o3 i8o3 1802 1802 1801 i 7 3i 1730 i 7 3o 1729 1728 1695 1694 1694 :6 9 3 r6 9 3 1660 i65 9 1 658 i658 1657 16,24 1624 i 1623 1623 1622 1 589 i58 9 1588 1 588 i58 7 1949 1948 1948 1947 1946 191 1 1911 1910 1909 1909 1874 i8y3 1873 1872 1871 1837 1 836 1 836 i835 i835 % 1800 ' 1800 1799 1798 1798 1764 i 7 63 1763 1762 1762 1728 1727 1727 1726 1725 1692 1692 1691 1690 1690 i65 7 1 656 1 655 1 655 1 654 1621 1621 1620 1620 1619 1 587 1 586 1 585 1 585 1 584 55 56 5 7 58 5 9 154' F55' 1 56' 1 57' 1 58' 159' 2 0' 2 1 2 2' 2 3' 2 4'. S. TABLE XXII. IT-* l Proportional Logarithms. S. i 2 3 4 h m 2 y h m 2 & h m 2 ? h m 2 8' h m 2 ^ h m 2 10' h m 2 11' h m 2 12 h m 2 I?/ k m 2 14' k m 215r S. 1 584 1 583 1 582 1682 ibi 1 549 1 548 1 548 i54 7 i54 7 i5i5 i5i4 i5i4 i5i3 l5l2 1481 i48o 1 479 i479 1478 i447 1 446 i446 )445 i445 i4i3 i4i3 14:2 1412 Mti i38o i3 7 9 1.370 t3^8 1378 i34 7 i346 1 346 1 345 1 345 i3i4 i3i4 i3i3 i3i3 I3l2 1282 I2&1 I2.8l 1280 12.80 I 249 i4g 1248 1248 124-7 i 2 3 4 5 6 7 8 9 i58i i58o i58o 1579 i5 7 8 1 546 1 546 1 545 1 544 1 544 1 543 i543 1 542 1 54 2 i54i l5l2 i5n i Ski i5io i5io 1478 1477 i477 i476 1476 i444 1 443 1 443 1 442 1 442 i4U i4o 1409 1409 i4o8 f 3 77 i3 77 i3 7 6 i3 7 6 i3 7 5 i344 1 344 1 343 i343 1342 1 331 i3ii i3io i3io i3o 9 I 2 79 I2 7 8 I2 7 8 I2 77 I2 77 12-76 12-76 I2 7 5 12 7 5 12 7 4 124 7 1246 1246 ia45 1245 5 5 8 9 10 ii 12 i3 i4 i5 7 8 i5 77 1 577 i5 7 6 !5 7 6 1 509 i5o8 i5o8 i5o 7 i5o 7 1475 1 474 1474 i473 i4 7 3 i44i i44i i44o 1440 i43 9 i4o8 i4o 7 i4o 7 i4o6 i4o6 i3 7 4 i3 7 4 !3 7 3 i3 7 3 l3 7 2 1 342 i34i i34o i34o i33 9 i33 9 1 338 1 338 i33 7 i33 7 1309 i3o8 i3o8 i3o 7 i3o 7 1244 1243 1243 1242 1242 I34f 1241 1 2.40 12.4*/ 1239 10 ii 12 1 3 i4 i5 16 17 18 '9 i5 16 7 18 '9 1 5-5 i5 7 4 5 7 4 1 573 i5 7 3 i54o i54o i53 9 ,539 1 538 i5o6 i5o6 i5o5 i5o4 i5o4 1472 1472 1471 i4 7 o i4 7 1 438 1 438 i43 7 43 7 1 436 i4o5 i4o4 i4o4 i4o3 i4o3 I3 7 2 i3 7 i i3 7 i i3 7 o i3 7 o 1 3o6 i3o6 i3o5 f3o4 i3o4 i2 7 4 J2 7 3 12 7 3 I2 7 2 J2 7 J 20 21 22 23 24 25 26 27 28 29 ,5 7 2 i5 7 i i5 7 i 5 7 o i5 7 o 1 538 i53 7 i536 1 536 1 535 i5o3 i5o3 1502 i5o2 i5oi 1469 1469 1 468 1 468 1467 1 436 i435 1 435 1 434 I43.J. l4f>2 1402 i4oi i4oi i4oo 1 369 1 368 1 368 i36 7 i36 7 i366 1 366 i365 i365 1 364 1 336 1 335 i335 i334 1 334 i3o3 i3o3 l3o2 J302 i3oi I2 7 1 I2 7 I 2 7 1269 1269 IV.39 J23b 12.38 I23 7 !23 7 rj36 1235 1235 1234 1234 20 21 22 23 24 "25 26 27 28 2 9 |56 9 !56 7 .56 7 1 535 1 534 1 534 i533 1 532 i5oo i5oo 1499 1 499 1498 1467 1466 i465 1 465 1 464 t'433 i43a U32 i43i i43i 1 399 1 3 99 1398 1398 i3 97 1 333 1 333 1 332 1 332 i33i i3oi i3oo i3oo 1299 1298 .368 I 2f)8 12() 7 1267 1266 3o 3i 32 33 34 i566 i566 i565 i565 1 564 1 532 i53i i53. i53o i53o 1498 i4 9 7 i4o6 1496 i495 1 464 i463 1 463 1462 i46i i43o 1429 1429 1428 1428 i39 7 1396 i3 9 6 i3 9 5 i3 9 4 1 363 1 363 1 36a 1 36a i36i i33i i33o 1329 l32 9 i328 1298 129-7 129 7 1296 1296 1266 1265 1264 t?6/ t ia63 1233 1233 J2>2 r;3u 123l 3o 31 32 33 34 35 36 37 38 3 9 4o 4i 42 43 44 '45 46 47 48 49 i563 i563 1 562 (562 i56i 1529 I5a8 i5a8 l52 7 I52 7 1495 1494 1494 i493 i493 i46i i46o i46o 1459 i45 9 142-7 l42 7 1426 1426 i425 i3 9 4 i3 9 3 i3 9 3 1392 I3 9 2 i36i i36o i36o i35 9 i35 9 1 3 2 8 132 7 l32 7 1 326 1 326 ~i3z5~ i3 2 5 1 324 i3 2 3 .323 J2 9 5 1295 1 294 1294 T9 9 3 ia63 1 2.(v> i 3fi:> t?T, ; I2? ;! 1260 1260 ,259 I25 9 1258 i3i > 2 3,0 12.3o 1229 1229 35 36 37 38 3 9 i56i i56o i55 9 i55o 1 558 1 526 1 526 i525 1 524 i5z4 1492 1491 1491 1490 1490 1 458 i458 1 45 7 i456 1 456 ~T455 i455 i454 i454 i453 1424 1424 i423 1423 1422 i3 9 i i3gi 1390 i38 9 i38 9 1 358 i35 7 i35 7 1 356 1 356 129? 1299 1291 1291 1290 1228 123 7 I22 7 1226 1226 /( > 4i 42 43 41 1 558 i55 7 1 556 1 556 1 5 55 i5a3 i5s3 1 52 2 1522 I 52 I 1 48 9 1489 i486 i48 7 i48 7 l422 l421 l42l l420 l4l9 1419 1418 i4i8 r4r 7 i4i 7 1 388 1 388 i38 7 i38 7 1 386 1 355 i355 1 354 1 354 i353 1322 l3?9 l32> i3 21 i3ao 130*1 1989 )v8y j;S8 1288 I25 7 I25 7 1256 12.56 1255 1225 1225 u.^4 1224 1223 45 4fi 47 48 49 5o 5i 52 53 54 1 555 1 554 1 554 1 553 i552 I 520 l52O 1519 1519 i5i8 i486 i486 i485 i485 1 484 i452 i45a 1 45 1 1 45 1 i45o 1 386 1 385 i384 i384 1 383 1 352 i352 i35i i35i i35o l320 1319 1319 i3i8 i3. 7 128-7 I28 7 1286 1285 1285 i? 55 1254 1254 1253 1253 r3 1222 1222 1221 IS21 1220 I2T 9 I2I 9 1218 I2l8 5o 5i 52 53 54 55 56 5? 5f J2. S. 55 56 57 58 59 1 552 i55i i55i i55o r55o i5i8 i5i 7 i5i6 i5i6 i5i5 1 483 i483 1482 1482 1481 i45o 1449 1 449 1 448 1 447 i4i6 i4i6 i4i5 i4i4 Mi4 1 383 i382 1 382 i38i i38i i35o. 1 349 1 34 9 1 348 1 348 i3i 7 i3i6 i3i6 i3i5 i3i5 1284 1284 1283 1283 1282 1252 1252 I25l 1250 1250 S. 2 5' 2 o' 2 7' 2 8' 2 9' 2 10' 2 11' 2 12' 2 13' 2 14' 2 15' PageJ44] TABLE XXJJ-. Proportional Logarithms. " '!';': "'; '' ' ; S. o i 2 3 4 S. A m 2 16 A m 2 17' A m 2 18' A m SPU? A m 2 20' A m 2 21' A m 2 22' A m 2 23' A m 2 24' A m 2 25' A m 2 26 i 2 3 4 5 6 8 .JL 10 1 1 12 i3 14 1217 1217 1216 1216 I2l5 1186 nS5 1184 1184 ii83 1 1 54 n53 u53 Il52 I I 52 1123 1122 1122 II2I I I 20 1091 1091 1090 1090 1089 1061 1060 1060 1059 io58 IOOO 1029 1029 1028 1028 0999 999 0998 0998 0997 0969 0969 0968 0968 0967 9 3 9 o 9 3 9 0938 0938 0937 0909 0909 0908 0908 0907 I2l5 1214 I2l4 i2i3 12 1 3 1212 121 I I 21 1 I 2 10 I 2 I u83 1182 1182 1181 1181 . n5i i i5i n5o ii5o 1149 I 120 I I 19 I 119 1118 1118 1089 1088 1088 1087 1087 io58 1057 1057 io56 io56 1027 1027 1026 1026 1025 0997 0996 0996 o 99 5 0995 0967 0966 0966 0965 o 9 65 0937 0936 o 9 36 o 9 35 0935 0907 09^6 c>9< 16 0905 0905 5 6 8 9 I lOo Il8o 1179 1179 1178 1149 ii48 ii48 Ii4 7 u47 III7 III7 1 116 1 1 16 ui5 1086 1086 io85 io85 1084 io55 io55 io54 io54 io53 1025 1024 1024 IO23 1023 0994 0994 0993 0993 0992 0964 0964 0963 0963 0962 oc;34 9 34 0933 0933 0932 0904 09114 0903 0903 0902 Iu 1 1 12 i3 i4 1 5 16 17 18 J9_ 20 21 22 23 24 5 16 '7 18 [9 I 209 I 209 1208 1208 I 207 1178 H77 "77 1 176 M75 n46 1 1 46 n45 n45 n44 ni5 1 1 14 1 1 1 4 ui3 in3 1084 io83 io83 1082 1082 io53 io5a 1052 io5i io5i 1022 1022 1021 IO2I IO2O 0992 0991 0991 0990 0990 0962 0961 0961 0960 0960 0932 0931 0931 0930 0930 0902 0901 OC,OI 0900 0900 20 21 22 23 24 ] 207 I 2O6 I 206 I2()5 iao5 i. 7 5 1 174 1 174 n 7 3 M 7 3 n43 ii43 1 142 1 1 42 i i4i TT4T i i4o i i4o life 1 139 I I 12 I I I 2 I I I I I III II 10 1081 1081 1080 1080 1079 io5o io5o 1049 1049 1048 1020 1019 1019 1018 1018 0989 0989 0988 0988 0987 009 OfySo 0958 o 9 58 0957 0929 0929 0928 0928 0927 0899 $ 0898 0897 25 96 27 28 29 3(" 3i 3 a 33 34 1 204 i 204 I 20 3 12 O2 I P.02 I 20.1 I 20 I 12 OO I2OO I1 99 1172 1 172 1171 1171 1 170 I I IO 1 109 1 109 1108 1 1 08 1079 1078 1078 1077 1076 1048 1047 1047 1046 1046 1017 1017 1016 1016 ioi5 0987 0986 0986 0985 098 5 0957 0956 0956 o 9 55 o 9 55 0927 0926 0926 0925 0925 0897 0896 0896 o8 9 5 o8 9 5 25 26 27 28 2 9 1 170 r 169 1 169 1 1 68 1168 u38 ti38 u3 7 ii3 7 1 1 36 1 107 1106 1 106 i io5 i io5 1076 1075 1075 1074 1074 1045 1045 1044 1044 1 043 ioi5 1014 1014 ioi3 ioi3 0984 0984 o 9 83 o 9 83 0982 0954 0954 0953 0953 0952 0924 0924 0923 092.3 0922 0894 0894 0893 0893 0892 3o 3i 32 33 34 35" 36 37 38 3 9 35 36 37 38 39 II 99 1198 1198 1197 1197 1 167 1167 1 1 66 1 1 65 ii65 n36 ii35 ii35 1 1 34 ii34 I K>4 i io4 i io3 iio3 I 102 1073 1073 1072 1072 1071 1071 1070 1070 1069 1069 io43 1042 1042 1041 1041 1012 1012 101 I IOI I I OK) 0982 098, 0981 0980 0980 0952 0951 0951 0950 oo5o 0922 0921 0921 0920 0920 0892 0891 0891 0890 0890 4o 4i 42 43 44 1 196 1196 i 195 1 195 1194 1164 n64 ii63 n63 1 162 u33 it3a ii3a u3i n3i I 102 I IOI I 1OI I 100 I 100 i o4o io4o 1039 1039 io38 1009 1009 1008 ioob 1007 0979 0979 0978 0978 0977 0949 0949 0948 0948 0947 0919 0919 0918 0918 0917 0889 0889 0888 0888 0887 4o 4i 42 43 44 ~45" 46 47 48 4 9 5o 5i 52 53 54 45 46 47 48 4 9 :, 9 3 1 193 1 192 1 192 1191 1 162 1 161 1 161 1160 1 160 i i3o i i3o 1129 1 129 1128 1099 1099 1098 1098 1097 1068 1068 1067 1067 1066 io37 1037 io36 io36 io35 To35 io34 io34 io33 io33 1007 1006 1006 ioo5 ioo5 0977 0976 0976 0975 0975 0974 0974 0973 0973 0972 0947 0946 0946 0945 o 9 45 0917 0916 0916 0915 0915 0887 0886 0886 o885 088 5 5o Si 52 53 54 55" 56 $7 58 5 V 1 191 1190 1190 1189 1189 i,5 9 1 1 59 u58 1 1 58 ii5 7 1128 1127 1127 1126 1 126 1097 1096 1096 1095 1095 1066 io65 io65 1064 1064 ioo4 ioo4 ioo3 ioo3 1002 0944 0944 0943 0943 0942 0914 0914 0913 0913 0912 0884 0884 o883 o883 o883 0882 0882 r,88l 0881 0880 1188 1188 1187 1187 1186 ii5 7 n56 n56 ii55 1 1 54 uaS (125 1 124 1 124 ' 1123 1094 1094 1093 1092 1092 io63 io63 1062 1062 1061 1032 io3a io3i io3i io3o 1 002 100 1 IOOI IOOO IOOO 0972 0971 0971 0970 0970 0942 0941 0941 0940 0940 0912 09*1 091 1 0910 0910 55 56 57 58 5 9 B. 2 16' 2 17' 2 18' 2 UK 2 '20' 2 21' 2 22' 2 23' 2 24' 2 25' 2 Stf S -TABLE XXII. [HH(ei45 Proportional Logarithms S h m 2 27' h m 2 28' Ii m 2 29' h m 230 / A m 2 31' h m 2 32' h m 2 33' h m 2 34' h m 2 35' h m 2 36' h m 2 37' S. o i 2 3 4 "5 6 1 8 9 10 ii 12 i3 i4 0880 0879 0879 0878 0878 08 5o o85o 0849 0849 0848 0821 0820 0820 0819 0819 0792 0791 0791 0790 0790 0768 0762 0762 0762 0761 o 7 34 o 7 34 o 7 33 o 7 33 7 32 o 7 o6 o 7 o5 o 7 o5 o 7 o4 o 7 o4 0678 0677 0677 0676 0676 0649 0649 0648 0648 0648 0621 0621 0621 0620 0620 o5 9 4 o5 9 3 o5 9 3 0592 0592 o i 2 3 4 5 6 8 9 0877 0877 0876 0876 o8 7 5 0848 0847 0847 0846 o846 0818 0818 0817 0817 0816 0789 0789 0788 0788 0787 0761 0760 0760 0759 0759 7 32 0731 073 1 0730 0730 o 7 o3 o 7 o3 0703 0702 0702 o6 7 5 0675 0674 0674 0673 0647 0647 o646 o646 o645 0619 0619 0618 0618 0617 0591 o5 9 . o5 9 i 0590 0590 "oTsT" 0589 o588 o588 o58 7 08 7 5 0874 o8 7 4 0873 0878 o845 o845 o844 o844 o843 0816 0816 68i5 o8i5 08 1 4 0787 0787 0786 0786 0785 o 7 5S o 7 58 0757 0757 07 56 0730 0729 0729 0728 0728 0701 0701 0700 0700 0699 0673 0672 0672 0671 0671 o645 o644 o644 o643 o643 0617 0616 0616 o6i5 o6i5 10 1 1 12 i3 14 i5 16 I~7 18 '9 0872 0872 0871 0871 0870 o843 0842 0842 084 1 0841 0814 o8i3 08 13 0812 0812 o 7 85 0784 0784 o 7 83 o 7 83 07 56 o 7 55 o-/55 o-54 o 7 54 0727 0727 0726 0726 0725 0698 0697 0697 0696 0696 0695 0695 0694 0670 0670 0670 0669 0669 0642 0642 0641 o64i 0641 o6r5 0614 o6i4 o6i3 061 3 0587 o586 o586 o585 o585 i5 16 17 18 1 9 20 21 22 23 24 0870 0869 0869 0868 0868 0840 0840 0839 0839 o838 08 1 1 0811 0810 0810 0809 0782 0782 0781 0781 0780 o 7 53 o 7 53 0752 0752 0751 0725 0724 0724 0723 0723 0668 0668 0667 0667 0666 ~ o666~ o665 o665 0664 0664 o64o o64o o63 9 0689 o638 0612 0612 0611 06 1 1 0610 o585 o584 o584 o583 o583 20 21 22 23 24 25 26 27 28 2 9 20 26 27 28 2 9 3o 3i 32 33 34 0867 0867 0866 0866 o865 o838 o83 7 o83 7 o836 08 36 0800 0808 0808 0807 0807 0806" 0806 o8o5 o8o5 0804 0780 0779 0779 0778 0778 o 7 5i o 7 5i o 7 5o 0750 0749 0722 0722 0721 0721 0721 0694 0694 0693 0693 0692 o638 o63 7 o63 7 c636 o65S 0610 0609 0609 0609 0608 o582 o582 o58i o58i o58o o865 0864 0864 o863 o863 o835 o835 o834 o834 o834 0777 0777 0776 0776 0775 0749 0748 0748 0747 074-7 0720 0720 0719 0719 0718 0692 0691 0691 0690 0690 066 3 o663 o663 0662 0662 o635 o635 o634 o634 o634 0608 0607 0607 0606 0606 o58o 0579 0579 0579 o5 7 8 3o 3i 32 33 34 35 36 3? 38 .3 9 4o 4i 42 43 44 0862 0862 0861 0861 0860 o833 o833 o83 2 o83 2 o83i 0804 o8o3 o8o3 0802 0802 0775 0774 0774 7?4 0773 0746 0746 o 7 45 o 7 45 o 7 44 0718 0717 0717 0716 0716 0609 0689 0688 0688 0687 0661 0661 0660 0660 o65 9 o633 o633 o632 o632 o63i o6<6 ooo5 0604 0604 o6o3 o5 7 8 o5 77 o5 77 o5 7 6 o5 7 6 35 36 37 38 39 0860 o85 9 0869 o858 o858 o83i o83o o83o 0829 0829 0801 0801 0801 0800 0800 0773 0772 0772 0771 0771 o 7 44 o 7 43 o 7 43 0742 0742 0715 0715 0714 0714 07 1 3 0687 0686 0686 0686 068 5 o65 9 c>658 o658 o()5 7 of>5 7 o63i o63o o63o 0629 0629 o6o3 0602 0602 0602 0601 o5 7 5 o5 7 5 o5 7 4 o5 7 4 o5 7 3 4o 4i 42 43 44 45 46 4? 48 49 0857 o857 08 56 08 56 o855 0828 0828 0827 0827 0826 0799 0799 0798 0798 0797 0770 0770 0769 0769 0768 o 7 4i o 7 4i 0740 0740 0740 0713 0712 0712 0711 0711 o685 0684 0684 o683 o683 c>656 o656 o655 .,655 (655 0628 o6?8 0628 0627 0627 0601 0600 0600 o5 99 o5 99 o5 7 3 o5 7 3 05 7 2 o5-2 o5 7 i 45 46 47 48 49 5o 5 1 52 53 54 o855 o855 08 54 o854 o853 0826 0825 0825 0824 0824 0797 0796 0796 0795 0795 0768 0767 0767 0766 0766 0789 0739 o 7 38 o 7 38 073 7 0711 0710 0710 0709 0709 0682 0682 0681 0681 0680 o654 o654 o653 o653 o65? 0626 0626 0625 0625 0624 0598 o5 9 8 0597 0597 0596 o5 7 i o5 7 o o5 7 o o56 9 0569 5o 5i 52 53 54 55 56 5 7 58 5 9 o853 o852 08 5 2 o85i o85i o8a3 0823 0822 0822 0821 0794 0794 0793 0793 0792 ^W o 7 65 o 7 65 0764 0764 o 7 63 o 7 3 7 o 7 36 o 7 36 o 7 35 o 7 35 2 31' 0-708 0-708 0707 O 7 C7 o 7 o6 0680 0679 0679 06-78 0678 o652 o65i o65i o65o o65o 0624 0623 0623 0622 0622 0596 0596 o5 9 5 o5 9 5 0594 o568 o568 o568 o56 7 o56 7 55 56 57 58 J2_ S. 8. 2 27' 2 28' 2 3(X 2^ 2 33' 2 34' 2 35' 2 36' 2 37' *agelU] TABLE XXII. Proportional Logarithms. S. 2 3 4 S. i 3 4 A m 2 38' h m 2 39' k m '? 40' m 41' h m 42' h m 2 43' m 44' rn 45' h m 2 46' h m 47' t m 48' o566 o566 o565 o'k>5 o r >64 o53 9 o538 o538 r53 7 o53 7 O5l2 o5ii o5ii o5io o5io o484 o484 o484 o483 o483 o458 o45 7 o45 7 o456 o456 o43 1 o43o o43o o43o 0429 0404 0404 o4o3 o4o3 o4o3 o3 7 8 o3 77 o3 77 o3 77 o3 7 6 o352 o35i o35i o35o o35o o326 o3 2 5 o325 o324 o324 o3oo 0299 0299 0298 0298 'j 6 8 _9_ 10 1 1 12 i3 i4 o56 4 o563 o563 o562 o562 o536 o536 o536 o535 o535 0509 0509 oSo8 o5o8 o5o 7 0482 0482 0481 0481 o48o o4 5b o455 o454 o454 o454 0429 0428 0428 0427 042 7 0402 0402 0401 0401 o4oo o3 7 6 o3 7 5 o3 7 5 o3 7 4 o3 7 4 o34 9 o34 9 o34 9 o348 o348 o323 o323 o323 0322 0322 0297 0297 0297 0296 0296 5 6 8 9 o562 o56i o56i o56o o5b'o o534 1 o534 o533 o533 o532 o5o 7 o5o 7 >5o6 o5o6 o5o5 0480 o48o 0479 0479 o4 7 8 o453 o453 o452 o452 o45i 0426 0426 0426 0425 0425 o4oo o3 99 o3 99 o3 99 o3 9 8 o3 7 4 o3 7 3 o3 7 3 03 7 2 o3 7 2 o34 7 o34 7 o346 o346 o346 0321 0321 0320 0320 o3i 9 0295 0295 0294 0294 0294 10 ii 12 i3 i4 i5 16 i 7 18 '9 o55o o55o o558 o558 o55 7 o532 o53i o53i o53i o53o o5u5 o5o4 o5o4 o5o3 o5o3 04-8 o4 77 o4 77 o4 7 6 o4 7 6 o45 1 o45o o45o o45o 0449 0424 0424 o423 0423 0422 o3 9 8 o3 97 o3 97 o3 9 6 o3 9 6 o3 7 i o3 7 i o3 7 o o3 7 o o3 7 o o345 o345 o344 o344 o343 o3i9 0319 o3i8 o3i8 o3i7 0293 0293 0292 0292 0291 i5 16 17 18 '9 20 21 22 23 24 20 21 19 23 24 o55y o55 7 o556 o556 o555 o53o 0529 o52*9 c>5a8 o5a8 o5oa 0502 o5o2 o5oi o5oi o4 7 5 o4 7 5 o4 7 5 o474 o474 o44Q 0448 o448 o44 7 o44 7 0422 0422 0421 0421 0420 o3 9 5 o3 9 5 o3 9 5 o3 9 4 0394 o36 9 o36 9 o368 o368 o36 7 o343 o342 o342 o34a o34i o3i7 o3i6 o3i6 o3i6 o3i5 0291 0291 0290 0290 0289 25 26 27 28 29 3o'~ 3i 3? 33 34 o555 o554 o554 o553 o r )53 ~5^' o552 (,552 o55i c>55i o52 7 O52~7 o5a6 5a6 o5a6 o5oo o5oo 0499 c>499 0498 o4 7 3 o4 7 3 04 7 2 04 7 2 o4 7 i o446 o446 o446 o445 o445 0420 0419 0419 0418 0418 o3 9 3 o3 9 3 o3 9 2 o3 9 2 0392 o36 7 o366 o366 o366 o365 o34i o34o o34o o33 9 o33 9 o3i5 o3i4 o3i4 o3i3 o3i3 0289 0288 02.88 0288 0287 25 26 27 28 29 o52.5 o525 o5^4 o5a4 o5a3 0498 0498 049-7 0497 0496 04- r 0471 0470 0470 0469 o444 o444 o443 o443 0442 0418 0417 0417 0416 0416 0391 0391 0390 0390 o38 9 o365 o364 o364 o363 o363 o33 9 o338 o338 o33 7 o33 7 o3i3 O3l2 O3l2 o3u o3n 0287 0286 0286 0285 0285 3o 3i 32 33 34 35" 36 37 38 3 9 35 36 37 38 3 9 4o 4t 42 43 44 655o o55o o549 0549 o548 o52.3 0522 o522 C)52I 0521 0496 o495 0495 0494 0494 0469 0468 0468 0467 0467 0442 0442 o44i o44i o44o o4i5 o4i5 o4i4 o4i4 o4i4 0389 o388 o388 o388 o38 7 o363 o362 o362 o36i o36i o336 o336 o336 o335 o335 o3io o3io o3io o3o 9 0309 O28D 0284 0284 0283 0283 o548 o547 o54? o546 o546 0521 0520 o520 o5i9 0519 0493 0493 o4 9 3 0492 0492 0467 0466 0466 o465 o465 o44o 0439 0439 o438 o438 o4i3 o4i3 0412 0412 o4n o38 7 o386 o386 o385 o385 o36o o36o o35 9 o35 9 o35 9 o334 o334 o33"3 o333 o333 o3o8 o3o8 0307 o3o 7 o3o7 0282 0282 0282 0281 0281 o r 40 4i 42 43 44 45' 46 47 48 49 5o 5i 52 53 54 55 56 57 58 5 9 S. 15 46 47 48 4Q o546 o545 o545 o544 o544 o5i8 o5i8 o5i7 o5i7 o5i7 0491 0491 0490 0490 0489 o464 o464 o463 o463 0462 o438 o43 7 o43 7 o436 o436 o4n o4io o4io o4io 0409 o384 o384 o384 o383 o383 o358 o358 o35 7 o35 7 o356 o332 o332 o33i o33i o33o o3o6 o3o6 o3o5 o3o5 o3o4 0280 027 9 0279 0379 mnH 5o 5i 52 53 54 55 56 57 58 & S o543 o543 o542 o542 o5^i o5i6 o5i6 o5i5 o5i5 o5i4 0489 0489 o488 o488 0487 0462 0462 o46i o46i o46o o435 o435 o434 o434 o434 0409 o4o8 0408 0407 0407 o38? o382 o38i o38i o38i o356 o356 o355 o355 o354 o33o o32 9 o32 9 o32 9 o3 2 8 o3o4 o3o3 o3o3 0302 02 7 8 02 77 02 77 02 7 6 o54i o54i o54o o54o o53 9 o5i4 o5i3 o5i3 O5l2 O5l2 0487 o486 o486 o485 o485 o46r o459 o459 o458 o458 o433 o433 o432 o432 o43i o4o6 0406 o4o6 o4o5 o4o5 o38o o38o o3 7 9 o3 7 9 o3 7 8 o354 o353 o353 o353 o35a o328 032 7 032 7 o3 2 6 o3a6 OvlO2 o3oi o3oi o3oo o3oo 02 7 6 02 7 5 02 7 r 0274 '2 38 2 '^ 2 P 40 2 41 2 42* 2 43 2 44 2 45' 2 46' 2 47 ________ 2 48 S. TABLE XXII. L i'ugei4? Proportional Logarithms. h m h m h m 2 50 2 51 k m 2 52 k m 2 53 It m 2 54 h m I h m 2 56' // m 2 57' li m 1 h m 2 59' s. I 2 3 4 5 6 8 9 0274 0273 0273 0273 02.72 0248 0248 0247 0247 0247 0223 0222 O222 0221 0221 0197 0197 0197 0196 0196 0172 0172 0171 0171 0171 0147 ci46 oi46 0146 OI22 0122 OI22 OI 2 1 0121 0098 0097 0097 0096 0096 0073 067*3 0072 0072 0071 0049 oo4 0048 0047 0047 0024 0024 002.3 0023 0023 o 2 3 4 5" 6 7 9 0272 0271 0271 0270 0270 0246 0246 0245 0245 0244 022.1 0220 0220 0219 0219 0195 0195 0194 0194 0194 0170 0170 0169 0169 0169 oi45 oi45 oi44 oi44 oi43 0120 0120 oi 19 or 19 0119 0096 0095 0095 0094 0094 0071 0071 0070 0070 0069 0046 0046 oc>46 oo45 0045 OO22 OO22 OO2I OO2I OO2I 4X CO (0 1-1 O 0270 0269 0269 0268 0268 0244 0244 0243 0243 0242 0219 O2I& 0218 0217 0217 0193 0193 0192 0192 0192 0168 0168 0167 0167 0166 0143 0143 0142 oi4i OIl8 OIl8 oi 17 0117 0117 oc. 9 3 0093 0093 0092 0092 0091 0091 0091 0090 0090 0069 0068 0068 0068 0067 006 0066 0066 0066 oo65 0044 0044 0044 oo43 0043 OO2O 0020 0019 0019 0019 IO 1 1 12 i3 i4 i5 16 17 18 0267 0267 0267 0266 0266 0242 0241 024 1 0241 0240 O2.l6 02l6 02l6 02l5 02 I 5 0191 0191 0190 0190 0189 0166 0166 oi65 oi65 0164 0141 0140 oi4o 0139 0116 oi 16 oi i5 0113 oi 14 0042 0042 00.42 (-041 0018 0018 0017 0017 0017 i5 16 17 18 '9 20 21 22 23 24 20 21 22 23 24 0265 0265 0264 0264 0264 0240 023o 0239 0238 0233 0236 0237 0237 0236 0236 02 I 4 0214 02 1 3 02l3 02l3 c c c c c OO CO OO CO CO -J OO CCO O 0164 oi63 oi 63 oi63 0162 0139 0139 oi38 oi38 oi37 oi 14 oi 14 on3 oi i3 OI 12 0089 0089 0089 0088 0088 oo65 0064 0064 oo64 oo63 oo4o oo4o 0039 0039 00l6 00l6 oo 1 5 oo 1 5 ooi 5 25 26 2"7 28 3o~ 3i 32 33 34 35" 36 37 38 39 4o 4i 42 43 44 45 46 47 48 49 '5o 5i 52 -53 54 0263 02.63 0262 02O2 026l O26l 026l 0260 0260 02.59 O2 I 2 O2 I 2 O2 I I D2.I I O2 I I 0187 0187 0186 0186 oi 85 0162 0161 0161 0161 0160 0137 oi36 oi36 oi36 oi 35 01 12 01 12 Oil I Oil I 01 10 0087 0087 0087 0086 0086 oo63 0062 0062 0062 0061 oo38 oo38 oc>38 0037 0037 ooi 4 ooi 4 ooi 3 oo 1 3 OOI 2 0012 0012 OOI I OOI I 00 1 25 2.6 27 28 29 02.35 0235 0235 0234 0234 0210 0210 0209 0209 0208 oi 85 oi 84 oi 84 0184 oi 83 oi8:> 0182 0181 0181 0160 0159 0169 oi 58 oi58 oi35 oi34 01 34 oi34 oi33 01 10 OI IO 0109 0109 0108 oo85 008 5 0084 0084 0084 0061 0060 0060 0060 0059 oc>36 oo36 oo36 oo35 oo35 3o 3 1 32 33 34 0259 0258 0258 0258 0257 0233 0233 0233 O232 O232 02i)8 0208 O2O7 O2O7 0206 oi 58 oi5 7 oi56 oi56 oi56 oi55 oi55 oi54 oi 54 oi33 Ol32 Ol32 oi3i oi3i 0108 0107 0107 0107 0106 oo83 oo83 0082 0082 0082 0059 oo58 oc>58 0067 0057 oo34 oo34 oo34 oo33 oo33 OOIO ooio 0009 0009 0008 35 36 37 38 39 0257 0256 0256 0255 O2.55 02.3 I 023 I 0230 02 30 O2.3O O2()6 O2C)5 O2o5 O2O5 O2O4 0181 0180 o 1 80 .0179 0179 oi3i oi 3o oi3o 0129 0129 0106 oio5 oio5 oio5 0104 0081 0081 0080 0080 0080 oo56 oo56 oo55 oo55 oo32 oo32 oo3 1 oo3i oo 3 1 0008 0008 0007 0007 0006 4o 4 1 42 43 44 45 46 47 48 49 5o 5] 52 53 54 55 56 57 58 02.55 0254 0254 0253 0229 0229 0228 0228 0227 0204 O2O3 O2O3 0202 0202 0179 0178 0178 0177 0177 oi53 oi 53 oi53 Ol52 Ol52 0129 0128 0128 0127 0127 OK>4 oio3 oio3 oio3 O1O2 0079 0079 0078 0078 0077 oo55 oo54 00 54 oo53 oo53 oo3o oo3o 0029 0029 0029 0028" 0028 0027 0027 0027 0006 0006 ooo5 ooo5 ooo4 O252 O2 5 2 0252 025l 025l 0227 0227 0226 0226 O225 O2O2 O2OI O2OI 0200 O2OO 0176 0176 0176 0175 0175 ci5i oi5i oi5i oi 5o 0160 0126 0126 0126 0125 0102 OIOI OIOI OIOO 0100 0077 0077 0076 0076 oo 7 5 oo53 00 5 2 0052 oo5i oo5i ooo4 OG94 ooo3 ooo3 OOO2 OCX) 2 OOO2 OOOI OOOI oooo 55 56 57 58 ~s7 02 5o 0250 6a5o 0249 0245 C.225 0224 O224 IO224 O223 O2OO 0199 0199 0198 0198 0174 0174 0:74 0173 0173 0149 oi49 0.48 01 48 oi48 0124 0124 0124 0123 0123 OIOO 0099 0099 0098 0098 0075 0075 0074 0074 0073 0()5l oo 5o oo5o 0049 0049 0026 0026 1 0025 0025 0025 2 49' 2 50' 2 51' 2 52' 25f3 2 54' 2 55' 2 5(5' j 2 57' 2 58' j 2 59' S. rag 1601 TABLE XXIV. Of Natural Sines. 535o o53 79 o54o8 ?9 863 79861 99860 #858 998.57 99855 99854 6976 700 5 7o34 7o63 7092 7121 7i5o w fo 99748 997^6 99744 9 8 7 6 5 4 2 7 8 9 ro 1 1 I 2 71 .5 r6 '7 18 9 20 2.1 22 2.3 24 O2()4 0233 0262 0291 0349 OOOOO OOOOO OOOOO 100000 99999 99999 i 9 4 9 1978 2007 2o36 2o65 02094 99981 99980 99980 99979 99979 99978 3693 3723 3752 3781 38io o383 9 99932 9993i 99930 999 2 9 999 2 7 9992.6 o543 7 o5466 o54 9 5 o552.4 o5553 o5582 99852 908 5 1 99849 99847 99 846 99844 7I7 9 >72o8 o 7 23 7 07266 99742 99/38 99736 99734 3 2 I O 47 46 45 44 43 42 6 8 8 9 x>436 oo465 00495 99999 99999 99999 99999 99999 99999 02123 >ai5a 02181 )22I I 99977 99977 99976 99976 99975 99974 o3868 03897 >3 9 2(5 o3 9 55 03984 o4oi3 99925 99924 99923 99922 99921 99919 o56u o564o o566 9 o56 9 8 05727 o5756 o58i4 o5844 o58 7 3 05902 o5 9 3i 05960" o5o8o 06018 06047 06076 o6io5 99842 99839 99838 99 836 99834 o 7 353 0741 i >744o 07460 ) 7 4 9 8 99729 9972.7 99725 99723 99721 997'9 9 10 1 1 1 1 12 12 13 i3 1 4 i5 i5 1 6 16 17 >o553 !o6i. x >64o 10669 x>6 9 8 99998 99998 99998 9999 s 99998 9999 s 12298 >a3a 7 .2356 02.385 >a4i4 02.443 99974 99973 99972 99972 9997i 9997" 04042 04071 o4ioo 04129 o4i59 04188 99918 999.7 99916 999 * 5 999' 3 999 1 a 99 833 99 83i 99829 99827 9982.6 99824 o 7 52. 7 1 07556 o 7 585 07614 o 7 643 07672 99716 997-4 99712 99710 99708 99705 4i 40 3 9 38 37 36 25 2.6 27 28 x) 7 56 00785 008 1 4 u>844 oo8 7 3 99997 99997 99997 99997 99996 99996 02472 025oi >a53o 02.560 02589 )26i8 99969 99967 99966 99966 042.17 04246 04275 o43c,4 o4333 o4362 999 !I 999 1 9999 99907 99906 999 o5 99822 9982, 998)3 07701 07730 07759 07766 07817 07846 997 o3 997 o. 99699 99697 99692 35 34 33 32 3i 3o 3 1 3 a 33 34 35 36 00902 0093 1 ( )( > 9 6< > 00989 01018 9999 9^ 99995 99995 99995 9999 02700 02734 0276^ 02792 999 65 99964 999 63 999 63 99962 9996 04391 04420 o4449 04478 o4536 999 0/ 99902 999" ' 999oc 99 8 9 8 99897 061 34 06 1 63 06 1 92 06221 06250 062.79 99812 99810 99808 99806 99804 99803 o 7 8 7 5 07904 07933 07962 07991 08020 99689 9968- 99 685 996l>: 996-8 20 28 27 2.6 25 18 18 1 9 19 2( 2O 21 21 22 22 2; 2* 25 26 2f 27 28 28 37 38 3 9 4< 4i 01076 01 io5 01 1 34 on64 01 (93 01222 9999- 9999- 9999 9999 9999 9999 0282 oa85o 02.879 02008 02 9 38 03967 99961 99959 99959 99958 999 5 999 5 o4565 04594 04623 o4653 04682 04711 99896 99894 99893 99892 99889 o63o8 o6366 o64?4 o6453 99801 99799 9979" 99795 99793 99792 08049 08078 08 TOT 08 1 36 081 65 08194 9967* 99673 9 ?668 99 66f 99?64 9966 9965? 99 654 9965 99649 23 2.2 2 2O I I, O O o o -^- o o o 4^ 4 r 46 47 48 5o 5 5 53 O I 2 5 I O128O or 338 01 367 oi3o6 9999 9999 9999 9999 9999 9999 o o o c o o CO CO CO CO CO OX ~ & en SSNQ M ss co Jx en s . 999 5 9995 999 5 999 5 999 5 999 5 04769 04798 04827 o4856 o4885 99 88b 99886 99 885 99 883 99882 9988, 06482 o65 1 1 o654<> 06069 o65 9 8 06627 99790 99-88 99786 99784 9978 997 8c 08223 08252 08281 o83ro o8368 oi454 oi483 oi5i3 9999 9998 9998 999 8 9998 o3i70 o3i 99 0322.8 o3286 o*33 16 9993 9994 999 4 9994 999 4 19994 04914 04972 oSooi o5o3o 99879 99878 99876 99875 99873 99872 o6656 o6685 06714 o6 7 43 06773 06802 9977 99776 99774 9977 9977 9976 08097 08426 o8455 o8484 o85i3 o8542 9964 99644 9964 9963 99 63 I 5 5 5 5 5 6 01600 01629 oi658 01687 01716 0174* 9998 9998 9998 999 s 9998 999 s o3345 o33 7 4 o34o3 o3432 o346i o34 9 r 999-^ 999^ 9994 9994 999- 999 3 o5o88 o5i46 o5i 7 5 o52o5 05234 : 99870 99869 99867 99866 99864 99 863 o683i 06860 06889 06916 06947 06976 N cos 9976 9976 9976 9976 9975 997 5 .IN. sin 08571 08600 0862.9 o8658 08687 08716 N. cos 9963 99 63 9962 9962 99 62. 0061 ~N.sin ] N. co N. sin 89 N. COS. iN. S1I 88 87 . 86 85 TABLE XXIV. r pa gi6i Of Natural Sines. Prop. 29 5 6 7 8 9 Prop. pan* 4 4 4 4 4 4 4 4 M N. sine. N. cos. N. sine N. cos. N. sine N. cos. N. sine. N. cos N. sine. N. cos G I I 2 2 3 c I 2 3 4 5 6 8 9 10 ii 12 08716 08 7 45 08774 08803 o883i 08860 08889 08918 08947 08976 09005 09034 09063 99619 99617 99614 99612 99609 99607 99604 10453 10482 io5n io54o 10569 10597 10626 99452 99449 99^46 99443 99440 9943 7 99434 I2l8 7 12216 12245 12274 12302 I233I i236o 99 255 99251 99248 99244 99240 99237 99233 ^917 i3 9 46 i3 97 5 i4oo4 i4o33 14061 14090 99027 99023 99019 99015 99011 99006 99002 1 5643 i56 7 2 15701 i5 7 3o i5 7 58 1 5 7 8 7 i58i6 98769 98764 98760 9 8 7 55 98-5 1 9 8 7 46 9874i 60 57 56 55 54 3 4 4 5 5 6 6 7 8 8 9 9 10 10 1 1 1 1 1 2 12 1 3 -3 H 14 IS "i5 i5 16 16 17 17 1 8" 18 '9 '9 20 2O 99602 99599 99596 995 9 4 99 5 9 i 99 588 io655 10684 10718 10742 10771 10800 9943 1 99428 99424 99421 99418 994i5 12889 12.418 12447 12476 i25o4 12533 99280 99226 99222 99219 99215 99211 14119 i4i48 14177 14205 14234 14263 98998 98994 98990 98986 98982 98978 1 5845 i58 7 3 15902 i5 9 3i i5 9 5 9 15988 98737 9 8 7 32 98728 98723 98718 987J4 53 52 5i 5o 4 9 48 47 46 45 44 43 42 4i 4o % 3 7 36 15" 34 33 32 3i 3o 4 3 3 3 3 3 ~3 3 3 3 3 3 ~3~ 3 3 3 2 2 .3 i4 1 5 16 17 18 09092 09121 09150 09179 09208 09237 99 586 99 583 99580 99 5 7 8 99575 99 5 7 2 10829 io858 10887 10916 io 9 45 10973 1 1002 no3i 1 1060 1 1089 11118 n\4i 99412 99409 99406 99402 99899 99896 12562 12591 1 2620 12049 12678 12706 99208 99204 99 200 99197 99198 99189 14292 14320 i4349 14378 14407 i4436 98973 98969 98965 98961 98957 98953 16017 16046 16074 16108 i6i32 16160 98709 98704 98700 98695 98690 98686 '9 20 21 22 23 24 09266 09295 09324 o 9 353 09882 09411 99570 99567 99564 99562 99 55 9 99556 99898 99890 99886 99 383 99880 99377 12735 12764 12793 12822 i285i 12880 99186 99182 V 9 I 7 8 99175 99I7I 99167 i4464 i4493 14522 i455i i458o 14608 98948' 98944 9 8 9 4o 9 8 9 36 9 8 9 3 1 98927 16189 16218 16246 16275 i63o4 i6333 98681 98676 98671 98667 98662 9 865 7 25 26 27 28 2 9 30 09440 ' 995^3 09469 99 55 1 ^9498 99548 o 9 ;v'7 1 99545 09556 1 99542 9 r '58 99540 1 1 176 I I2O5 1 1 234 1 1 263 11291 11 320 99874 99870 90867 99864 99860 9 9 35 7 12908 12937 12966 12995 i3o24 i3o53 99168 99160 99 1 56 991 52 99148 99144 14637 i4666 14695 i4723 i4752 14781 98923 98919 98914 98910 98906 98902 ^8897 98893 98889 98884 98880 98876 1 636 1 16890 16419 16447 16476 i65o5 98652 98648 9 8643 98688 9 8633 98629 2 2 2 2 2 2 3i 32 33 34 35 36 09614 09642 09671 09700 09729 097 58 99 53 7 99534 99081 99528 99528 1 1849 11878 1 1 407 1 1 436 1 1 465 n494 99354 99 35r 99847 99 344 9934i 99337 i3o8i i3no i3i39 1 3i 68 i3r97 18226 99'4i 99 l3 7 99 i33 99 I2 9 99125 99122 14810 i4838 1 486 7 14896 14925 i4954 i6533 i656 2 16591 16620 16648 16677 98624 98619 98614 98609 98604 98600 2 9 28 27 26 25 24 2 a 2 2 2 2 2 37 38 39 4o 4i 42 09787 09816 09845 09874 09903 09982 99520 995i7 995 1 4 99511 99 5o8 99506 1 1523 u552 n58o 1 1609 11688 11667 99334 99881 99827 99324 99820 99817 18254 18283 i33i2 i334i t33 7 o 1 33 99 99 n8 99^4 99110 99106 99102 99098 14982 iSoii i5o4o 1 5069 1 5097 i5ia6 98871 98867 9 8863 98858 98854 98849 16706 i6 7 34 i6 7 63 16792 16820 16849 985 9 5 9 85 9 o 98585 9 858o 985 7 5 98570 23 22 21 2O '9 18 21 21 3) 22 23 23 43 44 4 r - 46 47 48 09961 09990 10019 10048 10077 10106 995o3 99500 99497 99494 99491 99488 11696 11725 ii754 11788 11812 11840 99 3i4 99 3io 99307 99 3o3 99 3oo 99297 i342 7 i3456 1 348 5 i35i4 1 3 543 i35 7 2 99094 99091 99087 99 o83 99070 99075 i5i55 i5i84 l52I2 i5a4i 15270 1 52 99 98845 98841 9 8836 9 8832 98827 98823 16878 16906 16935 16964 16992 17021 98565 9S56i 9 8556 9 855i 98 546 9 854i 17 16 i5 i4 i3 12 II 10 I 7 6 O 24 24 25 25 26 26 P 5o 5i 52 53 54 ioi35 ior64 10192 IO22I IO25O 10279 99 485 99482 99479 99476 99473 99470 11869 11898 11927 11956 n 9 85 I2Ol4 99293 99290 99286 99 283 99279 99276 i36oo 13629 1 3658 i368 7 i3 7 i6 i3 7 44 99071 99067 99068 99059 99 o55 9905 1 i532 7 1 5356 i5385 i54i4 1 5442 1 547 1 98818 98814 98809 9 88o5 98800 98796 I7o5o 17078 17107 I 7 i36 17164 17193 o8536 9 853i 9 85 2 6 9 852i 9 85i6 9 85n 27 27 28 28 29 29 55 56 5 7 58 l 9 io3o8 io337 io366 10395 1042.4 io453 99467 99464 9946 r 99458 99455 99452 I2O43 12071 I2IOO I 2120 i2i58 12187 99272 99269 99265 99262 99258 99255 i3 77 3 18802 i383i 18860 18889 1891-7 99047 99 o43 99 o3o 9 9 o35 99 o3i 99027 i55oo i552 9 i555 7 i5586 i56i5 1 5643 98791 98787 98782 98778 98773 98769 17222 17250 17279 I 7 3o8 I 7 336 i 7 365 9 85o6 98501 98496 98491 98486 98481 5 4 3 2 I O o o o o N. cos. N. sine. N. cos. \. sine. N. cos. V. sine. N. cos. N. sine. N. c.s. N.sine. M 84 83 82 81 80 AK Pr"^ part 28 o O I [ 4 4 c f 6 ~6~ 7 7 7 8 8 9 9 10 10 M II T2 12 i3 i3 i4 1 4 5 e 162] TABLE XXIV. Of Natural Sines. 10 11 12 13 14 Prop, parts 6 6 6 6 6 6 6 5 5 ' 5 5 5 5 5 M N. sine . N. co N. sine.lN. co N. sine .N. co N. sine N. co N. sine N. co o i I 6 17365 i 7 3 9 3 17422 1745 1 17479 17508 17537 9848 98476 98471 98466 9 84tf 98455 9 845o 19081 19109 19138 19167 19195 19224 19262 19816 9815 9 8i5 9814 9814 9 8i3 9 8l2 20791 20820 20848 20877 20906 20 9 33 2.0962 9781 0780 9780 9779 9779 9778 9777 22495 22623 22552 22580 2.26o8 22637 22666 9743 9743 97424 974 1 974 1 974o4 97398 24192 24220 24249 24277 243o5 24333 24362 9703 9702 9701 9700 9700 9699 9698 6 5 5 5 5 5 5 8 9 10 1 1 17565 17594 17623 i765i 17680 17708 17737 17766 17794 17823 17862 17880 98445 9 844o 9 8435 9 843o 9 8425 08420 19281 19309 19338 19366 i 9 3 9 5 19423 98124 98118 9811 9810 9810 98096 20990 21019 21047 21076 21104 2II32 9777 9776 9776 9775 9774 9774 22693 22 7 22 22760 22778 22807 22835 9739 97384 97378 9737 97365 97 358 24390 2.44 1 8 2-4446 24474 2.45o3 2453 1 9698 9697 9696 9696 9696 9694 5 5 5 5 4Q 4 i3 i4 i5 16 17 18 984i4 98409 98404 9 83 99 983 9 4 98389 19452 19481 19509 19538 19566 19595 98oo( 98084 98079 9 8o 7 3 918067 08061 2Il6l 21189 2I2I8 21246 21275 2i3o3 9773 9772Q 97723 97717 9771 97705 22863 228 9 2 22020 22 9 48 22 9 77 23oo5 9735 97345 o-338 9733 97325 973 1 8 245.69 24687 246 1 5 24644 24672 24700 9693 9 6 9 3 9692 9691 9690 9690 4 46 45 44 43 42 5 5 5 4 4 4 9 20 21 22 23 24 17909 17937 17966 17995 18023 18062 98383 983 7 8 9 83 7 3 98 368 9 836 2 98357 19623 19652 19680 1 9709 19737 19766 98056 9 8o5o 9 8o44 9 8o3 9 9 8o33 9 8o27 2i33i 2i36o 2i388 21417 2i445 21474 97698 97692 97686 97680 97673 97667 23o33 23062 23o 9 o a3ii8 23 1 46 23i 7 5 97 3ir 973o4 97298 97291 97284 97278 24728 24756 24784 248 1 3 2484 1 24869 96894 9688 96880 9 68 7 3 96866 96853 4 4o 3 9 38 37 36 4 4 4 4 4 4 25 26 27 28 59 3o 1 808 1 18109 i8i38 18166 18195 1822.4 98352 98347 9834r 9 833b 9 833r o832.5 J 9794 19823 19851 19880 19908 19937 918021 9 8oi6 O^OIO 98004 97998 97992 2l5o2 2i53o 2i55 9 2i58 7 21616 21644 97661 97 655 97648 97642 97 636 9763o 23203 23231 23260 2.3288 233r6 23345 97271 .97264 97267 97261 97244 9723 7 24897 24926 24964 24982 26010 25o38 9686 9 6844 9 683 7 96829 96822 96816 35 34 33 32 3i 3o 20 28 27 26 25 24 4 3 3 3 3 3 r4 i5 i5 16 16 17 17 18 18 19 *9 20 20 21 21 21 22 22 3i 32 33 34 35 36 18252 18281 i83oo 1 8338 1 836- i83 9 5 98320 98 3. 5 983 10 9 83o4 98299 98294 i 99 65 19994 20022 2oo5i 20079 2OIO8 97987 97981 97975 97969 979 63 97958 2l6 7 2 2I70I 21-729 2i 7 58 21786 21814 97623 97617 97611 97604 975 9 8 97692 233 7 3 234oi 23429) 23458 23486 2 35i4 97230 97223 97217 97210 97203 97196 26066 26094 26122 25i5i 26,79 26207 96807 96800 967 9 3 96786 96/78 9677 1 3 3 3 3 3 2 2 2 2 2 2 2 2 2 I o o o o 3 7 38 3 9 4o 4i 42 18424 18452 1 848 1 18509 i8538 i856 7 98288 98283 918277 9)8272 9 8267 9 82.6r 20 1 36 2oi65 20193 20222 20250 202-9 97962 97946 9794o 979 34 97928 97922 21843 21871 2.1899 21928 2i 9 56 2 , 9 85 97585 %& 97 566 97 56o 97 553 23542 235 7 i 23599 23627 23656 23684 97189 97182 97176 97169 97162 97166 26235 26263 26291 25320 25348 253 7 6 96764 96766 96749 96742 96734 96727 23 22 21 2O 1 7 6 5 4 3 2 43 44 45 46 47 48 i85 9 5 18624 i865 2 18681 18710 i8 7 38 9 8 2 56 9 8 2 5o 9 8245 9)8240 9 82.34 9 822 9 2o3o 7 20336 2o364 20393 20.42 1 2o45o 97916 97910 97905 9,7899 97893 97887 220l3 22041 22070 22008 22126 22155 97547 9754i 97534 ,97528 97621 97 5 1 5 23 7 I2 2 3 7 4o 2 3 7 6 9 23 797 23825 23853 97i48 97141 97 1 34 97127 97120 97ii3 26404 25432 26460 26488 26616 2.5545 96719 96712 96706 96697 96690 96682 2.3 23 24 24 25 25 49 5o 5i 52 53 54 18767 18795 18824 i8852 18881 18910 9)8223 918218 9 82I2 98207 98201 98196 20478 20507 20535 20563 20692 20620 97881 978-5 97869 97 863 9785 7 9785 1 22183 22212 22240 2268 22 9 7 2325 97608 97602 974o6 97489 97483 97476 3882 3 9 io 3 9 38 3 9 66 3 99 5 4023 97106 97100 97086 97079 97072 55 7 3 56oi .6629 565 7 5685 5 7 i3 96675 96667 96660 o6653 9 6645 9 6638 I 1 6 26 26 27 27 28 28 55 56 57 58 5 9 60 18938 18967 r8 99 5 9024 9062 9081 98190 98 1 85 98179 98174 98168 98163 20640 20677 20706 o 7 34 o 7 63 0791 97845 9783o 97 S33 97827 97821 978 1 5 2353 2.382 24 1 o 2438 2467 24 9 5 97470 97463 9745 7 9745o 97444 9743 7 4o5i 4o 79 4108 4i36 4i64 4192 . cos. P 97066 97068 97061 97044 97037 97o3o 5 7 4i 5 7 69 6798 6826 5854 5882 o663o 96623 96616 96608 96600 5o3 5 4 3 2 1 O . COS. ^1. sine. . cos. . sine. . COS. . sine. >J. sine. . CCS. ? i. sine. I 79 78 77 76 75 1 - TABLE XXIV. [Pago lea Of Natural Sines. P. op parts 27 I I 2 2 3 ~ 4 4 5 5 5 "6 6 7 8 8 9 9 9 10 10 1 1 15 16 17 18 19 Prop parts 9 9 9 9 8 8 M o i 2 3 4 5 6 N. sine N. cos. N. sine N. cos N. sine N. cos. N. sine N. cos N. sine N. cos 25882 25910 2 5 9 38 25966 25994 26022 26o5o 9 65 9 3 9 6585 96578 96570 96562 9 6555 96547 2 7 564 27592 27620 27648 27676 27704 27-3 1 96126 96118 96110 96102 96094 96086 96078 29237 29265 29293 29321 29348 2 9 3 7 6 29404 9563o 95622 9 56i3 956o5 95596 95588 95579 30902 30929 30957 3o 9 85 3 1 O I 2 3io4o 3 1 068 9 5 1 06' 95007 95o88 95o?9 95070 95o6i 95o52 32557 32584 32612 32639 32667 32694 32722 94552 94542. 9 4533 94523 9 45 1 4 945o4 94495 60 5 9 58 5 7 56 55 54 II 8 9 JO ! 2 26v>79 26107 2 6i35 26163 26191 26219 9654o 96532 9 6524 96517 96509 96502 27759 27787 2 7 8i5 27843 27871 27899 96070 96062 96054 96046 96037 96029 29432 29460 29487 2 9 5i5 2 9 543 29571^ 95571 95562 9 5554 95545 95536 95528 31095 3iia3 3n5i 31178 3 1 206 3 1 233 95o43 95o33 95024 9-5o 1 5 95oo6 94997 3*749 32 777 32804 32.832 32859 32887 94485 944 7 6 94466 9445 7 9444 7 94438 53 52 5i 5o 49 48 8 8 8 8 7 7 7 7 7 7 6 6 ~6~ 6 6 6 6 5 T 5 5 5 5 5 i3 i4 i5 16 17 18 "i9 20 21 22 23 24 26247 26275 263o3 2633 1 26359 26387 96494 96486 96479 96471 9 6463 96456 27927 2 79 55 27983 28011 28039 28067 9602 1 9 6oi3 96005 95997 9 5 9 8 9 9 5 9 8i 2 9 5 99 29626 29654 29682 29710 29737 95519 955n 955o2 95493 95485 95476 3i26i 31289 3i3i6 3 1 344 3i372 3 1 399 94988 94979 94970 9496! 94952 94943 32914 32942 32969 32997 33oa4 33o5i 94428 944i8 94409 94399 94390 9438o 4 7 46 45 44 43 42 264 1 5 26443 26471 265oo 26528 26556 9 6448 9 644o 9 6433 9 6425 96417 96410 28095 28123 28i5o 28178 28206 28234 90972 95964 95 9 56 95948 95940 95931 29765 29793 29821 29849 29876 29904 95467 9 545 9 9545o 9544i 9 5433 95424 31427 3i454 3i482 3i5io 3i53 7 3i565 94933 94924 949i5 94906 94897 94888 33079 33 1 06 33i34 33i6i 33189 332i6 943 7 o 9436 1 943 5 1 94342 9 4332 94322 4i 4o 3 9 38 3 7 36 35 34 33 32 3; 3o ii 12 12 i3 1 3 M i4 1 4 i5 i5 16 16 25 26 27 28 26584 2.66 I 2 26640 26668 26696 26724 96402 96386 9 63 ? 9 96371 96363 28262 28290 283 1 8* 28346 2 83 7 4 28402 95923 95 9 i5 95907 95898 95890 95882 29932 29960 29987 3ooi5 3oo43 30071 9 Li4i5 95407 9 53 9 8 9538o 9538o 9 53 7 2 3i5 9 3 31620 3 1 648 3i6 7 5 3 1703 3 1730 94878 94869 94860 9 485 1 94842 9 4832 33244 33a 7 i 33298 33326 33353 3338 1 9 43 1 3 943o3 94293 942.84 94274 94264 94254" 94245 94235 94225 94215 94206 3i 32 33 34 35 36 26752 26780 26808 26836 26864 26892 96355 96347 96340 9 633 2 963a4 963i6 28429 2.845 7 28485 285 1 3 28541 28669 958 7 4 95865 9 585 7 96849 9584 1 9 583 2 30098 3oi;?6 3 i54 3oi82 30209 3o23 7 95363 9 5354 9 5345 9 533 7 95328 953i 9 3i758 3 1 786 3i8i3 3i84i 3 1 868 3 1 896 94823 04814 o48o5 94795 947^6 94777 334o8 33436 33463 33490 335i8 33545 29 28 2 7 26 25 24 4 4 4 4 4 4 17 17 18 18 18 ii J 9 20 20 21 21 22 3 7 38 39 4o 4i 42 26920 26948 26976 27004 27032 27060 963o8 963oi 96293 96285 96277 96269 285 97 28625 28652 28680 28708 28 7 36 95824 9 58i6 9 58o 7 95799 957Q' 9 5 7 2 3o265 30292 3o3io 3o348 3o3 7 6 3o4o3 953 10 953oi 95293 95284 9 5 27 5 95266 3i 9 23 3i 9 5i 32006 32o34 32061 94768 94758 94749 9474o 9473o 94721 335 7 3 336oo 3362 7 33655 33682 33 7 io 94196 94186 94176 94i6 7 94i5 7 94 1 47 23 22 21 20 1 17 16 i5 i4 i3 12 ii 10 i 6 3 3 3 3 3 3 43 44 45 46 47 48 27088 27116 27144 27172 27200 27228 96261 96253 96246 9 6238 9 6 2 3o 96222 28764 28792 28820 28847 28875 28903 95774 9 5 7 66 95757 9 5 749 95740 9 5 7 3 2 3o43i 30459 3o486 3o5i4 3o54a 3o5 7 o 95257 95248 95240 95 2 3i 95222 9 52i3 32089 32116 3 2 i44 32171 32199 32227 94712 94702 94693 94684 946 7 4 94665 33 7 3 7 33-64 33/92 338i 9 33846 338 7 4 94i3 7 94127 94118 9 4io8 94098 94088 3 2 2 2 2 2 22 20 23 23 24 24 25 25 26 26 27 27 P 5o 5i 52 53 54 55 56 5 7 58 5 9 60 27256 27284 27312 27340 2 7 368 27396 96214 96206 96198 96190 96182 96i74 2893 1 28959 28987 29015 29042 29070 95724 95715 95707 956 9 3 95690 9 568r 30597 3o6 2 5 3o653 3o68o 3o 7 o8 3o 7 36 95204 95 1 95 96186 95177 9 5i68 9 5i5 9 32254 32282 3a3o9 3 2 33 7 32.364 32392 94656 94646 9463 7 94627 94618 94609 33 9 oi 33929 33 9 56 33 9 83 34ou 34o38 34o65 34093 34120 34i4 7 34i 7 5 34202 94o 7 8 94068 94o58 94049 94039 94029 2 2 I I I I I I O O o o 27424 2 7 452 27480 27508 27536 27064 96166 96 1 58 96i5o 96142 96134 96126 29098 29126 29154 29182 29209 29237 9 56 7 3 9 5664 95656 9 564 7 9 563 9 9563o 30763 30791 30819 3o846 3o8 7 4 ^0902 9 5 1 5o 9 5i42 9 5i33 95124 9 5n5 95 1 06 32419 3244 7 324 7 4 3a5ou 32529 3255 7 9 45 99 94590 9458o o45 7 i 94 56 1 9 455 2 94o 1 9 94009 93999 9 3 9 8 9 939-79 9 3o6 9 5 4 3 2 I O N. cos. N. sine. N. cos. V. sine. \. fos. N T . s'ne. N. cos. \ sine. ' N. cos.,M. sine. i , .. ' M 740 73 72 71 70 Figeiw] TABLE XXIV. Of Natural Sines. rop. ara 11 II 11 10 10 IO 10 10 10 9 9 9 9 9 8 8 8 8 8 8 7 7 7 7 7 6 b 6 6 6 5 5 5 5 5 4 Prop, part. 27 o o I I J 2 3 20 21 22 23 V. sine. V. cos. 24 M V. sine. 1 34202 34229 3425 7 34284 343 1 1 3433 9 34366 V. cos. V. s'me.jN. cos. I. sine. |N. cos. \. sine. N. cos. 60 5^ 57 56 55 54 I 2 3 4 5 6 8 9 i 12 i3 i4 i5 (6 18 9 3 9 6 9 9 3 9 5 9 93949 93 9 3 9 93929 9 3 9'9 9 3 9 o 9 35837 35864 35891 35 9 i8 35 9 45 35 97 3 36ooo 93358 9 3348 9 333 7 9 332 7 933i6 933o6 932.95 3 7 46i 3 7 488 3 7 5i5 37542 3 7 56 9 3 7 5 9 5 37622 92718 92707 92697 9 2686 9 2675 9 2664 92653 39073 39100 39127 3 9 i53 39180 39207 3 9 234 92050 92.039 92028 9 20l6 92005 91994 91982 4o6 7 4 40700 40727 4o 7 53 40780 40806 4o833 9i355 91343 9 i33i 91819 91307 91296 91283 3 4 4 5 5 5 "IT 6 7 8 8 343 9 3 34421 34448 34475 345o3 3453o 93899 93889 93879 93869 93839 9 3849 3 60 2 7 36o54 36o8i 36 1 08 36 1 35 36162 9 3 2 85 93274 93264 9 3253 9 3243 93a32 37649 37676 3 77 o3 3 77 3o 37757 3 77 84 92642 92631 92620 92609 92598 92587 39260 39287 393*4 3 9 34i 39367 39394 91971 91959 91948 9 i 9 36 91925 91914 9 I 9 02 91891 91879 91868 9i856 9 i845 40860 40886 40913 40939 40966 40992 91272 91260 91248 91236 91224 91212 53 62 5i 5o 49 48 3455 7 34584 346 1 2 34539 34666 34694 93839 9382.9 9 38i 9 9 38o 9 93799 9 3 7 8 9 36 1 90 36217 36244 36271 36298 36325 93222 9321 1 93201 93190 93580 9 3i6 9 37811 3 7 838 37865 3-7892 3-7919 3 7 946 92576 92666 92554 9 2.543 92532 92521 39421 3 9 448 3 9 474 3950 1 39528 3 9 555 41019 4io45 41072 4 1 098 4ii25 4u5i 91200 91188 91176 91164 91 162 91 i4o 47 46 45 44 43 42 9 9 9 10 10 1 1 1 1 12 12 i3 i3 i4 '9 20 21 22 23 24 2:5 26 27 2.8 29 3o 34721 34748 34- 7 5 348o3 3483o 3485 7 9 3 779 93769 93759 93748 9 3 7 38 93728 36352 363 79 364o6 36434 3646 1 36488 9 3i5 9 93 1 48 9 3.3 7 93 1 27 93 1 1 6 93 1 06 37973 3 7999 3802.6 38o53 38o8o 38io 7 925 io 92499 92488 92.477 92466 92455 3 9 58i 3 9 6o8 39635 39661 3 9 688 3 97 i5 9i833 91822 91810 91799 91787 91775 41178 41204 4i23i 41267 412.84 4i3io 91 128 91116 91 u>4 91092 91080 91068 4i 4o 3 9 38 37 36 "35 34 33 32 3z 3o 29 28 27 26 25 24 34884 3 i9 1 2 34939 34966 34993 3 1)02 I 98718 93708 91698 93688 93677 91667 365 1 5 36542 36569 36596 36623 3665o 93095 93o84 93074 93o63 9 3o52. 98042 38 1 34 38i6i 38 188 382 1 5 3824i 382.68 9 2444 92432 9242 1 92410 92399 92.388 39741 39768 39795 39822 39848 39875 91764 91762 91741 91729 91718 9 1 706 4i33 7 4 1 363 4i3 9 o 4r4i6 4 1 443 4i46 9 91066 91044 91032 91020 91008 90996 90984 9097; 9 J96o 90948 9 -> 9 36 ! 90924 i4 r4 i5 1 5 (6 1 6 18 18 18 '9 3i 3-? 33 34 3 r > 36 3? 38 3 9 4o 4 1 42 35o48 35075 35io^ 35i3o 35i5 7 35.84 352fi 35239 35266 35293 35320 35.347 9 365 7 93647 93637 93626 93616 93606 PI" o3575 93565 9 3555 9 3544 36677 36704 3673i 36758 36785 368 1 2 "36839' 36867 36894 36 9 2 . 36948 36975 93o3i 93020 9.3010 92999 92988 92978 92^6? 92956 92945 92935 92924 92913 382 9 5 38322 38349 383 7 6 384o3 3843o "38456 38483 385io 3853 7 38564 38591 38617 38644 3867 1 38698 ,3879.5 38752 92.377 92.366 92.355 9 2343 92.3-32 92.321 92310 92299 92287 92276 92265 92254 39902 39928 39955 39982 4oob8 4oo35 91694 91683 91671 91660 91648 9: 636 97616 916.- 3 91601 91590 91573 9156; 4i4s>6 41622 4i549 4i575 41602 41628 40062 4oo88 4ou5 4oi4; 40168 40195 41655 41681 41707 4i734 41760 41^87 90911 90899 90887 908-6 | 908(53 90861 23 22 21 20 '9 i8 17 6 i5 i4 1 1 10 9 8 6 4 4 4 4 3 3 ~T 3 3 3 2 2 2 2 2 I I I I 1 I r '9 )O 20 21 9.1 22 43 44 45 46 47 48 35375 3 5 io 2 35429 35456 35484 3V>ii 93534 9352.4 9 35.4 9f3 93493 93483 37002 37029 37056 37083 371 io 3 7 i3 7 92902 92892 92881 92870 92859 92849 92243 92 2.3 1 92.220 92209 92 1 98 92186 402.21 40248 40276 4o3oi 4o328 4o355 91555 ; 91543 j 91 53 i 91619 91608 91496 4i8i3 4 1 840 41866 4? 892 41919 41943 90839 90826 90814 90802 90790 90778 2 2 2.3 23 23 24 ?4 49 5o 5i 52 53 54 35538 35565 35592 35619 35647 356-4 9347? 93462 93452 93441 9 343 1 93420 3 7 i64 37191 3 7 2i8 3 7 245 3 7 2 7 2 3-7299 92.838 92827 92816 92.805 92794 92784 38778 388o5 38832 3885 9 38886 38912 92176 92104 92152 92141 9 2i3o 9 2II 9 4o38i 4o4o8 4o434 4o46i 4o488 4o5i4 91484 91.472 91461 91449 91437 91426 41972- 41998 42024 42061 42077 42104 90766 90763 90741 90729 90717 90704 2.5 25 26 26 27 27 55 56 5? 58 59 60 35701 35728 35 7 55 35782 358 io 3583 7 N. cos 93410 93400 93389 9 33 7 9 93368 93358 373a6 3 7 353 3 7 38o 3 7 4o 7 37434 3 7 46i 92773 92702 92.751 92.740 9272.9 92718 38939 38966 3S993 39020 39046 39073 N. cos 92107 92096 92085 92073 92062 92.o5o 4o54i 40567 4o5 9 4 4062 1 4o647 40674 9i4i4 91402 9 i3 9 o 9 13~8 9; 366 9i355 42i3o 42166 421 83 42209 422.35 42262 90692 90680 90668 90666 oo643 9063 r o ~M . N. sine N. cos N. siiu N. sine N. ros N. sine N. cos N. sine ftP <]&- 67 66 65 1 TABLE XXIV. irag* u Of Natural Sines. Pro? parts 26 M o 2 3 4 5 6 8 9 10 ii 12 TJ i4 i5 16 17 18 25 26 27 2 N. sine 8 NTco7 29 Prop parts 14 ~i4 i4 i4 i3 i3 i.l i3 N. sine N. cos N. sine IN. cos N. sine N. cos N. sine N. cos. I I 2 2 3 42262 42288 423i5 4234i 4236 7 423 9 4 42420 9o63 1 90618 90606 90594 9 o582 90569 9o55 7 4383 7 43863 4388 9 43916 43942 43968 43 99 4 89879 89867 89854 8984 1 89828 89816 8 9 8o3 8 4545i 45477 455o3 45520 45554 89101 89087 89074 89061 89048 8 9 o35 89021 46947 469 7 3 46999 4 7 024 4 7 o5o 47076 47ioi 88295 88281 88267 .88254 88240 88226 88213 4848i 485o6 48532 4855 7 48583 48608 48634 87462 8-448 87434 87420 87406 87391 87377 60 5 7 56 55 54 3 3 4 4 5 ~6~ 6 7 7 8 4a446 42473 4249? 4a5a5 42552 425 7 8 9o545 9 o53 2 90520 90507 90495 90483 44020 44o46 44072 44098 44124 44i5i 89790 89777 89764 8 97 52 8 97 3 9 89726 4558o 456o6 45632 45658 45684 45710 89008 88 99 5 88981 88968 88 9 55 88942 47127 47i53 47178 47204 47229 47255 88199 88i8D 88172 88 1 58 88i44 88i3o 48659 48684 48710 48 7 35 48761 48786 8 7 363 87349 8 7 335 8 7 32i 8 7 3o6 8 7 292 53 52 5i 5o 49 48 12. I 2 12 12 II I I II II I I 10 10 10 42604 4263 1 4265 7 42683 42709 42 7 36 90470 90458 90446 9 o433 90421 90408 44i77 442o3 44229 44255 44281 443o7 897,3 89-700 8 9 68 7 8 9 6 7 4 89662 89649 45736 45762 45 7 8 7 458 1 3 4583 9 45865 88928 889 1 5 88902 88888 888 7 5 88862 47281 473o6 47332 47358 4?383 47409 47434 4746o 47486 475 1 1 4 7 53 7 4 7 56 2 88117 88io3 88089 88o 7 5 88062 S8o48 488 1 1 4883 7 48862 48888 489 1 3 48 9 38 8 7 2 7 8 8 7 264 8 7 25o 8 7 235 8 7 22I 87207 47 46 45 44 43 42 8 9 9 10 10 IO 9 20 21 22 23 24 25 26 27 28 2 9 3o 42762 42788 42815 42841 42867 42894 9 o3 9 6 90383 90371 90358 9 o346 9 o334 44333 4435 9 44385 444 1 1 4443 7 - 44464 8 9 636 89623 89610 895 9 7 8 9 584 8 9 5 7 i 45891 45917 45 9 42 45 9 68 45994 46020 88848 88835 88822 88808 88 79 5 8878: 88768 88 7 55 88741 88728 887 1 5 88701 88o34 88020 88006 87993 8-7979 8 79 65 48 9 64 48989 49014 49040 49065 49090 8 7 I 9 3 87178 87164 87150 87136 87121 4i 4o 37 36 "3T 34 33 32 3i 3o 10 9 9 9 I 8" 8 8 7 7 _J7_ 7 7 6 6 6 6 5 5 5 5 4 4 II II 12 12 13 1 3 42920 42946 42972 42999 43oa5 43o5i 90321 90309 90296 90284 90271 90259 44490 445 16 44542 44568 445 9 4 44620 8 9 558 8 9 545 S 9 53 2 8 9 5i 9 8 9 5o6 89493 46o46 46072 46007 46123 46149 46i 7 5 47588 476:4 4763o 47665 47690 47716 4774i 47767 47793 47818 47844 47869 8 79 5 1 87937 87923 87909 87896 87882 491 16 49141 49166 49192 49217 49242 87107 8 7 9 3 87079 8 7 064 8 7 o5o 87036 i3 i4 i4 i5 i5 16 3i 32 33 34 35 36 "37 38 3 9 4o 4i 42 43077 43io4 43i3o 43 1 56 43i82 43209 90246 90233 90221 90208 90196 90183 44646 44672 44698 44724 4475o 4477" 89480 89467 89454 89441 89428 894 1 5 46201 46226 46252 46278 463o4 4633o 88688 886 7 4 88661 88647 88634 88620 87868 8 7 854 87840 87826 87812 87798 49268 49293 4 9 3i8 49344 49369 4 9 3 9 4 87021 87007 86993 86978 86964 86949 29 28 27 26 25 24 16 16 17 l l 18 18 '9 ! 9 20 20 20 21 21 22 22 23 23 23 43235 4326i 43287 433 1 3 4334o 43366 90171 901 58 90146 90 1 33 90120 90108 44802 44828 44854 4488o 44906 44932 89402 8 9 38 9 8 9 3 7 6 89363 8 9 35o 8 9 33 7 46355 4638 1 464o 7 46433 46458 46484 88607 885 9 3 8858o 88566 88553 8853 9 47895 47920 47946 47971 4 799 7 48022 87784 87770 8 77 56 87743 87729 877 1 5 4 9 4i 9 4 9 445 49470 4 9 4 9 5 4 9 52i 4 9 546 86 9 35 86921 86906 86892 86878 86863 23 22 21 2O 1 17 16 i5 i4 i3 12 II 10 I 6 43 44 45 46 47 48 49 DO 5i 52 53 54 433 9 2 434 1 8 43445 4347i 43497 43523 90095 90082 90070 90057 90045 90032 44958 44984 45oio 45o36 4 5 06 a 45o88 89324 89311 89298 89285 89272 89259 465 10 46536 4656 1 4658 7 466 1 3 46639 88526 885 1 2 88499 88485 88472 88458 48o48 48oy3 48099 48124 48i5o 48i 7 5 87701 87687 8-673 8 7 65 9 8 7 645 8763 1 4 9 57i 4 9 5 9 6 49622 49647 49672 49697 86849 86834 86820 868o5 86791 86777 4 4 4 3 3 3 "3 2 2 2 i I 43l4 9 435 7 5 43602 43628 43654 4368o 90019 90007 89994 89981 89968 8 99 56 45i 14 45i4o 45i66 45192 45 2 i8 45243 89245 89232 89219 89206 89193 89180 4%64 46690 46716 46 7 42 46767 46 79 3 88445 8843 1 88417 884c>4 883 9 o 883 77 48201 48226 48252 48277 483o3 48328 87617 8 7 6o3 8 7 58o 8 7 5 7 5 8 7 56i 8 7 546 49723 49748 49773 49798 49824 49849 86762 86748 86 7 33 86719 86704 86690 24 24 25 25 26 26 55 56 57 5tf 59 60 43706 43733 4375o 43785 438 u 4383 7 N. tos. 8 99 43 89980 89918 8 99 o5 89892 89879 45269 45295 4532i 45347 453 7 3 453 99 89167 89 1 53 89140 89127 89114 89101 46819 46844 468 7 o 46896 46921 46947 88363 88349 88336 88322 883o8 88295 48354 48379 484o5 4843o 48456 4848 1 8 7 532 8 7 5i8 8 7 5o4 87490 87476 87462 49874 49899 49924 49950 49975 Soooo 86675 86661 86646 86632 86617 86603 5 4 3 2 I I I 1 O N. sin*. \. cos. \.sine. \. cos. \.siiie. N. cos. \. sine. N. cos. N. siir. IV! 64 63 fi2 ftt 60 l>; '^ l(i(i l TABLE XXIV Of Natural Sines. Prep puru 16 Prop. p.u s 25 30 31 32 33 34 M i 2 3 4 5 6 N. sine. N. cos. N. sine. N. cos. N. sine N. cos. N. sine N. cos. N. sine N. cos ~6o 5 9 58 5 7 56 55 54 O o 2 2 3 Soooo 5oo2.5 5oo5o 5oo 7 6 5oioi 50126 5oi5i 866o3 86588 865 7 3 8655 9 86544 8653o 865 1 5 5i5o4 5i52 9 5i554 5i5 79 5i6o4 51628 5i653 85 7 i 7 85-02 8568 7 86672 8565 7 85642 86627 856 1 2" 855 97 85582 8556 7 8555i 85536 62992 53oi 7 53o4i 53o66 53o 9 i 53u5 53i4o 84806 84789 84774 84769 84 7 43 84728 84712 54464 54488 545 1 3 5453 7 5456 1 54586 546io 8386 7 8385i 83835 838 1 9 838o4 83-88 83 772 66919 55 9 43 55o68 66992 56oi6 66040 66064 82904 82887 82871 82866 8283 9 82822 82806 1 6 16 i5 1 5 i5 16 3 3 4 4 5 5 8 9 to 1 1 5o 1 7 6 5O2OI 5022 7 60262 60277 5o3o2 865oi 86486 864 7 1 8645- 86442 8642 7 5i6 7 8 5i 7 o3 61728 5i 7 53 5i778 5!8o3 53 1 64 53i8 9 532i4 53238 53263 53288 84697 8468i 84666 84660 84635 84619 54635 5465 9 54683 64708 54 7 3 2 54 7 56 83-56 83 7 4o 83 7 24 83708 83692 83676 66088 66112 56 1 36 56 1 60 66184 66208 82790 82 77 3 82 7 5 7 82 7 4i 82724 82.708 53 52 5 1 5o 49 4t3 U 1 4 1 4 i3 1 3 i3 f> 6 6 8 ~8~ 8 9 9 10 1C) 1 3 i4 i5 16 18 5o3?7 5o35 2 5o3 77 5o4o3 5o428 5o453 864 1 3 863 9 8 86384 8636 9 86354 8634o 61828 61862 5i8 77 61902 6192-7 61962 85521 855o6 854 9 i 854 7 6 8546i 85446 533 1 2 53337 5336i 53386 534ii 53435 84604 84688 845 7 3 8455 7 84542 84626 54 7 8i 548o5 5482 9 54854 548 7 8 54902 8366o 83645 83629 836 1 3 835 97 8358i 56232 66266 66280 563o5 5632 9 56353 82692 82676 82669 82643 82626 82610 4 7 46 45 44 43 42 i3 12 ! 2 12 1 I 1 I '9 20 2J 22 23 24 25 26 27 28 ? 9 3o "37 32 33 34 35 36 37 38 3 9 4o 4i 42 5o4 7 8 5o5o3 5o5 2 8 5o553 50678 5o6o3 86325 863 10 86295 86281 86266 862,5 1 5 1 977 62002 62026 62061 52o 7 6 62101 8543 1 854i6 854oi 85385 853 7 o 85355 5346o 53484 535o 9 53534 53558 53583 845 1 1 84496 8448o 84464 84448 84433 6492-7 64961 54975 54999 66024 66048 83565 8354 9 83533 835i 7 835oi 83485 563 77 564oi 66425 56449 5^473 36497 82693 825 77 82661 82644 82628 82611 4i 4o 3 9 38 3 7 36 1 I I t IO IO IO IO IO 1 1 1 1 12 12 i3 i3 i3 i4 i4 i5 i5 50628 5o654 60679 5o 7 o4 60729 5o 7 54 8623 7 8622.2 86207 86192 86i 7 8 86 1 63 62126 62161 62176 62200 62226 62260 8534o 85325 853 10 86294 86279 86264 536o 7 53632 53656 5368 1 53 7 o5 5373o 844i7 844<>2 84386 843 7 o 84355 8433 9 55o 7 2 66097 66121 55i45 66169 55 1 94 83469 83453 R343 7 83421 834o5 8338 9 66621 56545 66669 565 9 3 66617 5664 1 82496 82478 82462 82446 82429 824i3 35 34 33 32 3i 3o 2 9 28 27 2.6 2.5 24 9 ') 9 8 9 8 ~8" 7 7 7 6 6 6 6 5 5 5 5o 779 5o8o4 60820 5o854 5o8 79 5o 9 o4 86 1 48 86 1 33 86119 86104 86089 86o 7 4 52.2 7 5 62299 62324 62349 62374 5 2 3 99 86240 85234 86218 86203 85i88 85i 7 3 53 7 54 53 779 538o4 5382.8 53853 538 77 84324 843o8 84292 842 77 84261 84246 66218 66242 66266 66291 553 1 5 55339 833 7 3 83356 8334o 83324 833o8 83292 56665 66689 667 1 3 56736 66760 56-84 8s3 9 6 8238o 82363 8234 7 8233o 823i4 i5 1 6 1 6 17 17 18 59 2 9 60964 5o 979 5 1 004 610291 5io54 86069 86o45 86o3o 860 1 5 86000 85 9 85 62423 62448 524 7 3 524 9 8 62622 5254 7 85i5 7 86142 8612-7 86112 86096 85o8i 53902 53 9 26 53 9 5i 53 97 5 54ooo 54024 8423o 842 r4 84198 84182 84167 84i5i 55363 55388 55412 55436 5546o 55484 00 OO O5 OO OO OO 1 COCOCOCOOOCO Co Co Co Co CO Co 1 Co Co Co Co Co Co vO "-> CoJX CTi-^1 vO to JX CTi<) Co en w -^j eo\o | en to oo jx o o> 66808 56832 56856 5688o 56 9 o4 66928 82297 82281 82264 82248 82.231 82214 23 22 21 2O 1 9 18 17 16 16 4 i3 12 18 18 T 9 '9 20 20 43 44 45 46 47 48 61079 5nq4 61129 5u54 61179 5 1 204 61229 5^54 5i2 79 5i3o4 5i32 9 5x354 85 97 o 85 9 56 85 9 4i 86926 86911 8580 525 7 2 62697 62621 62646 62671 5 2 6 9 6 85o66 85o5i 85o35 86020 86006 84989 54o4 9 54o 7 3 5409-7 54122 54 1 46 64171 84 1 35 84 1 2.0 84io4 84o88 84072 84o5 7 66609 55533 5555 7 66681 66606 5 r 63o 66962 56 97 6 5 7 ooo 5 7 024 67047 67071 82198 82/81 82166 82148 ha 1 3s 82115 82098' 82082 82066 82048 82032 82016 5 4 4 4 3 3 ~3 3 2 2 2 2 20 21 2 I 22 22 23 U a 3 :'4 24 2 5 25 4 9 5o 5 1 52 53 54 8588i 85866 8585i 85836 85821 858o6 52 7 20 52 7 45 52 77 O 52 79 4 62819 52.844 "62869" 62893 52 9 i8 52 9 43 62967 62902 84974 84969 84943 84928 849i3 848 97 54i 9 5 54220 54?.44 54v6o 542 9 3 543 1 7 84o4i 84026 84009 83 9 r /4 83 97 8 83962 55654 66678 66702 55 7 26 55 7 5o 55 77 5 83o82 83o66 83o5o 83o34 83oi 7 83ooi 67096 67119 5 7 i43 67167 67191 67216 I I IO I 6 5 4 3 2 55 56 5? 58 5 9 60 5i3 79 5i4q4 bi42 9 5 1 454 61479 5i5o4 N. cos. 86792 85 777 86762 85 7 4 7 86732 85- 1 7 848S.1 34866 848 5 1 84836 84820 84806 54342 54366 64391 544 i 5 5444o 54464 83 9 46 83 9 3o 83 9 i5 83899 83883 83867 55 799 55823 5584 7 558 7 i 56895 55919 82986 82 9 6 9 87963 82936 82920 82904 5 7 238 67262 67286 573io 57334 5 7 358 8i 999 8 I9?3 2 8i 9 65 8i 9 4 9 8193? 8i 9 ;5 I I I 1 C IN. sine. N. cos. N. sine* N. cos. V. sine. N. cos. N.sine. N. cos. N. sine. M 59 58 57 5(5 55 ~> TABLE XXIV. [i'agelCT Of Natural ISines. I'rop. pAJCtl 23 o i i 2 2 2 35 36 37 38 , i& Prop, iiaru 18 18 18 '7 17 17 17 16 ,VI N. sine. N. cos. N. sine. 58779 5S8oa 58826 58849 58873 588 V 6 58920 58 9 43 58 9 6 7 58990 546 1'4 5oo3 7 5oo6i N. cos. IN. sine. N. cos. N. sine N. cos. N. s : r,e. T)2 9 32 62955 62977 63ooo 63O22 63o45 63o68 M. cos. 77715 77696 77678 77660 77641 7762.3 776o5 o 1 2 3 4 5 6 57358 5 7 38i 574o5 57429 5 7 453 57477 575oi 81915 8 1 899 81882 81 865 81848 81 832 8i8i5 80902 8088 5 80867 808 5o 8o833 808.6 80799 60182 60205 60228 602 5 1 60274 60298 6o3a"i 79864 79846 79829 798" 79793 79776 79758 6 1 566 6t58 9 61612 6.635 6,658 61681 61704 61726 61749 61772 6.795 61818 6i84i 78801 78783 7 8 7 65 78747 7872.9 78711 78694 78676 -8658 78640 78622 78604 78586 60 5 9 58 ^"7 56 55 54 3 3 3 /4 4 5 ,- 6 6 7 7 -7 8 9 1 O 1 1 , a T3~ 1 4 i5 16 18 5 7 524 57548 5 7 5 7 2 57596 67619 5 7 643 8.798 81782 8 . 765 81748 81731 81714 80782 8o 7 65 80748 80730 807 1 3 80696 6o344 6o36 7 60390 6o4i4 6o437 6o46o 7974i 79723 79706 79688 79671 79 653 63090 63ii3 63i35 63 1 58 63 180 63203 77 586 77 568 77 55o 77 53i 77 5i3 77494 53 5 a 5i 5o 49 48 16 1 6 1 5 i5 .5 i4 i4 i4 i4 i3 i3 i3 57667 57691 577 1 5 5 77 38 57762 57786 81698 81681 8.664 8.647 8 1 63 . 8.6.4 8 . 597 8.58o 8 1 563 81 546 8i53o 8i5i3 59084 59108 59131 59164 59.78 59201 80679 80662 8o644 80627 806 K) 80593 6o483 6o5o6 60629 6o553 60576 60599 7 9 635 796,8 79600 79583 79565 79^47 6 1 864 61887 6.909 61932 6i 9 55 61978 78568 7855o 7 853 2 7 85i4 78496 78478 63225 63248 632 7 i 632o3 633,6 63338 77476 77458 7743 9 77421 77402 77 384 77366 77347 77^9 773 10 77292 772-73 47 46 45 44 43 42 TT 4o 3 9 38 37 36 7 8 8 8 9 9 '9 ao 21 22 2.3 24 25 26 27 28 59 3o ~3T 32 33 34 35 36 5 7 8io 57833 5 7 85 7 5 7 88i 57904 57928 59225 59*48 59272 59295 59318 59342 80576 8o558 8o54i 8o5a4 8o5o 7 80489 60622 60645 60668 60691 60714 60738 7953o 795 | 2 79494 79477 79459 79441 62001 62.0^4 62046 62069 62002 621 1 5 78460 78442 78424 784o5 7 838 7 7 836 9 63 36 1 63383 634o6 63428 6345 1 634 7 3 12 12 12 II 11 I I 10 10 10 1 1 i i 12 12 12 i3 1 3 i3 1 4 "77 i5 .5 .5 16 16 57952 57976 57999 58oal 58o47 58070 ~5~8o~97 58 1 1 8 58.4i 58 1 65 58 1 89 582 1 2 8.496 81479 81462 8.445 81428 81412 5 9 365 59389 594 1 2 5 9 436 59459 5 9 482 80472 8o455 8o438 80420 8o4o3 8o386 60761 60784 60807 608 3o 6o853 60876 79424 79406 79388 79371 79 353 79 335 62 1 38 62160 62183 62206 6222 9 6225 I 7835 1 78333 7 83i5 78297 78279 78261 63496 635i8 6354o 63563 63585 636o8 77 255 77236 77218 77199 77181 77162 35 34 33 32 3i 3o II IO 10 10 9 9 I 8 8 8 7 7 6 6 6 5 5 5 5 4 4 4 3 3 3 2 2 2 81395 8i3 7 8 8i36i 8 1 344 8,327 8i3io 59506 5 9 52 9 59552 59576 1>9":99 59622 8o368 8o35i 8o334 8o3.6 80299 80282 60899 60922 60945 60968 60991 6 1 o r 5 79 3,8 7 9 3oo 79282 79264 79247 79229 62274 62207 0232O 62342 62365 6 2 388 78243 78225 78206 78188 78170 7 8i5u 6363o 63653 636 7 5 636 9 8 63720 63742. 77i44 7712.5 77107 77088 77070 77o5i 29 28 27 26 25 24 3 7 38 3 9 4<> 4i 42 43 44 45 46 47 48 58^36 58260 58283 583o 7 5833o 58354 81293 81276 81259 812.42 81225 8. -208 ^i 19. 8 1 ( -4 8 n 5 7 8n4o 81,23- 81106 59646 '59669 5 9 6 9 3 597 . 6 39739 59763 80264 802.47 802 3o 802 1 2 80195 80.78 8 r (7i7i(7 80.43 80125 80108 8< >O9 1 8oo-3 6io38 6 1 '. >6 1 61084 6 1 107 611.30 6n53 7921 , 79193 79176 79 '58 79 1 4o 79122 6241 1 62433 62456 62479 62.502 62524 78i34 78116 7 8o 9 8 78079 78061 78043 63765 63 7 8 7 638 10 63832 63854 638 77 63899 63922 63 9 44 63 9 66 63989 64011 77033 770i4 76996 76977 76959 76940 23 22 21 20 1 9 18 16 '7 17 18 1.8 ^9 '9 20 HO uo 21 21 21 22 22 23 23 58378 584oi 58425 58449 58472 58496 59786 59809 59832 5 9 856 59879 59902 61 .76 61.99 6.222 61245 61268 6129. 79105 79087 79069 7905. 79o33 79016 62547 62570 62.592 626.5 62638 62660 78025 78007 779 88 77970 77962 779^4 7692 1 7 6 9 o3 76884 76866 7 684 7 76828 17 16 i5 i4 i3 12 II 10 7 6 49 5o 5i 52 53 54 585 19 58543 5856 7 58590 586.4 58637 81089 8.072 8io55 8io38 8.021 8ioo4 59926 39949 59972 5 999 5 600 1 9 60042 "60065" 60689 60 I 1 -2 60.35 60 1 58 60182 800 56 8oo38 80021 8ooo3 79986 7 99 68 6i3.4 6i33 7 6i36o 6t383 61406 61429 78098 78980 78962 78944 78926 78908 62683 62706 62728 62.75 1 62774 62.796 '62.6.9 62842. 62864 62887 6 2909 02932 77916 77897 77879 77861 77843 77824 77806" 77788 7776 7775i 77733 777 1 5 64o33 64o56 64078 64100 64123 64 1 45 76810 76791 76772 76754 7 6 7 35 76717 55 56 57 58 P 60 5866 1 80987 58684 80970 58708 80953 58 7 3i 8o 9 36 58 7 55 80919 58779 80902 799 5. 79934 79916 79864 6i45i 6 1 4-4 61497 6l 520 6.543 6 1 566 788 9 i 78873 78855 78837 78819 7880, 64167 64190 64212 64234 64256 64279 76698 76679 76661 76642 76623 76604 5 4 3 2 I 2 I I I & - N. cos. N. sine. N. cos. N. sine. N. cos.[N. sine. N. ,-os. N. sine. N. cos. N. sine. M 54 53 53 51 50 Page 1681 TABLE XXIV. Of Natural Sines. Prop, pans 19 ~^9 1 9 1 8 18 18 17 17 17 16 16 16 16 i5 Prop. pans 22 o I I 2 2 40 41 42 43 44 M i 2 3 4 5 6 8 9 10 1 1 r 2 N. sine. V. cos. V. sine. V. cos. V. sine. |N. cos. S T . sinu.iN. cos. N. sine. N. cos. 64279 643oi 64323 64346 64368 64390 i 644 1 2. 76604 7 6586 76567 76548 7 653o 765 1 1 76492 656o6 65628 6565o 66672 656 9 4 65 7 i6 65738 75471 7 5452 7 5433 754i4 753 9 5 753 7 5 7 5356 669 1 3 66 9 35 66956 66978 66999 67021 67043 743 1 4 74295 74276 74256 7423 7 74217 74198 60200 68221 682,42 68264 68285 68306 6832 7 7 3i35 73u6 73o 9 6 73 7 6 73o56 7 3o36 7 3o 1 6 6 9 466 69487 6 9 5o8 69529 69549 69570 6 9 5 9 i 71934 71914 7'94 7 ,8 7 3 7 i853 7 i833 7i8i3 60 r 5" 56 55 54 53 52 5i 5o 4 9 48 3 3 3 4 4 4 64435 64457 64479 645oi 64524 64546 76473 76455 76436 76417 7 63 9 8 7 638o 65 7 5 9 65 7 8i 658o3 65825 65847 65869 7 533 7 753i8 7 52 99 75280 752.61 7 524i 67064 67086 67107 67 1 29 67151 67172 74178 74i5 9 74 1 39 74 1 20 74 1 oo 7 4o8o 6834 9 68370 68391 68412 68434 68455 72996 72976 7295-7 7293-7 72917 728 97 696 I 2 60633 69654 69675 69696 69717 71792 71772 71752 71732 71711 71691 5 5 6 6 6 7 i3 14 i5 16 17 18 ^9 20 21 22 23 24 64568 64590 646 1 2 64635 6465 7 64679 ?636 1 7 6342 7 63 2 3 7 63o4 76286 76267 65891 65 9 i3 65 9 35 65956 65 97 8 66000 75222 752.o3 7 5.84 7 5i65 7 5i46 75126 6719.4 672 1 5 67237 67 2 58 67280 67301 7 4o6i 74o4i 74022 74002 73983 73963 68476 68497 685 18 6853 9 68 56 1 68582 72877 7 285 7 72837 72817 72797 72777 6 97 37 6 97 58 69779 69800 69821 69842 71671 7i65o 7i63o 71610 71590 71569 47 46 45 44 43 42 i5 i5 i4 i4 i4 i3 i3 i3 12 12 12 I 1 1 1 I I 10 10 10 10 7 7 8 8 8 _9. 9 1C 10 to I i 1 1 1 1 1 }. 1 '2 I 2 i3 i3 64701 64723 64746 64768 6479 64812 76248 76229 76210 76192 76t73 7 6i54 66022 66o44 66066 66088 66109 56i3i 75107 75o88 75069 75o5o 7 5o3o 75oi i 67323 6 7 344 6 7 366 6 7 38 7 67409 67430 73944 73924 7 3oo4 7 3885 7 3865 7 3846 686o3 68624 68645 68666 68688 68709 72757 72 7 3 7 72717 72697 72677 7 265 7 69862 69883 69904 69925 69946 69966 71549 71529 7i5o8 71488 71468 7 i447 4 1 4o 37 36 25 26 27 28 y 3o 64834 64856 64878 64901 64923 64945 76i35 76116 76097 76078 76059 7604 1 66[53 66i 7 5 66i9 7 66218 66240 66262 74992 74973 74953 74 9 34 74915 7 48 9 6 7 48 7 6 7485 7 7 4838 7 48 i 3 74799 74 7 8o 67452 67473 o74 9 5 6 7 5i6 6 7 538 67559 6 7 58o" 67602 67623 6 7 645 67666 67688 7 38 2 6 738o6 7 3 7 8 7 7 3 7 6 7 73747 7 3 7 28 68730 687 5 1 68772 68 79 3 6881 4 68835 7 263 7 72617 72.597 72577 72.557 72537 69987 70008 70029 70049 70070 70091 71427 71407 7 1 386 7i366 7i345 7 1 325 35 34 33 32 3i 3o 3i 32 33 34 35 36 649"7 64989 65oi i 65<>33 65o55 65(>77 76022 76003 76984 7 5 9 65 75946 75927 66284 663o6 66327 66349 663 7 i 663 9 3 7 3 7 o8 7 3688 7 366 9 73649 7 362 9 73i32 70.53 70174 70195 702 1 5 "70236 7025- 70277 70298 70319 7<>339 7 i3o5 71284 71264 71243 71223 71203 29 28 27 26 25 24 9 9 9 8 8 8 i4 M 1.4 1 5 i5 ID 3 7 38 3 9 4o 4! 42 43 44 45 46 4? 48 65 1 oo 65 I 22 65 1 44 65 166 65 1 88 652io 7 5 9 o8 7 588 9 7 58 7 o 7 585i 7 583a 7 58 1 3 66^4 66436 66458 66480 665o i 66523 74760 7474i 74722 74703 74683 74664 67709 67730 67752 67773 67795 67816 67837" 67859 67880 67901 67 9 23 6 79 44 7 35 9 o 7 35 7 o 7 355i 7 353, 735 1 1 73491 68983 69004 6902.5 69046 69067 69088 72397 72377 72357 7 233 7 7 23 17 72297 71182 71162 71141 71121 71 100 7 1 080 23 22 21 20 '9 18 7 7 7 6 6 6 5 5 5 4 4 4 ~~y 3 3 3 2 2 ) \ I O () 16 1 6 17 18 65232 65254 65276 65298 65320 65342 75794 75775 7 5 7 56 75738 75719 75700 66545 66566 66588 66610. 66632 66653 74644 74625 74606 74586 74567 74548 73472 7 345 2 7 343 2 734 1 3 7 33 9 3 73375 69109 69130 69. 5i 69172 6 9 i 9 3 69214 72277 72.2.57 72.236 72216 72.196 72.176 7o36o 7o38i 70401 70422. 7C443 70463 71059 71039 71019 70998 70978 70957 17 16 i5 i4 i3 12 II 10 9 8 7 6 r8 18 '9 '9 ! 9 20 49 5o 5i 52 53 54 v >5 56 57 58 % 65304 65386 654o8 6543o 65452 65474 7568o 7566 1 75642 7 56 2 3 756o4 7 5585 66675 66697 66718 66 7 4o 66762 66 7 83 668o5 66827 66848 66870 66891 66 9 i3 74528 74509 74489 74470 7445i 7443 1 6796? 67987 , 68008 68029 68o5i 68072 7 3353 7 3333 7 33i4 732 9 4 732 7 4 73254 69235 69256 69277 69298 K '9 69340 721 56 72 1 36 721 16 72095 72075 7 2o55 7<>484 7 o5o5 7o5a5 7 o546 7 o56 7 7 o58 7 70937 70916 70806 7 o8 7 5 70855 7 o834 20 21 i i 21 22 22 65496 655 1 8 6554o 65562 65584 656o6 7 5566 7 554 7 75528 75509 75490 7547' N sine *> 7 44 1 2 74392 743 7 3 74353 74334 743 1 4 68093 6811 5 68 1 36 68 1 57 68179 68200 7 32.34 7 32i5 7 3, 9 5 73T75 7 3i55 70 1 35 69361 69382 (k;.fo3 69424 6 9 445 6 9 466 72o35 720 1 5 7'995 71974 71954 71914 70608 70628 70649 70670 70690 70711 708 1 3 70793 70772 70702 70731 70711 5 4 3 2 I O IN. cos. X. ros. 4 N. sine N. cos. N. sine i\. ros. IN. sine. N. cos. N.sine. M 4 3 47 46 45 [Page JO!) TABLE XXV Of Logarithmic Sines, Tangents, and Secants to every Point and Quarter Point of the Compass. Points. Sine. Co-sine. Tangent. Co-tang. Secant. Co-secant. Inf. neg. I O. OOOOO Inf. neg. Infinite. 10. OOOOO Infinite. 8 o * 8.69080 9-99948 8.69132 ii.3o868 io.ooo52 ii .30920 7|j o h 8.99130 9.99790 8.99340 ii .00660 IO.O02IO ii .00870 7 h 0| 9.16652 9.99527 9.17125 10.82875 10.00473 10.83348 7 k I 9.29024 9.99157 9.29866 10.70134 10.00843 10.70976 7 i i 9. 3855 7 9.98679 9.39879 10.60121 IO.OI32I io.6i443 6 | I h 9.46282 9.98088 9.48194 io.5r8o6 10.01912 10.53718 6J i i 9.52749 9.97384 9.55365 10.44635 10.02616 10.47251 6J 2 9.68284 9.96562 9.61722 10.38278 io.o3438 10.41716 6 2 i 9.63099 9.95616 9.67483 io.325i7 io.o4384 10.36901 5 1 2 i 9.67339 9.94543 9.72796 10.27204 io.o5457 10.32661 54 2 | 9.71105 9.93335 9.77770 IO.2223O io.o6665 10.28895 5* 3 9.74474 9.91986 9.82489 10.17511 io.o8oi5 10.25526 5 3 * 9-775o3 9.90483 9.87020 10.12980 10.09517 10.22497 41 3 i 9.80236 9.88819 9.91417 io.o8583 10.11181 10.19764 4 h 3j 9.82708 9.86979 9.95729 10.04271 IO.l3o2I 10.17292 44 4 9.84949 9.84949 IO. OOOOO I O. OOOOO io.i5o5i 10. i5o5i 4 Co-sine. Sine. Co-tang. Tangent. Co secant. Secant. Points. TABLE XXVI. Logarithms of Numbers. No. 1 j 00. Log. 0.00000- ( J.OOOOO. No. Log. No. Log. No. Log. No. Log. No. Log. i o . ooooo 21 1.32222 4i 1.61278 Gi . 7 8533 81 .90849 2 o.3oio3 22 1.34242 42 1.62325 62 .79239 82 9i38i 3 0.477*2 23 1.36173 43 i .63347 63 .79934 83 .91908 4 0.60206 24 i.38o2i 44 1.64345 64 .80618 84 .92428 5 0.69897 25 1.39794 45 i. 6532 i 65 .81291 85 .92942 6 0.77815 26 1.41497 46 i .66276 66 .8i 9 54 86 i .93450 7 o.845io 27 i.43i36 47 i .67210 67 .82607 87 i .98952 8 o . 90809 28 i.447i6 48 1.68124 68 .8325i 88 94448 9 0.96424 2 9 i .46240 49 i .69020 69 .83885 89 .949-39 TO I. OOOOO 3o 1.47712 5o 1.69897 70 .845io 90 .95424 11 .04139 3i i. 49i36 5i 1.70757 7i .85i26 9i .95904 12 .07918 32 i.5o5i5 52 i .71600 72 .85 7 33 9 2 .06379 i3 .11394 33 i.5i85i 53 1.72428 73 .86332 93 .96848 i4 .i46i3 34 i.53i48 54 i. 7 3 2 3 9 74 .86923 94 . 97 3i3 i5 .17609 35 i . 54407 55 i.74o36 75 .8 7 5o6 9 5 97772 16 .204I2 36 i.5563o 56 1.74819 76 .88081 96 .98227 i? . 2 3o45 37 1.56820 57 i. 7 558 7 77 .88649 97 .98677 18 .25527 38 i . 57978 58 1.76343 78 .89209 98 .99^23 '9 .27875 3 9 i .59106 5 9 1.77085 79 .8 97 63 99 -99564 20 .3oio3 4o i .60206 60 i.778i5 80 .90309 100 2. OOOOO r*t*W] TABLE XXVI. Logarithms of Numbers. i 2 3 4 5 6 8 9_ 43 1 ,1 17 22 26 3o 34 h 41 12 4 8 i3 17 21 25 2 ,9 34 38 No. 100 1600. Log. 00000 20412. No. 1 2 3 4 5 6 7 8 9 100 101 IO2 io3 io4 ooooo 00432 00860 01284 01703 00043 oo475 00903 01326 oi 7 45 00087 oo5i8 00945 oi368 01787 ooi3o oo56i 00988 01410 01828 00173 00604 oio3o oi452 01870 00217 00647 01072 01494 01912 00260 00689 01116 oi536 oi 9 53 oo3o3 00732 01157 01578 oi 99 5 oo346 00776 01199 01620 O2o36 00389 00817 01242 01662 020-78 io5 106 107 1 08 109 02119 0253 1 02 9 38 o3342 o3 7 43 02160 02572 02979 o3383 03782 02302 026l2 03019 o3423 03822 02243 02653 o3o6o o3463 o3862 02284 02694 o3ioo o35o3 03902 02325 02735 o3i4i o3543 03941 02366 02776 o3i8i o3583 o3 9 8i 02407 02816 03222 o36 2 3 04021 02449 02867 03262 o36i63 04060 02490 02898 o33o2 o3 7 o3 04100 IIO I II 112 ri3 n4 o4i3 9 04532 o4q22 o53o8 05690 04179 04571 04961 o5346 05729 04218 04610 o5 7 6 7 o4258 o465o o5o38 o5423 o58o5 04297 04689 05077 o546i o5843 o4336 04727 o5n5 o55oo o588i o43 7 6 04766 o5i54 o5538 o5 9 i8 o44i5 o48o5 05192 o55 7 6 o5 9 56 04454 o4844 o523i o56i4 06994 04493 04883 06269 o5652 o6o32 40 "4 8 i } 10 20 24 28 3a 36 B8 1 8 1 1 1 5 J? 2 7 3o 34 i 2 3 4 5 6 8 9_ i 2 3 4 5 6 8 9 i 12 1 6 2 I 25 8 3? 39 4 8 12 1 6 20 23 27 3 1 35 n5 116 117 118 119 06070 o6446 06819 07188 o 7 555 06108 o6483 o6856 07225 07591 o6i45 o652i o68 9 3 07262 07628 06 1 83 o6558 06930 07298. 07664 06221 07335 07700 06258 o6633 07004 07372 07737 06296 06670 07041 07408 o 777 3 o6333 06707 07078 07445 07809 06371 06744 07116 07482 07846 06408 06-781 o 7 i5i 0-7618 0-7882 1 20 121 122 123 124 125 126 127 128 I2 9 07918 08279 o8636 08991 09342 07954 o83i4 08672 09026 09377 08707 09061 09412 08027 o8386 o8 7 43 09096 09447 o8o63 08422 08778 09132 09482 08099 o8458 088 1 4 09167 09517 08 1 35 08493 08849 09202 09552 08171 08529 08884 09237 o 9 58 7 08207 o8565 08920 09272 09621 08243 08600 08966 0930-7 09666 09691 10037 io38o 10721 11059 09726 10072 io4i5 io 7 55 1 1093 09760 10106 10449 10789 11126 o 979 5 ioi4o io483 10823 11160 09830 10175 io5i7 io85 7 11193 09864 10209 io55i 10890 11227 09899 10243 ro585 10924 11261 09934 10278 10619 10958 11294 09968 IOJI2 io653 10992 11827 iooo3 io346 10687 11026 u36i 11694 12024 12352 I 2678 i3ooi 1 3322 1 364o 13966 14270 14682 i3o i3i l32 i33 i34 i35 1 36 i3 7 1 38 i3 9 n3o4 11727 12057 12385 12710 11428 1 1 760 1 2090 12418 i2 7 43 11461 11793 I2I23 i245o 12775 11494 11826 iai56 12483 12808 n528 11860 12189 12616 1 2840 u55i 11893 I22i>2 12548 12872 11594 11926 12254 12681 12905 11628 11969 12287 ia6i3 12937 11661 11992 I232O 12646 12969 2 3 4 5 6 7 8 9_ 37 4 7 ii 16 '9 22 26 3o 33 ~X> 333 1 3354 13672 13988 i43oi i3o66 1 3386 i3 7 o4 1 4o 1 9 14333 13098 13418 i3735 i4o5i i4364 i3i3o i345o 1 3 7 6 7 14032 14395 i3i62 1 348 1 i3 7 99 i4n4 14426 13194 i35i3 i383o i4i45 i445 7 13226 i3545 1 3862 14176 14489 1 32.58 13577 i38 9 3 14208 i452o 13290 1 3609 13926 14239 i455i .4o i4i 142 1 43 1 44 r46i3 14922 15229 1 5534 1 5836 t4644 i4953 16269 1 5 564 1 5866 14675 14983 15290 15594 i58 97 14706 i5oi4 1 53 20 i56 2 5 15927 i4737 i5o45 1 535 1 1 5655 16957 14708 15076 1 538 1 1 5685 1 5 9 8 7 1 4799 16106 i54i2 i5 7 i5 16017 14829 i5i3 7 1 5442 16746 i6o4 7 1 4860 16168 i5473 16776 16077 14891 16198 i55o3 16806 16107 2 3 4 5 6 7 6 9 i 2 3 4 5 6 7 - 8 g 4 7 1 1 i4 18 21 25 AS 3 2 ~33 1 7 10 i3 17 20 23 26 3r 3 7 10 id i 7 20 24 27 3. J32 3 6 10 i3 ;6 19 22 ! 2 5 |29 1 45 .4<> 1*7 i4U i4; 16137 r6435 16732 17026 17319 16167 1 6465 16761 17056 i 7 348 16197 i6495 16791 17085 17377 16227 i6524 16820 i7n4 17406 1 62 56 i6554 i685o 17143 i 7 435 16286 i6584 16870 17:73 17464 i63i6 i66i3 16909 17202 17493 i6346 i6643 16938 17231 17622 16376 i66 7 3 16967 1-7260 I755-I 16406 16702 16997 17289 17680 i5o i5i 152 i53 i54 17609 17898 18184 18469 i8 7 52 17638 17926 i82i3 18498 18780 17667 17955 18241 18526 18808 17696 i79 8 4 18270 i8554 i883 7 17725 i8oi3 18298 i8583 1 8865 17754 18041 i832 7 18611 i88 9 3 17782 18070 i8355 i863 9 18921 17811 18099 i8384 18667 io49 17840 18127 18412 18696 189-77 17869 18166 1 844 1 18724 19006 1 55 i56 1 5 7 1 58 i5 9 19033 19312 19590 19806 2Ol4o 19061 19340 19618 19893 20167 19080 i 9 368 19645 19921 20194 19117 19396 19673 19948 20222 19145 19424 19700 19976 20249 19173 i945i 1972? 2O<-o3 20276 19201 $? 20000 2 o3o3 19229 19607 19783 20068 2o33o 19267 i 9 535 19811 2oo85 2o358 19286 19662 19838 201 I 2 ao385 No. 1 2 3 4 5 6 7 8 9 TABLE XXVI. [P**i Logarithms of Numbers. 2 | 8 9_ I 3 4 5 6 8 9 31 "1 6 9 12 1 6 19 23 25- ~si ~i 6 9 12 5 i? :4*J 23 9.8 ;W 3 6 9 i 3 16 ; iS 9. B 24 27 28 '7 6 8 1 2 i4 J7 >o ^2 2.5 *AJ ~3 5 8 JO il 16 18 9 3 133 24 5 7 rt 4 iJ 17 r > >2 ^^ 1 4 7 9 1 1 1 3 i5 18 90 20 4 4 6 8 10 12 i4 16 16 flo. 1600 2200. t Log. 520412- 34242. No. :6o 6i 162 1 65 1 64 ~i6T" 166 167 1 68 .69 1 2 3 4 5 *> 7 8 ; 9 2o4l2 20683 20952 2I2IO 21484 2o43 9 20710 20978 21245 aiSii 20466 20737 21005 21272 2i53 7 20493 20763 21032 21299 21664 20620 20790 21069 21325 21690 2c>548 20817 21086 21 352 21617 20676 20844 211 12 21378 21643 20602 ?. r 3 9 21406 21669 20629 20898 21166 243i 2 3 696 2o656 209-.) 5 2 J I<;2 2i458 25722 25986 22246 22606 22 7 J>3 a3;.j 1 9 2 1 7 48 2 201 1 22272 2 253 1 22789 21775 22037 22298 22557 22814 21801 22063 22324 22583 22840 21827 22089 2235O 22608 22866 2 1 854 22116 22376 22634 22891 21880 22l4l 22401 22660 22917 21906 22l6> 22427 2268 22943 21932 22194 22453 22712 22968 21968 2222O 22479 22737 22994 170 171 172 1 73 174 175 176 177 .78 179 23o45 233oo 23553 238o5 a4o65 23070 23325 235 7 8 2383o 24080 23096 2335o 2 36o3 23855 24106 23I2I 233 7 6 23629 2388o 24i3o 23i47 23401 23654 2 3oo5 24166 23l72 23426 236 79 23930 24180 23198 23462 23704 23 9 55 24204 23223 23477 23729 23980 24229 23249 23502 2 3 7 64 24006 24264 239. 7 4 2359.8 23-779 243o 242 7 9 243o4 24661 24797 25n4a 25285 24329 24576 24822 26066 253io 24353 24601 24846 26091 25334 243 7 8 24626 24871 26116 25358 244o3 24660 24896 26139 25382 24428 246 7 4 24920 26164 26406 24462 24699 24944 26188 2 543 1 24477 24724 24969 26212 25455 24602 24748 24 99 3 26237 26479 24527 ^4 77 3 a5m 8 269.61 2 56<>3 1 80 181 1 8?. 1 83 1 84 25527 25 7 68 26007 26245 26482 2555i 26792 26o3i 26269 26606 255 7 5 26816 26066 26293 26629 26600 26840 26079 263 1 6 26553 26624 26864 26102 26340 26576 26648 26888 26126 26364 26600 26672 26912 26160 2638 7 26623 26696 26935 26174 26411 26647 26720 26198 26435 26670 a6 7 44 269*3 26991 2fi45fc 26694 T a 4 f 6 8 9_ 2 a 3 4 6 I 2. i 2 3 A 5 6 8 9 i 2 3 4 5 6 7 8 9 27 ~3 ts 1 1 M '9 M 25 3 5 8 10 il ? r > ib 9J- 2.'J 3 5 7 9 12 i4 16 18 21 ~, 4 b 8 11 33 1 5 17 1 9 1 85 186 187 1 88 189 ~7^o~ 191 192 i 9 3 194 26717 26951 27184 27416 27646 26741 26975 27207 27439 27669 26764 26998 27231 27462 27692 26788 2702 1 27264 27486 27716 2681 1 27046 27277 27608 2 77 38 26834 27068 27300 2 7 53i 27761 26868 27091 2 7 3 2 3 27664 27784 26881 27114 2 7 346 27677 27807 26906 2 7 i3 27370 27600 2 7 83o *9? 2 7 jf>l 27391 2-693 27852- 27875 28io3 2833o 28556 28780 27898 28126 28353 28678 288o3 28^49 283 7 D 28601 28826 27944 28171 283 9 8 28623 28847 27967 28194 28421 28646 28870 27989 28217 28443 28668 28892 28012 28240 28466 28691 28914 28o35 28262 28488 28713 28937 28068 28286 28611 98 7 35 28969 28081 283. .-7 28533 28768 98981 <95 196 J 97 198 199 20003 29226 29447 29667 29885 29026 29248 29469 29688 29907 29048 29270 29491 29710 29929 29070 29292 29613 2 97 32 29961 29092 29314 2 9 535 29764 29973 29116 2 9 336 29667 29776 29994 29137 29358 29679 29798 3ooi6 29169 2 9 38o 29601 29820 3oo38 291 Si 294. .3 29693 99842 3oo6i > 99203 99426 V>45 ; 9 8 3i6i8 31827 32o35 3r2i8 31429 3i63 9 3 1 848 32066 3 1 239 3i45o 3 1 660 3 1 869 32077 3i26o 3i4?i 3i68i 3i8oo 32098 3.281 31492 3 1 702 3191 1 32118 3i3o2 3i5i3 3i723 3i 9 3i 32139 3i323 3i534 3 1 744 31962 3? 1 60 3 1 345 3 1 555 3 1 766 3i 97 3 32181 3 1 366 3 1 676 3i 7 85 31994 32201 32222 39.428 32634 32838 33o.|i 32243 32449 32654 39858 33o62 32263 39.469 32676 32879 33o82 32284 32490 32696 32899 33io2 39.3o5 32610 32716 3?9'9 33l22 32325 3 2 53i 32 7 36 32940 33i43 32346 32662 32766 32960 33 1 63 32366 32672 32777 32980 33i83 3238 7 32693 32797 33ooi 33203 .32408 39.6i 3 32818 33o2i 3329.4 134^5 33626 33826 34026 34223 33244 33445 336,(6 33846 34o44 3 3 264 33465 33666 53866 34004 33284 33486 33686 33885 34o84 333o4 335o6 33 7 o6 33oo5 34io4 333-iS 33520 33726 33926 34i24 33345 33546 33 7 46 33 9 45 34i43 33365 33566 33 7 66 33o65 34i63 33385 33586 33 7 86 33o85 34 1 83 334o5 336o6 338o6 34oo5 342o3 1 2 3 4 5 6 7 8 9 rage 172] TABLE XXVI. Logarithms of Numbers. 2 i 3 4 5 6 8 9 2 4 6 8 10 12 i4 iJ5 18 No. 2200 -2800. Log. 34242 44716. No. 1 2 3 4 5 6 7 8 9 220 221 222 223 224 34242 3443 9 34635 3483o 35025 34-262 3445o 34655 3485o 35o44 34282 344 79 346 7 4 34869 35o64 343oi 344o8 346 9 4 34889 35o83 3432i 345i8 34 7 1 3 34908 35io2 3434i 3453 7 34 7 33 34928 35122 3436i 3455 7 34 7 53 34 9 4 7 35i4i 3438o 345 77 34 77 2 34 9 6 7 35 160 344oo 345o6 34792 34986 35.8o 34420 34616 348n 35oo5 35199 225 22.6 22 7 228 220_ 23o 23l 232 233 234 352i8 354 1 1 356o3 35793 35 9 84 352.38 3543o 35622 358 1 3 36oo3 35 2 5 7 35449 3564i 35832 36o2i 352 7 6 35468 3566o 3585i 36o4o 352 9 5 35488 35679 35870 36o5 9 353 1 5 355o 7 35698 35889 36078 35334 355^6 35 7 i 7 35908 36097 35353 35545 35 7 36 35 9 2 7 36n6 353 7 2 35564 35 7 55 35946 36.35 353 9 2 35583 35 77 4 35965 36.54 36 1-3 36 36 1 36549 36 7 36 36922 36192 3638o 36568 36 7 54 36940 36211 36399 36586 36 77 3 36 9 5 9 36229 364 18 366o5 36 79 . 369 77 36248 36436 36624 368 10 36 99 6 36267 36455 36642 36829 37014 36286 364 7 4 3666i 3684 7 3 7 o33 363o5 36493 3668o 36866 3 7 u5i 3632.4 365ii 36698 36884 37070 36342 3653o 36 7 i 7 36903 3 7 o88 1 i 2 3 4 6 8 9 9 2 4 6 8 10 ;; i5 17 2 35 2 36 2.3 7 2 38 2 3 9 37107 37291 3 7 4 7 5 3 7 658 3 7 84o 3 7 i25 3 7 3io 3 7 493 3 7 6 7 6 3 7 858 3 7 i44 3 7 3 2 8 3 7 5u 3 7 6 9 4 3 7 8 7 6 3 7 i62 3 7 346 3 7 53o 3 77 I2 3 7 8 9 4 3 7 i8i 3 7 365 3 7 548 3 77 3i 3 79 I2 3 7 i99 3 7 383 3 7 566 3 77 49 3 79 3i 3 7 2i8 37401 3 7 585 3 77 6 7 3 79 4 9 3 7 236 37420 37603 3 77 85 3 79 6 7 3 7 254 3 7 438 37621 3 7 8o3 3 79 85 3 7 2 7 3 3 7 45 7 3 7 63 9 3-822 38oo3 240 24 1 242 243 244 38021 38202 38382 3856i 38739 38o39 38220 383 99 385 7 8 38 7 5 7 38o5 7 38238 384 1 7 385 9 6 38 77 5 38o-5 38256 38435 386 1 4 38 79 2 38093 38 27 4 38453 38632 388 10 38ii2 38292 384 7 i 3865o 38828 38i3o 383io 3848 9 38668 38846 38i48 38328 385o 7 38686 38863 38 1 66 38346 38525 38 7 o3 3888 1 38 1 84 38364 38543 38 7 2i 388 99 18 i 2 3 4 6 8 2 4 5 7 9 1 1 i3 i4 rfi 245 246 247 248 249 38 9 t 7 3 9 o 9 4 39270 39445 89020 38 9 34 3 9 iu 3 9 28 7 3 9 463 3 9 63 7 3 9 8u 3 99 85 4oi5 7 40329 4o5oo 38 9 52 3 9 i2 9 3 9 3o5 3 9 48o 3 9 655 389 7 o 3 9 i46 39322 3 9 4 9 8 3 9 6 7 2 38987 3 9 .64 3 9 34o 3o5t5 3 9 6 9 o 3ooo5 39182 3 9 358 3 9 533 3 97 o 7 3 9 o23 3919? 3 9 3 7 5 3 9 55o 39724 3 9 o4i 3 9 2 1 7 3 9 3 9 3 39568 39742 3 9 o58 3 9 a35 ~3 9 4io 3 9 585 3 97 5 9 3 9 o 7 6 3 9 252 3 9 428 39602 3 9777 250 25l 252 253 254 39794 39967 4oi4o 4o3 1 2 4o483 39829 40002 4oi 7 5 4o346 4o5 1 8 39846 40019 40192 4o364 4o535 3 9 863 4oo3 7 40209 4o38i 4o552 3 9 88i 4oo54 40226 4o3 9 8 4o56 9 J 9 8 9 8 40071 40243 4o4i5 4o586 3 99 i5 40088 40261 4o43a 4o6o3 39933 4o 1 06 402-78 4o44 9 40620 3 99 :x> 40123 4o2 9 5 4o466 4o63 7 37 i 2 3 4 5 6 8 9 2 3 5 7 9 10 12 i4 i5 255 256 25 7 258 _^2_ 260 261 262 263 264 4c>654 4082.4 40993 4 1 162 4i33o 4o6 7 i 4o84i 4ioio 411-79 4i34 7 40688 4o858 4l02 7 41196 4 1 363 4o 7 c5 4oS 7 5 4io44 4l2I2 4i38o 40 7 22 40892 41061 41229 4i3 97 4o 7 3 9 40909 41078 41246 4i4i4 40756 4o 9 26 4io 9 5 4i263 4i43o 40773 4o 9 43 4i 1 1 1 41280 4M4 7 40790 40960 41128 41296 4 1 464 40807 40976 4ii45 4i3i3 4i48i 4 1 49 7 4 1 664 4i83o 41996 42.160 4i5i4 4i68; 4i84 7 42012 42I 77 4i53i 4i6 97 4 1 863 4202 9 42i 9 3 4i54 7 4i 7 i4 4 1 880 42045 42210 4 1 564 4i 7 3i 4.8 9 6 42062 42226 4i58i 4i 7 4 7 4i 9 i3 420-78 422.43 4i5 9 7 4i764 4i 9 2 9 42o 9 5 4225 9 4i6i4 41780 41946 421 1 1 42275 4i63i 4i 797 41^3 42127 422 9 2 4i64 7 4i8i4 4i 979 42144 423o8 ] i 2 3 4 5 6 1 8 9 6 2 3 5 6 8 10 ii i3 r4 265 266 267 268 269 42325 49.488 4265 1 42813 42975 42341 425o4 4266-7 4283o 42991 4a357 42521 42684 42846 43oo8 4a374 4253 7 42700 42862 43o24 42390 42553 42-716 428 7 8 43<>4o 42406 425 7 o 42 7 32 42.8 9 4 43o56 42423 42586 42 7 4 9 42 9 I I 43o 7 2 4243 9 42602 42 7 65 42927 43o88 42455 4s6i 9 42781 42 9 43 43io4 424-72 42635 42 7 7 42959 43 1 20 270 271 272 2 7 3 274 43 1 36 43297 43457 436 1 6 43 77 5 43 1 52 433 1 3 434 7 3 43632 43 7 9i 43i6 9 433-; 9 4348 9 43648 438o 7 43i85 43345 435o5 43664 43823 43201 4336i 4352i 4368o 43838 432 1 7 453 77 43537 436 9 6 43854 44012 44i 7 o 443a6 44483 44638 43233 433 9 3 43553 43 7 i2 438 7 o 43249 43409 4356 9 43727 43886 43265 43425 43584 43 7 43 43oo2 43281 4344i 436oo 43 7 5 9 43 9 i 7 1 i 2 3 4 5 6 7 8 9 5 2 3 5 6 8 9 u ia i4 275 276 277 278 279 No. 43 9 33 44091 44248 444o4 4456c 43949 44io 7 44264 44420 445 7 6 43 9 65 44122 442-79 44436 44592 43 9 8i 44 1 38 442 9 5 444 5 1 446o- 43 9 o6 44 1 54 443 1 1 44467 44623 44028 44 1 85 44342 44498 44654 44o44 44201 44358 445 1 4 44669 44o5 9 4421-7 443 7 3 44520 44685 44o 7 5 44232 4438 9 44545 44 7 <*o 2 3 * 5 6 7 8 9 i'ABLE XXVI. [Page 173 Logarithms of Numbers. i 2 3 4 5 6 8 (y ] I 2 3 4 5 6 8 JL i 2 2 4 6 7 8 9 16 2 5 6 8 10 ii J3 15 2 3 iT e 8 9 II 12 i4 4 i 3 4 6 "7 8 10 ii i3 No. 2800 3400. Log. 4471G 53148. No. 1 2 3 4 5 6 7 8 9 280 281 283 284 44716 448 7 i 46026 461-79 45332 4473 1 44886 45o4o 45347 44747 44902 45o56 46209 45362 44762 44917 45o 7 i 46226 453 7 8 44778 44932 45o86 45393 4479 3 44948 452.55 454o8 44809 44963 45 1 17 452 7 i 45423 44824 45?33 46286 4543 9 4484o 44994 45 1 48 453oi 45454 44855 45oio 45 1 63 453 1 7 45469 286 286 287 288 289 291 292 2 9 3 2 9 4 45484 4563 7 45 7 88 45 9 3 9 46090 455oo 45652 458o3 45 9 54 46io5 455 1 5 4566 7 458 1 8 45o6 9 46120 4553o 45682 45834 45 9 84 46i35 45545 456 97 45849 46ooo 46 [5o 4556 1 46712 45864 46oi5 46 1 65 455 7 6 46728 458 79 46o3o 4Ci8o 455 9 i 45 7 43 458 9 4 46o45 46196 456o6 45 7 58 46909 46060 46210 46621 45773 46924 46o 7 5 46226 46240 4638 9 46538 4668 7 46835 46266 464o4 46553 46702 468 5o 46270 464 1 9 46568 46716 46864 46286 46^34 46583 46 7 3. 468 79 463oo 46449 465 9 8 46746 46894 463 1 5 46464 466 1 3 46761 46909 4633o 464 79 4662 7 46 77 6 46 9 23 46345 46494 46642 46-790 46938 46359 465o 9 46667 468o5 46 9 53 463 7 4 46523 46672 46820 46967 2 9 5 296 297 298 299 46982 47129 47276 47422 4 7 56 7 46997 47 1 44 47290 47436 47682 47012 4/3o5 4745 1 4 7 5 9 6 4-7026 47173 473 1 9 47465 47611 47o4 1 47188 47334 4748o 47626 47066 47202 4 7 34 9 4/494 47640 4 7 o 7 o 4 7 2I 7 4 7 363 4 7 5o 9 4-654 47378 47524 47669 47100 47246 47538 4 7 683 47261 47407 47553 47698 3oo 3oi 302 3o3 3o4 47712 48ooi 48 1 44 48287 47727 47871 48016 48i5 9 483o2 4774 1 4 7 885 48o2 9 48i 7 3 483 1 6 47756 47900 48o44 48i8 7 4833o 47770 48o58 48202 48344 4-7784 4-7929 48o-3 48216 48359 47799 47943 48087 4823o 483 7 3 47958 48101 48244 4838 7 4 7 8 2 8 4-79-72 48ii6 48269 484oi 47842 47986 48i3o 48273 484 1 6 3o5 3o6 3o 7 3o8 3o 9 4843o 48672 48 7 i4 48855 48996 48444 48586 48728 4886 9 4 9 oio 48458 486oi 48883 49024 484 7 3 486 1 5 48 7 56 488 97 49038 4848 7 48629 48 77 o 48911 49062 485oi 48643 48 7 85 48926 49066 485 1 5 4865 7 48 799 48 9 4o 49080 4853o 486 7 i 488 1 3 48964 49094 48544 48686 488 27 48968 49108 48558 48700 4884 1 48982 49122 Co Co Co Co Co -fc^ Co 10 -i O 4 9 i36 49276 494i5 49554 49693 49160 49290 49429 49668 49707 49164 49443 49682 49721 49178 4945 7 49696 49734 49192 49332 49610 49748 49206 49346 49485 49624 49-762 49220 49499 49638 49776 49234 49374 49613 4 9 65i 4979 49248 49388 4 9 665 4 9 8o3 49262 49402 49641 49679 49817 3i5 3i6 3i 7 3i8 319 4983i 49969 5oio6 50243 5o3 79 49845 49982 60120 60266 49869 49996 5oi33 602-70 5o4o6 49872 60010 5oi4 7 60284 60420 49886 60024 60161 5o433 49900 5oo3 7 5oi 7 4 5o3n 5o44 7 49914 60061 60188 5o3 2 5 5o46r 4992-7 60066 60202 5o338 5o4 7 4 4 99 4i 5oo 7 o 6021 5 5o352 60488 4 99 55 60092 50220 5o365 5o5oj 1 i 2 3 4 5 6 7 8 9_ 1 3 r 3 4 5 8 9 10 12 2 320 321 322 3 2 3 324 5o5i5 5o65i 60786 60920 5io55 60664 60934 61068 5o54a 5o6 7 8 5o8i3 6094-7 61081 5o556 60691 60826 60961 5io 9 5 60669 5o 7 o5 60840 50974 5 1108 5o583 60718 5o853 60987 61121 60696 5o 7 32 60866 5iooi 5n35 60610 5o 7 45 60880 61014 5ii48 60623 60-769 60893 61028 61162 5o637 60772 60907 5io4i 61176 325 326 32 7 328 32 9 5u88 5l322 5i455 61687 5l2O2 5i335 5 1 468 61601 5i 7 33 61216 5 1 348 5i48i 5i6i4 5i 7 46 61228 5 1 362 $1627 5i3 7 5 5i5o8 61640 61772 61266 5 1 388 61621 5 1 654 61786 61268 5 1 534 5i66 7 5 1 799 61282 5i4i5 5 1 548 5 1 680 61812 61296 5i4a8 61661 61693 61826 5i3o8 5i44i 5i5 7 4 61706 5i838 33o 33 1 332 333 334 5i85i 5i 9 83 62114 62244 523 7 5 5 1 865 61996 62127 52388 5ib 7 8 62009 622-70 62401 61891 62022 62163 62284 62414 5i 9 o4 52o35 62166 62297 62427 5i9i7 62048 621-79 523io 61930 62061 62192 52323 52453 5i 9 43 5 2 o 7 5 62206 52336 62466 61967 62088 62218 62349 62479 61970 62101 52231 62362 62492 2 3 4 6 7 8 9 i 2 4 5 6 8 10 ii 335 336 337 338 NoT 52.634 5 27 63 62892 53o2o 62617 62647 62776 62906 53o33 5253o 62660 62-789 52 9 i 7 53o46 52543 5 2 6 7 3 62802 53o58 62666 62686 53071 62669 62699 6282-7 62966 53o84 62682 62-711 62840 62969 5309-7 62696 62724 52853 62982 53iio 62608 62737 62866 62994 53l22 62621 62760 62879 53oo7 53i35 1 2 3 4 5 6 7 8 9 pa 174 J TABLE XXVI. Logarithms of Numbers. j 2 3 4 5 6 8 9 3 i 3 4 8 9 10 12 No. 3400 4000. Log. 53148- 602C6. No. 1 2 3 4 5 6 7 8 9 34o 34i 342 343 344 53i48 532 7 5 534o3 5352 9 53656 53i6i 53' 2 88 534 1 5 53542 53668 53i 7 3 533oi 53428 53555 5368i 53 1 86 533 1 4 5344i 5356 7 536 9 4 53i 99 53326 53453 5358o 53 7 o6 53212 5333 9 53466 535 9 3 53 7 i 9 53224 53352 534 79 536o5 53 7 3 2 53 2 3 7 53364 534 9 i 536 1 8 53 7 44 53 2 5o 533 77 535o4 5363 1 53 7 5 7 53263 53390 535i 7 53643 53 7 6 9 345 346 34 7 348 349 53 7 82 53 9 o8 54o33 54 1 58 54283 53 79 4 53920 54o45 54i 7 o 54295 538o 7 53 9 33 54o58 54 1 83 543o 7 53820 53 9 45 54070 54i 9 5 54320 53832 53 9 58 54o83 54208 54332 53845 53 97 o 54o 9 5 54220 54345 5385 7 53 9 83 54 1 08 54233 5435 7 538 7 o 53 99 5 ^4120 54245 543 7 o 53882 54oo8 54 1 33 542.58 54382 538 9 5 54020 54i45 542-70 543 9 4 35o 35 1 352 353 354 544o 7 5453 1 54654 54 777 54ooo 54543 5466 7 54-790 549i3 54432 54555 54802 54 9 25 54444 54568 546 9 i 548i4 54 9 3 7 54456 5458o 54704 5482 7 54 9 4 9 5446 9 545 9 3 54 7 i6 5483 9 54 9 6 2 5448i 54605 54728 5485 1 54 97 4 544 9 4 546i 7 5474i 54864 54 9 86 545o6 5453o 54 7 53 548 7 6 54998 54518 54642 54 7 65 54888 55ou 1 i 2 3 4 5 6 8 1 2 3 4 5 6 8 9_ It i 2 3 4 6 8 2 i 2 4 6 8 10 ii 1 i 3 4 6 8 9 10 > i 2 3 4 6 8 9 355 356 35 7 358 35 9 55o23 55i45 5526 7 55388 55o35 55i5 7 552 79 554oo 55522 55o4 7 55i6 9 552 9 i 554 1 3 55534 55o6o 55i8 2 553o3 55425 55546 55o 7 2 55i 9 4 553i5 5543 7 55558 55o84 552o6 55328 5544 9 555 7 o 55096 552i8 5534o 5546i 55582 55io8 55 2 3o 55352 55473 555 9 4 55i2i 55364 55485 556o6 55i33 55255 553 7 6 554 97 556 1 8 36o 36 1 362 363 364 "365 366 36 7 368 369 5563o 55 7 5i 558 7 i 55991 56uo 55642 55 7 63 55883 56oo3 56122 55654 55 77 5 558 9 5 56oi5 56 1 34 55666 55 7 8 7 55 9 o 7 56027 56 1 46 556 7 8 55 799 55 9 i 9 56o38 56 1 58 556 9 i 558n 55 9 3i 56o5o 56i 7 o 55 7 o3 55823 55 9 43 56o62 56i8 2 55 7 i5 55835 55 9 55 56o 7 4 56i 9 4 55 7 2 7 55847 55o6 7 56o86 56205 55 7 3 9 5585 9 55 979 56o 9 8 562 1 7 56229 56348 5646 7 56585 56 7 o3 5624i 5636o 564 7 8 56507 56 7 i4 56253 563 7 2 564oo 566o8 56 7 26 56265 56384 56502 56620 56 7 38 56*77 56396 565 1 4 56632 56 7 5o 5628 9 564o 7 56526 56644 56 7 6i 563oi 564 1 9 56538 56656 56 77 3 563 1 2 5643 1 5654 9 5666 7 56 7 85 56324 56443 5656 1 56 797 56336 56455 565 7 3 566 9 i 568o8 co co co Co co JX CO (0 1-1 O 56820 56 9 3 7 5 7 o54 57171 57287 56832 56 9 4 9 5 7 o66 5 7 i83 5 7 2 99 56844 56 9 6i 5 7 o 7 8 5 7 i 9 4 5 7 3io 56855 56 97 2 5 7 o8o 57206 5 7 322 5686 7 56984 5 7 ioi 5 7 2I 7 5 7 334 568 79 56 99 6 5 7 u3 5 7 22 9 5 7 345 568 9 i 5 7 oo8 5 7 i24 5 7 24i 5 7 35 7 56 9 02 5 7 oi 9 5 7 i36 5 7 252 5 7 368 56 9 i4 5 7 i48 57264 5 7 38o 56 9 26 57043 5 7 i5 9 57270 5 7 3 9 2 3 7 5 3 7 6 377 3 7 8 3 79 5 7 4o3 5 7 5i 9 5 7 634 5 77 49 5 7 864 5 7 4i5 5 7 53o 5 7 646 5 77 6i 5 7 8 7 5 5 7 426 5 7 542 5 7 65 7 5 777 2 5 7 88 7 5 7 438 5 7 553 5 7 66 9 5 77 84 5 7 8 9 8 5 7 44? 5 7 565 5 7 68o 5 779 5 5 79 io 57461 5 7 5 7 6 5 7 6 9 2 5 7 8o 7 5 7 4 7 3. 5 7 588 5 77 o3 5 7 8i8 5 79 33 5 7 484 5 7 6oo 5 77 i5 5 7 83o 5 79 44 5 7 4 9 6 57611 5 77 26 5 7 84i 5 79 55 5 7 5o 7 5 7 6 2 3 5 77 38 5 7 852 5 79 6 7 38o 38 1 382 383 384 ~385" 386 38 7 388 38 9 58092 58206 58320 58433 5 799 o 58io4 582i8 5833 1 58444 58ooi 58n5 58229 58343 58456 58oi3 58i2 7 5824o 58354 5846 7 58024 58 1 38 58252 58365 584 7 8 58o35 58i4 9 58263 583 77 584 9 o 58o4 7 58i6i 582 7 4 58388 585oi 58o58 58i 7 2 58286 583 99 585 1 2 58o 7 o 58 1 84 58a 97 584 10 58524 58o8i 58i 9 5 58422 58535 58546 5865 9 58 77 i 58883 58 99 5 58557 58670 58 7 82 588 9 4 5u 65 108 652o5 65302 04 9 24 65o2i 65n8 652 1 5 653 1 2 45o 45 1 452 453 454 6532i 654 1 8 655i4 656 io 65706 65 33 1 65427 65523 656 1 9 65 7 i5 6534i 6543 7 65533 65629 65 7 25 6535o 65447 65543 6563 9 65 7 34 6536o 65456 65552 65648 65 7 44 65369 65466 65562 65658 65 7 53 b33 7 Q 65475 655 7 i 6566 7 65 7 63 6538 9 65485 6558i 656 77 65 77 2 653 9 8 654 9 5 65591 65686 65 7 8a 654o8 655o4 656oo 65oo6 657 9 2 455 456 45 7 458 J5?._ No. 658oi 658o6 65992 66087 66181 658 1 1 65906 66001 66096 66191 65820 65916 66011 66106 66200 6583o 65 9 25 66020 66n5 66210 6583 9 65 9 35 66o3o 66124 66219 65849 65 9 44 66o3 9 66 1 34 66229 65858 65 9 54 66o4o 66i43 662.38 65868 65963 66o58 66i53 6624-7 658 77 65 97 3 66068 66162 66257 65837 65 9 8a 66077 66172 66266 _ 1 2 3 4 5 6 7 8 9 9 ! Pa s 176 1 TABLE XXVI. Logarithms of JNuniDers. 1 2 3 4 5 6 8 9 2 3 4 5 6 7 8 i 2 3 4 5 6 7 6 I .- 2 3 4 6 8 r\ \ 2 3 4 5 e 8 B i 2 2 3 5 5 6 7 No. 4GOO 5200. Log. G6376 71GOO. No. ~46o~ 461 462 463 464 1 2 3 4 5 6 7 8 9 66276 663 70 66464 66558 66652 66286 6638o 66474 6656 7 66661 66295 6638 9 66483 66677 66671 663o4 663o8 66492 66586 66680 663 1 4 664o8 66602 665o6 66689 66323 66417 665 1 1 666o5 66699 66332 66427 66621 666 1 4 66708 66342 66436 6653o 66624 66717 6635 1 66445 66539 66633 66727 6636i 66455 66549 66642 66 7 36 465 466 46 7 468 469 66745 66839 66932 6702.6 67117 66 7 55 66848 6694 1 67034 67127 66764 66867 66960 67043 67136 66 77 3 66867 66960 67062 67146 66 7 83 668 7 6 66969 6-7062 6 7 i54 66792 66885 66978 67071 67164 66801 66894 66987 67080 6 7 i 7 3 66811 66904 66997 67089 67182 66820 669 1 3 67006 67099 67191 66829 66922 6 7 oi5 67108 67201 470 471 472 473 474 476 476 477 479 48 1 482 483 484 . "485 486 48 7 488 48 9 490 491 492 493 494 496 496 497 498 499 5oo 5oi 502 5o3 5o4 5o5 606 607 608 609 67 2 I O 67302 67394 67486 67678 67219 67311 6 7 4o3 67496 67687 67228 6 7 32i 6 7 4i3 67604 67696 6 7 23 7 6 7 33o 67614 67606 67247 6 7 33 9 6 7 43i 67623 67614 67266 67348 67440 6 7 532 67624 6-7266 6 7 35 7 6-7449 6 7 54i 67633 67274 6 7 36 7 6 7 45 9 67660 67642 67284 67376 67468 67660 6 7 65i 6-7293 6 7 385 6 7 4 77 6 7 56 9 67660 67669 67761 67862 67943 68o34 67679 67770 67861 67962 68o43 67688 67779 67870 67961 68062 67697 67788 67879 67970 68061 67706 67797 67888 67979 68070 67716 67806 67897 67988 68079 67724 678 1 5 67906 67997 68088 6 77 33 67826 67916 68006 68097 67742 6 7 834 67926 6801 5 68106 67-762 67843 6-7934 68024 68116 68124 68216 683o5 683 9 5 68485 68 1 33 68224 683 1 4 684o4 68494 68142 68233 68323 684 1 3 68602 68161 68242 68332 68422 685 1 1 68160 68261 6834i 6843 1 68520 68169 68260 6835o 6844o 68629 68178 68269 68359 68449 68538 68187 68278 68368 68458 68547 68196 68287 683 77 68467 68556 68206 68296 68386 684-6 68565 68674 68664 68 7 53 68842 68931 68583 686 7 3 68762 6885i 68940 68692 68681 68771 68860 68949 68601 68690 68780 68869 68968 68610 68699 68789 68878 68966 68619 68708 68797 68886 68976 68628 68717 68806 68896 68984 68637 68726 688 1 5 68904 68993 68646 68735 68824 68 9 i3 69002 68655 68 7 44 68833 68 9 22 6 9 oii 69020 69108 69197 69286 6 9 3 7 3 69028 69117 69206 69294 6 9 38i 69037 69126 69214 69302 6939 69046 6 9 i35 69223 69311 6 9 3 99 69066 69144 69232 69320 69408 69064 69162 692.41 6 9 32 9 69417 69073 69161 69249 69338 69426 "69613 69601 69688 69776 69862 69082 69170 69268 69434 69090 69179 69267 6 9 355 6 9 443 69099 69188 69364 69462 69461 69648 69636 69723 69810 69469 6955-7 69644 6 97 3 2 69819 69478 69666 6 9 653 69740 69827 69487 69674 69662 69749 6 9 836 69496 69683 69671 69768 69845 69604 69692 69679 69767 6 9 854 69622 69609 69697 69784 69871 6 9 53i 69618 69706 6 979 3 69880 6 9 53 9 69627 69714 69801 69888 70070 70167 70243 69906 69992 70079 70 1 65 70262 69914 7000 1 70088 70174 70260 69923 70010 70096 70 1 83 70269 69932 70018 70106 70191 70278 69940 70027 70114 70200 70286 69949 7oo36 70122 70209 70296 69968 70044 70i3i 70217 7 o3o3 69966 70063 70140 70226 7o3i2 69976 70062 70148 70234 70321 70329 704 1 5 70601 70686 70672 7o338 70424 70609 70696 70680 70346 70432 70618 70603 70689 70355 7o44 1 70626 70612 70697 70364 70449 7 o535 70621 70706 70372 70458 7o544 70629 70714 7o38i 70467 7 o552 7 o638 70723 70389 70476 70661 70646 70731 70398 70484 -70669 70666 70740 70406 70492 70678 7 o663 70749 C M ro xr m to r--oo O m m m m m jm m n m m 70767 70842 70927 71012 71096 70766 70861 70935 71020 71106 70774 70869 70944 71029 7iu3 7 o 7 83 70868 70962 71037 71 122 70791 70876 70961 71046 7ii3o 70800 70886 70969 71064 71139 70808 7 o8 9 3 70978 7 io63 71147 70817 70902 70986 71071 71166 70826 70910 70996 71079 71164 70834 70910 7ioo3 71088 71172 71181 71266 7^33 71617 71189 71273 7 i35 7 7i44i 71626 71198 71282 7 1 366 71460 7 i533 71206 71200 71374 7 i458 -71642 71214 71299 7 1 383 71466 71660 71223 71307 71391 71476 71669 71231 7 i3i5 71399 7 i483 71667 71240 7 i4o8 71492 71676 712.48 7 i332 71416 71600 71684 71267 7i34i 71426 71608 71692 No. 1 3 4 5 6 7 8 9 TABLE XXVI. [Page 177 Logarithms of Numbers. T 2 3 4 5 6 7 8 _9_ ~T 2 3 1 I 9 9 i 2 3 4 5 5 6 8 8_ i 2 2 3 4 6 7 No. 5200 5800. Log. 71600 76343. No. 520 521 522 523 624 1 2 3 4 5 6 7 8 9 71600 71684 71767 7 i85o 71933 71609 71692 71775 7 1 858 7i94i 71617 71700 71784 71867 71950 71625 71709 71792 7 i8 7 5 7 i 9 58 7 i634 71717 71800 7 i883 71966 71642 7 I 7 25 71809 71892 71976 71660 71734 71817 71900 71983 71669 71742 71826 71908 71991 71667 71760 7 i834 71917 71999 71676 71769 71842 71926 72008 626 626 5 27 5 2 8 5 29 72016 72099 72181 72263 7 2.346 72024 72107 72189 72272 72354 72O32 72115 72198 72280 72362 72041 72123 72206 72288 72.370 72049 72l32 72214 72296 7 23 7 8 7 205 7 72140 72222 72304 7 238 7 72066 72148 72230 723i3 7 23 9 5 72074 72166 7223 9 72321 724o3 72082 72166 7224-7 72329 72411 7200X) 72173 72255 72337 7 24i 9 53o 53 1 532 533 534 ~535~ 536 537 538 5^9 7 2428 72509 72591 7 26 7 3 72 7 5/ 72436 725i8 72599 72681 72-762 72444 72526 72607 72689 72770 72452 72534 72616 72697 72779 72460 7 2542 72624 7 2 7 05 72787 72469 72660 72632 7 2 7 l3 72-796 72477 72668 72640 72-722 7 28o3 72486 72667 72648 72 7 3o 72811 72493 72676 72666 7 2 7 38 72819 7 25oi 7 2583 72666 72746 72827 7-835 72916 7^997 78078 7 3i5 9 /2843 72925 7 3oo6 7 3o86 73 1 67 72852 7 2 9 33 7 3oi4 73094 7 3i 7 5 72860 72941 7 3o22 7 3lO2 7 3i83 72868 -72949 7 3o3o 7 3ui 73191 72.8-76 72967 73o38 73119 73i99 72884 -72966 7 3o46 73127 73207 728 9 2 72973 7 3o54 7 3i35 7 32i5 72900 7 298i 7 3o62 7 3i43 73223 72908 7 2 9 8 9 7 3o 7 o 7 3i5i 7 3 2 3i 54o 54 1 54? 543 544 545" 546 547 548 549 7 3 2 3 9 7 33 20 7 34oo 7 348c 7 356o 73247 7 3328 7 34o8 7 3488 7 3568 7 3 2 55 7 3336 7 34i6 7 3496 7 35 7 6 7 3263 73344 73424 7 35o4 7 3584 732-72 73352 7 343 2 7 35i2 7 35 9 2 7 328o 7 336o 7 344o 7 352o 736oo 73288 7 3368 7 3448 7 35 2 8 7 36o8 7 32 9 6 73376 7 3456 7 3536 7 36i6 7 33o4 7 3384 7 3464 73544 7 3624 7 33i2 7 33 9 2 73472 73552 7 3632 7 364o 73-719 73799 7 38 7 8 73957 73648 73727 7 38o 7 7 3886 73965 7 3656 7 3 7 35 7 38i5 738 9 4 73973 73664 7 3 7 43 7 38 2 3 73902 7 3 9 8i 7 36 7 2 7 3 7 5i 7 383o 7 3 9 io 7 3 9 8 9 736 79 73 7 5 9 7 3838 7 3 9 i8 73 99 7 7 368 7 73767 73846 7 3 9 26 74oo5 7 36 9 5 73 77 5 7 3854 7 3 9 33 7 4oi3 7 3 7 o3 7 3 7 83 7 3862 73941 74020 73711 73791 7 38 7 o 7 3 9 4 9 74028 55o 55i 552 553 554 74o36 74n5 74194 7 42 7 3 7 435i 7 4o44 7 4i23 74202 7 428o 7 435 9 74o52 74i3i 74210 74288 7436 7 74060 74i3 9 74218 74296 743 7 4 7 4o68 7 4M 7 7 4225 7 43o4 7 438 2 74o 7 6 7 4 1 55 74233 7 43 1 2 743 9 o 7 4o84 74162 7424i 7 432o 7 43 9 8 74o 9 2 74170 7424 9 7432 7 744o6 7 4o 99 74i 7 8 7 425 7 7 4335 744 1 4 74107 74 1 86 74266 74343 7442i 555 556 55 7 558 55 9 74429 745o 7 74586 7 4663 7 4 7 4i 7 443 7 7 45 1 5 7 45 9 3 74671 74749 74445 74523 7 46oi 74679 74757 7 4453 7 453i 74609 7 468 7 7 4 7 64 7 446i 7 453 9 7 46i 7 7 46 9 5 7 4 77 2 74468 74547 74624 74702 74780 7 4476 7 4554 7 4632 7 4 7 io 74788 74484 74662 7464o 747i8 7479 6 7 44 9 2 745 7 o 74648 74726 748o3 745oo 745 7 8 74656 74733 748ii ; 2 3 4 5 6 j 9 r i i 2 O \J 4 4 5 6 6 56o 56 1 562 563 564 74819 7 48o6 7 49- 7 4 7 5o5i 7 5i28 7482 7 74904 74981 75o59 75 1 36 74834 74912 74989 75o66 7 5i43 74842 74920 74997 7 5o-4 76161 7 485o 7 4 9 2 7 7 5oo5 76082 7 5i5 9 74858 74 9 35 76012 7 5o8 9 7 5i66 74865 74943 76020 76097 76174 748 7 3 74 9 5o 76028 7 5io5 76182 74881 74 9 58 7 5o35 75n3 7 5i8 9 7 488 9 7 4o66 7 5o43 7 5l2O 75i 9 7 76274 7535 1 7542 7 7 55o4 7 558o 565 566 56 7 568 569 7 52.o5 76282 7 5358 7 5435 7 55ii 7 52i3 75289 7 5366 75442 75519 75220 75297 753 7 4 7 545o 75526 76228 7 53o5 7538 1 7 5458 7 5534 76 a 36 7 53i2 7 538 9 7 5465 7 5542 7 5243 7 532o 76397 75473 75549 76261 7 53 2 8 754o4 76481 7 555 7 76259 75335 76412 7 5488 7 5565 76266 7 5343 76420 7 54 9 6 7 55 7 2 b 7 o 5 7 i 5 7 2 5 7 3 5 7 4 7 558 7 7 5664 7574o 7 58i5 76891 7 55 9 5 756 7 i 75 7 47 7 58 2 3 75899 756o3 756 7 Q 7 5 7 55 7 583t 75906 7 56io 76686 76762 7 5838 76914 7 56i8 756 9 4 7 5 77 o 7 5846 7 5 9 2I 76626 76702 76778 7 5853 76929 7 5633 76709 76786 76861 75 9 3 7 7 564i 76717 76793 7 5868 75944 7 5648 76724 76800 76876 76962 7 5656 7 5 7 3 2 76808 76884 76969 5 7 5 5 7 6 5-7 7 5 7 8 5 79 7^967 76042 76118 76193 76268 75974 7 6o5o 76125 76200 762-75 7 5 9 82 76067 76 1 33 76208 76283 76989 7 6o65 7 6i4o 762 1 5 76290 75o9 7 7 00 7 2 7 6i48 76223 76298 76006 76080 76166 76230 763o5 76012 76087 76i63 76238 763 1 3 76020 76096 76170 76245 76320 76027 76103 76178 76263 7 6328 8 7 6o35 76110 76186 7 62/x> 7 6335 No. , 1 2 3 4 5 6 7 9 Pa e 178 J TABLE XXVI. Logarithms of Numbers. 8 No. 5800 6400. Log. 76343 80618. No. ~58o~ 58 1 58a 583 584 1 2 3 4 5 6 7 8 9 7 6343 76418 76492 7 656 7 76641 7635o 76425 76500 765 7 4 76649 "76723 76797 76871 76 9 45 77019 76358 76433 765o 7 7 6582 76656 7 6365 7644o 7 65i5 7 658 9 7 6664 76373 76448 7 6522 76597 76671 7 638o 7 6455 7 653o 76604 76678 7 6388 76462 7 653 7 76612 76686 7 63 9 5 76470 76545 76619 76693 76403 76477 7655a 76626 76701 76775" 76849 76923 76997 77070 76410 76485 7 655 9 7 6634 76708 a 3 4 5 6 7 8 i. i 2 3 4 5 6 8 9 i i t 3 4 6 6 7 2 3 4 4 6 6 585 586 58 7 588 58 9 590 691 5 9 2 5 9 3 5 9 4 76716 767-90 76864 7 6 9 38 77012 7673o 76805 7 68 79 7 6 9 53 77 026 7 6 7 38 -76812 76886 76960 77034 76745 76819 7 68 9 3 7 6 9 6 7 7704l 7 6 7 53 76827 76 9 oi 76 9 75 77048 76760 76834 76008 769-82 77056 76768 76842 76916 76989 77063 77137 77210 77283 77357 7743o 76782 76856 76 9 3o 77004 77078 77 o85 77i5 9 77232 77 3o5 77379 77093 77166 77240 773 1 3 77 386 77100 77173 77247 77320 77 3 9 3 77107 77181 77254 77327 77401 77II5 77188 77262 77335 77 408 77122 77195 77269) 77342 774i5 77129. 77203 77276 77349 77422 77144 77217 77291 77364 7743 7 77i5i 77225 77298 77371 77444 5 9 5 5 9 6 5 97 5 9 8 5 99 77452 77 525 775 9 7 77670 77743 7745 9 77532 77605 77677 7775o 77466 7753 9 77612 77 685 77757 77474 77546 776i 9 77692 77764 7748i 77554 77627 776 99 77772 77488 77 56i 77634 77706 77779 77495 77 568 7764i 777i4 77786 77 5o3 775 7 6 77648 77721 7779 3 775io 77 583 77 656 77728 77801 77517 77590 77 663 77735 77808 600 60 1 602 6o3 J5o4 60 5 606 607 608 6o 9 610 611 612 6i3 6i4 '78 1 5 77887 77 9 6o 78032 78104 78T76" 78247 7 83i 9 7 83 9 o 78462 77822 77895 77967 78039 78111 77 83o 77002 77974 78046 78118 7783 7 77909 77981 7 8o53 78125 77844 779i6 77988 78061 78 1 32 77 85i 77924 77996 78068 78140 77 85 9 77 9 3i 78oo3 7 8o 7 5 78i47 77866 77938 78010 78082 7 8i54 77873 77945 78017 78089 78161 77880 77952 78025 78097 78168 7 8i83 78254 78326 7 83 9 8 7 846 9 --HI 9 o 78262 ^8333 784o5 78476 78197 78269 7834o 78412 7 &483 78204 782^6 78347 78419 78490 78211 78283 78355 78426 78497 78219. 78200 78362 78433 7 85o4 78226 78297 7 836 9 7 844o 7 85i2 78233 7 83o5 78.376 78447 78519 78240 783 1 2 78383 78455 7 8526 78533 78604 7 86 7 5 78746 78817 7854o 78611 78682 78753 78824 78547 78618 7 868 9 78760 783 1 7 8554 78625 78696 78767 7 8838 7856i 78633 78704 78774 78845 7 856 9 7 864o 78711 78781 7 885 2 7 85 7 6 78647 78718 78789. 7 885 9 7 8583 7 8654 78726 78-796 78866 78590 78661 7 8 7 32 7 88o3 7 88 7 3 785 97 78668 78 7 3 9 78810 78880 6i5 616 617 6r8 6i 9 78888 7 8 9 58 7 9 02 9 7999 79'D'9 788 9 5 78965 79<>36 7 9 1 06 79176 78 9 02 78 9 72 79<"'43 79113 79 i83 78909 78979 79050 79120 79190 78 9 i6 78086 7957 7 9 J27 79 '97 7 8 9 23 78993 79064 79i34 79204 7 8 9 3o 79000 797i 7 9i4i 792H 7 8 9 3 7 79007 79078 79148 79218 78944 79014 79085 79i55 7ga5 7 8 9 5 1 70021 790 9 2 79162 7 9 2.32 ( i i 3 4 5 6 7 8 .i 5 i i 2 2 3 4 4 1 620 621 622 623 624 79 23 9 793o9 793/9 79449 795i8 7 9 246 7 9 3i6 79 386 7 9 456 79 525 79 253 79323 79 3 9 3 79463 79 532 79260 79 33o 79400 79470 79 53 9 79267 79337 79407 79477 79546 79274 79344 794i4 79484 7 9 553 79281 79 35i 79421 79491 79560 79288 79 358 79428 79498 79567 79295 79 365 79 435 7 9 5o5 79574 79802 79372 79.442 79 5ll 7968 1 6u5 626 627 628 62 9 79 588 79657 79727 79796 7 9 865 7 9 5 9 5 79664 79734 79 8o3 79872 79602 79671 7974 1 79810 79879 79609 79678 79748 79817 79886 7 9 6i6 79 685 79754 79824 79893 7 9 6?.3 79 6 9 2 7976i 79 83i 799o 7 963o 79699 79768 79837 -79906 79637 79706 79775 7 9 844 799 1 3 79644 79.71 3 79782 79 85i 79920 7 9 65o 70720 79789 79858 79927 63o 63i 632 633 634 79934 8ooo3 80072 8oi4o 8020 9 79941 80010 80079 80 1 47 80216 799 48 80017 8oo85 80 1 54 80223 799 55 80024 80092 80161 80229 79962 8oo3o 8oo 99 80168 80236 79969 80037 80106 8oi 7 5 80243 79975 8oo44 8on3 80182 8o25o 79982 8oo5i 80120 80188 80267 18SI 80127 80195 80264 79996 8oo65 80 1 34 80202 80271 635 636 63 7 638 63 9 80277 8o346 8o4i4 80482 8o55o 80284 8o353 80421 8o48 9 8o55 7 802 9 I 8o35 9 80428 8o4 9 6 8o564 80298 8o366 8o434 8o5o2 80570 8o3o5 8o3 7 3 8o44i 8o5o 9 8o5 77 8o3i2 8o38o 8o448 8o5i6 8o584 8o3i8 8o38 7 8o455 8o523 80691 8o325 8o393 80462 8o53o 8o5o8 8o332 8o4oo 8o468 8o536 80604 8o33 9 80407 80476 8o543 80611 No. 1 2 ] 3 4 5 6 7 8 9 TABLE XXVI. [Page 179 Logarithms of Numbers. No. 6400 7000. Log. 80618 84510. No. 1 2 3 4 5 6 7 8 9 640 64 1 642 643 644 80618 80686 80754 80821 80889 80626 8o6 9 3 80760 80828 8o8 9 5 8o632 80699 80767 8o835 800^)2 8o638 8o 7 o6 8o 77 4 80841 8o 9 o 9 8o645 8o 7 i3 8o 7 8i 80848 80916 80662 80 7 20 8o 7 8 7 8o855 80922 8o65 9 80-726 80794 80862 8o 9 2 9 80666 80733 80801 80868 80936 80672 8o 7 4o 80808 80876 8o 9 43 8o6 79 8o 7 4 7 808 1 4 80882 8o 9 4 9 81017 81084 81161 81218 81286 645 646 64 7 648 649 80956 81023 81090 81168 81224 8oo63 8io3o 8io 9 7 8n64 8i23i 8o 9 6 9 81037 81104 81171- 8 1 238 8o 97 6 8io43 81111 81178 81245 80983 8io5o 81117 81184 81261 80900 81067 81124 81191 81268 80996 81064 8ii3i 81198 81266 8ioo3 81070 8ii3 7 81204 81271 81010 81077 8n44 81211 81278 65o 65 1 652 653 654 81291 81 358 81426 81491 8i558 81298 8 1 365 8i43i 81498 8 1 564 8i3o5 81371 8 1 438 81606 81671 8i3n 8i3 7 8 8 1 445 81611 8i5 7 8 co m co xr >-i co m i- oo oo oo xx m m CO OO 00 CO CO 8i325 81891 8i458 8162.5 81691 8i33i 8i3 9 8 8i465 8i53i 81698 co m co xx oo o r~-oo c oo xxxrm ^o CO GO CO CO 00 8 1 345 8i4n 81478 8i544 81611 -. co m i-< r- m -H co m oo xx xx in -o CO OO OO CO OO 655 656 65 7 658 65 9 8162.4 81690 8i 7 5 7 81823 81889 8i63i 81697 8i 7 63 81829 81896 8i63 7 8i 7 o4 8i 77 o 8 1 836 81902 8i644 8i 7 io 8i 77 6 81842 8i 9 o8 81661 8I7I7 81783 81849 81916 8i65 7 8i 7 23 8i 7 oo 81856 8l 9 2I 81664 8i 7 3o 81-796 81862 81928 81671 8i 7 3 7 8i8o3 81869 8i 9 35 81677 8i 7 43 81809 81876 81941 8i684 8i 7 5o 81816 81882 8i 9 48 660 661 662 663 664 8i 9 54 82020 82086 82161 82217 81961 82027 82092 82168 82223 81968 82033 82099 82164 82230 8i 97 4 82040 82106 82171 82236 81981 82046 82112 821-8 82243 8i 9 8 7 82063 82119 82184 82249 81994 82060 82126 82191 82266 82.000 82066 82132 82197 82263 82007 82073 82i38 82204 82269 82334" 82400 82466 8 2 53o 82696 82014 820 79 82145 82210 822 7 6 665 666 66 7 668 669 82282 82347 82478 82543 82289 82354 82419 82484 82649 82296 82.360 82426 82491 82666 82620 82686 82 7 5o 82814 8 2 8 79 82802 8236 7 82432 824 97 82662 823o8 8 2 3 7 3 82439 82604 82669 823i5 82380 82445 82610 826-76 82321 8 2 38 7 82462 82.6 1 7 82682 82.328 8 2 3 9 3 82458 82623 82688 82341 82406 824-1 82536 82601 6 7 o 671 6 7 2 6 7 3 6 7 4 82607 82672 82737 82802 82866 82614 82679 82743 82808 82872 8262 7 82692 82-766 82821 82886 82633 82698 82 7 63 8282 7 82892 82640 82-706 82769 82834 82898 82646 82711 82776 82840 82906 82969 83o33 83o 97 83i6i 832*5 83353 834i7 8348o 83544 82653 82718 82782 82911 82669 82724 82789 82853 82918 82666 82 7 3o 8 279 5 82860 6 7 5 676 677 678 679 82930 82996 83o5 9 83i23 83 1 87 82937 83ooi 83o65 83 1 29 83i 9 3 82943 83oo8 83o 7 2 83 1 36 832oo 82960 83oi4 83o 7 8 83i42 832o6 82966 83o2o 83o85 83i49 832i3 82963 83027 83091 83i55 83219 82976 83o4o 83io4 83 168 83232 82982 83o46 83uo 83 1 7 4 83238 82988 83o52 83ii 7 83i8i 83245 680 68 1 682 683 684 8325 1 833 1 5 833 7 8 83442 835o6 833 2 1 83385 83448 835i2 83264 8332 7 833 9 i 83455 835i8 832 7 o 83334 83398 8346i 83525 832 7 6 8334o 834o4 8346- 8353i 83283 83347 834 10 83474 8353 7 83 2 96 8335 9 8342.3 83487 8355o 83302 83366 83429 83493 83556 833o8 833 7 2 83436 83499 83563 685 686 687 688 689 83569 83632 88696 83822 835 7 5 8363 9 83702 83 7 65 83828 83582 83645 83 7 o8 83 77 i 83835 83588 8365 1 8371$ 83 77 8 8384 1 83594 83658 83 7 2i 83 7 84 8384 7 836oi 83664 83 7 2 7 83 79 o 83853 83607 83670 83734 83797 8386o 836 1 3 836 77 83740 838o3 83866 83620 83683 83 7 46 838o 9 838 7 2 83626 8368 9 83 7 53 838i6 838 79 690 691 692 6 9 3 694 6 9 5" 696 097 698 699 83885 83948 84oii 84073 84 1 36 83891 83954 84017 84o8o 84 1 42 838 97 83960 84023 84o86 84 1 48 83904 83 9 6 7 84029 84092 84i55 83910 83 97 3 84o36 84o 9 8 84i6i 83 9 i6 83 979 84042 84io5 84i6 7 83 9 23 83 9 85 84o48 84m 84i 7 3 83929 83 99 2 84o55 84117 84 180 83 9 35 83 99 8 84061 84i23 84 1 86 83 9 42 84oo4 84o6 7 84i3o 84 1 92 84 1 98 84261 843a3 84386 84448 84206 84267 8433o 843o2 84454 84211 842 7 3 84336 843 9 8 8446o 842 1 7 84280 84342 844o4 84466 3 84223 84286 84348 844 10 8423o 842 9 2 84354 844i7 84479 84236 84298 8436i 84423 84485 84242 843o5 84367 84429 84491 84248 843 1 1 843 7 3 84435 844 97 84266 843 1 7 84379 84442 845o4 No. 1 2 I 4 1 5 6 7 8 9 **'>] TABLE XXVI. Logarithms of Numbers. i 2 3 4 5 6 7 8 _2. i 2 3 4 5 6 8 _9 i i 2 3 4 5 5 8 9_ 7 i ' 2 3 4 4 5 6 6 -*t \ 2 2 3 4 4 5 5 -- -* i a 2 3 3 4 4 No. 7000 7600. Log. 34510 88081. No. 1 2 3 4 5 6 ! 7 8 9 700 701 702 7 o3 704 70 5 706 77 708 709 845 10 845 7 2 84634 84696 845i6 84578 84640 84702 84763 84522 84584 84646 84708 84770 84528 84590 84652 847i4 84776 84535 845 97 84658 84720 84782 8454i 846o3 84665 84726 847'88 8454 7 846o 9 846 7 i 84 7 33 84 79 4 84553 846 1 5 84677 84739 84800 84559 84621 84683 84745 84566 84628 84689 848 1 3 84819 84880 8^942 '85003 85o65 85187 852.48 853o 9 85370 84825 84887 84948 85009 85o7i 1$5T72" 85193 85254 853 1 5 8 53 76 8483 1 848o3 84954 85oi6 85o 77 84837 84899 84960 85022 85o83 84844 84905 84967 85o28 85089 8485o 84911 84 9 73 85o34 85o 9 5 84856 849 i 7 84979 85o4o 85ioi 84862 84924 84985 85o46 85 1 07 84868 84930 84991 85o52 85ii4 84874 84936 84997 85o58 85i2o 710 711 712 73 7|4_ 7\6 717 718 719 85 1 38 85 1 99 8526o 8532.1 85382 85443" 855o3 85564 85625 85685 85 1 44 852o5 85266 85327 85388 85i5o 85an 852 7 2 85333 853 9 4 85i56 85217 852 7 8 8533 9 854oo 85x63 85224 85285 85345 854o6 85 1 69 8523o 852 9 i 85352 854i2 85i 7 5 85236 852 9 7 85358 854 18 85i8i 85242 853o3 85364 85425 G543i 85491 85552 856 1 2 856 7 3 8543 7 85497 85558 856i8 85679 8544 9 855<> 9 85570 8563 1 85691 85455 855i6 855 7 6 8563 7 856 97 8546 1 85522 85582 85643 85703 8546 7 85528 85588 85649 85 7 o 9 854 7 3 85534 855 9 4 85655 85 7 i5 85479 8554o 856oo 8566 1 85 7 2i 85485 85546 856o6 8566 7 85 7 2 7 720 721 -22 123 7 24 85 7 33 85794 85854 85914 85 97 4 85 7 3 9 858oo 8586o 85920 85 9 8o 85 7 45 858o6 85866 85926 85986 85 7 5i 858i2 858 7 2 85 9 32 85 99 2 85 7 5 7 858 1 8 858 7 8 85 9 38 85 99 8 85763 8582.4 85884 85 9 44 86004 85 7 6 9 8583o 858 9 o 85 9 5o 86010 85 77 5 85836 858 9 6 85 9 56 86016 85781 85842 85902 85 9 62 86022 85 7 88 85848 85 9 o8 8 5 9 68 86028 726 727 7 28 729 86o34 86094 861 53 862 1 3 86273 86o4o 86100 86i5 9 86219 86279 86o46 86106 861 65 86225 86285 86o5a 86112 86171 8623i 862 9 i 86o58 86118 86i 77 8623 7 86297 86064 86124 86 1 83 86243 863o3 86o 7 o 86i3o 86i8 9 8624 9 863o8 86o 7 6 86 1 36 86i 9 5 86255 863 1 4 86082 86i4i 86201 86261 86320 86088 86147 86207 86267 86326 7 3o 73 1 732 7 33 734 86332 86392 864 5 1 865 10 865 7 o 86338 86398 8645 7 865 1 6 865-6 86344 864o4 86463 86522 8658i 8635o 864io 8646 9 8652.8 8658 7 86356 864 1 5 864 7 5 86534 86593 86362 86421 8648 1 8654o 865 99 86368 8642 7 8648 7 86546 866o5 863 7 4 86433 86493 86552 86611 8638o 86439 86499 86558 86617 86386 86445 865o4 86564 86623 7 35 7 36 73 7 7 38 86629 86688 86 7 47 86806 86864 86635 86694 86 7 53 86812 86870 8664 1 86700 86 7 5 9 86817 86876 86646 86 7 o5 86764 86823 86882 86652 86711 86770 86829 86888 "86977 8 7 oo5 8 7 o64 8 7 I22 87181 86658 86717 86776 86835 86894 86664 86 7 23 86782 86841 86 9 oo "86558" 87017 8 7 o 7 5 87 1 34 87192 86670 86729 86788 86847 86906 86676 86 7 35 86794 86853 86911 86682 86741 86800 8685 9 86917 7 4o 7 4i 7 42 743 744 8692.3 86982 87040 87099 86 9 2 9 86988 87046 87105 87 '63 ^22," 87280 8 7 338 8 7 3o6 87454 86 9 35 87052 87111 87169 86 9 4i 86999 87058 87116 87175 86953 87011 87070 87128 87186 86964 87023 87081 87140 87198 86970 87029 87087 87 1 46 87204 86976 8 7 o35 8 7 o 9 3 8 7 i5i 87210 745 746 747 748 749 87216 87274 87332 87390 8 7 448 87227 87286 87344 87402 87460 87233 87349 8-7408 87466 8 7 23 9 87297 8 7 355 8 7 4i3 87471 8 7 245 8 7 3o3 87361 87419 8 7 477 8 72 5i 8 7 3o 9 8 7 36 7 87425 8 7 483 87256 8 7 3i5 8 7 3 7 3 8 7 43 1 87489 87262 87320 87379 8 7 43 7 87495 87268 87326 87384 87442 87500 7 5o 75 1 7 52 7 53 754 8 7 5o6 8 7 564 81622 87679 8 77 3 7 87512 8 7 5 7 o 87628 8 7 685 87743 87518 8 7 5 7 6 8 7 633 87691 87749 87523 87581 87639 87697 87754 8 7 52 9 8-58 7 87645 87703 87760 8 7 535 8 7 5o3 8 7 65i 8 77 o8 8 77 66 8 7 54i 8 7 5o 9 8 7 656 87714 87772 8 7 547 87604 87662 87720 87777 8 7 55 2 87610 87668 87726 8 77 83 87558 87616 87674 87789 7 55 7 56 758 87853 87910 87967 88024 87800 8 7 858 879 1 5 87973 88o3o 1 87806 87864 87921 87978 88o36 87812 87869 87927 87984 88041 87818 8 7 8 7 5 8 79 33 87990 88047 8 7 823 8 7 88i 8 79 38 8 799 6 88o53 87829 87887 87944 88001 88o58 8/835 67892 87950 88007 88064 87841 87898 87955 880 1 3 88070 87846 87004 87961 88018 88076 No. 2 3 4 5 6 7 8 9 TABLE XXVI. t l 'age 181 Logarithms of Numbers. No. 7600 8200. Log. 8S08] 91381. No. 1 2 3 4 5 6 7 8 9 760 761 762 7 63 ?64 7 65 766 767 768 769 88081 88 1 38 88i 9 5 88252 88809 88o8 7 88 1 44 88201 88268 883 1 5 88093 88160 88207 88264 88321 88098 88 1 56 88213 88270 88326 88104 88161 88218 88276 88332 88no 88167 88224 88281 88338 88.16 88. 7 3 88a3o 88287 88343 88121 88.78 88235 88*92 8834 9 88127 88.84 88241 88298 88355 8847?r 88468 88626 8858 1 88638 88.33 88.90 8824-7 883o4 8836o 88366 88423 8848o 88536 885 9 3 8o3 7 2 88429 88485 88542 88698 88377 88434 88491 88547 88604 88383 8844o 8849 7 88553 88610 88389 88446 88602 88669 886 1 5 883 9 5 8845. 885o8 88564 8862 1 884oo 8845? 885 1 3 88670 88627 88406 88463 885 1 9 88676 88632 884 1 7 88474 8853o 88687 88643 770 77i 772 773 774 88649 88 7 o5 88762 88818 88874 88655 88 7 i i 88-6 7 88824 88880 88660 88717 88 77 3 88829 88885 "8894? 88 997 89053 89109 89166 88666 88722 88779 88835 88891 88672 88728 88784 88840 88897 88677 88734 88790 8S846 88902 88683 88 7 3 9 88 79 5 88862 88908 88689 88 7 45 88801 88867 88918 88694 88 7 5o 88807 88863 88919 88700 88-56 88812 88868 88926 775 776 777 778 779 88930 88986 89042 89098 89 1 54 88986 88992 89048 89104 89.69 88947 89003 89069 89116 89170 88 9 53 89009 89064 89120 8 9 i 7 6 88968 89014 89070 89126 89.82 88 9 64 89020 89076 89181 89.8-7 88960 89026 89081 89. 3 7 89.93 88976 8908 1 89087 89143 89198 88981 89087 89092 89.48 89204 780 781 782 7 83 784 "785 786 787 788 789 89209 89265 8 9 32i 89376 8 9 432 89216 892 7 i 89326 8 9 38 2 8 9 43 7 89221 892-76 8 9 332 8 9 38 7 8 9 443 89226 89282 89337 8 9 3 9 3 8 9 448 89282 8 9 28 7 8 9 343 8 9 3 9 8 8 9 454 89237 892.93 8 9 348 89404 8 9 45 9 89243 89298 8 9 354 89409 8 9 465 89248 89304 8 9 36o 894 1 5 894-70 89264 89310 89865 89421 89476 89260 8 9 3i5 8987: 69426 89481 8 9 48 7 89542 895?7 8 9 653 89708 89492 89648 8 9 6o3 89668 8 97 i3 89498 89553 89609 8 9 664 89719 89604 89669 89614 89669 89724 89609 89664 89620 8 9 6 7 5 8 97 3o 89616 89670 89626 89680 8 97 35 89620 8 9 5 7 5 8963 1 89686 8 97 4i 89626 89681 89686 89691 89746 8 9 53i 89386 89642 89697 89762 89587 89692 89647 89702 89757 79 791 792 79 3 794 8 97 63 898 1 8 8 9 8 7 3 8992-7 89982 , 89768 89823 89878 8 99 33 89988 89774 89829 89883 89938 8 999 3 89779 8 9 834 89889 89944 89998 8 97 85 89840 89894 89949 90004 89790 8 9 845 89900 89966 90009 8 97 c;6 89861 89906 89960 900.5 89801 89866 8991. 89966 90020 8 9 8o 7 89862 89916 89971 90026 89812 89867 89922 89977 9008 . 79 5 796 797 7 9 8 799 9oo3 7 9009 1 90146 90200 90255 90042 90,097 90161 90206 90260 90048 90 1 02 9 oi5 7 9021 1 90266 90063 90108 90162 90217 90271 90069 901 1 3 90168 90222 902-76 90064 90? 19 90173 90227 90282 90069 9012.4 901-79 902.33 9028-7 90070 90129 90 . 84 90288 9 02 9 3 90080 9 o.35 90189 90244 90298 90086 90140 90.96 902.49 9o3o4 OO CO OO CC' OO o o o o o -ts CO 1O >-i O 90309 9o363 904 1 7 90472 90526 903 1 4 90869 90423 90477 9063 1 90320 903 7 4 90428 90482 90536 9 o325 90880 90434 90488 90642 9 o33i 9o385 90439 90493 9o54v 90886 90390 90446 90499 90553 90342 9(5896 9 o45o 9 o5o4 00668 90347 9 o4oi 90455 90609 90 563 90362 9040-7 90461 906 1 5 90669 903 58 904 . 2 90466 9 o55.0 9o5 7 4 8o5 806 807 808 809 ~8io~ 811 812 8i3 8x4 ~E7T 816 817 818 819 90680 90634 90687 90741 90-793 oo585 90639 90693 90747 90800 90690 90644 90698 90752 90806 90696 90660 90703 90767 9081 1 90601 9 o655 90709 90763 90816 90607 9066(3 90714 90768 90822 9 06 1 2 90666 90 7 20 90778 90827 906.7 90671 90726 9"779 90832 90623 90677 90780 90784 90888 90628 90682 90786 90780 9 0843 90849 90902 90966 91009 91062 908^4 90907 90961 91014 91068 91 i 21 9II74 QI228 91281 9 1 334 90869 909.3 90966 91020 9io 7 3 90866 90918 90972 91026 91078 90870 90924 90977 91080 91084 90876 90929 90982 9io36 91089 90881 90934 90988 91041 91094 90886 90940 90998 91046 91 TOO 90891 90945 90998 91062 91 106 9 o8 97 90950 91004 oio5 7 91110 911 16 91169 91222 912-76 91328 91 126 91 1 80 91233 91286 9 i33 9 91 132 91186 910.38 91291 9 i344 9. i3 7 91190 912.43 91297 91,350 91 142 91196 91249 9.302 9.355 9Il48 9 T20I 91954 9.307 9 .36o 91153 91 2O6 9.269 9l3l2 91 365 91168 912,2 91 2o:j 91818 9i3?i 91164 91217 912.70 9 i323 91^6 No. 1 2 3 4 5 6 7 8 9 p ^ ld *J TABLE XXVI. Logarithms of Numbers. 6 i i i\i 4 2 5 3 6 4 7 4 8 5 9i5 No. 8200 8800. Log. 91381 94448. No. 1 2 3 4 5 6 7 8 9 820 821 822 8a3 824 9 i3Si 9i434 91487 9r54o 91693 9 i38 7 91440 91492 9i545 9,598 91392 9i445 91498 9i55i 9 i6o3 9 [3 97 9i45o 9i5o3 9i556 91609 9i4o3 9i455 9.5o8 9.56i 91614 91408 9,461 915,4 9,566 9,6,9 9i4i3; 9,466 9 i5i 9 91572 9,624 91418 91471 91624 91677 9 i63o 91424 9'477 9,629 9,682 9,635 9,429 9,482 9,535 9,687 9,640 825 826 827 828 829 9 i645 91698 91751 91803 9i855 9 i65i 91703 91756 91808 91861 9i656 91709 91761 91814 91866 91661 91714 91766 91819 91871 91666 91719 91772 9182.4 91876 9,672 9,724 9 ! 777 91829 91882 9,677 9 , 7 3o 91782 9,834 9,887 9 ,682 91735 91787 91840 91892 91687 9, 7 4o 91793 9 ,845 9 ,8 97 91693 91745 9,798 9 .85o 91903 83o 83 1 832 833 834 91908 91960 920 I 2 92065. 92 1 1 7 91913 9 i 9 65 92018 92070 92122 91918 91971 92023 92075 92127 9.924 91976 92028 92080 92.32 91929 9198, 9 2.o33 92085 92187 91934 91986 92038 92091 92,43 91989 91991 92044 92096 92148 91944 9 '997 9 2.o4 9 9 2IOl 92 1 53 9 . 9 5o 92002 92064 92 1 06 92 1 58 9.955 92007 92069 92. . i 92 i'63 i i 2 3 4 5 6 7 8 9 i i 2 3 4 5 6 8 9 i i ;J 2 3 3 4 4 5 t i 2 } 2 3 3 4 835 836 83 7 838 839 92 1 69 92221 92273 92324 92376 92428 92.480 92 53 1 92583 9^.634 92174 92226 92278 92380 92381 92.179 92 2.3 1 92283 9 2335 9 238 7 92184 92286 922.88 92340 92392 9 2i8 9 9 22.4l 9 22 9 3 9 2345 9 23 97 9 244 9 9 2.5oo 9 2552 9 26o3 92655 92195 92247 92298 9235o 92402 92200 92262 92304 9 2355 92407 92206 92267 92309 92361 92412 92210 92262 92314 92366 924,8 92 2 1 ) 92267 923,9 9287. 92423 84o 84 1 842 843 844 92.433 92485 92536 92 588 92689 9 2438 92490 92542 9 2.5 9 3 92645 92448 9M95 92547 92.598 92650 92454 9 2.5o5 92557 92609 92.660 92459 9261 1 92662 926,4 92666 92464 92616 92667 926,9 92670 92469 92621 92672. 92624 926-76 92474 92626 92678 92620 92681 845 846 847 848 849 92686 92737 92788 92840 92891 92691 92742 92793 92845 92896 92696 92747 92799 9 285o 92901 92701 92.752 92804 92855 92906 9 27G5 9 2 7 58 92809 92860 92911 92711 9 2 7 63 92814 92865 92916 92716 92768 92819 92870 92921 92722 9-773 92824 92876 92927 92727 92778 92829 92881 92982. 92732 92783 92834 92886 92937 85o 85i 852 853 854 92942 9 2 99 3 9 3o44 08095 93 1 46 92947 92998 98049 93 100 93i5i 92952 98003 9 3o54 98 1 o5 98 1 56 92957 98008 9 3o5 9 93 1 10 98161 92962 93oi3 9 3o64 9 3ii5 98166 92967 o3oi8 9 3o6 9 9 3l20 98171 92973 98024 98076 9 3i25 9 3i 7 6 92978 98029 93080 9 3i3i 93181 92983 9 3o34 9 3o85 98 1 36 93,86 9 s 9 88 9 3o3 9 93090 93.4i 9 3i 9 2 855 856 85 7 858 859 93.97 98247 9 32 9 8 93349 9 33 99 98202 98252 933o3 9 3354 9 34o4 98207 9 3258 98808 9 335 9 93409 98212 93268 98813 9 3364 934i4 93217 98268 9 33i8 9 336 9 98420 93222 9 32 7 3 9 33 2 3 933 7 4 9 3425 93227 98278 93828 93379 9 343o 9 3232 9 3a83 9 3334 9 3384 9 3435 9 32.3 7 98288 9 333 9 9 338 9 9 344o 98242 93293 93344 93394 93445 860 861 862 863 864 9345o 935oo 9 355i 98601 9365 1 9 3455 9 35o5 9 3556 98606 93656 9 346o 9 35io 9356i 98611 98661 93465 9 35i5 98 566 98616 98666 98470 98520 98571 93621 936 7 1 93475 9352.6 9 35 7 6 98626 9 36 7 6 9 348o 9 353i 9 358i 9 363i 98682 9 3485 9 3536 9 3586 9 3636 9 368 7 9 34 9 o 9 354i 9 35 9 i 9 364i 9 36 9 2 9 34 9 5 93546 93596 9 3646 9 36 97 865 866 867 868 869 98-02 9 3 7 52 98802 9385a 93902 93707 98757 98807 9 385 7 98907 93712 93762 98812 98862 98912 98717 98767 98817 98867 98917 98722 98772 98822 98872 98922 9872.7 93777 93827 93877 939 2 7 9 3 7 32 9 3 7 82 9 3832 9 3882 98982 9 3 7 3 7 9 3 7 8 7 9 383 7 93887 9 3 9 3 7 9 3742 9 3 79 2 9 3842 9 38 9 2 9 3 9 42 98747 93797 98847 9,8897 9 3 9^7 8 TO Pvi 872 8-73 8 7 4 9 3 9 .52 94002 940 5 2 94 1 o i 94i5i 98957 94007 94057 94 1 06 9 4i56 98962 94012 94062 94 u i 94161 98967 1 94<>i7 94067 94. 16 9 4i66 98972 94022 94072 94.21 9 4i7i 9 3 97 7 94027 94077 94,26 94,76 98982 94o32 94082 9 4i3i 94.81 98987 94o3 7 94086 9 4.36 9 4i86 9 3 99 2 94042 9 4o 9 , 9 4i4i 9 4i 9 i 93997 94o47 94096 94,46 94196 8 7 5 ?y5 87? 3-8 879_ No. 94201 942.5o 94800 94349 94399 94206 94255 943o5 9 4354 9 44o4 94211 94260 94810 9 435 9 94409 2 942.6 9 42.65 9 43,5 9 4364 944.4 9 422I 9 427o 9 432o 9436 9 94419 94226 94275 9 4325 94374 94424 94231 94280 9 433o 94879 94429 94236 94286 9 4335 94384 9 4433 94240 9 42 9 9 434o 9 438 9 9 443& 94245 94*96 04345 94394 94443 1 3 4 5 6 7 8 | 9 8 TABLE XXVI. IPage 183 Logarithms of Numbers. No. 8800 9400. Log. 94448 9731 3. No. 1 2 3 4 5 6 7 8 9 880 88 1 882 883 884 94448 94498 94547 94596 94645 94453 o45o3 9 4552 94601 9 465o 94458 94507 9455 7 9 46o6 9 4655 9 4463 9 45i2 9 456a 9 46i i 9 466o 9 4468 9 45i 7 9 456 7 94616 94665 944 7 3 94522 945 7 i 94621 946-70 9 44 7 8 9 452 7 9 45 7 6 9 46 7 5 9 4483 9 4532 94581 9463o 94680 9 4488 94537 94586 9 4635 9 4685 94734" 94783 9 4832 94880 9492.9 94493 94542 9 45 9 , 9 464o 94689 885' 886 88 7 888 889 94694 94-792 9484i 9 48 9 o 94699 94 7 48 94797 9 4846 948 9 5 9 4 7 o4 9 4 7 53 9 48o2 9 485i 94900 9 4 7 oo 9480-7 94856 94905 9 47i4 94763 94812 94861 94910 94-719 94-768 948 1 7 94866 94915 94-724 94773 94822 948 7 i 94919 94729 94778 94876 94924 94 7 8 7 9 4836 9 4885 94934 890 891 8 9 2 8 9 3 8 9 4 8 9 5 896 897 898 899 949 3 9 94988 9 5o36 9 5o85 9 5i34 94944 94993 95090 9 5i3 9 94949 94998 95095 9 5i43 94954 95002 95o5i 95 1 oo 95 1 48 94959 95007 9 5o56 9 5io5 9 5 1 53 94963 95012 95o6 1 95 1 09 95i58 95207 9 5 2 55 953o3 9 535 2 95400 94968 96017 96066 95 1 14 95022 95071 95119 9 5i68. 949 7 8 95o2 7 96075 95124 9g83 95o8o 9 5i2 9 95182 9523i 9 5 2 7 9 9532.8 953 7 6 9 5i8 7 95284 9 533 2 9 538i 95i9 2 9 52.8 9 9533 7 95386 95245 95294 95390 95202 95299 95347 953 9 5 952 r i 95260 953o8 9 535 7 9 54o5 95216 9 5265 9 53i3 9 536i 95410 95221 953i8 9 5366 9 54 1 5 95226 952-74 95323 953 7 i 95419 900 901 902 oo3 9<>4 95424 954 7 2 95521 9 556 9 956 1 7 95429 954 7 -7 95525 955 7 4 95622 95434 95482 9553o 9 55 7 8 95626 95439 95487 9 5535 9 5583 9 563i 95444 95492 9554o 9 5588 95636 95448 9 5545 9 55 9 3 9 564i 95453 955oi 9 555o 9 55 9 8 95646 95458 9 5554 95602 9 565o 95463 955u 9 555 9 9560-7 9 5655 95468 9 55i6 9 5564 95612 9 566o 9 o5 9 o6 907 908 909 95665 9 5 7 i3 95-761 95856 95670 9 5 7 i8 9 5 7 66 958 1 3 9 586i 956 7 4 95722 95770 9 58i8 95866 95727 95 77 5 95823 95871 95684 95780 95828 9 58 7 5 95689 9573 7 9 5 7 85 9 583 2 95880 95694 95789 9 583 7 95885 95698 95746 95794 9 5842 95890 9 5 7 o3 9 5 7 5i 9 5 799 9584 7 9 58 9 5 95708 9 5 7 56 9 58o4 9 5852 95899 910 911 9,2 9.3 914 95904 95952 9 5 999 9 6r>4 7 9 6c 9 5 95909 95957 96004 96052 96099 95961 96009 96057 96 1 04 95918 90966 96014 96061 96109 95923 9 5 97i 96019 96066 96114 95928 9 5 97 6 96023 9 6o 7 i 96118 9 5 9 33 9 5 9 8o 96028 960-76 96123 9 5 9 38 9 5 9 85 9 6o33 96080 96128 9 5 99 o 96038 9 6o85 9 6i33 95947 9 5 99 5 96042 96090 9 6i3 7 in o t--oo Os Os Os Os Os Os 96,90 9623-7 96284 96147 96194 90242 962.89 96336 9 6i52 96199 962.46 96294 96341 961 56 96204 96251 96298 96 346 96 1 6 1 96209 96256 o63o3 9635o 96166 962 1 3 96261 963o8 9 6355 96171 96218 96265 963i3 9636o 9 6i 7 5 N 96223 96270 o63i 7 96365 916180 0622 7 9 6 27 5 9 6322 _9636_ 9 _ 96417 9 6464 o65n 9 6558 9 66o5 96185 96232 96280 9632-7 963 7 4 92O 9 2I 9 12 9 23 92.4 926 927 928 y3o 9 3i 9 32 9 33 9 34 9 63 7 9 96426 96473 96520 9 656 7 96384 9 643 1 96478 96525 9 65 72 9 6388 9 6483 9653o 965 77 96.193 9(^440 ?648 7 9 6534 9658s 96398 96445 96492 9653 9 96586 96402 y645o 96497 96544 9 65 9 i 9640-7 96454 965oi 9 6548 965 9 5 96412 9 645 9 9 65o6 o6553 96600 96421 96468 9 65i5 9 6562 96609 96614 96661 96708 96755 96802 966 1 9 96666 9 6 7 5 9 96806 9662.4 966-70 96717 96764 96811 96628 96675 9 6 7 22 96769 96816 96633 96680 96727 96774 96820 9 6638 96685 9 6 7 3i 96778 9 682.5 96642 96089 9 6 7 36 96783 9683o 96647 96694 96834 96652 96699 o6 7 45 96792 9683 9 96656 96-703 96-7 5o 96797 96844 96848 96895 96942 96988 9 7 o35 96853 96000 96946 96993 97039 96858 96904 9 6 9 5 1 96997 97044 96862 96909 96956 9 7 002 96867 96914 96960 9700-7 9 7 o53 96872 9 6 9 i8 96966 97011 97058 96876 96923 96970 97016 97063 96881 96928 96974 97021 97067 0886 96932 96979 97 025 9-70-72 96890 96937 96984 9 7o3o 97077 9 35 9f 937 9 3 9 9-7081 9-7128 97174 9 7 220 9 7 26 7 97086 97 1 32 97179 97225 9 7 2 7 I 97090 9-7 1 3 7 9 7 i83 9 7 2.3o 972-76 97095 9 7 l42 9 7 i88 9 7 234 9-7280 9 7 ioo 9-7 1 46 9-7192 97 2 3o 97285 97i4 97 i5i 97197 97243 97 2 9 97109 97 1 55 07202 97 2 9 4 97114 9 7i6o 9 72o6 97 2.53 97299 97 '1? 97 i65 97211 9725 7 97 3o4 971^3 97169 97216 97262 97 3o8 No. 1 a 3 4 5 6 7 8 9 Fagel84 J TABLE XXVI. Logarithms of Numbers. 9996. 5 i 2 3 4 6 8 9^ 4 2 3 4 5 6 81 0' No. 9400 10000. Log. 97313 9 No. 1 2 3 4 5 6 7 8 9 940 9 4i 942 943 944 ' 9 4-5" 946 947 948 9 4 9 960 95 1 9 52 9 53 954 97 JiJ o-?35o 974o5 9745 1 97497 97543" 9758 9 97 635 97681 97727 973i7 97364 974 10 9 7456 97502 9 7 322 97 368 97 4i4 97 46o 97606 97327 973 7 3 9-74 1 9 97 465 97 5ri 97 33 1 973 77 9-7424 97 4 7 o 9 7 5i6 97 336 9 7 38 2 9 7 428 9 7 4 7 4 9 7 52o 9734o 9738 7 97433 9 747 9 97525 97345 97391 9743 7 97483 97529 9 735o 97 3 9 6 97 44^ 97 488 9 7534 97354 97400 9744 7 974Q3 9753 9 97548 97594 97640 97 685 9773 1 97 55 2 975 9 8 97644 97 6 9 o 977 36 97 55 7 97 6o3 97 64 9 97 6 9 5 977 4o 97562 97607 97 653 97699 97745 9 7 566 9 7 6i2 9 7 658 97704 97749 9 757i 9 76i 7 9 7663 9 77o8 9 7754 97575 97621 9766 7 97713 97759 9 758o 9 7&26 97 6 7 2 9 7 7 i7 9 7763 97585 9763o 97676 97722 97768 97772 97818 97864 97909 97955 97777 97823 97866 979i4 97 9 5 9 977 82 97 82 7 97 8 7 3 979 i8 979 64 977 86 97 832 97 8 77 979 23 979 68 9779' 97836 97882 979-8 97973 97795 9784i 97886 97932 9 7 9 78 97800 9 7845 9 78 9 i 97937 97982 97804 9 7 85o 97896 9794i 97987 9 78o 9 97 855 979 oo 979 46 9-7991 97813 97859 9790^ 97950 97996 9 55 9 56 9^7 958 9 5 9 98000 98046 98091 9 8i3 7 98182 98005 98o5o 98006 98141 98186 9 8oo 9 o8o55 9 8ioo 9 8i46 98191 9 8oi4 9 8o5 9 9 8io5 9 8i5o 9 8i 9 5 98019 96064 98109 98 ( 55 98200 9 8o23 98068 98114 9 8i5 9 98204 98028 98073 98118 98 [64 98209 98032 98078 9812.3 98168 98214 98o3 7 98082 (^8127 9 8i 7 3 98218 98041 98087 98 1 32 98177 98223 960 961 962 963 964 98227 98272 9 83i8 98363 98408 98232 98277 98322 9 836 7 9 84i2 9 8236 98281 9 83 27 9 83 7 2 9 84i 7 9 824i 98286 9 833 1 9 83 7 6 98421 98245 98290 o6336 9 838i 9/8426 9 825o 9 o?f 90040 9 8385 9 843o 98254 98299 9 8345 98390 98435 98259 9 83o4 98349 98394 9 843 9 98263 o83o8 98354 9 83 99 9 8444 98268 983 1 3 98358 98403 98448 965 960 967 968 969 9 8453 98498 9 3543 9 8588 9 863 2 98457 9 85o2 98547 985 9 a 9 863 7 9 8462 9 85o 7 o8552 9 85 97 9 864i 98466 o85n 9 8556 98601 98646 9 84 7 i 9 85i6 9 856i c86o5 o865o 9 8475 9 852o 9 8565 98610 9 8655 98480 98525 98570 98614 9 865 9 9 8484 98529 985 7 4 986 1 9 98664 98489 9 8534 9857Q 9 86?.3 98668 98493 9 8538 98 583 98628 9 86 7 3 970 97' 972 973 974 9 8677 9 8 7 22 9 8 7 6 7 988 1 1 9 8856 9 8682 9 8726 9 8 77 i 9 88i6 9 886o 9 8686 9 8 7 3i 98776 98820 9 8865 98(391 9 8 7 35 98-780 98825 98869 9 8b 9 5 9 8 7 4o 9 8 7 84 9 882 9 9 88 7 4 9 8 7 oo 9 8 7 44 9 8 7 8 9 9 8834 9 88 7 8 98704 9 8 7 4 9 98-793 o8838 98883 98709 9 8 7 53 98798 98843 98887 98 7 t3 9 8 7 58 98802 9 884 7 9 88 9 2 98717 98762 98807 988 5 1 98896 975 976 977 978 979 98900 98945 98989 99 o34 99078 9 8 9 o5 98949 98994 99 o38 99 o83 98909 9 8 9 54 9 8 99 8 99043 99 o8 7 9 8 9 i4 9 8 9 58 99003 99 o4 7 99092 9 8 9 i8 98963 99 oo 7 oooSa 99096 98923 98967 990 I 2 99 o56 99100 98927 9 8 9 72 99016 99 o6i 99 io5 9 S 9 32 98976 99021 99065 99109 98 9 36 9 8 9 8i 99025 996 9 99" 4 9 8 9 4i 9 8 9 85 99029 99074 991 18 980 98, 982 9 83 9 84 o85 986 987 988 989 99*23 99167 99211 99255 99 3oo 99127 99171 99216 99260 99 3o4 "^348" 99 3 9 2 99436 99480 995a4 99i3i 99176 99 220 99264 99 3o8 99 1 36 99180 9922.4 99269 99 3 1 3 99 i4o 99 i85 99229 99273 99317 99145 99189 99^33 99277 99322 99 i4 9 99193 992.38 99282 99 3 2 6 99i54 99,98 99242 99286 99 3 3o 99 i58 99202 9924-7 99291 99 335 99162 9920^ 992 5 1 99295 99 33 9 99 344 99 388 9943a 99476 99.520 99 352 99396 9944i 99 484 99528 99 35 7 99 4oi 99445 $S3 9936 1 9940 5 99449 994Q3 99 53 7 99366 99410 99454 99498 99542 99 3-o 99 4i4 99 458 99502 99546 99 3 74 994i9 99463 99506 99550 99 3 7 o 99423 99467 ooSii 99355 99 383 99 42 7 99471 99 5.5 99 55 9 990 99' 99; 99 3 994 9 9 564 99607 99651 99 6 9 5 99739 99568 99612 99 656 &S. 995-72 99616 99660 997 o4 997 4 7 99 5 77 9962 1 99664 99708 99-52 99 58, 99625 99669 997 I2 997 56 99 585 99629 99 6 7 3 99717 99760 99590 996^4 996-77 99721 997 65 9<;5 9 4 99638 99 682 997 26 99769 99.^99 9964? 99686 9 97 3o 99774 99 6c3 9964 7 99691 99734 99778 99 5 996 997 998 999 99782 99 826 99 8 7 o 999 i3 999 5 7 gffi 99874 99917 99961 99-791 99835 99878 99922 99965 99 7 9 5 99 83 9 99 883 99926 9997" 3 99800 99 843 99 88 7 9993o 99974 99804 99848 9989. 999.35 99978 99808 99 85. 99896 999.^9 99-yS3 998 1 3 $856 99900 99944 999 8 7 99817 99861 99904 99948 99991 99822 99 865 99909 999 52 99996 No. 1 2 4 | 5 6 7 8 9 M TABLE XXVII. iPagtias Log. Sines, Tangents, and Secants. 179 Hour A.M. Hour p. M o o o o 8 o 16 ! o 24 32 Sine. Diff. 1 Cosecant Tangent. Diff.l Cotangen Secant. Cosine. M o ~e 6 8 9 1200 ii 59 52 59 44 59 36 59 28 Inf. Neg. 6.463 7 3 7 64 7 6 9408 5 7.06579 3oio^ 1-7609 12494 969 Infinite. l3.5362 7 23524 o5 9 i5 12.93421 Inf. Neg. 6.463 7 3 76476 94o85 7 .o65 7 9 3oio3 17609 12494 969 1 Infinite, i 3. 5362 7 23524 o5 9 i5 I2. 9 342I 10.00000 ooooo ooooo ooooo ooooo 10.00000 ooooo oocoo OOOOG DOOOO 60 5 9 58 5- se ii 59 20 5 9 12 5? 5t 58 48 o o 4o o 48 o 56 i ^ I 12 7. 16270 24188 3n882 36682 41797 7918 6694 58oo 5n5 45 7 6 i2.83 7 3o 7 58i2 69118 633 1 8 582o3 7. 16270 24188 3o882 36682 4i 7 9 7 7918 6694 58oc 5n5 45 7 6 i2.83 7 3( 7 58i2 691 1 8 633 1 8 582o3 10.00000 ooooo ooooo ooooo ooooo 10. ooooo ooooo ooooo ooooo ooooo 55 54 53 52 5i 10 ! I 12 i3 i4 ii 58 4o 58 32 58 24 58 16 58 8 I 20 I 28 i 36 i 44 I 52 7.463 7 3 5o5i2 54291 57767 6o 9 85 4i39 3 779 34 7 6 32i8 2997 12.53627 49488 45-709 42233 3 9 oi5 7 .463 7 3 5o5i2 5429 5 77 6 7 60986 4i3o 3 779 34 7 6 32I 9 2996 12.53627 4 9 488 45 7 o 9 42233 3 9 oi4 I O. OOOOO ooooo OMDOO ocooo OOl OO I O . OOOOO ooooo ooooo ooooo ooooo 5o 49 48 47 46 45 44 43 4a 4i 4o 3 9 38 3 7 36 1 5 16 17 18 '9 ii 58 o 5 7 52 5 7 44 5 7 36 5 7 28 020 2 8 2 16 2 24 2 32 7 .63 9 82 66784 69417 71900 74248 2802 2633 2483 2348 222 7 i 2 . 36o i 8 332i6 3o583 28100 25 7 52 7 .63 9 82 66 7 85 69418 7 i9oo 74248 2803 2633 2482 2348 2228 I2.36ot8 332i5 3o58 2 28100 25 7 52 10.00000 ooooo 00001 0000 1 0000 1 1C .00000 ooooo I 9-99999 99999 99999 1 1 >?. 23 34 II 5 7 20 5 7 12 5 7 4 56 56 56 48 o 2 4o 2 48 2 56 3 4 3 12 7 . 7 64 7 5 7 85 9 4 806 1 5 82545 84393 21 19 202 i 9 3o 1 848 i 77 3 12.23525 21406 19385 i 7 455 i56o 7 7. 7 64 7 6 7 85 9 5 806 1 5 82546 843 9 4 21 19 2O2O 1981 1848 i 77 3 12.23524 2i4o5 i 9 385 i 7 454 i56o6 10.00001 OOOOI 0000 1 OOOOI OOOOI 9-99999 99999 99999 99999 99999 25 26 27 28 29 ii 56 4o 56 32 56 24 56 16 56 8 3 20 3 28 3 36 3 44 3 52 7. 86166 87870 89509 91088 92612 1704 i63 9 1 579 i524 1472 I2.i3834 I2l3() 10491 08912 o 7 388 7 .86i6 7 8 7 8 7 i 8 9 5io 91089 9261^ i-7o4 i63 9 i5 79 i524 i4 7 3 i 2.i3833 121 2 9 io4 9 o o8 9 i i o 7 38 7 I O. OOOOI OOOOI OOOOI 0000 1 00002 9-99999 99999 99999 99999 9999 8 35 34 33 32 3i 3o 3i 3; 33 34 ii 56 o 55 52 55 44 55 36 55 28 o 4 o 4 8 4 16 4 24 4 32 7- 94o84 955o8 9 688 7 98223 99520 1424 1 3 79 1 336 1297 1259 12.05916 04492 o3i 1 3 01777 00480 7.94086 9 55io 96889 98225 99 522 1424 i3 79 i336 I2 9 7 I25 9 i2.o5 9 M o44 9 o o3i 1 1 oi 77 5 oo4 7 8 10.00002 00002 00002 00002 00002 9-9999 8 9999 8 9999 s 99998 9999 s 3o 2Q u8 27 26 35 36 3? 38 3 9 ii 55 20 55 12 55 4 54 56 54 48 o 4 4o 4 48 4 56 5 4 5 12 8.00-779 O2002 O3l92 o435o 05478 8.06578 07650 08696 09718 10717 1223 1190 ii58 1128 I IOO 11.99221 9 7 998 96808 9 565o 94522 8.00781 02004 03194 04353 o548i 1223 I IOO n5o I I 2.8 I IOO 11.99219 97996 96806 9564? 9 45i 9 IO.OOOO2 OOOO2 ooooc oooo3 oooo3 9-9999 8 99998 99997 99997 99997 25 24 2C 22 21 4o 4i 42 43 44 ii 54 4o 54 3 2 54 24 54 16 54 8 o 5 20 5 28 5 36 5 44 5 52 1072 1046 1022 999 976 ii .93422 9 235o 9i3o4 90282 89283 8.o658. o 7 653 o8 7 oo 09-722 I0 7 20 1072 io4 7 1022 998 976 ii . 9 34i 9 9 234 7 9 i3oo 002 7 8 89280 n.883o4 8 7 349 864 1 5 855oo 846o5 10.0000,: oooo3 oooo3 oooo3 ooco4 9-99997 99997 99997 99997 9999 6 2O '9 18 16 4b 46 4 7 48 4 9 IT 54 o 53 52 53 44 53 36 53 28 060 6 8 6 16 6 24 6 3 2 3.11693 12647 i358i i4495 15391 9 54 9 34 914 896 8 77 i i.883o 7 8 7 353 86419 855o5 84609 8.1l6o6 1 265 1 1 3585 i45oo i53 9 5 9 55 9 34 o.5 6 9 5 878 10.00004 00004 00004 00004 00004 9-99996 99996 99996 99996 99996 1 5 i4 i3 12 I I DO 5i 5;> 53 54 ii 53 20 53 12 53 4 52 56 52 48 o 6 4o . 6 48 6 56 7 4 7 12 8.16268 17128 i797i i8 7 98 19610 860 843 82 7 812 797 n.83 7 3a 828 7 2 82029 81202 60390 8.i62 7 3 I 7 i33 i 797 6 18804 10616 860 843 828 812 797 i i.83 7 a 7 8286-7 82024 81196 8o384 io.oooo5 ooooS oooo5 ooooS ooooS 9-99995 99995 99995 9999 5 9999 5 IO 7 6 5 4 3 .. i o bb 56 57 5P 5 9 60 M ii 52 4o 52 3a 52 2A 52 16 52 8 52 o 7 20 7 28 7 36 7 44 7 52 8 o 8 . 2o4o 7 21189 21958 22 7 l3 23456 24186 782 769 7 55 7 43 7 3o 717 1 1. -79593 78811 7 8o42 77 28 7 76544 7 58i4 8.2o4i3 2II 9 5 21964 22720 23462 24192 782 7 6 9 7 56 7 42 7 3o 718 11.79687 78805 78o36 77280 7 6538 7 58o8 I O . OOOO6 00006 00006 00006 00006 OOOO 7 9-99994 99994 99994 ' 99994 99994 9999 3 lour i>. M. Hour A.M. Cosine. W.I' Secant CotangentjDifi'. 1' Tangent. Cosecant. Sine. M agel8G] TABLE XXVII. Log. Sines, Tangents, and Secants. P 17^ M 3fftf A.M. HoiirP.M. Sine. JDiff.rjCoseoant. angent.lDiff.l'C /otaiigont Secant. Cosine. i 2 3 4 5 6 7 8 9 52 5i 521 5i 44 5i 35 5 1 28 o 8 o 8 8 8 16 8 24 8 3; 24i86| 24903 a56o9 263o4 26988 7 1 ? [i 706- 695 684 673 1.7*1814 75097 7439. 73696 73oi2 8 24192 24910 256 1 6 263 1 ? 26996 18 i 06 96 84 73 I.758o8 75oyo 74384 7 3688 7 3oo4 0. OOG07 | 99992 99997 99992 99993 9999. 10 1 1 1 2 1 3 i4 i 5o 4 5o 32 5o 24 5o 16 5o 8 o 9 20 9 28 9 36 9 44 9 52 .3o8 79 3.495 32io3 32702 33292 6.6 608 599 590 583 [i .69121 685o5 67897 67298 66708 8.3o888 3i5o5 32II2 32711 33302 6.7 607 599 5oi 584 .1 .691 12 68495 67888 67289 66698 o . 00009 00009 OOOIO 000 10 OOOIO 7-9999' 9999 ' 99990 99990 9999" i5 16 1-7 18 '9 i 5o o 49 52 49 44 4 9 35 49 28 O 10 10 8 10 16 10 24 10 32 .338 7 5 3445o 35<>i8 355 7 8 36t3i 5?5 568 56o 553 547 i. 66125 6555o 64982 64422 6386 9 8.3386 3446i 35o2 9 355 9 o 36i43 5 7 5 568 56 1 553 546 I.66..4 65539 64971 644 1 o 63857 0.000(0 OOOII OOOI I OOOII OOOI I 9.99990 99989 99989 99989 99989 20 21 22 23 *4 25 26 27 28 29 3o 3 3 3 3 3 3 j / ,: / / -. 4 4 < 5 f i I 49 20 49 12 49 4 48 56 48 48 o 10 4o 10 48 10 56 1 1 4 II 12 .36678 37217 3 77 5o 382 7 6 38 79 6 53 9 533 526 520 5i4 i .63322 62783 62250 6172.: 6120; 8.3668 9 37229 37762 38289 388o 9 54o 533 527 520 5.4 i. 633 1 1 6277. 62238 61711 61 .9. O . OOO I 2 OOOI 2 00012 000 1C OOOK 9.99988 99988 99988 99987 99987 i 48 4o 48 32 48 24 48 16 48 8 n 46 o 4? 52 47 44 47 36 47 ,8 O I I 2O II 28 n 36 ii 44 II 52 .39310 3 9 8i8 4o32 40816 4i3o7 5o8 502 496 491 485 i i . 60690 60182 5 9 68o 59184 58693 8.39323 3 9 83 4o33 4o83 4.32 509 502 496 491 486 i .60677 60168 59666 59170 58679 io.oooi3 000 1 4 OOO 1 4 ooo 1 4 ooo 1 5 i o . ooo . 5 ooo 1 5 000.6 00016 000.6 9.99987 99986 99986 99986 999 85 \ i 3 j g 8 6 12 12 f \i i 4 ,2 3 ,4i79 2 42272 42746 432.6 4368o 48o 474 470 464 459 ii .58^08 57728 5 7 25-4 56784 56320 8. 4 1 80 4228 4276 4323 436 9 48o 4 7 5 4~>o 464 46o .1.58193 5 77 i3 5 7 238 56 7 68 563o4 9-99985 999 85 99984 99984 99984 I I 47 20 4- 12 47 4 46 56 46 48 n 46 4o 46 32 46 24 46 16 46 8 12 4< 12 48 12 5f> i3 i3 i 8. 44 1 39 44594 45o44 45489 45 9 3< 455 45o 445 44 1 436 n.5586 554o6 5495 545i 5407 8.44i5 446i 45o6 455o 4594 455 45o 446 44 1 43 7 n.55844 5538 9 5493 544Q 54o5 I o . ooo i 7 00017 000.7 ooo 1 8 00018 9.99983 99983 99983 99982 99982 5 i 3 a n 9 s o o i3 >. i3 > i3 3 i3 4 i3 5 S.463b6 4679 4722(3 47(rx 48t.<><, 433 427 42.4 419 1 4i6 u.5363 5320 52 77 5235 5i93 8.4638 468. 4724 4 7 66 4808 432 428 424 420 4i6 412 4o8 4o4 4oi 3 9 7 n.536. 53.8 52 7 5 5233 5191 10.00018 00019 00019 000.9 000 2 C 9.9998. 999 8, 0098 1 9998. 99980 ii 46 o 45 52 45 44 45 36 45 28 o .4 i4 i4 i 14 2 i4 3 8.4848* 488 9 e 4i<. 4n > 4o8 4o4 | 4oo > 3 9 6 n.5t5i 5i 10 6069 5029 4989 8.485o 4891 4 9 32 497 2 5oi3 n.5i49 5io8 5o6 7 6027 498 7 IO.OOO2C OOO 2 . O002I 00021 OOO 2 2 9-9 99 8o 99979 999"9 99979 99978 4 ! ri 45 20 45 n 45 / 44 5* 44 4* o i4 4 i4 4 i4 5 i5 i5 i 8.5ob^ 5o8 9 - 5.28- 5 1 67^ 52o5 i 3 9 3 l 390 7 386 } 382 5 3 79 U.4949 4910 4871 4832 4794 8.5o52 5092 5.3 5.6o< 5207 3 9 3 383 38o 11.4947 4908 4869 483o 4792 IO. 00025 0002: 000 '). i 0002^ OOO2. 9.99978 99977 99977 99977 99976 C h ii 44 4< 44 3: 44 2^ 44 i< 44 ! 44 < 15 2 15 2 i5 3 i5 4 i5 5 16 8.5243, 528i< 53i8 5355 53 9 i 5428 \ 3 7 6 3 3 7 3 3 36 9 2 36 7 y 363 2 36o n.4756 4719 468 1 4644 4608 45 7 i 8.5245 5283 5320 535 7 53 9 4 543o Cotangei 3 7 b 3 7 3 3 7 o 36 7 363 3 36i t|l>iflT. ii .4754 4716 4679 4642 46o5 4569 IO.OOO2' 000 2 f 0002' 000 2 ( OOO2( OOO 2 9-99976 99975 99975 99974 ij 999* N 99974 M Hour A. Cosine Diff.l ' Secant Taiigcn Cosecant. 1 Sine. 88 9i c TABLE XXVII. [Page 1ST Log. Sines, Tangents, and Secants. i] 177 C M i ) 2 3 4 5 6 8 9 Hour A.M. Hour P.M. Sine. ,I)iff.l' Cosecant. Tangent. Dtfr.l'|CotangeKl Secant, i Cosine. M ii 44 o 43 5. 4* 44 43 36 43 28 o 16 o 16 8 16 16 16 a4 16 32 Q ,. 54282 54642 %m 557o5 36o 35 7 355 35i 349 M.45 7 i8 45358 45ooi 44646 44295 8.543o8 54669 55027 55382 55 7 34 36 1 358 355 352 34 9 i i .4^692 4533i 449 7 3 446 1 8 44266 10.00026 00027 00027 00028 00028 9.99974 99973 999?3 9997' 99972 60 5 9 58 5 7 56 55 54 53 52 5 1 II 43 20 43 12 43 4 42 56 42 48 o 16 4o 16 48 16 56 17 4 17 12 8.56o54 564oo 56 7 43 5 7 o84 57421 346 343 341 33 7 336 11.43946 436oo 43 2 5 7 42916 425 7 9 8.56o83 5642 9 56 77 3 57114 5 7 452 346 344 34i 338 336 ~33T 33o 328 326 323 ii .43 9 i 7 435 7 i 4322 7 42886 4^548 10.00029 00029 ooo3o ooo3o ooo3i 9.99971 9997' 99970 9997" 99969 10 1 1 I 2 i3 i4 ii 42 4o 42 32 4^ 24 42 16 42 8 o 17 20 17 28 17 36 17 44 17 52 8.5 77 5 7 58o8 9 584i9 58 7 4 7 590-72 332 33o 328 325 3 2 3 ii .42243 41911 4i58i 4i253 40928 8.5 77 88 58(2. 5645 1 58779 59105 ii .42212 4 1 8-79 4 1 549 4i22r 4o8 9 5 io.ooo3i ooo32 OOO32 ooo33 ooo33 9 -999 6 9 99^8 99968 99967 99967 5o 4 9 48 4 7 46 .5 1 6 17 18 '9 I I 42 4i 52 4i 44 4i 36 4i 28 o 18 o 18 8 18 16 18 24 18 32 8.5 9 3 9 5 5 97 i5 6oo33 6o349 60662 320 3i8 3i6 3i3 3u i i .4060 5 40285 39967 3 9 65i 3 9 338 8.59428 59749 60068 6o384 60698 321 3i 9 3i6 3i4 3u ii .4o5 7 2 4o25i 39932 39616 39302 io.ooo33 ooo34 ooo34 ooo35 ooo36 9-99967 99966 99966 99965 99964 45 44 43 42 4i 20 21 22 23 24 11 4 1 20 4i 12 4r 4 4o 56 4o 48 o 18 4 18 48 18 56 19 4 19 12 8.6o 97 3 61282 61589 61894 62196 3o 9 3o 7 3o5 302 3oi I I .3 9 02 7 38718 384 1 1 38 1 06 3 7 8o4 8.61009 6r3i 9 61626 61931 62234 3io 307 3o5 3o3 3oi 11.38991 3868 1 383 7 4 38o6 9 3 77 66 io.ooo36 00037 ooo3 7 ooo38 ooo38 9 . 999 64 99 9 63 99963 99962 99962 4o 3 7 36 25 26 27 28 29 u 4o 4o 4o 32 4o 24 4o 16 4o 8 o 19 20 19 28 19 36 19 44 19 52 8.6249 7 62795 63091 63385 636 7 8 298 296 294 293 290 288 287 284 283 281 u .375o3 3 7 2o5 36909 366 1 5 36322 8.62535 62834 63i3i 63426 63718 299 297 295 292 291 n.37465 3 7 i66 3686 9 36574 36282 io.ooo3 9 ooo3 9 ooo4o ooo4o 00041 9.99961 99961 99960 99960 99959 35 34 33 32 3i 3o 29 28 ? -> 26 a5 24 23 22 21 3o 3i 32 33 34 ii 4o o 3 9 52 3 9 44 3 9 36 3 9 28 II 39 20 39 12 39 4 38 56 38 48 O 20 20 8 20 1 6 20 24 20 32 8.63 9 68 61256 64543 64827 65 1 10 n.36o3a 35 7 44 3545 7 35i 7 3 34890 8.64009 64298 64585 648 7 o 65 1 54 289 287 2.85 284 281 11.35991 35 7 o2 354 1 5 35i3o 34846 i^73~4565 34285 34007 33 7 3i 3345 7 io.ooo4i 00042 00042 ooo43 ooo44 "g& 99 9 53 99957 99 9 56 35 36 37 38 3 9 4o 4i 4 a 43 44 o 20 40 20 48 20 56 21 4 21 12 8.653 9 i 656 7 o 65947 66223 66497 279 277 276 2 7 4 2 7 2 i i . 34609 3433o 34o53 33 77 7 335o3 8.65435 657i5 66993 66269 66543 280 278 276 2/4 2 7 3 io.ooc44 ooo45 00045 00046 ooo46 io.ooo4 7 00048 00048 00049 00049 9-99956 99 9 55 99 9 55 999V 9 < ;9 >4 ii 38 4o 38 32 38 24 38 16 38 8 O 21 20 21 28 21 36 2t 44 21 52 8.66769 67089 6 7 3o8 6 7 5 7 5 6784 1 2 7 269 26 7 266 263 n.3323. 32 9 6. 32692 32425 32159 8.66816 67087 6 7 356 67624 67890 2 7 I 269 268 266 264 n.33i84 32 9 i3 32644 323 7 6 32IIO 9.99953 99959 99952 999 5i 999 5 1 2O '7 1 6 45 46 4-7 48 49 5o 5i 52 53 54 55 56 5 7 r,8 5 9 60 M u 38 o 3 7 52 3 7 44 3 7 36 3 7 28 22 O 22 8 22 l6 22 24 22 32 8. 68104 6836 7 68627 68886 6 9 i44 263 260 25 9 258 256 11.31896 3)633 3i3 7 3 3in4 3o856 8.68i54 684 1 7 686 7 8 68938 69196 263 261 260 258 9,5 7 n.3i846 3 1 583 3l322 3 1 062 3o8o4 io.ooo5o ooo5i ooo5i OO052 000 52 9 . 999 5o 99949 9994s 99948 99948 i5 i4 id 12 I I 10 | 6 ~5 4 3 2 I M II 37 20 3 7 12 3 7 4 36 56 36 48 22 40 22 48 22 56 23 4 23 12 8.6 9 4oo 6 9 654 69907 70159 70409 254 253 252 250 249 ~^T ?46 244 243 2.42 ?4o i i . 3o6oo 3o346 30093 29841 2 9 5 9 i 8.69453 69-708 69962 7 02l4 7 o465 255 254 252 25l 249 i i . 3o54 7 30292 3oo38 29786 29535 11.29286 29038 28792 28547 2 83o3 28060 io.ooo53 ooo54 ooo 54 ooo55 ooo56 9.9994-7 99946 999 46 og945 99944 9.99944 99 9 43 999^3 1 99942 9994i i 9994o ii 36 4o 36 32 36 24 36 16 36 8 36 o O 23 2O 23 28 2 3 36 23 44 23 52 24 8.70658 70905 7 i i5i 7'3 9 5 7i638 71880 1 1 .29342 29095 28849 28605 28362 28120 8. 7 o 7 i4 - 70962 71208 7T453 71697 71940 248 246 245 244 243 24 1 i o.ooo 56 ooo5 7 ooo58 ooo 58 ooo5g 00060 Hour p.M.'.I'/ur A.M. Cosiiio. JDiflT.r Secant. Cotangent jDiff.1 Tangent. Oosecant. ' Sine. sr I>a * el8 3 TABLE XXVII. Log. Sines, Tangents, arid Secants. 3 Yi(? .M lour A.M. lour P.M. Siiie. JDiffl' Cosecant. 'angent. 1 otangcnt Secant. Cosine. M o 9 8 7 6 o i 3 4 5 6 8 9 1 O 1 2 i3 ii 36 o 35 52 35 44 3*5 36 35 28 o 24 o 24 8 24 16 24 24 24 32 .71880! 721 20 72359 72597 72834 23 9 238 9.3 7 235 1.28.20 2-7880 2 7 64i 2 7 4o3 2-7166 8 . 7 i 940 72181 72420 7 265 9 72896 24 1 23 9 23 9 23 7 236 i . 28060 2 7 8.9 2 7 58o 2 7 34i 2 7 I04 0.00060 00060 00061 00069. 00062 999*0 99939 999 38 99938 i: 35 20 3.i <:2 35 4 34 56 34 48 o 24 4o 24 48 24 56 25 4 25 12 . 7 3o6 9 7 33o3 7 3535 7 3 7 6 7 73997 234 232 9.32 230 299 i . 26 9 3 i 26697 26465 269.33 26oo3 8. 73 1 32 7 3366 7 36oo 7 3832 7 4o63 9.34 9.34 232 23l 229 I . 26868 26634 26400 26.68 25 9 3 7 o . ooo63 00064 00064 0006 5 00066 7.99937 999 36 99936 99935 99934 5 4 3 ii 34 4o 34 32 34 24 34 16 34 8 25 20 25 28 2 5 36 25 44 25 52 .74226 74454 74680 74906 7 5i3o 29.8 2.26 226 224 223 n.25774 25546 25320 25o 9 4 248 7 o 8. -74292 7 452i 7 4 7 48 75I99 229 22 7 226 225 224 1.25-708 25479 25252 25026 24801 o . oo( >66 00067 00066 00066 00069 99933 99932 999 3 1 o 4 9 48 16 i5 16 17 18 12 x> 21 92 9.3 24 25 26 27 9.8 3o 3i 3 a 3 3 ir 34 <> 33 52 33 44 33 36 33 28 o 26 o 26 8 26 16 26 24 26 32 .75353 7 55 7 5 75795 7601 5 762.34 222 22O 220 2I 9 217 1 1 . 2464-7 24425 242O5 23 9 85 28766 8.75423 7 5645 75867 7 6o8 7 7 63o6 222 222 22O 2. 9 2I 7 2.6 2l5 214 2l3 1.24577 24355 24.33 a|oi3 2 36 9 4 O.OOO 7 O 000 7 I 000 7 I 000 7 2 ooo 7 3 9.9993.. 99929 99929 99928 99927 \t 4- 42 4i u 33 20 33 12 33 4 32 56 32 48 o 26 4o 26 48 26 56 27 4 27 12 . 7 645 i 7 666 7 7 6883 77097 773 10 2.6 216 2.4 2l3 212 u.23549 23333 23lI 7 22903 22690 '76742 7 6 9 58 77 i 7 3 77387 1.23475 23258 23042 2282-7 2261: o.ooo 7 4 00074 ooo 7 5 00076 00077 9.99926 99926 99925 99924 999 23 9.99923 9992 i 99921 999 2( 999 20 9.999.9 99918 99917 99917 999 if 4o 3 9 38 3 7 36 i 32 4o 32 32 32 24 ' 32 if 32 8 o 27 20 27 28 27 36 27 44 27 52 '77733 77943 781 52 7 836c 21 I 210 20 208 208 I I .224 7 8 2226 7 2205 7 21848 21640 8.77600 778., 78022 78232 7844 211 21 I 210 20 9 208 1 1 .22400 22189 2i 7 68 2i55 9 10.0007.7 00078 00079 00080 00080 35 34 33 32 3i II 32 3i 52 3. 44 3. 3f 3i 28 28 28 8 28 16 28 24 28 39 8.7856b 78774 78979 79 '8 79 386 206 205 204 203 202 1 1 .21432 21 221 21O2 208 I" 206 1 4 8.78649- 7 8855 7906 7 9 266 7947< 2o6 206 205 204 203 ii. 2.35 21 145 20939 2o 7 34 2o53c 10.00081 00082 0008: 0008: 00084 t. 27 06 25 2; 22 2 1 35 3- 38 3? 4o 49 43 4-1 45 46 47 48 - 9 .1 3. 2C 3i i 3i 4 3o 56 3o 48 o 28 4c 28 48 28 56 29 4 29 12 8. 79 588 79789 7999 80189 8o388 201 201 99 '99 I I . 2C>4 1 2021 20010 Ifil 8.7967 7987 8007 8027 8047 202 201 20. 20I2D 19924 I9 7 23 1952.4 i 0.0008 5 00086 00087 00087 00088 9-999' 5 999 - 9991 9991 9991 i i 3o 4o 3o 32 3o 24 3o .6 3o 8 O 29 20 29 ?S 29 36 29 44 29 52 8.8o585 80-782 8o 97 8 81173 8i36 7 '96 195 194 i 9 3 i i .1941 1921 1902 1882 1 863 8.8067 8087 8106 8126 8i45 ,98 , 9 6 , 9 6 io5 .9198 .8 9 3 i8 7 36 1 854 10.00089 00091 00091 00091 00092 9.9991 999 u 999 999 999 o 2.0 19 .8 17 16 u 3o c 29 5? 29 4' 29 3f 29 26 o 3o o 3o 8 3o 16 3o 2.4 3o 3 8.8.56t 8i 7 52 81944 82.34 82324 192 192 190 190 i8 9 n.i844 i8o5 1-786 i 7 6 7 8.8i65 8184 82o36 829.3C 8242C , 9 3 192 192 190 190 ii.i834 i8i5 1796 1777 i 7 58 10.0009. 0009/1 0009!: 0009^ 0009^ 9.9990 9990 9990 999 9990 5o 5. 59. 5: 5* 56 5 7 58 59 60 II 29 2C 2 9 IS 2 9 i 28 5( 28 4t o 3o 4 3o 4 3o 5 i 3i \ 3i i 8.82.51 2 82701 82886 83o 7 ~ 8326. 8T8344C 8363c 838i: 83 99 ( 84 17- Cosine 1 88 .87 187 1 86 i85 11.1748 1729 1711 1692 i6 7 3 8.826.C 82 79 S 8208- 83i 7 - 8336 189 ) 1 88 .88 1 86 1 86 11.1739 i -720 I 70 K 1682 .663 I O . OOC 9 " 00096 00099 OO I OC O01OI 9.99903 99902 ) 99901 > 99900 99899 ii 9.8 4< 9.8 3: 9.8 2. 2.8 If 28 I 28 < ) 3l 2 1 3l 2 i 3. 3 3 3i 4 3 3i 5 ) 32 xr oo oo . | T~ CO CO CO CO 00 CO '5= . i.i655 i63 7 1618 1600^ 1 589 1 564 'j S<-<-ant 8.8354- 83 7 3; 839 if 84 1 o( 849.8- 8446. Colangm i .85 .8/4 i 184 ) 182 182 \ 182 1 1. .645 1626 1608 .590 i5 7 ' i553 i 0.0010: ooio: OOIO/! oo.of ooio( 9.99898 99898 \ 99 8 97 ( 9989^ > 99^9') } W&9* . Sine. 2 O IV! t Dirt'. '] Tangent, , Cosec;uil ~HnnrA.f 93" TABLE XXV II. I*** 8189 Log. Sines, Tangents, and Secants. 4 175 M Hour A.M. Hour P.M. Sine. Difl'. 1 Cosecant. Tang-en t. Diff.l Cotangent Secant. Cosine. M o i 2 3 4 5 6 7 8 9 I I 28 2 7 52 27 44 27 36 27 28 32 32 8 32 16 32 24 32 32 8.84358 8453 9 84718 84897 85<> 7 5 181 '79 1 79 178 177 ii . i 5642 i546i 15282 i5io3 14925 8.84464 84646 84826 85oo6 85.85 182 1 80 1 80 179 i 7 8 1 1. 1 5536 1 5354 16174 i4994 i48i5 10.00106 00107 00108 00109 00109 91.99894 99 8 9 3 99892 99891 99891 60 3 5 7 56 II 27 20 27 12 27 4 26 56 26 48 o 32 40 32 48 32 56 33 4 33 12 8.85252 85429 856o5 86781 85 9 55 177 176 i 7 5 i 7 5 , 7 3 ii.i4748 i457i i43 9 5 14220 Uo45 8.85363 8554o 85 7 i 7 ^ 177 177 176 176 i?4 ii.i463 7 i446o 14283 14107 i3 9 3i I O . OO I I O 001 II 001 I 2 ooi 1 3 ooi 14 9.99890 99889 99888 99887 99886 55 54 ^3 59 5i 1 1 > 1 1 u i3 1 4 u 26 4o 26 32 26 24 26 1 6 26 8 o 33 PO 33 28 33 36 33 44 33 52 8.86128 863oi 86474 86645 86816 i 7 3 i 7 3 171 171 171 u i38 7 2 i36 99 i3526 i3355 i3i84 8.86243 86417 86691 86 7 63 86935 i 7 4 i 7 4 I 7 2 172 171 11.13757 i3583 1 34o 9 i3 2 37 i3o65 lo.ooi i5 ooi 16 ooi 17 00118 00119 9.99886 99884 99 883 99882 99881 5o 4 9 48 47 46 i5 16 17 18 '9 1 1 26 o 25 52 2.5 44 25 36 25 28 o 34 o 34 8 34 16 34 24 34 32 8.86987 87. 56 8 7 3a5 87494 87661 ,69 169 169 '67 1 68 i i . i 3o i 3 12844 12675 i 2 5o6 i233 9 8.87106 87277 87447 87616 8 77 85 171 170 I6 9 I6 9 1 68 i i . i 2894 12723 12553 12384 I22l5 IO. 00120 OOI 2 I OOI 2 I 00122 00123 9.99880 99879 99879 99878 99877 45 44 43 42 4i 20 21 22 23 24 II 25 20 25 12 25 4 24 56 24 48 o 34 4<> 34 48 34 56 35 4 35 12 8.87829 87995 88161 88326 88490 166 166 1 65 i64 164 1 1 .12171 12005 11839 11674 1 1 5 1 o 8.87953 88120 88287 88453 88618 167 167 1 66 1 65 i65 1 1 . I 2047 11880 H7i3 1 1 547 n382 10.00124 00126 00126 00127 00128 9.99876 99875 99874 99 8 7 3 99872 4o 3 9 38 37 36 35 34 33 32 3i 25 26 ^7 28 2.9 i i 24 40 24 32 24 24 24 16 24 8 o 35 20 35 28 35 36 35 44 35 52 8.88654 88817 88980 89142 89304 1 63 1 63 162 162 1 60 ii.n346 in83 1 1020 io858 10696 8.88783 88948 89111 89274 8 9 43 7 1 65 1 63 1 63 1 63 161 ii .11217 11062 10889 10726 io563 10.00129 ooi3o ooi3i 00 1 32 oo 1 33 9.99871 998 7 o 99869 99868 99867 3o 3i 32 33 34 I I 24 23 52 23 44 2 3 36 23 28 o 36 o 36 8 36 16 36 24 36 32 8.8 9 464 89625 89784 8 99 43 90102 161 159 i5 9 1 59 1 58 ii .io536 io3 7 5 10216 10057 09898 8.8 9 5 9 8 8 97 6o 8 99 2o 90080 90240 162 160 160 1 60 169 I I . 1O4O2 10240 10080 09920 09760 io.ooi34 oo 1 35 ooi 36 00 1 37 oo 1 38 9.99866 99866 99864 99 863 99862 3o 11 27 26 35 36 3 7 38 3 9 4<> 4i 42 43 44 II 23 20 23 12 23 4 22 56 22 48 o 36 4o 36 48 36 56 3 7 4 37 12 8.90260 90417 90574 9 o 7 3o 90885 i5 7 1 5 7 1 56 i55 i55 ii .09740 o 9 583 09426 09270 09115 8 -$8 90715 90872 91029 1 58 1 58 167 1 5 7 1 56 II .09601 09443 09285 09128 08971 10.00139 ooi4o ooi4i 00142 ooi43 9.99861 99860 99869 99 858 99867 25 24 23 22 21 It 22 40 22 32 22 24 22 l6 22 8 37 20 3 7 28 3 7 36 3 7 44 37 52 8.91 o4o 91195 9i34 9 91502 9i655 1 55 1 54 1 53 1 53 162 i i . 08960 o88o5 o865i 08498 o8345 8.91185 9i34o 9i4Q5 9 i65o 91803 i55 i55 i55 i53 1 54 11.08816 08660 o85o5 o835o 08197 io.ooi44 ooi45 ooi 46 ooi 47 oo 1 48 9.99866 99 855 99 854 99 853 99 852 20 \l IJ 16 45 46 47 48 49 II 22 21 52 21 44 21 36 21 28 o 38 o 38 8 38 16 38 24 38 32 8.91807 9'9 5 9 92110 92261 92411 152 i5i i5i i5o i5o 11.08193 08041 07890 07739 o 7 58 9 8.91957 921 10 92262 92414 92565 1 53 152 162 i5i i5i i i .08043 07890 o 77 38 o 7 586 o 7 435 10.00149 ooiSo OOI 52 oo 1 53 00 1 54 9.99861 99860 99848 99847 99846 i5 i4 1 3 12 I I 10 1 6 5o 5i 62 53 54 55 56 57 58 69 JO II 21 20 21 12 21 4 20 56 20 48 o 38 4o 38 48 38 56 3 9 4 3 9 12 8.92561 92710 9 285 9 93007 9 3i54 i4 9 149 1 48 i4 7 147 i47 1 46 1 46 i45 i45 1 44 ii .07439 07290 07141 o6 99 3 06846 8.92716 92866 93o [6 93 1 65 933 1 3 i5o i5o 149 1 48 149 ii .07284 071 34 06984 o6835 06687 io.ooi55 oo 1 56 00167 oo 1 58 00169 9-99845 99844 99 843 99842 9984f II 20 40 20 32 20 24 20 l6 20 8 20 O 39 20 3 9 28 3 9 36 3 9 44 39 62 4o o 8. 9 33oi 9 3448 935 9 4 93740 9 3885 94o3o i i . 06699 o655 2 06406 06260 o6n5 05970 8.93462 93609 9 3 7 56 93903 94049 94i95 i47 147 1 47 1 46 1 46 145 1 1. o6538 06391 06244 10.00160 00161 00162 oo 1 63 00164 00166 9.99840 99 83 9 99 838 99837 99836 99 834 5 4 3 2 1 M Hourp.M.jHourA.iw. Cosine. Diff.l' Secant. Cotangent] Diff. l' Tangent. Cosecant. Sine. M P: ' 8e19 ' 1 TABLF XXVII. Log. Sines, Tangents, and Secants. Of. A A B B C 3 174 M Hour A.M. Hour P.M. Sine. Diff. 2 4 7 9 Cosecant. Tangent. Diff. Cotangent Secant. Diff. o o o o o o o o o o o o Cosine. M i 2 3 4 II 20 00 19 52 19 44 19 36 19 28 o 4o o 4o 8 4o 1 6 4o 24 4o 32 8.94o3o 94i74 943i7 9446i 946o3 ii .06970 06826 o5683 o53 97 8.94196 9 434o 94485 9463o 94773 o 2 4 7 9 1 1. 06806 06060 06616 06370 06227 10.00166 00167 00168 00169 00170 9.99834 99 833 99 832 99 83 1 99 83o 60 69 58 67 56 5 6 8 9 ii 1920 19 12 19 4 18 56 18 48 o 4o 4o 4o 48 4o 56 4i 4 4l 12 8.94746 94887 96029 96170 953 10 ii i3 16 18 20 11.06264 o5u3 o4 9 7i o483o o46 9 o 8.94917 96060 96202 9 5344 9 5486 ii i3 i5 18 20 ii.o5o83 o4 9 4o o47 9 8 04656 o45i4 10.00171 00172 00173 00176 00176 9.99829 99828 99827 99826 99824 55 54 53 52 5i !O ! 9 i3 i4 75 1 6 17 18 '9 ii i 8 4o 18 32 18 24 18 16 18 8 o 4 1 20 4i 28 4i 36 4i 44 4i 62 8.96460 9 558 9 96728 96867 96006 22 24 26 ^3 35 3 7 3 9 42 ii.o455o o44i i 04272 o4i33 o3 99 5 8.96627 96767 96908 96047 96187 22 24 27 1? 33 35 38 4o 42 11.04373 04233 o4o 9 2 o3 9 53 o38i3 10.00177 00178 00179 00180 00181 9.99823 99822 99821 99820 99819 5d 49 48 47 46 ii 18 o 17 62 17 44 1-7 36 17 28 o 42 o 42 8 42 16 42 24 42 32 8.96143 96280 96417 9 6553 96689 i i.o3857 03720 03583 o3447 o33n 8.96326 96464 96602 96739 96877 ii .03676 o3536 o33 9 8 o326i o3i23 io.ooi83 00184 00186 00186 00187 9.99817 99816 99816 9 9 sl3 45 44 43 42 4i 4o 3 9 38 3 7 36 2 I 23 2/4 26 27 28 29 3o 3i 32 33 34 II 17 20 17 12 17 4 16 56 16 48 o 42 4 42 48 42 56 43 4 43 12 8.96826 96960 97096 97229 97 363 44 46 48 5o 53 "55 57 64 o3o4o O2 9 o5 0277! 02637 8.97013 97160 97286 97421 97 556 44 46 53 io.02 9 87 02860 02716 O257 9 02444 10.00188 00190 00191 00192 00193 o 9.99812 99810 99809 99808 99807 ii 16 4o 16 32 16 24 16 16 16 8 43 20 43 28 43 36 43 44 43 62 8.97496 97629 97762 97894 98026 ii .02604 02371 02238 02106 or 9 74 8.97691 97826 97969 98092 98226 55 58 60 62 64 II .O23o 9 02176 02041 oi 9 o8 01776 10.00194 00196 00197 00198 00199 9.99806 99804 99803 99802 99801 35 34 33 32 3i 1 1 16 o i5 62 i5 44 16 36 i5 28 o 44 o 44 8 44 1 6 44 24 44 32 8.98167 98288 98419 98649 98679 66 68 70 72 75 ii.oi843 01712 01681 01461 Ol32I 8. 9 8358 98490 98622 9 8 7 53 98884 66 69 7 3 75 II .01642 01610 01378 01247 on 16 10.00200 00202 O0203 00204 O0205 9.99800 99798 99797 99796 99796 3o 2 9 28 27 26 35 36 3 7 38 3 9 11 l5 20 l5 12 i5 4 i4 56 i4 48 o 44 4o 44 48 44 56 45 4 45 12 8.98808 9 8 9 3 7 99066 99194 99322 77 79 81 83 86 ii .01 192 oio63 00934 00806 00678 8.99016 99145 99276 99406 99534 77 80 82 84 86 n .oo 9 85 00866 00726 oo5 9 5 00466 10.00207 O02O8 O020 9 O02IO 00212 9.99793 99792 99791 99790 99788 25 24 23 22 21 C - ?J 00 XT xrxrxrxrxr ii i4 4o i4 32 1 4 24 i4 16 i4 8 ii i4 o i3 62 i3 44 i3 36 i3 28 o 45 20 45 28 45 36 45 44 45 62 8.99460 99 5 77 99704 99 83o 99966 88 90 92 94 96 ii .00660 00296 00170 ooo44 8.99662 99791 999 '9 9 . ooo46 00174 89 93 9 5 97 i i. oo338 0020 9 00081 io. 999 54 99826 IO.002I3 002 1 4 00215 00217 002l8 9.99787 99786 99786 997 83 99782 2O '9 18 17 16 45 46 47 48 49 o 46 o 46 8 46 16 46 24 46 32 9.00082 00207 oo332 oo456 00681 99 101 io3 io5 107 i o . 999 i 8 99793 99668 99644 99419 9 .oo3oi 00427 oo553 00670 00806 100 102 io4 1 06 1 08 10.99699 99573 99447 99321 99 T 9 5 10.99070 98946 98821 98697 98673 IO.OO2I 9 OO22O OO222 OO223 OO224 9.99781 99780 99778 99777 99776 i5 i4 i3 12 I I 5o 5i 52 53 54 II 1 3 20 l3 12 13 4 12 56 12 48 o 46 4o 46 48 46 56 47 4 47 '2 9 . 00704 00828 00961 01074 01 196 no 112 ii4 116 118 10.99296 99172 99049 98926 98804 9 .oo 9 3o 01066 SIS 0142? III "7 120 122 124 126 128 1 33 IO.OO225 O0227 00228 O022 9 0023 1 9-99775 99773 99772 99771 99769 10 6 55 56 67 58 ii 12 4o 12 32 12 24 12 l6 12 8 12 O o 47 20 47 28 47 36 47 44 47 52 48 o 9 .oi3i8 oi44o 01661 01682 oi8o3 01923 121 123 125 127 I2 9 l32 10.98682 98660 9 843 9 983i8 98197 98077 9 .oi55o 01673 01796 01918 O2040 02162 10.98460 9 832 7 98204 98082 97960 97 838 10.00232 00233 00235 00236 00237 0023 9 Diff. 9.99768 99767 99765 99764 99763 b 4 3 2 I O M Hour p.M.lHour A.M. Cosim 1 Diff. Secant. Cotangent|Diff. Tangent. Cosecant. Sine. M 950 A A B B C C 84' 1 s & 3 1 4' 5' 6' 7- f A 16 33 49 66 82 99 n5 Prop, oarts of cols. < B '7 33 5o 66 83 IOC 1 16 ( C o o o i 1 i 1 s G M > Hour A.M. n TABLE XXVII. LOJT. Sines, Tangents-, and Secants. A ' A B B C C <7:* r: {Jour P.M. Sine. Ditr. Cosecant. Tung-em. [Diff. Coiai.ffnn Secant. Dirt'. Cosine Al 60 56 55 54 53 52 5i i 2 3 I I 12 II 52 ii 44 ii 36 n 28 o 48 o 48 8 48 16 48 24 48 32 9.01923 07O43 O2i63 0^283 2 4 6 10.98077 97957 9783 7 97717 97598 9.02162 02283 02404 02525 02645 o 2 4 6 8 10.97838 97717 97596 97475 97 355 IO.OO9.3 9 00240 0024 1 00243 00244 o o 9976o 99759 99757 99756 5 6 8 9 ii ii 20 II 12 ii 4 10 56 10 48 o 48 4o 48 48 48 56 49 4 49 12 9.02.520 02639 02757 02874 02992 9 1 1 i3 i5 10.97480 9 7 36i 97243 97126 97008 9.02 7 66 02885 o3oo5 03242 9 1 1 i3 i5 7 10.97234 971 1 5 9 6 99 5 968-6 96758 10.00245 00247 00248 00249 OO25l o o o o o 9.99-55 99753 99752 9975 1 99749 10 1 1 12 i3 (4 ii 10 4o IO 32 10 2.4 10 16 10 8 o 49 20 49 28 49 36 49 44 49 52 9 .o3 109 0322.6 o3342 o3458 o35 7 4 '9 20 22 24 26 10.96891 9^.774 96426 9-o336i o34 7 9 o35 97 03714 o3832 23 24 26 10.96639 96521 96403 96286 96168 10.00252 00253 00255 00256 002.58 9-99748 99747 99745 99744 99742 5o 4 9 48 47 46 16 '7 18 [9 II IO 9 52 9 44 9 36 9 28 o 5o o 5o 8 5o 16 5o 24 5o 32 9-o36oo o38o5 03920 o4o34 04149 28 3o 3 1 33 35 37 3 9 4i 43 44 10.96310 96195 96080 9 5 9 66 9 585i 9.03948 o4o65 04181 04297 o44i3 28 3o 32 34 36 10.96052 9 5 9 35 95819 95703 9 558 7 10.00259 00260 00262 00263 00264 9.99741 9974o 99738 99737 997 36 45 44 43 4i 20 21 22. 2.3 9.4 II 9 20 9 12 9 4 8 56 8 48 o 5o 4o 5o 48 5o 56 5i 4 5l 12 9.0.4262 04876 04490 o46o3 0471 5 10.95738 95624 95397 9 5285 9.04528 o4643 04873 04987 38 3o 43 45 10.95472 9 535 7 95242 95127 95o 1 3 10.00266 00267 00269 00270 00272 o 9.99734 997 33 9973 1 99728 4o 3 9 38 3 7 36 25 2.6 2.8 2 9 3, 3 ) 33 34 35 36 3 7 38 39 ii 8 4o 8 32 8 24 8 16 8 8 O 5l 20 5 1 28 5i 36 5i 44 5 1 52 9.04828 o4 9 4o o5o52 o5i64 05275 46 48 5o 52 54 56 57 59 61 63 10.95172 95060 94948 9 4S36 94725 9-o5ioi o52i4 o5328 o544i o5553 4 7 49 5i 53 54 10.94899 94786 94672 94559 94447 10.00273 00274 00276 00277 00279 9.99727 99726 99724 99723 99721 35 34 33 32 3 1 3V, 29 *7 26 n 8 o 7 52 7 44 7 36 7 2.8 52 52 8 52 16 52 2/j 52 32 9 .o5386 05497 05607 05717 o582 7 9-o5 9 37 06046 06 1 55 06264 06372 10.94614 9 45o3 94093 9.o5666 05778 05890 06002 061 1 3 56 58 60 62 64 66 68 69 7' 73 10.94334 94222 941 10 9 3 99 8 9 388 7 10.00280 00282 00283 00284 00286 9.99720 99718 99717 997.6 997 '4 II 7 20 7 12 7 4 6 56 6 48 o 52 4o 5 -i 48 52 56 53 4 53 12 65 67 69 70 72 i o . 94o63 93 9 54 93845 9 3 7 36 93628 9.06224 o6335 o6445 o6556 06666 10.93776 9 3665 9 3555 93444 9 3334 10.00287 00289 00290 00292 00293 9.99713 99711 99710 99708 99707 25 24 23 2.2 21 4i 43 44 1 1 6 4o 6 32. 6 2.4 6 16 6 8 o 53 20 53 28 53 36 53 44 53 52 9.06481 06589 06696 06804 0691 1 74 76 78 80 Si 10.93519 933o4 93196 9 3o8 9 9.06775 o6885 06994 07 1 o3 0721 1 75 77 79 81 83 10.93225 93.1*5 93006 92897 92789 10.00295 00296 00298 00299 oo3oi 9.99705 99704 90702 99701 99699 '9 18 '7 16 45 46 47 48 49 ii 60 5 52 5 44 5 36 5 28 o 54 o 54 8 54 16 54 2.4 54 32 9.07018 07124 07231 o 7 33 7 07442 83 85 87 89 9' 10.92982 92876 92^9 92663 92558 9.07320 0742.8 o 7 536 o 7 643 07751 84 86 88 9 92 10.92680 92572 92464 9 235 7 92.249 io.oo3o2 oo3o4 oo3o5 00307 oo3o8 9.99698 99696 99 6 9 5 99693 99692 i 5 i3 I 2 10 I 6 4 3 2 I O 5o 5i r )2 53 r >1 55 56 57 58 5 9 (k> 3! I I 5 20 5 12 5 4 4 56 4 48 o 54 4o 54 48 54 56 55 4 55 12 9.07548 o 7 653 o 77 58 07863 07968 93 IOO 10.92452 92.34-7 92242 9 2i3 7 92032 9.07858 07964 08071 08177 08283 9 r 96 98 99 101 10.92142 92036 91929 91823 9'7'7 io.oo3io oo3i i oo3i3 oo3i6 9.99690 99689 99^7 99686 99684 u 4 4o 4 32 4 24 4 :6 4 8 4 o o 55 20 55 28 55 36 55 44 55 52 56 o 9.08072 08 1 76 08280 o8383 08486 o858 9 102 104 1 06 107 I0 9 I I I 10.91928 91824 91720 91617 9i5i4 91411 9.08389 08495 08600 08705 08810 08914 io3 io5 107 109 10.9161 i 9 i5o5 91400 91295 91190 91086 i o . oo3 i 7 00319 OO32O 00322 oo3 2 3 oo39.5 9 99 683 99681 99680 99678 99677 996/5 Flour P. M.I Hoar A.M. Cosine. Diff. Secant. Cotangent Diff. Tangent. Cosecant. Sine M C 83 Seconds of time ' . 1 s 2" 3" 4 s 5 s r>' 7" (A i4 sB 42 56 69 83 97 Prop, ijarts ol'ools. < B i4 28 42 56 70 84 96 I C o I i i , Pa 5 T M o i 2 3 4 se 192] TABLE XXVII. Log. Sines, Tangents, and Secants. G> A A B B C C 172 H.rur A M. Hour P.M. Sine. Diff. Cosecant. Tangent. |Diff. Cotangent Secant Diff. o c o o o o Cosine. 99 6 7 4 99 6 7 2 99670 99669 M 60 5 9 58 57 56 55 54 53 52 5, II 4 3 52 3 44 3 36 3 28 o 56 o 56 8 56 1 6 56 24 56 32 o 56 4o 56 48 56 56 5 7 4 5 7 12 9 .o858 9 1 o86 9 2 o8 7Q 5 08807 08999 2 3 5 6 10 1 1 i3 i4 10.9141 i 9i3o8 91205 91 ,o3 91001 9.089,4 09019 09,23 0922-7 o 2 3 5 7 8 ,0 ii i3 ,5 10. 9 , 086 9 o 9 8 1 9 o8 77 90773 90670 io. 9 o566 9 o36o 90258 9 oi55 io.oo325 oo326 oo328 oo33o oo33. 5 6 7 8 9 i : 3 20 3 12 3 4 2 56 2 48 9.09101 09202 09304 09405 09506 io.oo8 99 9 o 79 8 9o6 9 6 9 o5 9 5 90494 9 .o 9 434 09537 o 9 64o 97 42 09845 io.oo333 oo334 oo336 oo33 7 00339 9.99667 99666 99 664 99 663 90661 i i 1 2 1 3 i4 11 2 40 2 32 2 24 2 16 2 8 o 57 20 57 28 5 7 36 57 44 5 7 52 9.09606 09707 09907 10006 16 18 ! 9 2 I 22 26 2 7 2 9 3o io. 9 o3 9 4 90293 9 o, 9 3 9 oo 9 3 8 999 4 9 .o 99 47 ioo4 9 ioi5o I025c io353 16 18 20 21 23 io. 9 oo53 8 99 5t 8 9 85o 8 97 48 89647 io.oo34i 00342 oo344 oo345 oo34 7 o 19.99659 c 996.58 o 996^6 o 99655 o 99653 5o 4 9 48 47 46 i5 16 17 18 II 20 I 52 i 44 i 36 i 28 o 58 o 58 8 58 ,6 58 24 58 32 9 . i o i 06 10205 , io3o4 10402 io5oi io.8 9 8 9 4 8 979 5 8 9 6 9 6 89598 89499 io.8 9 4oi 8 9 3<>3 8 9 2o5 8 9 oio 9 . io454 io555 io656 io 7 56 1 08 56 24 26 28 3? 10.89546 89445 89344 89244 89,44 10.00349 oo35o oo352 oo353 oo355 o o 9 . 99 65, 9965o 99648 99647 99645 44 43 42 4i 20 21 22 23 24 II I 20 I 12 i 4 o 56 o 48 o 58 4o 58 48 58 56 5 9 4 5 9 12 9.10599 10697 10-795 io8 9 3 10990 32 34 35 3 7 38 9 .io 9 56 iio56 in55 11254 1 1 353 33 34 36 3 7 39 10.89044 88944 88845 88746 88647 io.oo35 7 oo358 oo36o oo362 oo363 9.99643 99642 99640 99638 99637 4o ll 3 7 36 25 26 27 28 29 ii o 4o 32 o 24 o 16 o '8 o 5 9 20 5 9 28 5 9 36 5 9 44 5 9 52 9. 1 108-7 11184 11281 1 1 377 4o 42 43 45 46 io.88 9 i3 88816 88 7 i 9 88623 88526 n55i n64 9 H747 n845 4i 42 44 46 47 io.88548 8844 9 8835 1 88253 88 1 55 io.oo365 oo36 7 oo368 oo3 7 o oo3 7 i -- 9.99635 99 633 99 632 99630 99629 35 34 33 32 3i 3o 3i 32 33 34 II 00 10 59 52 59 44 59 36 5 9 28 I O o 8 o 16 o 24 32 9.11570 11666 11761 u857 11952 48 5o 5i 53 54 56 58 59 61 62 io.8843o 88334 88 2 3 9 88i43 88o48 9 .n 9 43 12040 I2i38 12235 12332 t 52 54 55 10. 88057 87960 87862 8 77 65 8-7668 10.00373 oo3 7 5 oo3 7 6 oo3 7 8 oo38o 9.99627 99625 99624 99622 99620 3o 3 27 26 35 36 37 38 3 9 4o 4i 42 43 44 1C 59 20 59 12 5 9 4 58 56 58 48 i o 4o o 48 o 56 4 12 9.1204-7 12,42 12236 i233i 12425 10.8-7953 8 7 858 8 77 64 87669 8 7 5 7 5 9 . 1242? 12525 12621 1*717 12813 5 7 59 60 62 64 io.8 7 5 7 2 8 7 4 7 5 8 7 3 79 8 7 283 87187 io.oo382 oo383 oo385 oo38 7 oo388 9.996,8 99617 996,5 996,3 99612 25 24 23 22 21 10 58 4o 58 32 58 24 58 16 58 8 I 20 28 36 44 52 9.1*519 I 26 1 2 12706 12799 12892 64 66 6 7 69 7 o 10.87481 8 7 388 87294 87201 87108 9 . I2 9 9 1 3oo4 i3o 99 13194 i3 2 8 9 65 67 68 7 o 7 2 10 '86996 86901 86806 86711 io.oo3oo 00392 00393 00395 0039-7 9.99610 99608 99607 99603 20 I 9 18 1 7 16 45 46 47 48 49 10 56 o 5 7 52 5 7 44 5 7 36 5 7 28 120 2 8 2 16 2 24 2 32 9. 12985 i3o 7 8 i3i 7 i i3263 i3355 9-i344 7 1 353 9 i363o l3 7 22 i38,3 72 7 4 7 5 77 78 10.87015 86922 86829 86 7 3 7 86645 9 .i3384 i34 7 8 i35 7 3 i366 7 i3 7 6i 7 3 77 78 80 10.86616 86522 86427 86333 86239 10.00399 oo4oo 00402 oo4o5 9 . 99 6oi 99598 99596 1 4 ,3 12 , I 5o 5, 52 53 54 IO 57 20 5 7 12 5 7 4 56 56 56 48 I 2 40 2 48 2 56 3 4 3 12 80 82 83 85 87 io.86553 8646 r 863 7 o 86278 86187 9 .i3854 i3 9 48 i4o4i i4i34 81 83 85 86 88 10.86,46 86o52 85 9 5 9 85866 85 77 3 io.oo4o 7 00409 oo4i i 00412 oo4i4 2 2 2 2 2 2 9 99 5 9 3 99501 99588 99 586 IO 6 55 56 5- 58 5 9 60 10 56 4o 56 32 56 24 56 16 56 8 56 o I 3 20 3 28 3 36 3 44 3 52 4 o 9 .i3 9 o4 i3 99 4 i4o85 14266 i4356 88 90 96 ,0.86096 86006 859 1 5 8582.5 857 'M 85644 9.14320 14412 i45 97 i46S8 14780 9 96 io.8568o 85588 8 54 9 6 85463 853,2 85220 io.oo4i6 00419 00421 00425 9 . 99 584 99 582 99 58, 99579 99 5 77 99575 4 3 2 I O M M Hour P.M. Hour A.M. Cosine. Diff. Secant. Cotargcnt Diff. Tangent. Cosecant. Diff. Sine. (J7 o A A B B U V Vi- Seconds of time 1" 2 s 3 s 4" 5 6 s 7* f A 12 24 36 48 60 72 84 Prop, parts of cols. 3 B 12 24 37 49 61 73 86 tc i ! i i 1 1 s 3 M TABLE XXVII. Log. Sines, Tangents, and Secants. A A B B C Diff [Page 193 G C 171 lour A.M. Hour P.M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent Secant. Cosine. M 2 3 4 o 56 o 55 5a 55 44 55 36 55 28 i 4 o 4 8 4 16 4 24 4 32 9.14356 i4445 i4535 14624 i4?i4 i 3 4 6 0.85644 85555 85465 853 7 6 85286 9.14780 14872 14963 i5o54 i5i45 o i 3 4 6 IO.8522O 85i28 85o37 84946 84855 lo.oo425 00426 00428 oo43o oo432 o o o 9.99575 99 5 7 4 995-72 995-70 9 9 568 60 % 57 56 5 6 7 8 9 o 55 20 55 12 55 4 54 56 54 48 i 4 4o 4 48 4 56 5 4 5 12 9-i48o3 14891 14980 1 5o6 9 i5i5? 8 10 1 1 i3 0.85197 85 1 09 85o20 8493i 84843 9.i5236 i53 27 i54i7 i55u8 i55 9 8 7 9 10 12 i3 10.84764 846 7 3 84583 84492 84402 ;o. oo434 oo435 00437 oo43 9 00441 o o 9. 99 566 99565 99 f>63 99 56i 99 55 9 55 54 53 52 5i 10 1 1 12 i3 i4 i5 1 6 18 r 9 10 54 4o 54 32 54 24 54 16 54 8 I 5 20 5 28 5 36 5 44 5 52 9 .i5245 1 5333 1 542 1 i55o8 15596 i4 16 17 18 20 0.84755 8466-7 845 79 84492 844o4 9.i5688 15777 i586 7 i5 9 56 16046 4 16 17 '9 ao io.843i2 84223 84i33 84044 83 9 54 io.oo443 00444 oo446 oo448 oo45o o 9 . 99 55 7 oo556 99554 99 55 2 99 55o DO <4o 47 46 10 54 o 53 52 53 44 53 36 53 28 i 6 o 6 8 6 16 6 24 6 32 9 .i5683 15770 i585 7 i5944 i6o3o 9. 161 16 i6ao3 16289 i63 7 4 1 646o 21 23 24 25 27 10.84317 8423o 84 1 43 84o56 83970 9. i6i35 16224 i63i2 i64oi 16489 22 23 25 26 27 10.83865 83776 83688 83599 83511 io.oo452 oo454 oo455 oo45 7 00459 o 9 . 99 548 99546 99 545 99 543 9954. 45 44 43 42 4i 4o i* 37 36 iO 21 22 23 24 10 53 20- 53 12 53 4 52 56 5 2 48" i 6 4o 6 48 6 56 7 4 7 12 28 3o 3i 32 34 10.83884 83 7 97 83 7 u 83626 8354o 9.16577 1 6665 i6 7 53 1 684 1 16928 Q 9 3o 32 33 35 10.8349.3 83335 8324 7 83i5 9 83o 7 2 10.00461 oo463 oo465 00467 oo468 9 . 99 53 9 99 53 7 99535 99533 99 532 25 26 27 28 2 9 10 52 4o 52 32 52 24 52 16 52 8 i 7 20 7 28 7 36 7 44 7 52 9.16545 1 663 1 16716 16801 16886 35 37 38 g io.83455 8336 9 83284 83,99 83u4 9.17016 17103 17190 17277 i 7 363 36 37 3 9 4o 42 10.82984 8289 7 82810 82 7 23 8263 7 10.00470 00472 oo4i4 00476 00478 9.99530 9 9 5a8 99626 99524 99 522 35 34 33 32 3i 3o 3i 3? 33 34 35 36 3 7 38 3 9 10 52 5i 52 5i 44 5i 36 5i 28 i 8 o 8 8 8 16 8 24 8 32 9.16970 I7o55 17139 17223 17307 9.17391 17474 i 7 558 i 7 64i 17724 4a 44 45 47 48 io.83o3o 82945 82861 82777 82693 9.i745o i 7 536 17622 17708 17794 43 45 46 48 49 5o 52 53 55 56 io.8255o 82464 823 7 8 82292 82206 10.00480 00482 oo483 oo485 00487 9.99520 99 5i8 99 5l7 99 5i5 99_5i3 3o ?o 28 2 7 26 25 2^ 2C 22 'i\ 20 '9 l8 17 16 75 i4 K 12 II 10 5l 20 5l 12 5i 4 5o 56 5o 48 i 8 4o 8 48 8 56 9 4 9 12 49 5i 52 54 55 10.82609 82526 82442 8 2 35 9 82276 9.17880 i- 9 65 iBo5i i8i36 18221 10.82120 82o35 81949 81864 8i 779 10.00489 00491 00493 . 00495 00497 9.99511 99509 99 5o 7 99 5o') 99 5o3 4o 41 42 43 44 10 5o 4o 5o 32 5o 24 5o 16 5o 8 i 9 20 o 28 $ 36 9 44 9 52 9.17807 17890 17973 i8o55 i8i3 7 56 58 > 61 62 10.82193 82110 82027 8i 9 45 8 [863 9.i83c6 18391 i84 7 5 i856o 1 864*' 58 59 61 62 63 10.81694 81609 8i525 8i44o 8 1 356 10.00499 oo5oi oo5o3 oo5o5 oo5o6 9.99501 99^99 99497 99 4 9 5 99 4 9 4 45 46 47 48 49 10 5o o 49 52 49 44 49 36 49 28 I IO O 10 8 10 16 10 24 IO 32 9.18220 i83o2 i8383 1 8465 i8547 63 65 66 68 69 10.81780 81698 81617 8i535 8t453 0.1 3 7 28 18812 18896 18970 19063 65 66 68 69 7i 10.81272 81188 81104 81021 8o 9 3 7 io.oo5o8 ooSio oo5 1 2 oo5i^ oo5i6 I I I 2 2 9 . 99 4 9 2 99490 99 488 99 486 99 484 5o 5i 52 53 54 55 56 5? 58 5 9 6c 10 49 20 49 12 49 4 48 56 48 48 i 10 4o 10 48 10 56 ii 4 II 12 9.18628 18709 18790 18871 18962 7i 72 73 7 5 76 10.81372 81291 81210 81 129 81048 9.19146 19229 19312 i 9 3 9 5 19478 72 74 75 76 78 io.8o854 80-771 80688 8o6o5 80522 io.oo5i8 oo520 O0522 oo52^ oo526 2 2 2 2 2 9-99482 99480 99478 99476 994?4 IO O 8 6 10 48 4o 48 32 48 24 48 16 48 8 48 c I II 20 II 28 ii 36 1 1 4^ II 52 12 O 9.19033 191 K I 9 ! 9 3 1927; 19353 1943,1 78 79 80 82 83 85 Diff 10.80967 80887 80807 80727 80647 8o56 7 9.19561 19643 19725 19807 19889 19971 79 81 82 84 85 87 10.80439 8o35 7 80275 80193 80111 80029 10.00528 oo53o oo532 oo534 oo536 oo538 2 2 2 2 2 2 9-99472 9947" 99 468 99466 99464 99 46a c i I O M Hour P. M Hour A. M Cosine. Secant. Cotangen Diff Tangent. Cosecant Diff Sine. M 96 C C 810 1" Os T <1 8 5 6 s 7" (A 1 1 21 32 42 53 63 74 Prop, parts of cols. < B 1 1 22 32 43 54 65 76 ( C o () ' i i i 3 Pageiy1 ' TABLE XXVJI. Log. Sines, Tangents, and Secants. G'. 9 A A B B C C 170 M lour A.M. Hour P.M. Sine. Diff.J Cosecant. Tangent. D ff. 'Cotangent Secant. Diff. Cosine. 9-99462 99 46o 99458 99456 99 454 M i 2 3 4 o ^8 o 47 5; 47 44 47 36 47 28 I 12 G 12 8 12 l6 12 24 12 32 9. i 9 433 i 9 5i3 19693 19672 19751 o 3 4 io.8o56 7 80487 8o4o8 8o328 80249 2oo53 20 1 34 202 1. 6 2O2 97 o I 4 5 10.80029 79947 79866 79784 797Q3 10. -79622 79460 79 3 79 79 2 99 10.79218 791 38 79058 78978 78898 io.oo538 oo54o 00542 oo544 oo546 o ; o i o 60 58 57 6 8 9 10 47 20 47 12 47 4 46 56 46 48 I 12 40 12 48 12 56 i3 4 l3 12 9.19830 20067 2oi45 6 8 9 10 ii i o . 80 i 70 80091 80012 79933 79855 9 .2o3 7 8 20459 2o54o 20621 20701 6 8 9 10 12 io.oo548 oo55o oo552 oo 5 54 oo556 o o 9.99452 99 45o 99 448 99 446 99444 55 54 53 52 5i 10 I 2 i3 i4 10 46 4o 46 32 46 24 46 16 46 8 i 1 3 20 i3 28 i3 36 i3 44 i3 52 9.20223 20302 2o38o 20458 2o535 i3 i4 i5 16 18 io.7 9777 79698 79620 79543 79 465 9.20 7 82 20862 20942 21022 21 102 i3 i4 16 17 18 io.oo558 oo56o oo562 oo564 oo566 o o 9 . 99 442 99 438 99436 99434 5o 47 46 i5 16 18 '9 10 46 o 45 52 45 44 45 36 45 28 i 14 o i4 8 i4 16 r4 24 i4 3* 9 . 2061 3 206 9 I 20-768 2o845 20 9 22 20 21 23 24 io. 79 38 7 7 9 232 79 .55 79 o 7 8 9.21182 2126l 2i34i 21420 21499 1 9 21 22 23 25 10.78818 78739 7 865 9 7 858o 7 85oi io.oo568 oo5 7 i oo5 7 3 oo5 7 5 00577 9-99432 99429 99427 99425 99423 45 44 43 42 4i 20 21 22 23 24 25 26 27 28 29 IO 45 20 45 12 45 4 44 56 44 48 i i4 4o 1 4 48 i4 56 i5 4 15 12 9.20999 2I0 7 6 3ii53 21229 2i3o6 25 26 28 ~3T 33 34 35 37 io. 79 ooi 7 8 9 24 78847 78771 786 9 4 9.21578 2i65 7 2i 7 36 21814 21893 26 27 28 3o 3i 10. 7 8422 78343 78264 78186 7810-7 i o. 00579 oo58i oo583 oo585 oo58 7 9-99421 99419 99417 994 1 5 994 ' 3 9-994" 99409 99407 99402 4o 3 9 38 37 36 10 44 4o 44 32 44 24 44 16 44 8 I 1 5 2C i5 28 1 5 36 1 S 44 IS 52 9.21382 2i458 2 1 534 21610 2 1 685 10.78618 7 8542 78466 7 83 9 o 7 83i5 9.219-71 2.2049 22I2 7 222O5 22283 32 34 35 36 38 10. -78029 77873 77795 77717 io.oo58 9 oo5 9 i oo5 9 3 oo5 9 6 oo5 9 8 35 34 33 32 3i 3o 3 1 3 2 33 34 35 3 7 38 39 10 44 o 43 52 43 44 43 36 43 28 i 10 o 16 8 16 16 1 6 ->4 16 32 9.21-761 2 1 836 21912 2198-7 22062 38 39 4o 42 43 10.78239 78164 78088 78013 77938 9 .2236l 22438 22516 225 9 3 22670 3 9 4o 4i 43 44 io. 77 639 77 562 77484 774o7 77 33o 10.00600 00602 00604 00606 00608 9.99400 99398 99 3 9 6 99 3 9 4 99 3 9 2 3o 11 27 26 25 23 25 21 IO 43 20 43 12 43 4 42 56 42 4b i 1 6 4o 16 48 16 56 17 4 17 13 9.2213-7 2221 1 22286 2236l 22435 44 45 47 48 49 io. 77 863 777 8 9 777'4 77 63 9 77 565 9.22747 22824 22901 2297- a3o54 45 47 48 49 5o 10.77253 77176 77099 77023 76946 10.00610 006 12 006 1 5 00617 006 1 9 9 . 99 3 9 f 99 388 99 385 99383 99 38, 4o 4 1 42 43 44 10 42 4o 42. 32 42 24 42 16 42 8 I I 7 '20 1J 28 17 36 i 7 .44 17 5. 9.22509 22583 22657 22 7 3. 22805 5o 52 53 54 55 io. 77 4 9 i 774i7 77343 7726 77 1 9 5 9.23i3o 23206 23283 2 335 9 23435 52 53 54 56 5 7 10.76870 76794 76717 76641 76565 10.00621 00620 00625 00628 oo63o 9.99379 99377 99372 2O '9 1 8 16 45 46 47 48 49 to 42 o 4i 52 4i 44 4i 36 4i 28 i 18 o 18 8 18 16 18 24 18 32 9.22878 2295? 23025 23098 23171 57 58 59 60 62 10.77122 77048 76975 76 9 02 7682 9 9.235io 23586 2366 1 2 3 7 3 7 238 I 2 58 60 61 62 63 10.76490 7633 9 76263 76188 io.oo632 006 3^ oo636 oo638 00641 9.99368 99 366 9936j 09359 9 '^1 99353 99 35i 99 348 \L 12 I I 5o 5i 53 54 10 4i 20 4l 12 4i 4 4o 56 4o 48 i 18 4o 18 48 18 56 19 4 19 12 23390 23462 23535 63 64 65 67 68 io. 7 6 7 56 7 6683 76610 7 6538 76465 9. 2 388 7 23962 24112 24186 65 66 67 69 70 io. 7 6i i3 7 6o38 75888 7 58i4 io.oo643 oo645 oo64 7 00649 oo652 2 2 2 10 8 6 55 56 57 58 5 9 60 10 4o 4o 4o 32 4o 2^ 4o 16 4o 8 4o c I 19 21 19 28 19 36 19 44 19 52 20 o 9.23607 23679 23 7 52 23823 23895 2 3 9 6 7 69 72 73 74 76 io. 7 63 9 3 7 632i 76248 76177 7 6io5 7 6o33 9 . 24261 24335 244io 24484 24558 24632 73 74 75 76 78 io. 7 5 7 39 7 5665 7 5590 7 55i6 7 5442 7 5368 io.oo654 oo656 oo658 00660 oo663 oo665 | 2 ! 2 2 2 2 i)iff 9.99346 99344 99 342 9934c 99337 99 335 t i M Hour A.M Cosine. Diff Secant. Cotangent Diff Tangent. Cosecant. Sine. A! I*? A A B B C U 80< Seconds of time 1" 2" 3' 4' 5' H' 7" ( A 9 1 9 28 38 47 57 66 B 10 W 29 39 49 58 68 C c i i i i TABLE XXVII. [Page 195 Log. Sines, Tangents, and Secants. G '~ 10 A A B E C C 169 M I lour A.M. Hour P. M Sine. Diff. Cosecant. 1 angent. Diff. Cotangent Secant. Diff.l Cosine. M o i 2 q 4 10 4 3 9 52 3 9 44 39 36 3 9 28 tO 39 20 39 12 3 9 4 38 56 38 48 I 2O O 20 8 20 16 20 24 20 32 9.23967 24039 24 no 24181 24253 o i 2 3 5 io.76o33 7 5 9 6. 7 58 9 o 7 58. 9 75747 9-24632 24706 24779 24853 24926 i 2 4 5 io. 7 5368 75294 75221 75i47 75o 7 4 io.oo665 0066-7 00669 00672 00674 9 . 99 335 99333 99 33. 99 3 2 8 99 320 60 5 9 58 57 56 55 54 53 52 5i 6 7 8 9 i 20 4o 20 48 20 56 21 4 21 12 9.24324 2 43 9 5 24466 24536 24607 6 8 9 10 10.75676 7 56o5 7 5534 75464 7 53 9 3 9 .25ooo 25o 7 3 25i46 252I 9 252 9 9 6 7 8 9 1 1 10.75000 74927 74854 74781 74708 10.00676 00678 00681 oo683 oo685 9 . 99 3-;4 99322 99319 99 3,7 99 3.5 10 1 1 12 1 3 i4 10 33 4o 38 32 38 24 38 16 38 8 I 21 20 21 28 21 36 21 44 21 52 9 24677 24748 24818 24888 24 9 58 1 1 i3 i4 i5 16 10 7 5323 7 5 2 52 7 5i8 2 75 I 12 7 5o42 9 . 25365 2543 7 255io 25582 25655 12 i3 i4 i5 1.6 10.74635 74563 744 9 o 744 1 8 74345 10.00687 00690 00692 00694 00696 o I I 9 . 99 3i3 99 3.o 993o8 99806 99 3o4 5o 49 48 47 46 i5 16 18 '9 10 38 o 3 7 52 3? 44 3 7 36 3 7 28 I 22 22 8 22 l6 22 24 22 32 9.25028 25o 9 8 2 5 1 68 a5a3 7 253o 7 17 18 19 20 22 I0. 7 4 97 2 74902 7 483 2 74 7 63 746 9 3 9 .25 7 2 7 2 5 799 258 7 i 2 5 9 43 260 1 5 18 19 20 21 22 10.74273 74201 74 129 740^7 7 3 9 85 i o . oo6 99 00701 oo 7 o3 00706 00708 I I I 9 . 99 3oi 99 2 99 99 2 97 99294 99 2 9 2 45 44 43 42 4i 20 21 22 23 24 10 37 20 3 7 12 3 7 4 36 56 36 48 I 22 40 22 48 22 56 23 4 23 12 9 .253 7 6 25445 255i4 25583 25652 23 24 25 26 27 10.74624 74555 7 4486 7447 74348 9 . 26086 26 1 58 2&22 9 26301 263 7 2 24 25 26 27 28 10.73914 7 3842 73771 73699 7 3628 10.00710 00712 oo 7 i5 oo 7 1 7 00719 I I I I I 9-99 2 9 99 2.88 99 a85 99 283 99 28l 4o 37 36 a 5 26 27 98 29 10 36 4o 36 32 36 24 36 16 36 8 I 23 20 23 28 23 36 23 44 23 52 9.25721 25790 25858 25927 2 5 99 5 28 3o 3i 32 33 10.742791 74210 74142 74o/3 74oo5 9 . 26443 265 1 4 26585 26655 26-726 3? 32 33 34 io. 7 355 7 7 3486 7 34i5 7 3345 732 7 4 10.00-722 00-724 00-726 00 7 2 9 oo 7 3 1 I I I I I I I 9-99 2 78 99 2 76 99 2 74 99271 99 2 69 35 34 33 32 3i Jo 3i 39 33 34 35 36 37 38 3 9 10 36 o 35 52 35 44 35 36 35 28 I 24 24 8 24 16 24 24 24 32 9.26063 26i3i 26.99 26267 2.6335 34 35 36 38 3-9 10.73937 7 386 9 7 38oi 7 3 7 33 7 3665 9 .26 797 2686 7 2 6 9 3 7 2 7 oo8 2 7 7 8 35 36 38 3 9 4o 10.73203 73 1. 33 7 3o63 72992 72922 io.oo 7 33 oo 7 36 oo 7 38 oo 7 4o oo 7 43 9-99267 9 9 264 99262 99260 992.57 3o 20 28 27 26 10 35 20 35 12 35 4 34 56 34 48 i 24 4o 24 48 24 56 25 4 25 12 9 . 264o3 26470 26538 26605 26672 4o 4i 42 43 44 10.73597 7 353o 73462 7 33 9 5 73328 9 .2 7 i48 2 7 2l8 2-7288 2 7 35 7 27427 4i 42 44 45 46 I0. 7 2852 72782 7 2 7 .2 7 2643 7 25 7 3 io.oo 7 45 oo 7 48 00760 007 5 2 00755 I 2 9 . 99 255 99252 99 2.5o 99248 99245 9.99243 99241 99 238 99236 99233 25 2<^ 2: 22 21 20 1 9 6 4o 4i 42 43 44 10 34 4o 34 32 34 24 34 16 34 8 I 25 20 25 28 25 36 25 44 25 52 9.26739 26806 268 7 3 26940 27007 45 47 48 i 9 5o 10.73261 73i94 73i27 7 3o6o 72993 9 .2 7 4 9 6 2 7 566 2 7 635 2 77 o4 27773 47 48 & 52 10.72504 72434 72365 72296 7222-7 10.00757 00759 00762 00764 00767 2 2 2 2 2 45 46 47 48 4 9 10 34 o 33 52 33 44 33 36 33 28 I 26 26 8 26 16 26 24 26 32 9.27073 27140 27206 272 7 3 27339 5i 52 53 55 56 10.72927 72860 72794 72727 7266! 9 . 27842 27 9 n 279)80 28o4 9 28117 53 54 55 56 58 59 60 61 62 63 io. 7 2i58 72089 72020 71951 7 1 883 io.oo76 9 00771 00774 00776 oo77 9 2 2 2 2 2 2 2 2 2 2 9.99231 99229 99226 99224 99221 r Z I I 10 8 6 5o 5i 52 53 54 55 56 57 58 5 9 60 10 33 20 33 12 33 4 32 56 32 48 i 26 4o 26 48 26 56 27 4 27 12 9-2 7 4o5 27471 2 7 53 7 2 7 602 2 7 668 5 7 58 r 9 60 6. 10.72595 72529 72463 7 23o8 72332 9 . 28186 28254 , 283 2 3 2 83 9 i 2 845 9 10.71814 7 1 7 46 71677 71609 7i54i 10.00781 oo 7 83 00786 00788 O07 9 i io.oo7 9 3 00796 oo7 9 8 00800 oo8o3 oo8o5 9.99219 99217 99214 99212 99209 10 32 4o 32 32 32 24 32 16 32 8 32 I 27 20 27 P.8 27 36 27 44 27 52 28 o 9.27734 27799 27864 27930 27995 28060 63 64 65 66 67 68 10.72266 72201 72136 72070 7 2005 71940 9 . 28527 285 9 5 28662 28730 28 79 8 28865 65 66 67 68 69 71 10.71473 7r4o5 7 i338 7 I2 7 71202 7 ii35 2 2 2 2 2 2 9.99207 99204 99202 99200 99197 99 i 9 5 c 4 I O M Hour P. M Hour A. M Cosine. Diff Secant. Cotanger ' Diff Tangent. Cosecant. Diff. Sine. M 100 A A B B C C 79 Seconds of time i- 2 B 3 3 4" 5- 6 s 7- (A 9 17 26 34 ^3 5i 60 Prop, parts of cols. < B 9 18 26 35 44 53 62 ( C o i i i i 2 2 Pageiiu] TABLE XXVII. Log. Sines, Taiigonts, and Secants. 11 A A B B C G . C 168 ;! lour A.M.! Hour P.M. Sine. DirT. Cosecant Tangent. Oiff.C Cotangent Secant. Jiff. Cosine. M 2 3 4 5 6 7 8 9 10 1 1 12 i3 i4 32 3i 52 3i 44 3i 36 3 1 28 1 28 28 8 28 16 28 24 28 32 .28060 28125 28:90 28254 28319 i 2 3 4 5 6 7 8 9 0.71 940 71876 71810 71746 71681 9- 28866 28933 29000 29067 29134 o I 2 3 4 o. 7 u35 71067 71000 7 o 9 33 70866 o. 0080 5 00808 00810 008 1 3 00816 o >. 99196 99 '9 3 99 i 9 o 99,87 99 1 85 ?. 99 l82 99180 99!?7 99176 99172 i ^7 56 3l 20 3l 12 3i 4 3o 56 3o 48 i 28 4o 28 48 28 56 29 4 29 12 .28384 28448 285 12 2 85 77 28641 0.71616 7 i55 2 7 t488 7i423 7.359 9- 29201 29268 2 9 335 29402 29468 5 6 8 9 10 0.70799 70732 70666 70698 70632 0.00818 00820 00823 00826 00828 o o o R ,5 54 53 52 61 o 3o 4o 3o 32 3o 24 3o i6| 3o 8 I 29 20 29 28 29 36 29 44 29 52 9.28705 28769 28833 28896 28960 10 ii 12 i3 i4 0.71295 7ia3i 71167 71104 71040 9- 2 9 535 29601 29668 29-34 29800 ii 12 i3 i4 i5 i 0.7046 5 7o3 99 7o332 70266 70200 o.oo83o 008 3 3 oo835 oo838 00840 9.99170 99167 99166 99162 99160 5o 49 48 47 46 i5 16 17 .8 |9 o 3o o 29 5 2 29 44 29 36 29 28 i 3o o 3o 8 3o 16 3o 7 A 3o 3a 9.29024 29087 29150 29214 29277 16 17 18 9 20 0.70976 70913 7o85o 70786 70723 9.29866 29932 3oi3o 16 17 18 1 9 20 10.70134 70068 70002 6 99 36 69870 io.oo843 oo845 00848 008 5o oo853 -- 9. 991167 99 i55 99 l52 99160 99^7 45 44 43 42 4i 4o 3 9 38 37 36 20 21 i2 a 3 a4 o 29 20 29 I 2 29 4 28 56 28 48 i 3o 40 3o 48 3o 56 3i 4 3l 12 9.29340 29403 29466 29529 2 9 5 9 , 21 22 23 24 25 o . 70660 70597 7 o534 70471 70409 9 3oi 9 5 3o26i 3o326 3o39i 3o45 7 22 23 24 26 26 10.69806 69739 69674 69609 69643 10.00866 00868 00860 oo863 00866 9-99'45 99142 99140 991 3 7 9 9 i35 25 ^6 28 2 9 10 28 4o 28 32 28 24 28 16 28 8 J 3 1 20 3i 28 3i 36 3. 44 3i 52 9.29654 29716 29779 29841 291903 26 27 28 3? 10.70346 70284 70221 70169 70097 9 .30522 3o58 7 3o652 30717 30782 27 28 ? 9 3o 3i 10.69478 69413 6 9 348 69283 6Q2l 10.00868 00870 00873 00876 00878 9.9913? 99.- 3o 9912- 99124 99122 35 34 33 \q 3j 3. 3- 3 a 33 3/j 3 T 3( 3 38 3 9 4> 4 42 4 44 4 T 4< 47 58 10 28 o 27 52 27 44 27 36 27 28 I 32 32 8 32 16 32 24 32 32 9.29966 30028 30090 3oi5i 3O2K 3i 32 33 34 35 1 . 70034 6997? 69910 69849 69787 9.30846 3091 1 30976 3io4o 3 1 10^ 32 33 35 36 3 7 I0.69l54 69089 69026 68960 68896 10.00881 oo883 00886 00888 00891 9.99119 99117 99114 99112 99109 3o 29 2.8 2.7 26 10 27 20 27 12 27 4 26 56 26 48 i 32 4c 32 48 32 56 33 4 33 1-2 9.30275 3o33f 3o3 9 8 3o45o 3o52i 36 ' 37 38 3 9 4o 10.69726 69664 69602 6 9 54i 69479 9 .3n68 3i233 31297 3i36 3i4^5 38 3/9 4o 4i 42 io.68832 68767 68703 6863 9 685 7 5 10.00894 00896 00899 00901 00904 2 2 2 2 2 9.99106 99104 99101 99099 99096 26 1L 23 22 2.1 10 26 4o 26 32 26 Ii 26 l( 26 8 i 33 20 33 28 33 36 33 44 33 5? 9.3o582 3o643 30704 3o?6! 3o82C 4i 42 43 45 46 10.69418 6 9 35 7 69,96 69235 69174 o.3i48c 3i552 3i6i6 31679 3 1 7 43 43 44 45 46 47 10.686*1 68448 68384 6832 6826 10.00907 00909 00912 0091^ 00917 2 2 2 2 2 2 2 2 2 2 9.99093 99091 99088 99086 99083 20 6 10 26 o 25 52 25 44 2 5 36 25 28 i 34 o 34 8 34 16 34 24 34 32 9.3o88- 3094- 3ioo8 3 1068 31125 47 48 49 5c 5i 10.691 i3 6 9 o53 %$ 6887 9. 3 i 806 3i8 7 c 3i 9 33 3 1996 32069 i 9 5o 5i 62 53 10.6819 68i3 6806 6800 6794 10.00920 00922 00925 00928 oo 9 3o 9.99080 99078 9 975 9.9072 99070 5t i 5 5 5-4 5 56 5 r 5 6 10 25 20 25 12 25 4 24 50 24 48 i 34 4c 34 4b 34 5f 35 4 35 i 9.31189 3i25c 3.3ic 3i3 7 e 3i43r 5? 53 54 55 56 10.6881 68760 68690 6863r 685 7 t 9.3212 32.8 3224 323 1 3a37 54 55 56 57 58 10.6787 6781 6775 6768 6762 10.00933 00936 00938 00941 0094^ 2 2 2 2 2 0.09067 99064 99062 99069 99066 10 ( 10 24 4o 24 32 24 24 24 iC 24 24 c i 35 20 35 2 35 3 35 4 35 5 36 9.3i49< 3i54 3 1 60 3i66c 3l 7 2 3i 7 8 57 58 5 9 60 61 62 10.685! 6845 6839 6833 6827 6821 9 .3 2 43( 324 9 3256 3262.: 3268 C 32 7 4- , 5 9 60 6, ! 63 64 , 65 n;ff 10.6766 6760 6 7 43 6 7 3 7 6731 6726 Tangent 10.00946 00949 00952 oo 9 54 00967 00960 Cosecant 2 2 2 !5 I 3 I>iff 9.990^4 99061 99 o48 99046 99043 99040 Sine. M JM Hour i>. M 101 Hour A. M A A B B C C 78 Seconds of time 1* 2 3' 23 24 ' i 4 5" lo~ 40 a 6 7* 54 57 3 ( A Prop, partf ot com < B I C 8 !6 10 ! 3i 32 i 4-7 49 a - TARI/E XXVII. ^ Page 197 I og. Sines, Tangents, and Secants. w ' 12 3 A A B B C C 167 >I Hour A.M. Hour P.M. i 36 o 36 8 36 16 36 24 36 32 Sine. Diff. Cosecant. Tangent. |Diff.jCotang-cnt Secant. Dift. Cosine. AI o 4 10 24 23 52 23 44 23 36 23 28 9.31788 3 1 847 31907 3 1 966 32025 i 2 3 4 10.68212 68 1 53 68o 9 3 68o34 67975 9.32747 328-10 32872 32 9 33 32 99 5 2 3 4 10.67253 67190 67.28 67067 67005 10.66943 6688 1 66820 66758 66697 i o . 00960 00969. oo 9 65 oo 9 68 oo 97 o o o o o o 9.99040 99 o38 99 o35 9932 99 o3o 60 5 9 58 57 56 55 54 53 52 5i K 6 8 9 10 23 20 23 12 23 4 22 56 22 48 i 36 4o 36 48 36 56 3 7 4 37 12 9.32084 32143 32202 32261 3 2 3i9 5 6 8 9 10.67916 6 7 85 7 67798 67739 67681 9 .33o5 7 33ii 9 33 1 80 33242 333o3 5 6 7 8 9 .10.00973 00976 00978 0098 1 00984 9.99027 99024 99 022 99 '9 99016 10 1 1 i 2 i4 IO 22 4o I 37 2O 22 32 3y 28 22 24 3 7 36 22 1 61 3 7 44 22 8! 3? 52 9 .3?3 7 8 3243 7 32495 32553 32612 IO 10 II 12 i3 10.67622 6 7 563 6 7 5o5 67447 6 7 388 9 . 33365 33426 33487 33548 336o 9 10 ii 12 i3 i4 io.66635 665 7 4 665.3 66452 663 9 . io.6633o 66269 66208 66147 66087 10.00987 00989 00992 0099^) 00998 o 9.99013 990 1 1 99008 9900 5 99002 5o 49 48 47 46 1 D 16 i? 18 19 10 22 O 21 52 21 44 21 36 21 28 i 38 o 38 8 38 16 38 24 38 32 9.32670 32728 32786 32844 32902 i4 i5 16 17 18 10.67330 67272 67214 67 1 56 67098 0. 33670 33 7 3i 337 9 2 33853 33 9 i3 i5 16 17 18 *9 IO.O1OOO oioo3 01006 01009 010. I 9 . 99000 9 8 997 98994 9 8 99' 9 8 9 8 9 45 44 43 42 4i 20 21 22 23 a4 10 21 20 21 12 21 4 20 56 20 48 i 38 4o 38 48 38 56 39 4 39 12 9.32960 33o.8 33o 7 5 33 1 33 33 1 90 1 9 20 21 22 23 10.67040 66982 66925 66867 668 1 o 9.33974 34o34 34o 9 5 34.55 342 1 5 20 21 22 23 24 10.66026 65966 65oo5 65845 65 7 85 10.0101/4 01017 01020 01022 O1025 9.98986 9 8 9 83 98980 98978 98975 4o % II 35 34 33 32 3i 25 a ^7 28 29 10 20 40 20 32 20 24 20 1 6 20 8 I 30 20 3o 28 3 9 36 3 9 44 3952 9 .33248 333o5 3336p. 33420 33477 24 25 26 27 28 10.66752 666 9 5 66638 6658o 66523 9 . 34 2 76 34336 343 9 6 34456 345 1 6 25 26 2 7 28 29 10.65724 65664 656o4 65544 65484 10.01028 o i o3 1 oio33 oio36 oio3 9 9-9 8 972 9 8 9 6 9 98967 98964 9 8 9 6i 3o :h 3j 33 34 10 20 19 52 19 44 19 36 19 28 i 4o o 4o 8 4o 16 4o 24 4o 32 9.33534 335 9 i 33647 33 7 o4 33 7 6i 2 9 2 9 3o 3i 32 10.66466 66409 66353 66296 66239 9.34576 34635 346 9 5 34 7 55 348.4 3o 3i 32 33 34 10.65424 65365 653o5 65245 65.86 IO.OIO42 01045 01047 oio5o oio53 2 2 9 . 9 8 9 58 9 8 9 55 9 8 9 53 98960 98947 3o 29 28 27 26 35 36 3 7 38 3 9 4<> 4i 4^ 43 44 IO 19 20 19 12 19 4 18 56 18 48 i 4o 4o 4o 48 4o 56 4i 4 4i 12 r 4i 20 4i 28 4i 36 4i 44 4i 52 9.338.8 338 7 4 33o3i 33 9 8 7 34o43 33 34 35 36 37 10.66182 66126 66069 660 r 3 65 9 5 7 9.34874 34 9 33 34992 35o5i 35m 35 36 37 38 3 9 io.65i26 65o6 7 65oo8 64 9 4 9 6488 9 io.oio56 01059 01062 o 1 064 01067 2 2 2 2 2 2 2 2 2 2 9-98944 98941 9 8 9 38 9 8 9 36 98933 25 24 23 22 21 jo i 8 4o 18 3 2 18 24 18 16 18 8 9 . 34 1 o'o 34i56 34212 34268 34324 38 3 9 4o 4r 42 10.65900 65844 65788 65 7 3 2 656 7 6 9.35170 35229 35288 35347 354o5 4o 4i 42 43 44 io.6483o 64771 64712 64653 645 9 5 i o . o i 070 01073 01076 01079 01081 9.98930 98927 98924 9 8 9 2i 9 8 9'9 2O '9 .8 '7 1 6 45 46 47 4S 49 10 18 o 17 52 17 44 17 36 17 28 1C 17 20 17 12 17 4 16 56 16 48 i 42 o 42 8 42 16 42 24 42 32 9.3438o 34436 344oi 34547 34602 43 44 45 46 47 48 48 4 9 5o 5i 52~ 53 54 55 56 j>7_ DirT. 10.65620 65564 655o 9 65453 653 9 8 9.35464 35523 3558i 3564o 356 9 8 45 46 47 48 A 5 52 53 54 io.64536 64477 644 1 9 6436o 643o2 10.01084 01087 01090 oio 9 3 01006 2 2 2 2 2 9 . 9 8 9 i6 989.3 98910 98907 98904 i5 i4 .3 I 2 I I 10 8 6 So 5i 52 53 54 i 42 4o 42 48 42 56 43 4 43 12 9.34658 3471 3 34769 34824 348 7 9 10.65342 6528 7 65 2 3i 65 176 65i2i 9 .35 7 5 7 358i5 358-3 35 9 3i 35989 10.64243 64 1 85 64127 64069 64oi i io.oio 99 01 102 01 104 01 107 01 I 10 2 2 2 2 3 9.98901 98898 98896 9 88 9 3 98890 56 56 5~ 58 5 9 60 10 16 4o 16 32 16 24 16 16 16 8 16 o i 43 20 43 28 43 36 43 44 43 52 44 o 9.34934 34989 35o44 35099 35 1 54 35209 io.65o66 65oi i 64956 64 9 o i 64846 64791 9.36o47 36io5 36.63 3622. 36279 36336 55 56 57 58 r 9 60 10.63953 63895 ' 6383 7 63779 63 7 2i 63664 10.01 i i3 OI I l6 01 1 19 OI 122 01 125 oi 128 Cosecant.) 3 3 3 3 3 3 9.98887 98884 9 888i 98878 9 88 7 5 9 88 7 2 5 4 3 2 I O M Tour P.M lour A.M. Cosine. Secant. Cotangent DilT. Tangent. ixr. Sine. M 102 A A B B C Seconds of time 1 s 9 s :V /! 5' fi s 7 f A Prop, parts of "ols. < B 7 *f i4 i5 - 1 22 29 3o 36 37 43 45 ^>O 52 I C I 9 a- 1 c ir- Fage 1 1 JS| S'. 13 TABLE XXVII. Log. Sines, Tangents, and Secants. A A B B C G C 166 > ai o 2 3 4 our A.M.IIIourp.M. Sine. 1 >iff.C Cosecant. Tangent. )iff. otanger. Secant. DiiT. Uosine. o 16 o i5 5. 1 5 441 i5 36 1 5 28 i 44 o 44 8 44 16 44 24 44 32 }. 35209 35263 353i8 353 7 3 3542 7 I 2 3 4 o. 64 7 9i 64 7 3 7 64682 6462 7 645-3 9.36336 363 9 4 36452 365o 9 36566 i 2 3 4 0.63664 636o6 63548 634 9 1 63434 o.oi 128 Oi l3i ou33 oii36 on3 9 o s o o .98872 98869 98867 9 8864 98861 5 6 8 9 O I 5 20| l5 I2i i5 4. i4 56 i4 48 i 44 4" 44 48 44 56 45 4 45 12 j. 3548i 35536 355 9 o 35644 356 9 8 4 i 5 6 8 0.64519 64464 644 1 o 64356 643o2 9.36624 3668 1 36 7 38 36 7 95 36852 5 6 6 8 o.633 7 6 633 1 9 63262 632.o5 63 1 48 c.oi 142 on45 ou48 01 i5i 01 154 o o o >. 98858 98855 98852 98849 98846 1 O 11 12 i3 i4 o i4 4o i4 32 i4 24 i4 16 i4 8 i 45 20 45 28 45 36 45 44 45 52 9 .35 7 5 2 358o6 3586o 35914 35968 9 10 ii ii 12 0.64248 64194 64i4o 64o86 64o32 o . 36909 36966 3-02: 3 7 o8o 3 7 i3 7 9 10 1 1 12 i3 o.63( 91 63o34 6-J 977 62920 62863 O.OI ID 7 01 1 60 oi i63 01 166 oi 169 7. 9 S843 98840 988*7 98834 9883i i5 ! 6 18 19 o i4 o i3 52 1 3 44 i3 36 i3 28 i 46 o 46 8 46 16 46 24 46 32 O.36O22 36o 7 5 36129 36:82 36236 i3 i4 (5 16 17 o.639 7 8 63 9 25 638 7 i 638 1 8 63 7 64 9.371^3 37250 3 7 3o6 3 7 363 3j4i9 M i5 16 17 18 10.62807 62 7 5o 62694 62637 62 58 1 10.01 1 7 9 or i 7 5 oi t 7 8 oi 181 01184 9.98828 98825 98822 9 88i 9 98816 i 1 l ; ! 20 21 22 23 24 l3 20 13 12 i3 4 12 56 12 48 i 46 4o 46 48 46 56 47 4 47 12 9.36289 36342 363 9 5 36449 365o2 18 18 19 20 21 o.63 7 u 63658 636o5 6355i 1 63498 9 .3 7 4 7 6 3 7 532 3 7 588 3 7 644 3 77 oo 9 .3 77 56 3 7 8i2 3 7 868 37924 3 79 8o 19 19 20 21 22 10.62524 62.468 62412 62356 623oo 10.01 187 oi 190 oi 193 01196 01199 9 . 9 b8i3 9 88 1 o 98807 98604 98801 25 2f> 37 28 2 9 o 12 4o 12 32 12 It. 12 l6 12 8 i 47 20 47 28 4 7 36 47 44 47 52 .365551 366o8 3666o 36 7 i3 36 7 66 22 23 24 25 25 0.63445 633 9 2 6334o 6328 7 632.34 2C Ii 25 2O 2 7 "^8" 2 9 3o 3i 32 10.62244 62188 62132 62076 62020 IO.OI2O2 01205 01208 OI2II OI2i4 9 . 9 8 79 8 9 8 79 5 98792 9 8 7 8 9 9 8 7 86 - 1 3o 3i 32 33 34 12 II 52 ii 44 ii 36 ii 28 i 4 o 48 8 48 16 48 24 48 32 9.36819 368 7 . 36 9 24 36 97 6 37028 26 2 7 28 2 9 3o IT 32 32 33 31 io.63t8i 63129 63o 7 6 63o24 629-72 9.38o35 38091 38 1 47 38202 3825 7 10.619*5 61009 6i853 61798 6i 7 43 IO.OI2I 7 01220 01223 01226 01229 2 2 2 2 2 0.98783 98-780 ?8 777 9S/ 7 4 9877' 6 35 3C 37 38 9 o 1O II 20 II 12 ii 4 10 56 10 48 i 48 4o 48 48 48 56 49 4 49 i? I 49 20 4 9 28 49 36 49 44 4o 52 9.37081 3 7 i33 3 7 i85 3 7 23 7 37289 10.62919 62867 62815 62 7 63 62-71 1 9- 383 1 3 38368 38423 384 7 9 38534 32 33 34 35 36 10.61687 6i63a 6 1 577 6i52i 6 1 466 IO.O1 232 01235 01238 01241 01244 2 2 2 2 2 9.98768 9 8 7 65 9 8 7 62 9 8 7 5 9 9 8 7 56 > j 1 a i |O 4 4 4^ 4^ 4- 4 4 4 4 r C I 10 10 4o 10 32 10 .2Z 10 16 10 & 9 .3 7 34i 3 7 3 9 3 3 7 445 3 7 497 3 7 549 9.37600 3 7 652 3 77 o: 3 77 5: 3 7 8o6 9 .3 7 85 3 79 ,-c 3 79 6c 38oi 38o6 973877 38.6 382i 3826 383 1 3836 35 36 3 7 38 3 9 10.62659 6260-7 62555 6s5o3 62451 9.38589 38644 386 9 s 38 7 5.' 388o 3 7 38 39 4o 4i io.6i4i i 6 1 356 6i3oi 61246 6lI 9 2 I0.0124 7 01250 01254 OI25 7 01260 2 2 2 2 2 9 . 9 8 7 53 9 8 7 5o 9 8 7 46 9 8 7 43 98 7 4o 6 13 10 C 9 5, 9 4^ ?3C o 2, i > i j > 1 i jo < 5o 8 5o 16 5o 2/ *><> 3p 3 9 4o 4 42 43 10.62400 62348 6229-7 62245 62194 9- 3886: 38 9 i 38 97 : 3 9 02' 3 9 o8- 42 43 44 45 45 10.6 6 6 6 6 ii3 7 1082 1028 o 97 3 o 9 i8 0864 o8ic o 7 5f 7 OI 064- 10.0126^ OI26C 0126^ Oi2 7 : oi2 7 : 2 2 2 2 2 ,9-9873 7 98 7 34 9 8 7 3, 98728 98725 5 -1 (3 a 1 1 10 9 2c 9 IS 9 8 5( 8 4^ 10 8 4< 8 3 8 2 8 i 8 8 5o 4< 5o 4 5o 5<: 5i - 5i i 5l 2 5i 2 5i 3 5i 4 5i 5 52 44 45 46 4 7 4 7 4b 49 5c 5i 52 53 10.6214^ 62091 62040 6. 9 Sc 6i 9 3fc 9 .3 9 ,3( 3 9 .9< > 3924 ) 3929 i 3 9 35 46 4? 48 49 5o 10.6 6 6 6 6 IO.OI2 7 ^ 0128 oiaSf oust 0129 3 3 3 3 3 9.98722 98719 987.5 987.2 98709 10 9 8 i 10.6188- 6i83( 6178? 6i 7 3. 6168, 6i63 '. Secant. __ A 7 9.3940 ) 3 9 46 ] 3 9 5. | 3 9 56 ] 3962 \ __J^7 Cotangei _J. B 5i 52 53 54 55 56 Dif io.6o5 9 J 6o53c 6o485 6o43 1 6o3 7 - 6o32: ". Tangent. B 10.0129-; 0129- oi3oc oi3o^ oi3o( oi3i( Cosecant .. C 3 3 3 3 3 3 jTO 5.98706 98703 9 8700 9869.7 98694 9 86 9 o 5 4 3 a i 11 1M Hour?.?.! Ho 103 UTA.J Cosine ^ A Dif C 76 Seconds of time 1" 2 s 3 s 20 21 I 4 s 26 28 2 5 s 33 35 2 6 s "17 42 2 7 ~46~ 49 | 5 1 T^ 1 Prop, paita of cols. < B 1 C 7 7 o i3 i4 i TABLE XXVII. tragei Log. Sines, Tangents, and Secants. 14 A A B B C C 16 fd 5 M 31 Hour 4.M. Hour P.M. Sine. Diff. Cosecant. Tangent. Diff. vctangent Secant. Dff. Cosine. o i 2 3 4 5 6 7 8 9 10 8 o 7 52 7 44 7 36 7 28 I 52 52 8 52 16 52 24 52 32 9.38368 384 18 38469 385 1 9 38570 o i 2 2 3 ~T 6 7 7 io.6i632 6i582 61 53 1 6i48i 6i43o 9.39677 39731 39785 39838 39892 2 3 3 io.6o3a3 60269 602 1 5 60162 60108 TO.Ol3lO Oi3i3 oi3i6 01319 Ol322 o o o o 9 . 9 b6 9 o 98687 98684 98681 98678 60 58 5"> 56 10 7 20 7 12 7 4 6 56 6 48 i 52 4o 52 48 52 56 53 4 53 12 9.38620 386 7 o 38 7 2i 38771 3882i io.6i38o 6i33o 61279 61229 61179 9-39945 39909 40062 4o 1 06 4oi5 9 4 5 6 8 io.6oo55 60001 59948 5 9 8 9 4 5 9 84i 10 oi325 01329 oi33a oi335 oi338 9.98675 98671 98668 98665 98662 55 54 53 5a 5i 10 1 1 12 i3 i4 10 6 4o 6 32 6 24 6 16 6 8 i 53 20 53 28 53 36 53 44 53 52 9 .388 7 i 38 9 2i 38 97 r 30021 39071 8 9 10 ii ii 12 i3 i4 i5 i5 io.6t 129 61079 61029 60979 60929 9.40212 40266 4o3i9 4o3 7 2 4o4a5 9 10 10 11 12 10.59788 59734 5 9 68i 59628 5o575 io.oi34i 01 344 oi 348 oi35i oi354 9.98659 98656 98652 98649 98646 5o 49 48 47 46 i5 16 17 18 '9 10 6 o 5 52 5 44 5 36 5 28 i 54 o 54 8 54 16 54 24 54 32 9.39.2, 39170 39220 39270 3 9 3i 9 10.60879 6o83o 60780 60730 60681 9.40478 4o53i 4o584 4o636 40689 i3 i4 i5 16 17 10.59522 5 9 46 9 5 9 4i6 5 9 364 593ii io.oi357 oi36o oi 364 01 367 01370 9.98643 9 864o 9 8636 98633 9863o 45 44 43 42 4i 20 21 22 23 24 IO 5 20 5 12 5 4 4 56 4 48 i 54 40 54 48 54 56 55 4 55 12 9.3 9 36 9 3 9 4.8 39467 39517 3 9 566 16 17 18 '9 20 io.6o63i 6o58 2 6o533 6o483 6o434 9.40742 40795 40847 40900 40952 17 18 9 20 21 10.59258 59205 5 9 i53 59100 59048 10.01373 oi 377 oi38o oi383 oi386 9.98627 98623 98620 986.7 98614 4o 3 9 38 37 36 25 26 27 28 29 10 4 '4o 4 3 2 4 24 4 16 4 8 i 55 20 55 28 55 36 55 44 55 52 9.3 9 6i5 3g664 3 97 i3 39762 39811 2O 21 22 23 24 24 25 26 27 28 29 29 3o 3i 32 io.6o385 6o336 60287 60238 60189 9 .4ioo5 4io57 41109 4i 161 41214 22 23 23 24 25 10.58995 58 9 43 588 9 i 5883 9 58786 10.01390 01393 oi3 9 6 oi3 99 oi4o3 2 2 9.98610 98607 98604 98601 _98597 9-985 9 4 9 85 9 , 9 8588 98584 9 858i 35 34 33 32. 3i 30 29 28 27 26 25 24 23 22 21 3o 3i 3?. 33 34 35 36 37 38 3 9 10 4 o 3 52 3 44 3 36 3 28 i 56 o 56 8 56 :6 56 24 56 32 9.39860 39909 3995? 4ooo6 400*35 T n.6oi4o 60091 60042 59994 5 99 45 9.41266 4i3i8 41370 4l422 4i474 26 27 28 ?9 3o ~3o~ 3i 32 33 34 10.58734 58682 5863o 585 7 8 58526 io.oi4o6 01409 01412 01416 01419 2 2 2 2 2 2 2 2 2 2 10 3 20 3 12 3 4 2 56 2 4& i 56 4o 56 48 56 56 5 7 4 57 12 9 .4oio3 4oi52 40200 4o24 9 40297 io.5 9 8 9 7 5 9 848 5 9 8oo 59761 59703 9-4i526 4i5 7 8 41629 41681 4i733 10.58474 58422 583 7 i 583 1 9 58267 10.01422 01426 01429 oi432 oi435 9 . 9 85 7 8 9 85 7 4 9 85 7 i 98568 9 8565 4o 4i 42 43 44 45 46 47 48 49 5o 5i 52 53 54 10 2 40 -2 32 2 24 2 16 2 8 I 57 2O 5 7 28 5 7 36 57 44 5 7 52 9 .4o346 4o3 9 4 4o44a 40490 4o538 33 33 34 35 36 10.59654 5 9 6o6 5 9 558 5 9 5io 5 9 462 9.41784 4 1 836 41887 41939 41990 35 36 36 37 38 10.58216 58 1 64 58u3 58o6i 58oio 10.01439 oi44^ oi445 01449 01452 2 2 2 2 2 9. 9 856i 9 8558 9 8555 9 855i 98548 20 !S 17 l6 10 52 44 36 28 i 58 o 58 8 58 16 58 24 58 32 9 .4o586 4o634 40682 40730 40778 3 7 3? 38 3 9 4o 10.59414 5 9 366 5 9 3.8 59270 59222 9.42041 42093 42i44 42195 42246 3 9 4o 4i 42 43 43 44 45 46 4 7 10.57959 57907 5 7 856 5 7 8o5 57754 io.oi455 oi45 9 01462 oi 465 01469 2 3 3 3 3 9.98545 9 854i 98538 9 8535 9 853i 1 4 Io II 10 20 12 4 o 56 o 48 i 58 4o 58 48 58 56 5 9 4 5 9 12 9.40825 4o8 7 3 40921 40968 4ioi6 4i 42 42 43 44 10.59175 59127 59079 59082 58 9 84 9.42297 42.348 42399 4245o 425oi 10.57703 5 7 652 57601 5 7 55o 57499 10.01472 oi475 01479 01482 oi 485 3 3 3 3 3 9.98528 9 85 2 5 98521 9 85i8 9 85i5 10 6 55 56 5 7 58 59 60 10 o 4o 32 o 24 o 16 o 8 o o i 59 20 5 9 28 5 9 36 5 9 44 59 52 200 9.41 o63 4> 1 1 1 4ii58 4i2o5 41252 4i3oo 45 46 46 47 48 49 io.58 9 37 58889 58842 58 79 5 58 7 48 58700 9.42552 42603 4a653 42704 42 7 55 42805 48 I 9 5o 5o 5i 52 io.5y448 57397 5 7 347 57296 5 7 245 57195 10.01489 01492 01495 oi499 01502 oi5o6 3 3 3 3 3 3 9.98511 985o8 9 85o5 9 85oi 98498 984 9 4 5 4 3 2 I M Ho'.irp.M. Hour A.M. Cosine. Diff. Secant. Cotangent Diff. Tangent. Cosecant. Diff. Sine. M 114 C 75 Seconds of time 1" 9 s ? s 4 s f> s (1 s 7- (A 6 12 18 24 3i 3 7 43 Prop, parts of cols. ^ B 7 i3 20 26 33 3 9 46 I C I I 2 2 a 3 l';i 5' 15 ;\i ie ~ a ^ TABLE XXVII. Log. Sines, Tangents, and Secants. A A B B C C 1C>4? lour A.M. lour P.M. Sine. Diff. o a 2 3 Cosecant. Tang-ent. Difl'. yotangenl Secant. |Diff Cosine. M o I 7 r\ i 2 3 4 5 6 7 8 _9 10 1 1 i '). i3 i4 O O 9 69 52 5 9 44 5 9 36 59 28 9 59 20, g" 09 4l 58 56; 58 48 200 o 8 o 16 o 24 32 3 40 o 48 o 56 4 12 9.41 3oo 4 1 34 7 4i3 9 4 4i44i 4 1 488 . 58700 58653 586o6 5855 9 585i2 9.42805 42856 42906 42 9 5 7 43oo 7 o i 2 2 3 4 5 6 7 7 0.57195 5 7 i44 5-7094 5 7 o43 56 99 3 O.oi5o6 Oi5o 9 1 5 I 2 oi5i6 oi5i 9 o . 9 84 9 4 9 84 9 i 9 8488 9 8484 9848 1 9-4i535 4i58 2 41628 4i6 7 5 41722 4 5 5 6 7 0.58465 584 1 8 58372 58325 582 7 8 9.43o5/ 43 108 43 1 58 432o8 43 2 58 o.56 9 43 568 9 2 56842 56792 56 7 42 o.oi523 0026 Ol52 9 oi533 01 536 o o I .98477 98474 98471 98467 98464 5 4 3 52 5i 9 58 4o 58 32 58 24 58 16 58 8 2 20 28 36 44 52 9.41768 4i8i5 41861 41908 41954 8 8 9 10 n io.58232 58i85 58i3 9 58092 58o46 9.433o8 43358 434o8 43458 435o8 8 9 10 ii 1 1 10.56692 56642 565 9 2 56542 564 9 2 o.oi54<> 01 543 o.54 7 | oi55o oi553 9.98460 9 845 7 9 8453 9 845o 9 844 7 5o 1 46 i5 16 17 18 i? 20 21 22 23 24 9 58 o * 5 7 52 5 7 44 57 36 5 7 28 220 2 8 2 16 2 24 2 32 9.42001 42047 42093 42140 42186 ii 12 i3 i4 i4 ~TT 16 17 17 18 10.5-7999 5 7 953 5-790-7 5 7 86o 5 7 8i4 9.43558 436o 7 4365 7 43 7 o 7 43 7 56 12 i3 i4 i5 16 10.56442 563 9 3 56343 562 9 3 56244 io.oi557 oi56o 01 564 01 567 01571 9.98443 9 844o 98436 98433 98429 45 4- / 4^ 42 4. 9 D7 20 5 7 12 5 7 4 56 56 56 48 2 2 40 2 48 2 56 3 4 3 12 9.42232 42278 42324 423 7 o 42416 io.5 77 68 57722 5 7 6 7 6 5 7 63o 5 7 584 9-438o6 43855 43 9 o5 43 9 54 44oo4 16 17 18 9 20 io.56i 9 4 5645 56o 9 5 56o46 55 99 6 IO.OI 574 01578 oi58i 0.585 01 588 9.98426 98422 9 84i 9 94i5 9 84i2 4o 3y 38 3 7 36 35 34 33 32 3i 26 ^8 :! 9 9 56 4o 56 32 56 24 56 16 56 8 2 3 20 3 28 3 36 3 44 3 52 9.42461 42507 42553 42599 42644 '9 20 21 21 22 io.5 7 53 9 5 7 493 57447 5 7 4oi 5 7 356 9-44o53 44 1 02 44i5i 44201 4425o 2O 21 22 23 24 io.55 9 4 7 55898 5584 9 55 79 9 557o io.oi5 9 i o.5 9 5 oiS^ 0.602 Qi665 9 . 98409 98405 98402 983 9 8 9 83 9 5 ;io 3 1 33 34 9 56 o 55 52 55 44 55 36 55 28 240 4 8 4 16 4 24 4 32 9.42690 42 7 35 42781 42826 42872 23 24 24 25 26 27 27 28 I 9 3o io.5 7 3io 5 7 265 5 7 2i9 57174 57128 9.44299 44348 4439 7 44446 44495 25 25 26 27 28 10.55701 5565a 556o3 55554 555o5 i o . o . 6o 9 01612 016.6 oi6i 9 0162: 2 2 J 2 2 9 . 9 83 9 , 9 8388 9 8384 9 838i 3o 2() 2 2 7 2(> 35 36 3? 38 3q 9 55 20 55 12 55 4 54 56 54 48 244' 4 48 4 56 5 4 5 12 9.42917 42962 43oo8 43o53 43o 9 8 10.57083 5 7 o38 56 99 2 56 9 4 7 56902 9-44544 44592 4464i 44690 44 7 38 29 y 3o 3 1 32 10.55456 554o8 5535 9 553io 55262 10.01627 o 1 63o oi634 01 637 01641 9 . 9 83 7 3 o83 7 o 9 8366 9 8363 98359 25 Ii 4' 4 4? 43 44 9 54 4o 54 32 54 24 54 16 54 8 2 5 2C 5 28 5 36 5 44 5 52 9.43.43 43 1 88 43a33 43278 43323 3o 3i 32 33 33 10.56857 568i2 56 7 6 7 56 7 22 566 77 9.44787 44836 44884 44933 44981 33 34 34 35 36 io.552i3 55i64 55n6 55o6 7 55oi 9 lo.o. 644 01 648 oi65i oi655 01 658 2 2 2 3 3 ~F 3 3 3 3 9 . 9 835b 9 8352 9 834 9 9 8345 9 8342 4o 4( 47 48 49 5o 5 5 5 5-4 9 54 o 53 52 53 44 53 36 53 28 260 6 8 6 16 6 24 6 32 9.43367 434i2 4345 7 435o2 43546 34 35 36 36 37 10.56633 56588 56543 564 9 b 5645 4 9.45029 45o^8 45.26 45i74 45222 37 38 38 3 9 4o 10.5497 54922 548 7 4 54826 54778 10.01662 01666 01669 0167: 01676 9>9 833b 9 8334 9 833i 9 8327 9 8324 10 74 9 53 20 53 12 53 4 52 56 52 48 2 6 4o 6 48 6 56 7 4 7 12 9.43591 43635 4368o 43724 43769 9.438i3 43857 43901 43946 43 99 c 44o34 38 ! 4i i o. 56409 56365 56320 562 7 6 5623 9.45271 453.9 4536- 454 1 5 45463 4i 42 43 43 44 10.54729 5468 54633 5458 5453 7 10.01 680 01 683 01687 oi6 9 i o.6 9 z io.oi6 9 8 01701 01705 01709 01712 01716 3 3 3 3 3 ~r 3 3 3 3 4 ]1)U_ 9 83.7 ^313 9 83o 9 983o6 9 . 9 83o2 98299 98296 9829 98788 9-8284 Sine. - C 5 5f 5 58 ~> 5 \ lite 9 52 4o 52 32 52 24 52 16 52 8 52 2 7 20 7 28 7 36 7 44 7 5 8 o 42 43 43 44 45 46 Diff io.56i8 7 56 1 43 56099 56c54 56oio 55 9 66 9.455;i 45559 456oC 45654 45 7 o2 45 7 5c 45 46 47 47 48 49 io.5448 9 5444 543 9 4 54346 54298 54250 Hour p. M - :-j Hour A. M Cosine. A Secant. ____ A Cotangen .. B Diff i Tangent _ B Cosecant C Sec >nds of time I" Prop, parts of cols. < B r 3' 18 4. 5 s ()' 7" 23 1^8~ 17 4o 25 3i 37 43 2 2 3 3 TABLE XXVII. [ pa * B5i01 ^ Log. Sines, Tangents, and Secants. 16" A A B B C C 163 M I 2 3 4 5 6 S 9 Hour A.M. [Hour P.M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent Secant. Dff. Cosine. M o 52 o 5i 52 5i 44 5i 36 5i 28 280 8 8 8 16 8 24 8 32 9 .44o34 44078 44122 44i66 44210 i i 2 3 io.55o66 55 9 22 558 7 8 55834 55790 9.4575o 45797 45845 458 9 2 45 9 4o i 2 2 3 io.5425o 54ao3 54 1 55 54 1 08 54o6o 10.01716 01710 oi 7 23 OI 7 2 7 oi 7 3o o 9.98284 98281 98277 9 82 7 3 98270 60 59 58 5-7 56 9 5 1 20 5l 12 5i 4 5o 56 5o 48 2 8 4o 8 48 8 56 9 4 9 ' a 9.44253 44297 4434i 44385 44428 4 4 5 6 6 10.55747 55 7 o3 5565 9 556 1 5 555 7 2 9.45987 46o35 46082 46i3o 46177 4 5 5 6 7 io.54oi 3 53 9 65 53 9 i8 536 7 o 53823 io.oi 7 34 oi 7 38 oi 7 4t oi 7 45 oi 7 4 9 I 9.98266 98261! 9 825 9 9 8 2 55 9 8 2 5r 55 54 53 52 5 t 56 49 A8 47 46 10 1 1 12 i3 i4 9 5o 4o 5o 32 5o 24 5o 16 5o 8 2 9 20 9 28 9 36 9 44 9 52 9.44472 445 1 6 4455 9 44602 44646 8 9 9 10 ii ii 12 i3 i4 i4 i5 16 16 17 18 18 1 9 20 21 io.55528 55484 5544i 553 9 8 55354 9.46224 46271 463 1 9 46366 464 1 3 8 9 9 10 ii 10.53776 53 7 2 9 5368i 53634 5358 7 IO.OI 7 52 oi 7 56 oi 7 6o oi 7 63 01767 9 . 9 8248 9 8244 98240 98237 98233 1 5 16 i? 18 12 20 21 22 23 24 9 5o o 49 52 49 44 4 9 36 49 28 2 10 10 8 10 16 10 24 10 32 9.44689 44733 44776 44819 44862 io.553i i 55267 55224 55i8[ 55 1 38 9.46460 46507 46554 466oi 46648 12 12 13 i4 i5 i5 16 17 1.8 '9 io.5354o 53493 53446 533 99 53352 10.01771 01774 01778 01782 oi 7 85 9.98229 98226 9 8222 9 82i8 9 82i5 45 44 43 42 4i 4o 3 9 38 3 7 36 9 49 20 49 12 4Q 4 48 56 48 48 2 10 40 10 48 10 56 ii 4 II 12 9.44905 44948. 44992 45o35 45077 io.55o95 55o5 2 55oo8 54965 54923 9.46694 46741 46788 46835 46881 io.533o6 532 5 9 53212 53!65 53n 9 io.oi 7 8 9 oi 79 3 01796 01800 01804 9.98211 98207 98204 98200 98196 a 5 26 27 28 29 9 48 4o 48 32 48 24 48 16 48 8 2 II 2O II 28 ii 36 ii 44 II 52 9.45120 45 1 63 45206 45249 45292 io.5488o 5483 7 54794 54 7 5 1 54708 9.46928 46975 47021 47068 47ii4 '9 20 21 22 22 10.53072 53oa5 52 979 52 9 3t 52886 10. 01808 0181 1 01816 oi8i 9 01828 2 9.98192 98180 981 85 98181 9 8 i77 35 34 33 32 3i 3o 3 1 32 33 34 9 48 o 4? 52 47 44 4? 36 47 28 2 12 12 8 12 l6 12 24 12 32 9 .45334 453 77 454i9 45462 455o4 21 22 23 23 24 10.54666 54623 5458 1 54538 54496 9.47160 47207 47253 47299 47346 23 24 25 26 26 10. 52.84() 5 2?9 3 53747 52701 52654 10.01826 oi83p 01 834 oi838 01841 2 2 2 2 2 9 . 9 8i74 98170 98166 98162 9 8i5 9 3o 2 9 28 27 26 ,35 36 3 7 38 3 9 9 47 20 4? 12 47 4 46 56 46 48 2 12 40 12 48 12 56 i3 4 l3 12 9-45547 4558 9 45632 456 7 4 45 7 i6 25 26 26 27 28 10.54453 544n 54368 54326 54284 9.47392 47438 47484 4 7 53o 475 7 6 27 28 29 ? 9 3o 10.52608 52562 5 2 5i6 52470 5242.4 io.oi845 oi84 9 oi853 oi856 01860 2 2 2 2 2 9 . 9 8i55 9 8i5i 98147 98144 98140 25 24 23 22 21 4o 4i 42 43 44 45 46 47 48 49 o 46 4o 46 3 2 46 24 46 16 46 8 2 l3 20 i3 2.8 i3 36 i3 44 i3 52 9 .45 7 58 458oi 45843 45885 45927 28 29 3o 3i 3i ~3T 33 33 34 35 10.54242 54iQ 9 54i5 7 54u5 54073 9.47622 47668 477M 47760 47806 3i 32 32 33 34 10.52378 52332 52286 52240 52i 9 4 10.01864 01868 oi8 7 i oi8 7 5 oi&7 9 2 3 3 3 3 ~3~ 3 3 3 3 9 . 9 8i36 9 8i3 2 9 8i2 9 9 8i2.5 98121 20 '9 1 8 '7 1 6 9 46 o 45 52 45 44 45 36 45 28 2 l4 i4 8 i4 16 14 24 i4 32 9-45969 46oi i 46o53 46095 46 1 36 io.54<>3i 53 9 8 9 53 9 4 7 53 9 o5 53864 9-47^52 47897 47943 47989 48o35 35 36 36 3 7 38 10.52148 52io3 52o5 7 52OI I 5io65 io.oi883 01887 01800 01894 01898 9 98117 98113 981 10 98106 98102 i5 t4 i3 12 II 5o 5i 52 53 54 9 45 20 45 12 45 4 44 56 44 48 2 14 4o i4 48 i4 56 i5 4 l5 12 9.46178 46220 46262 463o3 46345 36 36 3 7 38 38 10.53822 53 7 8c> 53 7 38 536 97 53655 9.48080 48126 48171 48217 48262 3 9 3 9 4o 4i 42 I0.5l 9 20 5 1 874 5i82 9 5i 7 83 5i 7 38 10.01902 01906 01910 01913 01917 3 3 3 3 3 9.98098 98094 98090 08087 9 8o83 IO T 6 55 56 ST 58 59 60 9 44 4o 44 32 44 24 44 16 44 8 44 o 2 1 5 20 1 5 28 i5 36 i5 44 i5 52 16 o 9-46386 46428 4646 9 465 1 1 46552 46594 38 4i 4r 42 43 io.536i4 535 7 2 5353i 5348 9 53448 534o6 9.48307 48353 483 9 8 48443 4848 9 48534 43 43 44 45 46 46 io.5i6 9 3 5 1 647 5 1 602 5i55 7 5i5n 5 1 466 10.01921 01925 0192(7 01933 01937 01940 3 3 4 4 4 4 9.98079 9 8o 7 5 98071 98067 9 8o63 98060 5 4 2 I O M M Hour P.M. Hour A.M. Cosim>. ! Diff. Secant. Cotangent Diff. Tangent. Cosecant. DfF.i Sine. 106 C 73" Seconds of time ! 2' 3' 4' 5 s 6* 7' f A 5 ii 16 21 27 32 3? Prop, parts of cols < B 6 12 17 23 2 9 3^ 4i 1 (c J 1 * 2 2 3 3 1>age202] TABLE XXVII. Log. Sines, Tangents, and Secants. 17 A A B B G'. M Hour A.M. illonr P.M. Sine. IDiff (Cosecant Tangent. Diff| o i 2 3 Cotangent Secant. Diff. Cosine. M o i 2 3 4 9 44 o 43 52. 43 44 43 36 43 28 210 16 8 16 .6 16 24 16 32 9-46594 ' 46635 46676 46717 46758 o 2 3 io.534o6 53365 53324 53283 532.42 9-48534 485 79 4862.4 48669 48 7 i4 io.5i466 61421 5i3 7 6 5i33i 6.286 i o . o . 940 01944 Oio48 01966 o o 9 . 98060 98062 98048 9 8o44 60 5 9 58 56 5 6 7 & 9 9 43 20 43 12 43 4 42 56 42 48 2 16 4o 1 6 48 16 56 17 4 17 12 2 17 20 17 28 17 36 17 44 17 52 9 468oo 4684 1 46882 46923 46964 3 4 5 5 6 7 7 8 9 9 10.53^00 53.5 9 53 1,8 53077 53o36 10.52995 52955 52914 62873 5-2.832 488cM 48849 48804 4 4 5 6 7 10.5.241 51196 5n5i 5uo6 61061 10.01960 01964 I 968 01971 01975 o o 9.98040 9 8o36 98032 9802.9 98026 55 54 53 52 5: 5o 48 4? 46 45 44 43 42 4i 10 1 1 12 i3 9 42 4o 42 32 42 24 42 16 42 8 9.47005 47086 47127 47168 9.48984 49029 49118 49163 8 9 10 10 10.61016 50971 60927 60882 5o83 7 10.019-79 01983 01987 0199. 01996 9.98021 98017 98013 98009 98006 9.98001 97997 97993 97989 97986 1 5 .6 17 18 '9 9 42 o 4i 52 4i 44 4i 36 4i 28 2 1 8 18 8 18 16 18 24 18 32 9.47209 47249 47290 4 7 33o 10 1 1 1 1 12 i3 10.52-791 62761 52 7 10 52670 52629 9.4920-7 492.62 49296 49385 1 1 12 12. i3 i4 10.60793 60748 60704 60669 606 1 5 10.01999 02003 02007 0201 I 020.4 20 2 I 22 23 2.4 9 41 20 4i 12 4i 4 4o 56 4o 48 2 18 4o 18 48 18 56 19 4 19 12 47452 47492 47533 _ 47573 47654 47M 47734 47774 i3 i5 i5 16 17 '7 18 '9 20 21 21 22 23 10.52589 62648 525o8 62467 '49474 49619 4 9 563 i5 16 16 17 18 10.50670 5o48i 5o43 7 5o3 9 3 10.020.8 02022 02026 02030 02034 2 9.9798'-* 97978 97974 979/0 97966 3? 3-' 36 i 33 32 3, 2.5 26 28 29 3o 3 i 32 33 35 36 37 38 9 i i I > I i \ i 4 5 46 48 49 5o 5 1 52 53 54 o j^o <4o 4o 32 4o 24 4o 16 4o 8 2 19 20 19 28 19 36 19 44 19 62 io.5238 7 52346 523o6 52266 62226 9.49662 49696 49784 49828 18 '9 20 21 21 io.5o348 5o3o4 60260 60216 60172 10.02038 02042 02046 02o5o 02064 2 2 2 2 2 9.97962 979 58 979 54 97960 97946 9 4o o 3 9 52 39 44 3 9 36 3 9 28 2 2O 20 8 20 1 6 20 24 20 32 47854 47894 47934 47974 10.52186 62106 62066 62026 9.49872 49916 49960 60004 5oo48 22 23 2/4 24 25 10.60128 60084 60040 49996 49962 io.o2o58 02062. 02066 02070 02074 2 2 2 2 2 9.97942 979 38 97934 97930 97926 3o 28 26 V 3 9 20 39 1 2 39 4 38 56 38 48 2 20 4 20 48 20 56 21 4 21 12 9.48014 48o54 48094 48.33 48i 7 3 23 24 25 25 26 10.51986 61946 61906 5i86 7 5i82 7 9 . 60092 5oi36 60180 60223 60267 26 26 27 28 2 9 10.49908 49864 49820 497-7 49733 10.02078 02082 02086 02090 02091 2 2 2 3 3 9.97922 97918 979 i 4 97910 97906 25 24 22 2 I 2O [0 ,8 17 .6 9 38 40 38 32 38 2.4 38 16 38 8 2 VI 2.0 21 2.8 2. 36 21 44 21 52 9.482.3 48252 48292 48332 483-1 27 27 28 29 29 io.5i 7 8 7 5i 7 48 61-708 5 1 668 61629 9.5o3i i 5o355 5o3 9 8 5o485 I 9 3o 3i 32 32 10.49689 49645 49602 49668 49616 10.02098 02102 02106 021 10 021 l4 3 3 3 3 3 3 3 3 3 9.97902 97898 9794 9-7890 9 7 886 9 38 o 3 7 52 37 44 3 7 36 3 7 28 2 22 22 8 22 l6 22 24 22 32 4845o 48490 4852 9 48568 3o 3i 3i 32 33 10.61689 5i55o 5i5io 5i432 9.60629 5o5 7 2 60616 60669 6070$ 33 34 35 35 36 10.49471 49428 49384 49297 10.02118 02122 02126 02l3o 02 1 34 9.9-7882 97878 97874 97870 97866 i > i4 1 3 1 2 . I 9 37 20 3 7 12 3 7 4 36 56 36 48 2 22 4o 22 48 22 56 23 4 23 12 9.48607 48647 48686 48 7 25 48-64 33 34 35 35 36 "37 37 38 39 39 4o io.5i3 9 3 5i353 5i3i4 5i2 7 5 5 1 236 9.60746 60789 5o833 60876 60919 37 38 39 4o 10.49264 49211 49167 49124 49081 10. C c c c c 2i3o 2i43 2147 2l5. 2i55 2169 2i63 2167 2171 2.76 2179 3 3 3 4 4 9.9786. 97867 97 853 9784Q I C) 6 5 4 3 a i o 55 56 57 58 r 9 60 M 9 36 4o 36 32 36 24 36 16 36 8 36 o 2 23 20 23 28 23 36 23 44 23 52 24 o 9_488o3 48842 48881 48920 48959 48998 io.5. 19-7 5u58 61119 5 1 080 5io4i 61002 9.60962 5ioo5 5io48 61092 5ii35 61178 4o 4i 42 43 43 44 io.49o38 48 99 5 48962 48908 48865 48822 IO.C c 4 4 4 4 4 4 9.97841 97837 97 833 97829 97826 97821 Hour P.M. Hour A.M. Cosine Diff. Secant. Cotangent Din. Tangent. Cosecant. 'Diff. Sine. M 107 \ A B B C C 72* Seconds of time 1- 2' 3 4 . 20 22 2 5 s 25 28 2 6' 5o 33 3 7' "35" 39 3 (A Prop, pnrts of cols. < B ( C 5 10 6 ii I 16 i? i TABLE XXVN. [Page203 Log. Sines, Tangents, and Secants. '-' 18 \ A B B C C )<>r M Hour A.M. [Hour " M. bine. Diff. Cosecant. Tangent. JDifT. jCotn^ent Sei-aiil. iDiff. Cosine. M D I I 3 4 9 36 o 35 52 35 44 35 36 35 28 2 24 24 8 24 16 24 '24 24 3? 9.48998 49087 49076 49U5 49153 o i 2 3 I0.5I002 50963 50924 5o885 5o847 9.51178 5l22l| I 5l264 1 5i3o6' 2 61349 3 10.48822 48779 48 7 36 48694 4865 1 10.02179 021 83 02188 02192 02196 o o o 9.97821 978i 7 97812 97808 97804 60 5 9 58 57 56 55 54 53 52 5i So" 49 48 4? 46 5 6 7 8 _9 10 1 1 12 i3 i4 9 35 20 35 12 35 4 34 56 34 48 2 24 4o 24 48 24 56 25 4 25 12 9.49192 4923i 49269 4 9 3o8 49347 3 4 4 5 6 io.5o8o8 50769 5o 7 3i 60692 5o653 9.61392 5i435 61478 61620 5 1 563 3 4 5 6 6 10.48608 48565 48622 4848o 4843y IO.O22OO O22O4 02208 O22I2 022l6 o 9.97800 97796 9779 2 97788 97784 9-97779 97775 97771 97767 97763 9 34 4o 34 3a 34 24 34 16 34 8 2 25 20 25 2.8 25 36 25 44 25 52 9.49385 49424 49462 495oo 49539 6 8 8 9 io.5o6i5 5o5 7 6 5o538 5o5oo 5o46i 9.61606 61648 61691 5i 7 34 5] 776 8 8 9 10 10.48394 48352 483o 9 48266 48224 IO.0222J O2225 02229 02233 02237 i5 16 17 18 1? 20 21 22 23 24 9 34 o 33 52 33 44 33 36 33 28 2 26 26 8 26 16 26 24 26 3s 9.49577 49615 49654 49692 49730 9 IO 1 1 1 1 12 io.5o423 5o385 5o346 5o3o8 60270 9.61819 61861 61903 61946 61988 IO 1 1 12 i3 i3 ~T4~ i5 i5 16 '7 10.48181 48. 3 9 48o 97 48o54 48012 10.02241 02246 O2250 62254 02258 9.97759 97754 97760 97746 97742 9-97738- 97734 97720 97726 9772 r 45 41 43 42 4i 4<- 3y 3!'. 3-; 3i> 9 33 20 33 12 33 4 3 2 56 3 2 48 2 26 40 26 48 26 56 27 4 27 12 9.49768 49806 49844 49882 49920 i3 i'3 i4 i4 i5 10.50232 50194 5oi56 60118 5oo8o 9.52o3i 62073 62116 52i5 7 62200 i 0.47969 47927 47885 47843 47800 10.02262 02266 02271 02276 02279 2D 26 11 2 9 9 32 4o 32 32 3a 24 3a 16 32 8 2 27 20 27 28 27 36 27 44 2 7 52 9.49958 49996 5oo34 50072 5ono 16 16 17 18 18 io.5oo42 5ooo4 49966 49928 49990 9.62242 62284 62326 52368 62410 17 18 W 20 20 10.47758 477i6 47674 47632 47590 10.02283 02287 02292 02296 02300 2 2 2 9.97717 977 ' 3 97708 97704 97700 35 31 3j- 32 3i 3o 29 28 27 26 3o 3i 32. 33 34 9 32 o 3i 62 3i 44 3i 36 3i 28 2 28 28 8 28 16 28 24 28 32 9.50148 5oi85 50223 5o26i 60298 '9 20 2O 21 21 10.49852 49815 49777 49739 49702 9.62462 62494 62536 62.578 62620 21 22. 22 23 24 10.47548 4?5o6 47464 474" 4738o io.023o4 02309 O23lO 02317 02321 2 2 2 2 2 9-9/696 97691 9768 7 97683 97679 35 36 37 38 3 9 9 3i 20 3 I 12 3i 4 3o 56 3o 48 2 28 4<> 28 48 28 56 29 4 29 12 9 .5o336 5o3 7 4 5o4n 5o449 5o486 22 23 23 24 25 10.49664 4962(5 49589 4955 1 495 1 4 9.62661 52 7 o3 62745 62787 62829 24 25 26 27 27 10.47339 47297 47255 472i3 47171 10.02326 0233o 02334 02338 02343 2 3 3 3 3 9-976 7 4 97670 97666 97662 97657 25 24 23 J>2 21 4o 4i 42 43 44 45 46 47 48 49 9 3o 4o 3o 32 3o 24 3o 16 3o 8 2 29 20 29 28 29 36 29 44 29 52 9 .5o523 5o56t 5o5o8 5o635 5o6 7 3 25 26 26 27 28 10.49477 49439 49402 49365 49327 9.62870 52912 52 9 53 62996 53o3 7 28 29 I 9 3o 3i 3i 3a 33 <4 34 io.47i3o 47088 47047 47006 46 9 63 10.02347 0235i 02355 0236o 02364 3 3 3 3 3 9. 97 653 97649 97645 97640 97 636 2O V 1 8 '7 1 6 9 3o o 29 52 29 44 29 36 29 28 2 30 3o 8 3o 16 3o 24 3o 32 9.50710 5o 7 4 7 5o 7 84 5o82 1 5o858 28 2 9 3o 3o 3r 10.49290 492.53 492 1 6 49179 4914^ 9.53078 53 1 20 53i6i 53202 53^44 10.46922 46880 4683 9 46798 46 7 56 IO.O2368 02372 02377 0238i 02385 3 3 3 3 3 9.97632 9-7628 97623 976! 9 9 7 6i5 i5 M i3 I 2 I I 5o 5i 52 53 54 9 29 20 29 12 29 4 28 56 28 48 2 3o 4o 3o 43 3o 56 3i 4 3l 12 9 . 50896 5o 9 33 50970 5-i 1x17 5.o43 31 3a 33 33 34 10.49104 49067 49o3o 48993 48957 9.53285 5332 7 53368 53409 5345o J5 J6 J6 37 38 10.46716 466 7 3 46632 465 9 i 4655o IO.O23OO 02394 02398 O24o3 02407 4 4 4 4 4 9.9:7610 9-7606 9/602 97597 97^93 IO 6 55 56 57 58 59 60 9 28 4o 28 32 28 *4 28 16 28 8 28 o 2 3 1 20 3 1 28 3 1 36 3 1 44 3 1 52 32 9. 5 1080 5i i 17 5ii54 5i 191 5l22 7 5 1 264 35 35 36 3? 3 7 3 10.48920 48883 48846 48809 48 77 3 4736 9.53492 53533 535 7 4 536 [5 53656 536 97 38 3 9 4o 4i 4i 42 10.46608 46467 46426 46385 46344 463o3 10.0241 i 02416 02420 02424 02429 02433 4 4 4 4 4 4 9- 9758 9 97584 97680 97676 97571 97667 5 4 3 i i o M 12 Hour P.M Hour A.M. Cosiiu:. Diff. Secant. Cotangent Diff. Tangent. Cosecant. Diff. Sine. 108 Seconds of time 1 ! 2' 9 3 9 i4 4 19 5 s 6* 7 s (A 5 24 28 33 Prop, parts of coin. * B 5 !O 16 21 26 3i 3 7 (c 1 . I 2 2 3 I 3 4 p s> ( i 2 3 i e E c ^ e204 J TABLE XXVIT. Log. Sines, Tangents, and Secants. A A B B C C 100 Hour A.M. I lour .'.M Sine. )iff.| Cosecant. 'angent. >i<'.C oUiiii^ent Sec- ant. Diff.l Cosine. 9 p8 o 2 7 52 2 7 44 27 36 27 28 32 ci 32 H 3a 16 32 24 32 32 5. 264 5.338 5.3 7 4 5i4i. I i I 2 2 0.487.36 486 99 48( >(>;. 48626 48689 9.53697 53 7 38 53 779 53820 5386. O I 2 3 o.463o3 46262 46221 46180 46i3 9 0.02433 0243 7 02442 r o o .97667 97 563 9-7668 97554 97 55o 9 27 20 27 12 27 4 26 56 > 26 48 2 3? 4<> 32 48 32 50 33 4 33 12 -5.44 7 5 1 484 61620 5 1 55~ 5 1 5 9 : 3 4 4 5 5 0.48553 485.6 4848o 48443 484o 7 9.5390; 5 3 9 4 3 54o65 3 i 4 5 5 6 0.46098 46o,6 45 97 5 45 9 35 0.02455 02464 02468 024-72 97545 9-764. 97536 97 532 9-7628 1C T \: \ n > 9 26 4o 26 32 I 26 24 } 26 1 6 i 26 8 2 33 20 33 28 33 36 33 44 33 62 .5.629 5 1 666 5l 7 02 5i 7 3C 5i 77 4 (i 7 8 8 0.4837 i 48334 48298 48262 48226 9.64106 54i4 7 54i8 7 54228 54269 7 7 8 9 9 io.458 9 4 45853 458,3 45^72 45 7 3. 0.024 77 0248. 02485 02,490 02494 2 2 2 2 2 9-762.3 9-73,6 9-7610 i I 1 I ) 9 26 o 3 26 62 7 26 44 3 25 36 ) 25 28 2 34 o 34 8 34 1 6 34 24 34 32 5i84 7 5i883 5.910 5i 9 55 9 IO 10 1 1 II 0.48189 48i53 48117 48081 48o45 9.543oy 5435o 543 9 o 5443. 544 7 i IO 1 1 12 i3 0.46691 4565o 456 10 4556 9 46629 0.02499 0260^ 02608 02612 026.6 . 97 5oi 97497 97492 97488 97484 2 2 2 2 2 3 9 25 20 I 25 12 2 25 4 3 24 56 4 24 48 2 34 4o 34 48 34 56 35 4 35 12 .5.991 6202-7 62063 62099 62 1 35 12 I 2 i3 0.48009 4 797 3 4 79 3 7 4-790 4 7 865 9 .545.2 54552 54693 54633 546 7 3 i3 i4 16 i5 .6 0.45488 45448 45407 4536 7 45327 o'. 0262 1 02626 0253o 02534 02639 97479 974 7 5 974 7 o 97466 9746i 2 ; 3 2 2 3 3 1 5 9 24 4o 6 24 32 7 2-4 24 8 24 16 9 24 8 2 35 20 35 28 35 36 35 44 35 52 9.6217 62207 62242 62278 16 i5 16 17 '7 ic,.4 7 82. 9 4 77 9 47758 4772 4768 9 .54 7 >4 54 7 54 54 7 9 54835 548 7 5 17 7 18 '9 9 10.45286 45246 4520 45r6 4612 10.02643 02647 0255 0255 0266 9. 97 45 7 97453 97448 97444 97 43 9 o 9 24 o I 23 52 * 23 44 3 23 36 /i 23 28 2 36 o 36 8 36 16 36 24 36 3 9 .5235o 52385 62421 52456 62.492 18 18 19 20 20 10.4766 4 7 5 7 4754 4 7 5o '54955 54995 55o35 55o 7 5 20 21 21 22 2J io.45o8 45o4 45oo 4496 4492 10.0266 0267 0267 02679 02583 2 2 2 2 3 9.97435 9743o 97426 97421 97417 7 6 4 3 i iM "0 5 9 23 20 16 23 12 h 23 4 J8 22 56 } 9 22 48 2 36 4c 36 48 36 56 ' 37 t- 37 ' 9.62627 52563 62698 52634 6266^ 21 21 22 23 10.4747 4743 4736 4 7 33 o en en en en en en en en en en -j eoso en - en en en en en 23 24 25 25 26 10.4488 4484 448o 4476 4472 10.02688 02692 02697 02601 02606 3 3 3 3 9.974.2 97408 974o3 97399 97394 {<> 9 22 4c fl 22 32 ^2 22 2^ ^3 22 if 44 22 2 37 2 3 7 2 3 7 3 37 4 3 7 5 9.5270? 62740 62.81 5284( 24 2<; 26 26 10.4-729 4-726 4 7 22 4 7 i8 4 7 i5 9 .553i5 55355 553 9 5 55434 27 27 2.8 29 29 10.4468 4464 446c 4456 4452 10.026.0 02616 026.9 02624 02628 3 3 3 3 3 3 3 4 4 9.97390 97 385 97 38. 97 3 7 6 97 3 7 2 43 9 22 c 46 21 5: / 21 4^ 48 21 3f 49 21 2C > 2 38 38 38 i > 38 2 > 38 3 529i( 53< 2 27 27 28 2 io.4 7 ' i 4 7 o8 4 7 o4 4701 469-7 9 .555iz 5555^ 555 9 : 5563: 6667-' 3o 3i 3i 32 33 10.4448 4444 444o 4436 4432 10.02633 0263- 02642 0264" 02661 9-9736- 97363 97 358 V 97 353 97349 50 9 21 2( 5i 21 i: 52 21 ^ 53 20 5( 54 20 4! > 2 38 4 i 38 4 i 58 5 3 39 ^ J 3 9 . 9 .53o5< 53o 9 53,2 53.6 53ic>< 3 3 3 3 3 10.469^ 468 7 4683 9.5571 : 55 7 5'. 55 79 5583 558 7 c 33 34 35 35 36 10.4428 44M 44 2 < 44.3 10.0266^ 02660 0266^ 02660 10.0267^ 0268: 02.68* 0269: 0269- 0270 Cosecant 1 n 4 4 4 4 IlT > 4 > 4 A j t t 9- 97 344 9?| 9 26 9^97322 973 1 7 9 73i 2 9 73o8 9 73o3 T Sine. J- -* C ' '5 9 20 4< 56 ' 20 3 5 7 20 2< 58 20 i 69 20 60 20 ) 2 3 9 2 ? . 3 9 2 i 3 9 ^ 3 3 9 4 3 3 9 5 3 4o en en en en en en CO CO CO CO CO CO JX CO CO CO 10 !0 C -J Co O CT> Co 3 3 3 3 3 3 io.46 7 6 46 7 3 4669 4666 4663 46.39 9 .55 9 u 55 9 4c 55 9 8c 56o2.5 56o6- 56io- 3- 38 7 3^ 7 4 ( 10.4409 44"5 44o 43 97 43 9 3 4389 M :IO,,M>.> jIIonrA.. Cosi ie .1 ! I) i nil . Tan^ei i n 109 Seconds of time 1' 2* Os 4 s 5" 6" 7- ( A Prop, parts of cols. ;] TABLE XXVII. Log. Sines, Tangents, and Secants. r '' A A B 15 C C 158 -Jo:!-- I'.V . Sine. >itf.{Cosecant. 'angent. I )iff. otan^ent Secani. )\ff.\ Cosiiu-. M 9 12 o I I 52 ii 44 ii 36 ii 28 2 48 -i / - ! 48 ;> 48 i'. 48 2,' 4i> 3, j. 55433 55466 55499 55532 55564 o i 2 2 0.44567 44534 445oi 44468 44436 9 .584i8 58455 584 9 3 5853 1 5856 9 o i r 2 2 0.4l582 4i545 4 1 5o 7 4>46 9 4i43i 0.02985 0300f; 02995 02999 o3oo4 o J 9 1 o .97015 97010 97co5 97001 9699(1 K> 1? >7 V3 9 1 1 20 II 12 ii 4 10 56 10 48 2 4i- 4 48 4'i 48 &:> 49 4' 49 12 ). 555 97 5563o 55663 556 9 5 55 7 a8 3 3 4 4 5 o.444o3 443 7 o 4433 7 443o5 44272 9.586o6 58644 5868 1 58 7 i 9 58 7 5 7 3 4 4 5 6 o.4i3 9 4 4 1 356 4i3i 9 41281 4i243 o . o3oo 9 o3oi4 o3oi 9 o3o24 o3o2 9 S I 1 I >. 96991 96986 9698, 969-6 96971 15 54 53 ^2 5i 5o . c 47 46 45 44 43 42 4i 4o 3o 38' 3 7 36 9 10 4o 10 32 10 24 10 16 10 8 2 49 20 49 28 49 36 49 44 49 52 o.5!/76i 55 79 3 55 C ,?6 55* !# S5C 9 .T .55023 55o56 55o88 56o2i 56o53 5 6 6 7 7 [o.4423 9 44207 44i74 44i42 44109 9 .58 79 4 58832 5886 9 58907 58 ?44 6 7 7 8 9 9 IO IO I I 12 0.41206 4u68 4n3i 4io 9 3 4io56 o.o3o34 o3o38 o3o43 o3o48 o3o53 I I I I I '96966 96962 96957 96962 96947 i5 16 17 18 i? 20 21 22 2: 2^ 9 10 i! 9 5. o 44] 9 36 9 28! 2 5o O 5o 8 5o 16 5o 24 5o 32 JJ 9 9 IO 10 10.44077 44o44 44012 43 979 43 9 47 9.58981 59019 5 9 o56 5 9 o 9 4 59i3i io.4ioi 9 4o 9 8i 4oo44 4o 9 o6 40869 o.o3o58 o3o63 o3o68 o3o 7 3 03078 I I I 2 j. o6 9 4 2 9 6o3 7 9f> ^927 9699.2 9 9 20 9 ,2 9 4 8 56 8 48 2 5o 4o 5o 48 5o 56 5i 4 5i 12 ,56o85 56 118 56i5o 56.82 562 1 5 I i 1 1 12 12 i3 10.4391 5 43882 4385o 438 1 8 43785 9.59168] 59205 59243 59280 5 9 3. 7 12 i4 M i c io.4o83a 4o 79 5 4o 7 5 7 40720 4o683 o.o3o83 o3o88 o3o 9 3 o3o 97 O3l02 2 2 2 2 2 9-9 6 9'7 96912 96907 9690.3 9 68r/; 25 2t) 28 2O 9 8 4o 8 3., 8 24 8 1 6 8 8 1 5l 20 5 1 28 5 1 36 5i 44 5i 52 9.56247 56279 563 1 56343 56375 i3 i4 i4 1 5 ,6 0.43753 43725 43689 A3 1 1 4362 9-59354 5939 1 59429 59466 59503 i5 16 17 17 18 10.40646 40609 40671 4o534 40497 10.03107 03)12 o3i 17 O3l22 O3l27 2 2 2 2 2 9.96893 96888 96883 96878 96873 3b 3. 3i 20 2 27 26 o 2 33 34 980 7 52 7 44 7 36 7 28 2 52 O 52 8 52 1 6 52 2.4 52 3 a 9.564o8 5644o 56472 565o4 56536 16 17 17 18 18 io-4359 4356 435^ 4340 4346 9.5954oi 19 59577 '9 59614 20 50651 20 59688 2, io.4o46< 4042 4o38b 4o34 4o3t io.o3i32 o3.3 7 o3i42 o3i4 7 o3i5a io.o3i5 7 o3i6? o3i6 7 o3 1 72 o3i77 2 3 3 3 3 9 . 9 6868 9 6863 06858 9 6853 ^848 35 36 37 38 ?1 ? no 4> ia 43 44 9 7 20 7 12 7 4 6 56 6 48 2 52 4o 52 48 52 56 53 4 53 12 9.56568 565 99 5663. 56663 566 9 5 1 9 1 9 20 20 21 io.4343 434o 4336 4333 433o 1j &8 5 9 8 7 2 22 2^ 23 24 10.4027 4023 4020 4oi6 4012 3 3 3 3 3 9.96843 o6838 96833 96828 96823 |a!) 24 23 2-2 31 9 6 4o 6 32 6 24 6 it 6 & 2 53 20 53 28 53 36 53 44 53 52 9.56727 56 7 5 9 56 79 c 56822 5685^ 21 22 22 23 24 24 25 25 26 26 10.4327 4324 432i 43i 7 43 1 4 9- ^999 5 99 46 5 99 83 60019 6oo56 ;25 25 26 27 27 i o . 4009 4oo5 4ooi 3 99 8 3 99 4 io.o3i82 o3i87 o3 1 9 2 o3i 97 03202 3 3 3 4 4 9.968:8 968 1 3 96808 o68o3 96798 2O '9 18 '7 1 6 45 46 47 48 4 ? 5o 5i 5 a 53 54 o 6 c 5 5? 5 M 5 3C 5 a 2 54 o 54 8 54 16 54 24 54 32 9 .5688e 5691- 56 9 4c -56981 5701: io.43i i 43o8 43o5 4302 4298 0.6009: 6oi3c 6oi6 6020' 6oa4c 28 28 ? 9 3o 3o io.3 99 o 3 9 8 7 3o83 3 979 3 97 6 10.0320- 03212 o32i- 03222 0322^ 4 4 4 4 4 9.96793 96788 9 6 7 83 96 77 8 9677? ID i4 1 3 I 2 1 I 9 5 2e 5 i: 5 i 4 5( 4 4 2 54 4< 54 48 54 56 55 i 55 i 9.5704^ 5707' 5710- 57i3* 57i6< 27 27 28 28 29 io.42 9 5 42 9 2 428 9 4286 4283 9 .6o2 7 ( 6o3t: fo34c 6o38( 6,42: 3i 3 1 32 33 33 io.3 9 -2 3 9 68 3 9 65 3o6i 3 9 5 7 io.o323, o32.3J 0324: o324 o3 2 5: 4 4 4 4 4 96762 96757 96752 9 6 7 47 I 6 55 56 57 58 5$ (k 9 1 f: 4 2, 4 i< 4 i 4 < 2 55 20 55 28 55 36 55 M }\ 55 5 J 56 c 9.5720 V 5 7 23 5726, 5729 5 7 32< 5735 29 3o 3o 3i 32 32 10.4279 4276 42 7 3 4270 4267 4264 9 .6o45< 60/9 6o53 6o56! 6o6c 6o64 34 35 35 36 36 37 io.3 9 54 3 9 5o 3 9 46 3 9 43 3939 3?35 io.o325L o3p.6: o326J 0327: o3a7? o3a8: D 5 5 5 5 5 DitT 9-967^ 96737 96702 9672- 9672: 0671-; Sine. 4 3 a o ^ M 1 1 Hour kMi.) Hour A.M . 1 i" Cosine. |Diff i A Secant A Cotangent Uitf.j rangen B B C C G8' J TABU: xxvn. ^"* I jO g- Sines, Tangents, and Secants. 29 A A B B C [Page 07 G'. C 157 M Hour A.M. Hour I'.M. Sine. Dinr. Cosecant. Tangent. Diff Cotangent Secant. Difl'. Cosine. 9 . 96717 9 6 7 I! 96706 06701 96696 M o i 2 3 4 9 4 o 3 52 3 44 3 36 3 28 2 56 o 56 8 56 16 56 24 56 32 9 .5 7 358 5 7 38 9 5 7 42o 5 7 45i 5 7 482 o i i 2 2 10.42642 42611 4258o o. 6064 . 60677 607 1 4 6o 7 5o 6o 7 86 o 1 2 2 io.3935 9 3 9 32.3 39286 3 9 25o 3 9 2i4 io.o3283 o328 9 o32 9 4 o32 99 o33o4 o o o 60 56 5 6 8 9 9 3 20 3 12 3 4 2 56 2 48 2 56 4o 56 48 56 56 5 7 4 5 7 12 9 .5 7 5i4 5 7 545 5 7 5 7 6 5 7 6o 7 5 7 638 3 3 4 4 5 10.42486 42455 42424 42362 9 . 608 23 60869 6o 9 3i 6o 9 67 3 4 4 5 5 io.3 9 i77 39141 3 9 .o5 3 9 o6 9 39033 io.o33o 9 o33.4 o33. 9 o3324 o333o o 9 . 9 66 9 i 96686 9 668i 916676 96670 55 54 53 52 5. 10 1 1 12 i3 i4 9 2 4o 2 32 2 24 2 l6 2 8 2 5 7 20 5 7 28 5 7 36 5 7 44 5 7 52 9 .5 7 66 9 67700 5 77 3i 5 77 62 5 779 3 5 6 6 7 7 io.4233r 42300 42238 42207 9 .6ioo4 6io4o 61076 6l I 12 6n48 6 7 8 8 10.38996 38 9 6o 38 9 24 38888 38852 io.o3335 o334o o3345 o335o o3355 9.96666 96660 9 6655 9 665o 9 6645 5o 1 47 46 i5 1 6 18 '9 920 I 52 i 44 i 36 i 28 2 58 o 58 8 58 16 58 24 58 32 9 '57855 5 7 885 5 79 4 7 8 8 9 9 10 10.42176 42i45 42ii5 42084 42o53 9.61184 6.220 6i256 6l2 9 2 6i328 9 10 10 1 1 1 1 10.388.6 38 7 8o 38 7 44 38 7 o8 386 7 2 io.o336o o3366 o33 7 6 o338. 9.96640 9 6634 96629 96624 966.9 45 44 43 42 4i 20 21 32 23 24 9 i 20 I 12 i 4 o 56 o 48 2 58 4o 58 48 58 56 5 9 4 59 12 9 '58oo8 58o3 9 58o 7 o 58ior 10 1 1 1 1 12 12 10.42022 41992 41961 4i 9 3o 4i8 99 9. 6.364 6.400 6.436 6>4 7 2 6i5o8 12 i3 id i4 i4 10.38636 386oo 38564 38528 384 9 2 10.38456 3842i 38385 3834 9 383 1 3 io.o3386 o33 9 2 o33 97 o34o2 2 2 2 2 2 9.96614 96608 9 66o3 o65 9 8 9 65 9 3 4o 3 9 3ft 37 36 25 26 27 28 2 9 3o 3i 3 a 33 34 9 o 4o 32 o 24 o 16 o 8 2 59 20 69 28 59 36 59 44 5 9 52 9.58.3i 58i62 58 1 02 58123 58253 13 i3 i4 i4 16 io.4i86 9 4i838 4 1 808 4.777 4i747 9 .6i544 61 5 79 61616 6i65i 6.687 16 i5 16 17 17 10.034.2 o34i8 03428 o3433 2 2 2 2 3 9 . 9 6588 9 6582 96677 9=6572 9 6567 35 34 33 32 3. 900 8 59 52 59 44 69 36 59 28 3 o o o 8 o 16 o 24 32 9.68284 583t4 58345 583-5 68406 i5 16 16 17 17 10.4.716 4.686 4i655 41625 4i5 9 4 0.61722 ' 6i 7 58 61794 6i83o 6.865 18 18 '9 20 20 10.38278 38242 38206 38 1 70 38i35 io.o3438 o3444 o3449 o3454 o345 9 3 3 3 3 3 9.96662 9 6556 9 655i ^546 96641 3o 20 28 27 26 35 36 37 38 39 8 59 20 59 12 59 4 58 56 58 48 3 o 4o o 48 o 56 i 4 I 12 9.58436 5846 7 584 97 5852 7 5855 7 18 18 9 20 20 21 21 22 22 io.4i564 4.533 4i5o3 4 1 443 9 .6i 9 oi 6i 9 36 6i 9 72 62008 62043 21 21 22 23 23 10.38099 38o64 38028 37992 3 79 5 7 io.o3465 o34 7 o o34 7 5 o348o o3486 3 3 3 3 3 9. 96535 ^530 96520 9 65i4 25 ").(. 22 2 1 20 I 9 18 17 .6 4o 4i 42 43 44 8 58 4o 58 32 58 24 58 16 58 8 3 i 20 1 28 i 36 i 44 I 52 9.58588 586.8 58648 586 7 8 58 7 o 9 io.4i4i2 4i382 4i352 4i3aa 4l2 9 I 9. 62079) 621 14 62160 62185 6^22 1 24 25 26 26 io.3 7 92i 3 7 886 37860 3 7 8i5 3 777 9 io.o34 9 i o34 9 6 o35o2 o35o 7 o35.2 3 4 4 4 4 9.96609 9 65o4 9 64 9 8 9 64 9 3 9 6488 45 46 47 48 4 9 8 58 o 5 7 52 5 7 44 5 7 36 5 7 28 320 2 8 2 16 2 24 2 32 9 .58 7 3 9 58 7 6 9 58 799 5882 9 5885 9 23 23 24 24 25 10.41261 4i23i 41201 41171 9 . 62256 622 9 2 62327 62362 623 9 8 2.7 2.7 28 29 io.3 77 44 37708 3 7 6 7 3 3 7 638 3 7 6o2 ro.o35. 7 o352.3 o3528 o3533 o353 9 4 4 4 4 4 9 . 9 6483 96477 96472 9.6467 9 646i r I I o ~ ro XT m m m m m 8 5 7 20 5 7 12 5 7 4 56 56 56 48 3 2 4o 2 48 2 56 3 4 3 12 9 .5888 9 58 9 , 9 58 9 4 9 58 979 59009 25 26 26 27 ?-7 10. 4i . i i 41081 4io5i 4l02l 4o 99 i 9.62433 62468 62504 62539 62574 3o 3o 3i 32 32 io.3 7 56 7 3 7 53 2 37496 3 7 46i 37426 io.o3544 o354 9 o3555 o356o o3565 4 4 5 5 5 9 . 9 6456 9 645. 06445 9 644o o6435 10 8 6 r, 2 O 55 56 57 58 69 60 8 56 4o 56 32 56 24 56 16 56 8 56 o 3 3 20 3 28 3 36 3 44 3 52 4 o 9 .5 9 o3 9 5 9 o6 9 5 9 o 9 8 5 9 .28 5 9 .58 5 9 .88 28 28 2 9 3i DifT io.4o 9 6i 4o 9 3i 40 9 02 40872 40842 40812 9.62609 62645 62680 62715 62760 62785 33 33 34 35 35 36 10.3739. 3 7 355 3 7 32o 3 7 285 3 7 25o 3 7 2i5 io.o35 7 i o35 7 6 o358i o358 7 o35 9 2 o35 97 5 5 5 5 5 5 9 . 9 642 9 96424 96419 9 64.3 96408 9 64o3 M Hour P.M. IIourA.M. Cosine. Secant. Cotangent Tangent. Cosecant. Diff. Sine. M 112 C Seconds of time . l 9s 3 4" 5- 6* 7 s (A 4 8 ii i5 19 23 2 7 Prop, parts of cols. J B 4 9 i3 .8 22 27 3 1 I C i i 2 3 3 4 5 I>l 8 e3)81 ' TABLE XXVII. Log. Sines, Tangents, and Secants. $J A A B B C G . C 156 i M i 2 3 4 5 6 7 8 9 our A.M. 1 lour P.M. Sine. IDiff. Josecanl. raiigeni. >iflV 'oiaii-ent Secanl. >iff. o Cosine. M b 56 o 55 52 55 44 55 36 55 28 34o 4 8 4 16 4 24 4 32 ? . 5 9 i88 59.fi 5 9 24v 59277 5 9 3o 7 2 0.40812 40782 40753 4o 7 a3 4o6 9 3 9.62785 62820 62855 62890 62926 o 2 2 o.372i5 3 7 i8o 3 7 i45 37110 37074 o.o35 97 o36o3 o36o8 o36i3 o36 1 9 . 9 64o3 60 96397 59 96392 58 9638 7 5 7 96381 55 8 55 20 55 12 55 4 54 56 54 48 3 4 4o 4 48 4 56 5 4 5 12 9 .5 9 336 5 9 366 59396 59425 5 9 455 2 3 3 4 4 o.4o664 4o634 4o6o4 4o5 7 5 4o545 9.62961 62996 63o3. 63o66 63ioi 3 3 4 5 5 0.37039 37004 36 9 6 9 36 9 34 368 99 0.03624 o363o c3635 o364o o3646 >.o63 7 6 5c 9 63 7 o ^ 96365 53 96360 5: o6354 5 10 1 1 12 i3 i4 8 54 4o 54 32 54 24 54 it) 54 8 3 5 20 5 28 5 36 5 44 5 52 9.59484 5 9 5i4 5 9 543 5 9 5 7 3 59602 5 5 6 6 7 7 8 8 9 9 o.4o5i6 4o486 4o457 40427 4o3 9 8 9 .63i35 63 1 70 632o5 6324o 63275 6 6 7 8 [0.36865 3683o 36 79 5 36 7 6o 36 72 5 o.o365 i o365 7 o3662 o366 7 o36 7 3 p. 96349 5c 9 6343 4< 96338 4! 96333 4 963 2 7 4 I 1 7 ) i5 16 '7 18 '9 8 54 o 53 52 53 44 53 36 53 28 3 6 o 6 8 6 16 6 24 6 32 9 .5 9 63 2 5 9 66i 5 9 6 9 o 59720 59749 io.4o368 4o33 9 4o3io 40.280 402 5 1 9 .633io 63345 633 79 634 1 4 6344 9 9 9 10 10 1 1 io.366 9 o 36655 3662.1 36586 3655 1 o.o36 7 8 o3684 o368 9 o36 9 5 o3 7 oo 2 2 9.96322 4 9 63.6 4 9 63n 4 9 63o5 4 96300 i j \ i 20 21 22 8 53 20 53 12 53 4 52 56 52 48 3 6 4o 6 48 6 56 7 4 7 12 9.59778 59808 5 9 83 7 5 9 866 5 9 8 9 5 10 10 1 1 ii 12 10.40222 4oi 9 2 4oi63 40 1 34 4oio5 9 . 63484 635i 9 63553 63588 63623 12 12 i3 i3 i4 io.365i6 3648 1 3644 7 364i2 363 77 o o3 7 o6 o3 7 u o3 7 i6 03 7 2.2 O3 7 2 7 2 2 2 2 2 9.96294 4 96289 3 96284 3 962-78 3 962-73 3 9 8 j( 2* 29 8 52 4o 52 32 52 24 52 16 52 8 3 7 20 7 28 7 36 744 7 5i? 9.59924 59954 5 99 83 60012 60041 9.60070 60099 60128 60 1 57 60186 t 4 10.40076 40046 40017 3 99 88 3 99 5 9 0.6365-; 63692 63726 63761 S3 79 6 9 .6383o 63865 638 99 63 9 34 63 9 68 i4 i5 16 16 17 17 18 18 '9 20 io.36343 363o8 362 7 4 3623 9 36204 io.o3 7 33 o3 7 38 o3 7 44 o3 7 4 9 o3 7 55 2 2 2 3 3 9 .962.6 7 3 96262 3 06256 .5 0625 i : 962.45 : 2 T 3o 3i 3 a 33 3 8 52 o 5i 52 5i 44 5i 36 5i 28 3 8 o 8 8 8 16 8 24 8 32 i5 i5 i5 16 16 io.3 99 3o 3 99 oi 3 9 8 7 2 3 9 843 3 9 8i4 io.36i 7 o 36i3 36io 36o66 36o3 io.o3 7 6o o3 7 66 o3 77 i o3 777 o3 7 82 3 3 3 3 3 9.9624 ; ^23 : 9-6229 : 96223 : 9621 ,0 9 ,8 I 1 .6 3* 36 3 38 3 8 5i 20 5l 12 5i 4 5o 56 5o 48 3 8 4 8 48 8 56 9 4 9 12 9. 6021 5 60244 6o2 7 3 6o3o2 6o33i 17 17 18 18 '9 io.3 97 85 3 97 56 39727 3o6 9 8 39669 9>64oo3 64o3 7 64072 64 ioc 64i4c 20 21 21 22 22 10.3599 35 9 6 35 9 2 358 9 3586 io.o3 7 88 o3 79 3 o3799 o38o4 o38io 3 3 3 3 4 9.9,6212 : 9.620-7 : ^20! : 96190 9 6i 9 o i i. <3 12 ). I 1C 4 4 4 4- \ 8 5o 4o 5o 32 5o it 5o 16 5o 8 3 9 20 9 28 9 36 9 44 9 52 9.6o35c 60 388 604 1 7 6o446 6o474 '9 20 2O 21 21 10.39641 3961 2 3 9 583 3 9 554 39526 9. 64i75 64209 6424i 642 7 643 1 2 23 24 24 25 25 , 26 26 , 27 > 28 i 28 10.3582 35 7 o 35 7 5 35 7 2 3568 io.o38i5 o382i o382.6 o3832 o3838 4 4 4 4 4 | 9 . 9 6i85 1 9 6i 79 9617^ 96168 96162 4 4 4 4 1 8 5o c 49 52 4Q M 49 36 49 28 3 10 o 10 8 10 16 10 24 10 32 o.6o5o: 6o53a 6o56i 6o58 5 606. fc 22 22 23 23 24 10.39497 3 9 468 3 9 43 9 3 9 4u 3 9 382 9.6434C 6438 644 iJ 6444c 6448: 10.3565 356i 3558 3555 355i io.o3843 o3849 o3854 o386o o3865 4 4 4 4 4 9 . 9 6.5 7 96161 96146, 96140 9 6i35 1C) ^ 5? 8 49 2c 49 is 49 t 48 5f 48 4 3 10 4o 10 48 10 56 > ii 4 i II 12 9.6064^ 6o6 7 f 6070^ 6073: 6076 24 25 25 26 26 io.3 9 354 3 9 325 3 9 2 9 6 39268 3 9 23 9 9.6451- 6455: 6458( 6462( 6465, 1 29 \ y ) 3o ) 3i < 3i 10.3548 3544 354i 3538 3534 10. o o o IO.O Cose i 6" 22 26 A jo 7 i 38 7 7 3882 3888 38 9 3 38 9 c 3 9 o5 3 9 ic 3 9 i6 3 ii M \ II 53 ) 12 C 9.60780 608 1 6o84^ 6087' 6090: 6o 9 3 27 27 28 28 29 2 9 10.39211 39182 3 9 i54 39125 39097 39069 9.64681 6472: 64 7 5( 6479< 6482; 648 51 J 32 , 32 5 33 > 33 I 34 5 35 io.353i 352 7 3524 352i 35i 7 35i4 Hour p. M . Hour A. M Cosine Diff Serai A - Cotangen B p~~ar~ t D.fl - - ' 3' Tai 4' ige B 5 18 22 1 113 A Seconds of time . ( A Prop, parts of cols.,! B 4 7 4 9 ii i3 i5 17 a TABLE XXVII. [Page am ^ Log. Sines, Tangents, and Secants. &* 'M A A B B C C 155 M i 2 4 Hour A.M. [Hour P.M Sine. Diff Cosecant. Tang-ent. Diff. i i 2 2 ~~3 3 4 4 5 Cotangent Secant. D ff. Cosine. M 8 48 o 4 7 52 4 7 44 47 36 47 28 3 12 12 8 12 16 12 2/ 12 32 9 . 6o 9 3 i 6o 9 6o 6o 9 88 6 1 o i (: 6io45 O o I I 2 io.3oo6 9 3 9 o4o 3 9 OI2 38 9 84 38 9 55 9. 64858 64892 64926 64960 64994 io.35i42 35io8 35074 35o4o 35oo6 io.o3 9 27 03933 o3 9 38 o3 9 f 4 o3 9 5o io o 9.96073 96067 9 6o62 960 56 9 6o5o 60 % 57 56 6 8 9 8 47 20 47 12 47 4 46 56 46 48 3 12 4o 12 48 12 56 i3 / l3 12 9 . 6 1073 61 101 6 1 I2 9 6n58 61186 2 3 3 4 4 10.38927 388 99 388 7 i 38842 388 1 4 9 .65o28 65o62 65oo6 65i3o 65 1 64 10.34972 34938 34904 348 7 o 34836 io.o3 9 55 o3 9 6i 03966 03973 o3 97 8 9 . 9 6o45 96o3 9 96034 96028 9 OO22 55 54 53 52 5i 10 1 1 12 i3 1 4 8 46 4o 46 32 46 24 46 16 46 8 3 i3 20 i3 28 i3 36 i3 44 i3 52 9.612.4 61242 61270 6i2 9 8 6i3a6 5 5 6 6 6 io.38 7 86 38758 38 7 3o 38702 386 7 4 9 .65i 97 6523 1 65265 652 99 65333 6 6 7 8 io.348o3 34?6 9 34 7 35 34701 3466 7 io.o3 9 83 03989 o3 99 5 o4ooo o4oo6 9.96017 O60II o6oo5 96000 9 5 99 4 5o 49 48 4-? 46 f* 16 ' 7 18 '9 8 46 o 45 52 45 44 45 36 45 28 3 14 o i4 8 i4 if 14 24 14 32 9 .6.354 6i38 2 6i4i i 6i438 6 1 466 7 7 8 8 9 10.38646 386 1 8 3858 9 38562 38534 9.65366 654oo 65434 6546 7 655oi 8 9 9 10 1 1 ii 12 12 i3 i3 io.34634 346oo 34566 34533 34499 io.-o4oi2 o4o 1 8 04023 0.4029 o4o35 I 2 2 2 2 9 . 9 5 9 88 93982 95977 9597' 95 9 65 45 44 43 42 4i 4o 3 9 38 3 7 36 20 21 22 23 24 8 45 20 45 12 45 4 44 56 44 48 3 i4 4o i4 48 i4 56 i5 4 l5 12 9 .6i4 9 4 6i5a2 6i55o 6r5 7 8 61606 9 10 10 ii 1 1 io.385o6 38478 3845o 38422 38394 9. 65535 65568 65602 65636 65669 io.34465 34432 343 9 8 34364 3433. io.o4o4o o4o46 o4o52 o4o58 o4o63 2 2 2 2 2 9.95960 9 5 9 54 9 5 9 48 9 5 9 42 9 5 9 3 7 2.5 26 2? 28 2 9 8 44 4o 44 32 44 24 44 16 44 8 3 i5 20 i5 28 i5 36 1 5 44 i5 52 9.6i634 61662 6i68 9 61717 6i 7 45 12 12 12 i3 i3 ~i4 i4 i5 i.5 16 10.38366 38338 383n 382.83 38255 9.65703 65 7 36 65770 658o3 6583 7 i4 i5 i5 16 16 17 17 18 18 *9 10.34297 34264 3423o 34i 9 7 34i63 io.o4o6 9 04075 04080 04086 o4o 9 2 2 2 3 3 3 ~3~ 3 3 3 3 9 . 9 5 9 3. 95925 9 5 9 20 9 5 9 i4 9 5 9 o8 35 34 33 32 3i 3o 3i 32 33 34 35 36 3 7 38 3 9 8 44 o 43 52 43 44 43 36 43 28 3 16 o 16 8 16 16 16 2.4 16 32 9. 6i 77 3 61800 61828 6i856 6 1 883 10.38227 38200 38i 7 2 38 1 44 38n 7 9.65870 65 9 o4 65 9 37 65 9 7i 66004 io.34i3o 34096 34o63 34029 33 99 6 i o . o4o 9 8 o4io3 o4io 9 o4i 1 5 04121 9.95902 9 58 97 9 58 9 i 95885 9 58 79 3o 2 9 28 2T 26 8 43 20 43 12 43 4 42 56 42 48 3 16 4o 16 48 16 56 17 4 17 12 9.61911 fr939 6i 9 o6 6i 99 4 62021 16 17 17 18 18 io.38o8 9 38o6i 38o34 38oo6 37979 9 .66o38 66071 66104 66 1 38 66171 20 2O 21 21 22 io.33o62 33o2 9 338 9 6 33862 338a 9 10.04127 o4i32 o4i38 o4i44 o4i5o 3 3 4 4 4 9 . 9 58 7 3 9 5868 9 5862 95856 9 585o 25 24 23 25 21 4o 4 1 42 43 44. 8 42 4o 42 32 42 24 42 16 42 8 3 17 20 17 28 17 36 17 44 17 52 9.62049 62076 62104 62i3i 62i5 9 18 19 1 9 20 20 io.3 79 5i 3 79 24 3 7 8 9 6 3 7 86 9 3 7 84i 9.66204 66238 66271 663o4 6633 7 22 23 23 24 25 ~25~ 26 26 27 27 io.337 9 6 33762 33729 336 9 6 33663 io.o4i56 04161 04167 o4i 7 3 o4i7 9 4 4 4 4 4 9- 9 5844 9 583 9 95833 9 58 27 9 582. 2O 17 16 75 i4 i3 12 II 10 I 6 45 46 4 7 48 49 8 42 o 4i 52 4i 44 4r 36 4 1 28 3 18 o 18 8 18 16 18 2.4 18 32 9 . 62186 62214 62.241 62268 622 9 6 21 21 22 22 23 io.3 7 8.4 3 77 86 3 77 5 9 3 77 32 3 77 o4 9 .663 7 i 664o4 6643 7 66470 665o3 io.3362 9 335 9 6 33563 3353o 334 97 io.o4i85 o4 9 o o4i 9 6 04202 04208 4 4 5 5 5 9 . 9 58i5 9 58io 9 58o4 95798 9 5 79 2 bo 5i 52 53 54 8 4r 20 4i 12 4i 4 4o 56 4o 48 3 18 4o 18 48 18 56 19 4 I 9 12 9.62333 6235o 62377 624o5 62432 23 24 24 24 25 io.3 7 6 77 3 7 65o 3 7 623 3 7 5 9 5 3 7 568 9.66537 665 7 o 666o3 66636 66669 28 28 ? 9 3o 3o 10.33463 3343o 33307 33364 3333i 10.04214 04220 04225 0423 1 o423 7 5 5 5 5 5 9.95786 9 5 7 8o 95775 95-69 9 5 7 63 bo 5(5 5 7 58 5 9 60 8 4o 4o 4o 32 4o 24 4o 1 6 4o 8 4o o 3 i 9 20 19 28 i 9 36 i 9 44 I 9 52 20 9 .6245 9 62486 625 1 3 62541 62568 62.5 9 5 25 26 26 27 27 28 io.3 7 54i 3 7 5i4 3 7 48 7 3 7 45 9 3 7 43 2 3 7 4o5 9.66702 66 7 35 66768 66801 66834 66867 3i 3i 32 32 33 33 io.332 9 8 33265 33232 33i 99 33i66 33 1 33 10.04243 o424 9 o4255 04261 04267 04272 5 5 5 6 6 6 9 . 9 fi-5 7 9 5 7 5i 95745 9 5 7 3 9 9 5 7 33 9 5 7 28 5 4 3 2 I :>1 M Hour P.M. Hour A.M. Cosine. Diff. Secant. Cotangent Diff. Tangent. Cosecant. 1 Diff. Sine. 114 C C G5 C Seconds of* time . . 1 s 2* Prop, parts of cols. I'i 3 4 7 8 y 4 s 5' 0* 7- 10 i4 17 21 24 i3 '7 21 25 ,9 1 f Pa .S''. M o i 2 3 4 -e 2lO n TABLE XXVII. Log. Sines, Tangents, and Secants. A A B B C fji'. C 154 lour A. M.I I lour P.M. Sine. Diff. Cosecant. 1'ai igent. Diff. Sotangfcnt Secant. Diff.| Cosine. M 60 5 9 58 57 56 S 4o o 39 52 3 9 44 3 9 36 3 9 28 3 20 20 '8 20 1 6 20 24 20 32 9.62595 62622 62649 626/6 62703 o o i i 2 io.374o5 3 7 3 7 8 3 7 35i 3 7 3 2 4 37 2 97 9.66867 66900 66 9 33 66966 66999 o i i 2 2 io.33i3? 33ioo 33o67 33o34 33ooi 0.04272 042-8 04284 04290 04296 o o }. 957 2(0 95722 95716 90710 95704 6 7 8 9 8 39 20 39 12 39 4 38 56 38 48 3 20 4o 20 48 20 56 21 4 21 12 '62757 62784 62811 62.838 a 3 3 4 4 4 5 5 6 6 0.37270 3 7 243 3 7 2i6 3 7 i8 9 37162 9- 67032 67065 67098 67 1 63 3 3 4 4 5 10.32968 32935 32902 32869 3a83 7 O.O43O2 o43o8 o43i4 o432o 04326 I 9.95698 96602 9 5686 9 568o 55 54 53 52 5i 5o 47 46 10 ii 12 i3 8 38 4o 38 32 38 24 38 16 38 8 3 21 20 21 28 21 36 21 44 21 52 9.62865 62892 62918 62945 62972 io.37i35 37108 37082 37055 37028 9 . 67 i 96 67229 67262. 67295 6 7 32 7 5 6 7 7 8 0.32804 32771 32 7 38 32705 32673 10.04332 o433 7 o4343 04349 o4355 9 . 9 5668 9 5663 9565 i 9 5645 i5 16 17 18 '9 8 38 o 3 7 52 37 44 3 7 36 3 7 28 3 22 22 8 22 1 6 22 24 22 32 9.62999 63o26 63o5 2 63079 63 1 06 7 8 8 8 9 10 10 1 1 10.37001 36 97 4 36948 3692 1 368 9 4 9- 6 7 36o 6 7 3 9 3 67426 6 7 4 58 6749' 6 7 556 6 7 58 9 67622 6 7 654 8 9 9 10 10 32607 325 7 4 32542 32309 io.o436i o436 7 o43 7 3 o4385 2 2 2 9 5627 95621 9 56i5 45 44 43 42 4i 20 21 22 23 24 8 37 20 37 12 3 7 4 36 56 36 48 3 22 4o 22 48 22 50 23 4 23 12 o.63i33 ' 63i5 9 63 186 632 1 3 63239 10.36867 3684i 368 1 4 3678 7 36 7 6i II I [ 12 1 2 F3 10.32476 32.444 324 1 1 32378 32346 10.04391 04397 o44o3 04409 o44i5 2 2 2 2 2 9.93609 9 56o3 95597 95585 4o 3 9 38 37 36 25 26 27 28 29 8 36 4o 36 32 36 24 36 16 36 8 3 23 20 23 28 23 36 ^3 44 2.3 5 a 9.63266 632 9 2 633 19 63345 633 7 2 9". 63398 63425 6345i 634 7 8 635o4 1 1 1 1 I 2 12 i3 10.36734 36 7 o8 3668 1 36655 36628 9 67687 67719 67785 67817 i4 i5 i5 16 10.32.3.3 32281 32248 322l5 32i83 10.04421 04427 o4433 o443 9 o4445 3 3 3 3 3 3 3 3 3 9-95579 95573 95567 9556i 95555 35 34 33 32 3i 3o 3i 32 33 34 3d 3 7 38 39 i< 4i 42 43 44 8 3t> o 35 52 35 44 35 36 35 28 3 2.4 o 24 8 24 j6 24 24 24 3;. i3 i4 .5 i5 io.366o2 365 7 5 36549 36522 364 9 6 9.67850 67882 67915 67947 67980 16 17 18 18 io.32i5o 32118 32o85 3ao53 32O2O io.o445i o4457 o4463 04469 o44 7 5 9.95549 9 5543 95537 9553i 95525 3o 29 28 27 26 8 35 20 35 12 35 4 34 56 34 48 3 24 4o 24 48 24 56 25 4 25 1 2 9. 6353i 63557 63583 636io 63636 i5 16 16 17 10.36469 36443 364 1 7 363 9 o 36364 9 68012 68o44 68077 68109 68142 20 20 2.1 21 i o . 3 i 988 3. 9 56 31923 31891 3i858 10.04481 04487 04493 o45o6 4 4 4 4 4 9.95519 95507 95494 25 24 2.2 21 8 34 4o 34 32 34 24 34 16 34 8 3 25 20 25 28 25 36 25 44 25 52 9.63662 63689 63 7 i5 6374 1 63767 18 18 '9 '9 io.36338 363 1 1 36285 36233 9 68174 68206 68239 68271 683o3 22 22 23 23 24 10.31826 31794 31761 31729 31697 10. 045 12 045 ! 8 04524 o453c o4536 4 4 4 4 4 9.95488 95482 95476 95470 95464 20 1 5 1 2 [ I 45 46 47 48 49 8 34 o 33 52 33 44 33 36 33 28 3 26 o 26 8 26 16 26 24 26 32 9.63794 63820 63846 638 7 2 638 9 8 20 20 21 21 22 2.2 23 23 23 24 10.36206 36 1 80 36i54 36i28 36 1 02 9 68336 68368 684oo 68432 68465 24 25 25 26 27 i o . 3 i 66^ 3i632 3 1 600 3 1 568 3 1 535 io.o4542 o454o o4554 o4'56o o4566 b 5 5 5 5 9 . 9 5458 95446 9544o 95434 5o 5i 5 a 53 54 8 33 20 33 12 33 4 32 56 32 48 3 26 4o 26 48 26 56 27 4 27 12 9.6392^ 63 97 6 64002 64028 10.36076 36o5o 36024 35 99 8 35 97 2 9 .68497 6852 9 6856 1 685 9 3 68626 27 28 28 29 29 io.3i5o3 3i47' 3 1 439 3 1 407 3i3 7 4 04579 o4585 04591 04597 5 5 5 5 9.95427 95421 9 5{.5 95409 IO 9 8 6 t i M 55 5b 57 58 60 M 32 4o 32 32 32 24 32 16 32 8 32 3 27 20 27 28 27 36 27 44 2 7 52 28 o 9.64o54 64o8o 64 1 06 64 1 32 64 1 58 64 1 84 24 25 25 26 26 26 10.35946 35920 358 9 4 35868 35842 358i6 9.68658 68690 68722 68 7 54 68786 68818 3o 3o 3i 3i 32 33 io.3t342 3i3io 3i2 7 8 3 1 246 3i2i4 31182 Tangent. io.o46o. 04609 04616 04622 04628 o4634 Cosecant. b 6 6 6 6 6 ttifi 9.95397 o5384 9 53 7 8 95372 9 5366 Sine. flour P.M HOUTA.M Cosine. Diff. Secant. Cotangent Diff its 3 A A B B C C 64 Seconds of time 1* & 3 s 4' 5> l> 9 7' ~2T 28 5 ( A Prop, parts of cols. < B J r< 3 4 7 8 10 12 i3 17 16 20 20 TABLE XXVII. I"* 65 " 1 Log. Sines, Tangents, and Secants G '- 26 A A B B C C 153 31 Hour A.M. Hour P.M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent Secant. Diff. o i o Cosine. y. 96 366 9536o 9 5354 95348 95341 M i 2 3 4 ') 6 8 9 8 32 o 3i 52 3i 44 3i 36 3i 28 3 28 o 28 8 28 16 28 24 28 32 9.64l84 64210 64236 64262 64-^.88 o o I I 2 io.358i6 35790 35764 35 7 38 35 7 i2 9.68818 6885o 68882 68914 68946 i i 2 2 10. 3i 182 3 1 i5o 3iit8 3 1 086 3io54 io.o4634 o464o o4646 04662 04669 60 69 58 67 56 8 3i 20 3l 12 3i 4 3o 56 3o 48 3 28 4o 28 48 28 56 29 4 29 12 9.64313 64339 64365 64391 644i7 2 3 3 3 4 io.3568 7 3566 1 35635 356o 9 35583 9.68978 69010 69042 69074 69106 3 3 4 4 5 IO.3lO22 30990 3o 9 58 30926 30894 10.04666 04671 04677 o4683 04690 ). 9 5335 95329 953a3 9 53. 7 953io 55 54 53 52 5. 10 1 1 I 2 .3 i4 8 3o 4o 3o 32 3o 24 3o 16 3o 8 3 29 20 29 28 29 36 29 44 29 5a 9-64442 64468 64494 645 .9 64545 4 5 5 5 6 10.35558 35532 355o6 3548i 35455 9.69138 69170 69202 69234 69266 5 6 6 7 7 10.30862 3o83o 30798 3o 7 66 3o 7 34 10.04696 04702 04708 o47i4 04721 9.96304 96298 96292 96286 96279 5o 49 48 47 46 i5 16 1-7 18 1 9 8 3o o 29 52 29 44 29 36 29 28 3 3o o 3o 8 3o 16 3o 24 3o 32 9.64571 645 9 6 64622 64647 646 7 3 6 8 8 10.35429 354o4 353 7 8 35353 3532 7 9.69298 6 9 3 29 69361 69393 69425 8 8 9 9 10 1 1 1 1 12 12 1 3 10.30702 30671 3o63g 3o6o 7 3o5 7 5 10.04727 o4733 04739 o4 7 46 04762 2 2 2 2 2 2 2 2 2 3 9.96273 96267 9626. 96264 96^48 45 44 43 42 4( 20 21 22 23 24 8 29 20 29 12 29 4 28 56 28 48 3 3o 4o 3o 48 3o 56 3i 4 3f 12 9.64698 64724 64749 64775 64800 8 9 9 10 10 io.353o^ 352 7 6 3525i 35225 352oo 9.69457 6 9 488 69520 6 9 552 6 9 584 io.3o543 3o5i2 3o48o 3o448 3o4i6 10.04768 04764 04771 o4777 04783 9.96242 95336 96-9 96 22 3 9621 ; 4o ll 37 36 25 26 27 28 29 8 28 4o 28 32 28 24 28 16 28 8 3 3t 20 3i 28 3i 36 3i 44 3i 52 9.64826 6485. 64877 64902 64927 i 1 ii 1 1 12 12 10. 35174 35.49 35i23 35o 9 8 35o 7 3 9.696.5 69647 69679 69710 69742 i3 i4 i4 1 5 i5 io.3o385 3o353 3o32i 30290 3o^58 10.04789 04796 04802 04808 o48i5 3 3 3 3 3 9.9621; 9620^ 95.9^ 96192 96.86 35 3/1 33 32 3. 3o 3i 32 33 34 8 28 o 27 52 27 44 27 36 27 28 3 32 o 32 8 32 16 32 24 32 32 9.64953 64978 65oo3 65029 65o54 13 i3 i4 i4 i4 io.35o47 35022 34997 34971 34946 9.69774 6 9 8o5 6 9 83 7 69868 69900 16 16 17 17 18 18 i9 20 20 21 IO.3O226 3oi 9 5 3oi63 3oi3 2 3oioo 10.04821 04827 04833 o484o o4846 3 3 3 3 4 9.96179 9 5i 7 3 96167 96160 95,54 3o 29 28 27 26 35 36 3? 38 3 9 4o 4i 42 43 44 8 27 20 2 7 12 27 4 26 56 26 48 3 32 4o 32 48 32 56 33 4 33 12 9.66079 65io4 65i3o 65i55 65 180 9.652o5 65 2 3o 65255 6528i 653o6 i5 i5 16 16 16 10.34921 34896 34870 34845 34820 9. 69932 6 99 63 6 999 5 70026 70o58 io.3oo68 3oo3 7 3ooo5 29974 29942 10.04862 04869 04866 04871 04878 4 4 4 4 4 9.96148 96141 95i35 96129 96122 25 2.4 23 2.2 21 20' '9 18 17 16 8 26 4o 26 3a 26 24 26 16 26 8 3 33 20 33 28 33 36 33 44 33 52 17 '7 18 18 '9 10.34/95 34770 34 7 45 34719 34694 9.70089 7012 1 70162 70184 702 1 5 9-70247 70278 70309 7 o34i 70372 21 22 22 23 23 ~^4~ 24 26 26 26 10.2991 i 29879 29848 29816 29786 10.04884 04890 04897 04903 04910 4 4 4 5 5 ~T 5 5 5 5 9.961 16 96110 96103 96097 96090 45 46 47 48 4 9 5o 5i 52 53 54 8 26 o 25 52 a5 44 25 36 25 28 3 34 o 34 8 34 16 34 24 34 32 9.6533i 65356 6538 1 654o6 6543 1 1 9 1 9 20 20 21 10.34669 34644 34619 345 9 4 3456 9 10.29763 29722 29691 29669 29628 10.04916 04922 04929 04935 04941 9.96084 96078 95071 96066 96069 1 5 14 i3 I 2 1 1 10 I 7 8 25 20 25 12 25 4 24 56 24 48 3 34 4o 34 48 34 56 35 4 35 12 9-65456 6548 1 655o6 6553 1 65556 21 22 22 22 23 io.34544 345i 9 34494 3446 9 34444 9.70404 7 c435 70466 70498 70629 26 27 27 28 28 10.29696 29565 2 9 534 29602 29471 ic .04948 04964 04961 04967 04973 5 5 5 6 6 9.95062 96046 96039 9 5o33 96027 55 56 5 7 58 | 8 24 4o 24 32 24 24 24 16 24 8 24 o 3 35 20 35 28 35 36 35 44 35 52 36 o 9-6558o 656c5 6563o 65655 6568o 66705 23 24 24 25 25 25 10.34420 343 9 5 34370 34345 34320 34?- 9 5 9.70660 70692 70623 70664 70686 70717 y 3o 3o 3i 3i 32 10.29440 29408 29377 29346 2 9 3i5 29283 10.04980 04986 04993 04999 06006 06012 6 6 6 6 6 6 9.96020 96014 96007 9600 1 94995 94988 5 4 3 2 I M M Hour P.M. Hour A.M. Cosine. Diff. Secant. Cotangent Diff. Tangent. Cosecant. Diff. Sine. 116 tiff Seconds of time ! & 3 s 4 s 5 s 6' 7' (A 3 6 10 i3 16 9 22 Prop, parts of cois / B 4 8 12 16 20 4 28 1 r- . A 4 ; ft >7 mwq TABLE XXVII. Log. Sines, Tangents, and Secants G '- A A B B ' C C 158 r i i. 23 5: 23 4^ 23 3( 23 2* 8 23 2C 23 i: 23 / 22 5( 22 4 336 36 ' 36 . 36 2 36 3 9.65 7 0: 657 2 c 65 7 5/ 65 77S uin o v/osecan i 10. 3429 3427 3424 3422 34196 1 aiigent. 9.7071- 7074* 70/7$ 708 ic 70841 Difl f O i i > i ) 2 ~1 L t jCotan,>>-ei 10.2928 2926 2922 29,9 2916 Secant. I 0.060 ii o5o3i o5o3 iDfl o o o Cosine 9.9498 94 9 8 9497 9496 9496 31 Go 69 58 67 66 3 36 4 364 36 5 3 7 3 7 i 9.66828 65853 658 7 fi 66902 66927 10.3417 34.4 34i2 34o 9 & 34o 7 3 9.7087; 7090 7093 7096 7099 10.2912 2906 2 9 o3^ 2900; 10. 06044 0606 1 05057 06064 06070 9-94956 9494 9494 94 9 36 55 54 53 52 5i 8 22 4r 22 32 22 24 22 if 22 fc 3 37 2 3 7 2 3 7 3 3 7 4 3 7 5 9.65962 659 7 6 6600. 66026 66060 6 io.34o4< 34024 33 999 33 97 5 33 9 5o 9.7102 7106 7109 71 12 71.5 6 6 10.2897 2894 289. 2887 2884 io.o5o 77 o5o83 06089 06096 06102 9.9492 9491 9491 94904 94898 5o 49 48 47 46 16 .6 2 8 22 ( 21 5; 21 44 2. 36 21 28 3 38 o 38 8 38 if 38 24 38 3 9,60075 66099 66.24 66.48 66. 7 3 b 6 8 10.33926 3390 338 7 6 33852 33827 9.71.8 7121 7124 7127 7 i3o 8 8 9 9 10 10 1 1 ii 12 12 1C 14 M 10.2881 2878 2876 2872 2869 o5i .5 06.22 06129 o5i35 ; 2 9.9489 9 488 9 48 7 8 948 7 9 486 45 44 43 42 4i 82. 20 21 .2 21 4 20 56 20 48 3 38 4c 38 48 38 56 9.66.97 66221 66246 662-70 6629 8 Q 9 10 io.338o3 33779 33 7 5/ 33 7 3c 33 7 o5 9 .7i33 7 i4o 7i46 10.2866 2863o 28699 28669 28538 061 48 o5i55 06161 06168 2 2 2 3 3 3 3 1 3 3 3 9.94868 9 485 9484 9483 9 9483 4o 3 9 38 37 36 a6 28 29 8 20 4o 20 32 20 24 20 1 6 20 8 3 . 9 % 3 9 20 3 9 3f 39 44 3 9 52 3 4o o 4o 8 4o .6 4o 24 4o 32 9.663.9 6634 66368 663 9 664i6 10 ii ii ii 12 io.3368 3365 7 33632 336o8 33584 9-7i49 71624 7.55 71686 7161 10.28607 28476 2844 28414 2838. io.o5. 7 4 06181 o5i8 7 06194 06201 948.9 9 48.3 9 48o6 94799 35 34 33 32 3i 8 6 1 i 3o 8 20 '95 19 44 19 3( 19 28 9.6644 66465 6648 9 665.3 6653 7 4 io.3355 9 33535 335it 3348- 33463 9.7.648 71679 7.709 7177 i5 16 16 17 17 10.2835 2832 2829 28260 28229 I0.o520 7 0621 0622 0622 0623 3 3 4 4 4 9.94793 9 4 7 86 94773 94767 1C to '9 8 19 20 1 9 .2 1 8 5f 18 48 3 4o 40 4o 48 4o 56 4i 4 4i 12 9.66662 66586 666.0 66634 66658 4 c c K, 16 io.33438 334.4 333 9 o 33366 33342 9.71802 7i833 7 i863 71894 7i 9 25 18 '9 '9 20 20 10.28195 28167 28 13- 28ic 28076 06253 06260 06266 4 4 4 4 4 9.94760 94753 94740 94734 4i 44 45 7 48 9 5 1 55 3 i 55 -7 58 9 o I 8 18 4o 18 32 18 2-4 1 8 i6 18 8 3 4. 20 4. 28 4. 36 4. 44 4i 62 9.66682 66706 66 7 3. 66 7 55 66 77 9 16 17 17 17 18 0.333.8 332 9 4 33369 33245 33221 9.71966 7.986 72017 72048 72078 21 21 22 22 23 o.28o45 2801^ 2 79 83 2 79 22 io.o52 7 3 06280 06286 06293 o53oo 4 4 5 5 9.94727 94720 947 '4 94707 94700 8 18 o 17 62 17 44 17 36 17 28 3 42 o 42 8 42 .6 42 24 42 32 9.66800 668 2 7 6685. 668 7 5 66899 18 1 9 1 9 1 9 20 '33l?3 33.49 33.25 33io. 9.72109 72140 72170 72201 7223l 23 24 24 25 26 0.2 7 8 9 I 27860 2 7 83o 27799 27769 io.o53o6 o53i3 o532o o532.6 o5333 5 5 5 5 5 9.94694 9 468o 94674 94667 8 17 20 17 12 16 56 16 48 3 42 4o 42 48 42 56 43 4 43 12 .66922 66946 669 7 o 66994 6 7 o.8 20 21 21 21 22 0.33078 33o54 33<>3o 33oo6 32982 9.72202 72293 72323 72354 72384 26 26 27 27 28 o.2 77 38 2770-7 27677 27646 27616 o.o534o o5346 o5353 o536o o5366 6 6 6 6 6 9.94660 9*654 94647 9 4634 o 7 ?. 16 4o 1 6 32 1 6 24 r6 .6 16 8 16 o 3 43 20 43 28 43 36 43 44 43 62 44 o .6-7042 67066 6-7090 6?!3 7 67161 22 23 23 23 24 24 >iff. 0.32958 32 9 34 32910 32887 32863 32839 9.724.5 72445 72476 72606 7 253 7 72667 28 29 3o 3 1 o. 27686 2 7 555 27624 27494 2 7 463 2 7 433 o.o53 7 3 o538o o5386 o53 9 3 06407 6 6 6 6 6 7 ^.94627 94620 9.46.4 94607 94600 94693 5 4 2 O our P.M. lour A.M. Cosine. 1 Secant. otangeut Diff. 'angent. Cosecant. >iff. Sine. I U7 A A B B C C GSP Seconds of time | 2' 6 8 2 3 s 4 F2 .5 3 5* 6' I 5 3 _ 7 1 21 ? 6 (A Prop, parts of cols. < |j ( C 3 4 i 9 .2 2 16 '9 4 TABLE XXVII. [Pise aw Log. Sines, Tangents, and Secants. :>$> A A B JB C C 151 M Hour A.M.; Hour I>.M. Sine. .Diff. Cosecant. Tangent. Diff. Cotang-eiU Secant. |Dff. Cosine. M c i 2 3 4 8 16 o i5 52 1 5 44 i5 36 :5 28 3 44 o 44 8 44 1 6 44 24 44 32 9.67161 o 67185 o 67208 I 67232 I 67256 2 ID. 3 2.839 32.8.5 32792 32768 3 2 7 44 9.72567 7 25 9 8 72628 72659 72689 i I 2 IO .27433 27402 27372 27341 273. [ io.o54o 7 o o54i3 o 05420 o C)542 7 o5433| o 9.94593 945B7 9458o 945 7 3 9456 7 60 ll 5 7 56 5 6 7 8 9 10 i i I 2 3 i i 8 i5 20 [5 12 i5 4 1 4 56 i4 48 3 44 4o 44 48 44 56 45 4 45 i2 9.67280 6 7 3o3 6 7 32 7 67350 67374 2 2 3 3 3 10.32720 32697 32673 32.65o 32626 9.7272.0 72750 72780 728 1 i 72841 3 3 4 4 5 10.27280 27250 27220 27189 2.7 1 59 [O.o544 6544? o5454 c>546o 05467 9.94560 9 4553 94546 9454o 9 4533 55 54 53 5 3 5i 5o 49 48 47 46 8 14 4o i4 32 i4 M 14 16 14 8 3 45 20 45 28 45 36 45 44 45 52 9.67398 674? i 67445 67468 6-492 4 4 5 5 5 ~6 6 7 7 7 8 8 9 9 9 10.32602 325 79 32555 32532 325o8 9.72872 72902 72932 7 2 9 63 72993 5 6 6 7 7 1^.27128 27038 27068 27037 27007 10.0.5474 o548. 05487 o5494 o55o. 9.94526 945i9 9 45.3 945o6 94499 i r > f6 17 f8 '9 8 14 o i3 52 i3 44 i3 36 i3 28 3 46 o 46 8 46 16 46 24 46 32 9.67515 6 7 53 9 67562 6 7 586 67609 10.32485 32461 32438 324.4 3 2 3 9 i 9.73023 7 3o54 7 3o84 7 3n4 7 3i44 8 8 9 9 IO 10.26977 26946 26916 26886 26856 io.o55o8 o55.5 o552i o5528 o5535 2 2 2 2 2 9.94492 94485 9.4479 94472 94465 45 44 43 42 4i 4o 3 9 38 37 36 20 2 I 2 2 2.3 M 8 i3 20 l3 12 i3 4 12 56 12 48 3 46 4o 46 48 46 56 47 4 4? 12 9.67633 6 7 656 67680 67703 67726 10.32.367 32344 3232.O 32297 322 7 4 9. 7 3i 7 5 7 32o5 7 3235 7 3265 7 32 9 5 10 1 1 1 1 12 12 10.2682.5 26795 2.6765 26735 26705 [o. 65542 o5549 o5555 o5562 o556 9 2 2 3 3 3 9-94458 944 5 1 94445 94438 9443 1 25 26 .'7 a 8 '9 3o 3i 32 33 34 8 12 4o 12 32 12 24 12 l6 12 8 3 4? 20 47 28 47 36 4y 44 47 52 9.67750 67773 67796 6-7820 6 7 843 10 10 10 1 1 1 1 I0.322.5o 32227 32204 32.180 3 2 i5 7 io.32i3'4 321 10 32087 3ao64 32041 9 . 7 3326 7 3356 7 3386 7 34.6 73446 l3 i3 i4 i4 .5 10. 26674 26644 26614 26584 26554 10.05576 3 o5583| 3 05590 3 o55o6i 3 o56o3| 3 9.94424 94417 944io 944o4 94397 35 34 33 32 3. 8 12 II 52 ii 44 n 36 ii 28 8 II 20 II 12 ii 4 10 56 10 48 3 48 o 48 8 48 16 48 24 48 32 9.67866 67890 67913 6 79 36 67959 12 12 12 13 i3 9.73476 7 35o 7 7 353 7 7 356 7 735 97 i5 [6 16 17 '7 10.26524 26493 26463 26433 a64o3 io.o56.o o56 1 7 o5624 o563i o5638 3 4 4 4 9.94390 9 4383 94376 9 436 9 94362 3o 29 28 27 26 35 36 37 38 39 4o 4i 4 ;. 43 44 3 48 4o 48 48 48 56 49 4 49 12 9.67982 68006 68029 68o5a 68o 7 5 i4 i4 i4 i5 i5 10. 320 l8 3 1 994 3i97i 3i 9 48 3.925 9.7362-7 7 365 7 7 368 7 73717 73747 18 1 8 9 IO 20 10. 263 7 3 26343 263.3 26283 26253 . o.'. >5645 9565? o5658 o5665 05672 4 4 4 4 4 9.94355 94349 94342 94335 94328 25 24 2.3 22 2 1 8 10 4o IO 32 10 24 10 16 10 8 3 49 20 49 28 49 36 49 44 49 52 9.68098 68121 68i44 68167 68190 16 16 16 17 17 i o . 3 1 9( > 2. 31879 3i856 3.833 . 3(8.0 9.73777 7 38o 7 7 383 7 7386 7 73897 20 21 21 22 22 10.26223 26193 26163 261 33 26.o3 IO;p56 7 9 o5686 05693 o5 7 oo 05707 5 5 5 5 5 9.9432. 943 1 4 943c>7 9 4 3 oo 9 42. 9 3 2O 1 6 45 46 il 4o 49 5b 5 1 r r>. 53 54 8 to o 9 52 9 44 9 36 9 28 3 5o o 5o 8 5o 16 5o 24 5o 32 9.68213 68237 68260 68283 683o5 17 18 18 '9 [9 10.31787 3 1 763 3i 7 4o 3.717 3 . 695 9-73927 73957 73987 740.7 74^47 23 2.3 24 24 25 .0.260-3 26o43 2.601 3 25983 25 9 53 10.05714 05721 05727 o5 7 34 05741 5 5 5 5 6 9.94286 942-79 9*1273 94266 94259 i5 i4 .3 1 1 10 9 8 6 8 9 20 9 I2 9 4 8 56 8 48 3 5o 4o 5o 48 5o 56 5i 4 5l 12 9.68328 6835i 683 7 4 68397 68420 '9 20 2.O 21 21 10.31672 3 1649 3.626 3.6o3 3i58o 9.74077 74107 7 4i3 7 7^(66 7 4i 9 6 25 26 26 27 27 10.25923 25893 25863 5.5834 2.58o4 10.05748 o5755 05762 05769 05776 6 6 6 6 6 9.94252 94245 94238 9 4a3i 94224 55 56 $7 r 8 59 Go 8 8 4o 8 32 8 24 8 16 8 8 8 o 3 5i 20 5i 28 5i 36 5 1 44 5i 52 52 9-68443 2t 68466 22. 68489 22 685 I 2; 22 68534' 2,3 6855 7 23 ic. 3 1 557 3 1 534 3.5u 3.488 3 1 466 3i443 9.74226 28 7 4 a 56 2.8 74286 29 743.6' 29 74345 3o 743 7 5| 3o 10. 25774 25 7 44 25 7 i4 25684 25655 25625 io.o5783| 6 c5-90j 6 057971 7 o58o4! 7 o58ii| 7 o58.8j 7 9.94217 94210 94ao3 94196 94189 94182 5 4 3 2 I M He isr P.M. t lour A.M. Cosmo. JDifl'. 1 Secant. Cotangent. Diff. Tangent. Cosecant. |D ff. Sine. M 118 A A B B C 1 s 9s 3' 4 s 5" f) s 7" (A Prop, parts of cols. < B ( C 3 4 6 8 2 9 1 1 3 1 2 i5 3 i5 '9 4 17 23 5 20 26 6 61 C Page 2i4] S'. 29 M Hour A. M . Hour p. M TABLE XXVII. Log. Sines, Tangents, and Secants. Sine. DiffCosecan Tangent DiffJCotan-e, Secant C C 15 o 8 8 < i 7 5 2 7 4/ 3 7 3( 4 7 2* J 3 52 I 52 \ 52 I ) 52 2 i 52 3 9-6855 6858 6860 6862 6864 o o io.3i44 3i35 9-743 7 f 744of 7443? 7446 C 7449^ o i 2 10.2562 255 9 2556 2553 255o 'o582.! o583: o583 s 5 o ) o o > o > o 9.94182 9 4i 7 5 94168 94161 5 8 7 2c 6 71: 7 7 z 8 6 5t 9 6 4 ) 3 52 4 52 4 i 5 2 5 > 53 53 i 9.6867 6869 6871 68 7 3 6876 4 4 t e io.3i32 3i3o 3i28 3 1 26 9- 7 452/ 7 455^ 74583 746 r^ 74643 2 3 3 4 4 10.2547 2544 254 1 2538 2535 10.0585'- o586c 0586- 05874 o588i io.o5888 05895 o5oo2 o5 9 ic o5 9 i 7 -! T 9 . 9 4i4 7 94 M 9 4i33 9.4126 o4i 10 o 8 6 4c i 6 3p 2 6 2 3 6 i 4 6 3 53 2 53 2 53 3 53 4 53 5 9.6878 6880 68829 6885 688 7 5 I0.312J 3 1 19; 3i 17 3u4 3lI2 74702 74732 74762 7479 ' 5 5 6 6 7 8 8 9 9 252 9 1 2526 2523 2520 2 9.9411 a 94 10' 94098 9 4o 9 o 586 6 55 7 5 4 8 53 9 5 2 3 54 54 54 i 54 2 54 3 9.68897 68920 68942 68 9 65 68987 6 6 6 7 7 10. 3i 10 3 1 080 3io58 3io3 9.74821 7485, 7488o 74910 74939 10.25(7 25l2( 25o 9 o 25o6 io.o5 9 24 o5 9 3[ o5 9 38 o5 9 45 o5 9 5 2 2 2 2 2 94069 94062 9 4o55 94048' 9-94o4i 9^o3^ 94027 94020 94012 o 8 5 2 i 5 i 2 5 4 3 4 56 4 4 48 3 54 4o 54 48 54 56 55 4 55 12 9.69010 6 9 o3 2 6 9 o55 69077 69100 8 8 9 9 10.30990 3o 9 68 3o 9 45 3o 9 2; 3o 9 oo 9.74969 7 4 99 8 75028 7 5o58 7 5o8 7 10 10 1 1 1 1 12 io.25o3 a5oo 24 9 72 24 9 4' 24 9 i3 io.o5 9 5 o5 9 6 o5 9 7 o5 9 8 o5 9 8 2 3 3 3 3 5 8 4 4o 6 43 7 4 24 8 4 16 9 48 3 55 20 55 28 55 36 55 44 55 52 9.69122 69144 69167 69189 69212 9 10 10 10 II II 12 12 12 13 i3 i3 i4 i4 i5 io.3o8 7 8 3o856 3o833 3o8u 3o 7 88 ' 7 5i46 7 5i 7 6 752o5 75235 1 2 i3 i3 i4 14 10.2488 24854 24824 24795 24765 io.o5 99 0600 0600 0601 0602 3 3 3 3 3 9. 9400 5 9 3 99 [ 9 3 9 84 93977 o 8 4 o , 3 52 2 3 44 3 3 36 4 3 28 3 56 o 56 8 56 16 56 24 56 3 a 9.69234 6 9 256 69279 69301 69323 io.3o 7 66 3o 7 44 3072 1 3o6 99 3o6 77 9.75264 73*94 7 53 2 3 75353 75382 i5 i5 16 16 17 10.24736 24706 24677 24647 24618 io.o6o3 o6o3 0604 o6o5 o6o5 4 4 4 4 4 9 . 9 3 9 7o 9 3 9 63 9 3 9 48 9394 > ! 3 4 4 4 4 4 5 8 3 20 1 3 12 7 3 4 3 2 56 ? 2 48 3 56 40 56 48 56 56 .69345 6 9 368 6 9 3 9 o 69.412 6 9 434 o.3o655 3o63 2 3o6io 3o588 3o566 7544 754/o 755oo 7 552 9 17 18 18 1 9 '9 10.24589 24559 2453< 245oo 24471 10.06066 0607 0608 06088 o6o 9 5 4 4 4 5 5 9.93934 93927 93920 93912 3 8 2 40 [ 2 32 2 2 2Z 3 2 l6 ^ 2 8 3 5 7 20 5 7 28 5 7 36 57 44 57 52 .6 9 456 6 9 479 69501 6 9 523 6 9 545 i5 1 5 16 16 16 o.3o544 3o52i 3o4 99 3o4 77 3o455 9. 7 5558 7 5588 756i 7 75647 7 56 7 6 20 20 21 21 22 10.24442 244 I 2 24383 24353 24324 10.06102 06109 06116 06124 ooi3r 5 5 5 5 5 9.98898 9 38 9 i 9 3884 9 38 7 6 9 386 9 xr XT xr xr xr : m m m r> m ) 8 2 ) 52 7 44 5 36 > 28 3 58 o 58 8 58 16 58 24 58 32 .6 9 56 7 6 9 58 9 69611 6o633 6 9 655 17 17 '7 18 18 io.3o433 3o4u 3o38 9 3o36 7 3o345 9- 7 5 7 o5 75735 75/64 75793 7 5822 22 23 23 24 24 10.24295 24265 24236 24207 24178 o.o6i38 o6i45 06 1 53 06160 06167 5 5 6 6 6 * 9 3855 9 3847 9 384o 9 3833 ) 8 20 12 4 o 56 o 48 3 58 40 58 48 58 56 59 4 59 12 .6 9 6 77 69699 69 7 2i 69743 6 97 65 '9 9 1 9 20 20 20 21 21 22 22 22 io.3o323 3o3o i 302-79 3o25 7 3o235 9. 7 5852 7 588i 75^69 25 25 26 26 27 10.24148 24119 24090 24061 0.06174 06181 o6i8 9 06106 06203 6 6 6 6 6 , 9 3826 9 38, 9 9 38i i 9 38o4 9 3 797 5 f 5( 5F 5c, 60 M 8 o 4o 32 o 24 o 16 o 8 3 59 20 5 9 28 5 9 36 5 9 44 5^5, 4 o o .6 97 8 7 6(7809- 6983? 69853 69875 6 9 8 97 o.3c>2i3 30191 3oi6 9 3oi4 7 3oi25 3oio3 9.75998 76027 7 6o56 76086 761 1 5 76i44 27 28 28 29 29 29 10.24002 2 3 97 3 23 9 44 23 9 .4 23885 23856 Tangent. 0.06211 06218 06225 06232 06240 7 7 7 7 7 7 W. 93789 93782 93775 9 3 7 68 93760 93 7 53 o r P.M. our A.M. Dosine. )i(T. Secant. otangent Jiff osecant. Sino. 119 C (jff ' Seconds of time ! 2 s 3' 4- 5* 6- 7 (A 3 6 8 TJ i4 17 20 Frop. parts of cols. < B 4 7 ii i5 18 22 36 (c i 2 3 4 4 5 6 TABLE XXVII, [."ageais 9. Leg. Sines, Tangents, and Secants. G> ' W A A B B C C 349 M Hour A.M. I lour P.M. Sine. Dill Cosecant. Tangent. Diff Cotangent Secant. DilF. Cosine. M >o 5S t>7 56 55 54 53 5? 5i o 2 3 4- "5 6 7 8 9 800 7 5 9 52 5 9 44 5 9 36 5 9 28 4 o o o 8 o 16 o 24 32 9.69897 69919 69941 6 99 63 69984 o o I I I 2 2 3 3 3 4 4 5 5 ic.3oio3 3oo8i 3oo3 7 3ooi6 9 . 76 i 44 76173 76202 76231 76261 o I I 2 10.23856 23827 23798 23-769 2 3 7 3 9 0.06247 06264 06262 06269 06276 Ii o 9 . 9 3 7 53 o3738 9 3 7 3, o3?24 7 5 9 20 5 9 12 5 9 4 58 56 58 48 4 o 4o o 48 o 56 4 12 9 . 70006 70028 70o5o 70072 7OO 9 3 10.29994 29972 29950 29928 29907 9^6290 76319 7 6348 763 77 76406 2 3 3 4 4 10.23-710 2368 1 23652 23623 235 9 4 10.06283 06291 06298 o63o5 o63i3 i 2 2 93-709 93-702 9 36 9 5 9 368 7 10 i i I 2 i3 i4 7 58 4o 58 32 58 24 58 16 58 8 4 20 28 36 44 52 9 .7on5 70137 70i5 9 70 1 80 70202 10.29885 2 9 863 2 9 84i 20.820 2 979 8 9 . 7 6435 76522 7 655i 5 5 6 6 7 10.23565 23536 235o 7 234 7 8 23449 io.o632o o632 7 o6335 o6342 o635o 9 . 9 368o 9 36 7 3 9 3665 9 3658 9 365o 5o 49 48 47 46 i5 16 17 j.8 '9 7 58 o 57 52 57 44 5 7 36 5 7 28 2 8 2 16 2 24 2 32 9 . 70224 70245 70267 70288 7o3io 5 6 6 6 7 IO.2 977 6 2 97 55 2 97 33 2 97 I2 2 9 6 9 o 9.76580 76609 7 663 9 76668 76697 8 8 9 9 10.23420 233 9 i 2 336i 23332 233o3 io.o635 7 o6364 o63 7 2 o63 79 o6386 2 2 2 2 2 9-93643 93636 9 36 2 8 9 362 1 9 36i4 45 44 43 42 4i 4o 39 38 3 7 36 20 21 22 23 24 7- 57 20 5 7 12 5 7 4 56 56 56 48 4 2 4o 2 48 2 56 3 4 3 12 9 '70353 70375 7o3 9 6 70418 i 8 8 9 10.29668 29647 29604 29582 9.76725 76754 7 6 7 83 76812 7 684i 10 IO II 1 1 12 10.232 7 5 23246 232I 7 23 1 88 23i5 9 10.06394 06401 06409 06416 o6423 2 3 3 3 3 9.93606 9 35 99 93591 93584 9 35 77 25 26 2 7 28 29 7 56 4o 56 32 56 24 56 16 56 8 4 3 20 3 28 3 36 3 44 3 52 9> 7o43 9 70461 70482 9 9 10 10 10 II II II 12 12 10.29561 2 9 53 9 2 9 5i8 2 9 4 9 6 9. -768-70 76899 76928 76957 76986 12 13 i3 i3 i4 io.23i3o 23lOI 230 7 2 23o43 23oi4 10. o643 i o6438 o6446 o6453 o646i J 3 3 3 4 9 . 9 356 9 93562 9 3554 9354 7 9 353 9 35 34 33 3: 3i CO Co CO Co Co lix CO V3 - O 7 56 o 55 52 55 44 55 36 55 28 4 4 o 4 8 4 16 4 24 4 32 9-70547 7 o568 7o5 9 o 7061 1 70633 io.2 9 453 2 9 432 2 9 4 I 29389 29367 9.77016 77044 77073 77101 77 i3o i4 16 16 16 16 10.22986 22956 2292-7 22899 228-70 10.06468 o64 7 5 o6483 06490 06498 4 4 4 4 4 9 . 9 3532 9 3525 9 35i 7 935io 9 35o2 3o 29 28 2 7 26 35 36 3 7 38 3 9 7 55 20 55 12 55 4 54 56 54 48 4 4 4o 4 48 4 56 5 4 5 12 9 . 70654 70675 7o6 9 7 70718 7 o 7 3 9 i3 i3 i3 i4 10.29346 2 9 3 2 5 29303 29282 29261 9.77169 77i88 77217 77246 77274 17 17 18 18 10.22841 22812 22 7 83 22 7 54 22-726 io.o65o5 066 1 3 06520 06528 o6535 4 4 5 5 5 9 . 9 34 9 5 9 348o 9 34 7 2 9 3465 25 24 23 22 21 4o 4i 4 a 43 44 7 54 4o 54 32 54 24 54 16 54 8 4 5 20 5 28 5 36 5 44 5 5 2 9 . 7 o 7 6i 70-782 70803 70824 70846 i4 i5 i5 i5 16 10.29239 29218 29176 29154 9 ' 77 332 77 36i 77390 774i8 '9 20 20 21 21 10.2269-7 22668 2263 9 22610 22582 io.o6543 o655o o6558 o6565 o65 7 3 5 5 5 5 5 9-9 3 45 7 9 345o 93442 9 3435 2O I 9 1 8 17 16 45 46 47 48 49 5o 5. 52 53 54 7 54 o 53 52 53 44 53 36 53 28 4 6 o 6 8 6 16 6 24 6 32 9. 70867 70888 70 9 o 9 70 9 3t 70 9 52 ib 16 17 17 18 10.29133 291 12 200 9 I 29069 29048 9-77447 77476 77 5o5 77 533 77562 22 22 23 23 24 10. 22553 22624 22495 2246-7 22438 io.o658o o6588 o65 9 5 o66o3 06610 6 6 6 6 6 9.93420 93412 93397 9 33 9 o 9 . 9 3382 933 7 5 9 336 7 9 336o 9 335a r i4 i3 ii 10 I 6 7 53 20 53 12 53 4 52 56 52 48 4 6 4o 6 48 6 56 7 4 7 12 9 . 70973 70994 71016 7io36 7io58 18 18 9 '9 I0.2902 7 2 9 006 2 8 9 85 28 9 64 28 9 42 9-7759I 77619 7 7 648 77677 77706 24 25 25 26 26 10.22409 22381 22352 22323 2229/1 10.06618 06625 o6633 o664o 06648 6 6 6 7 7 55 56 5 7 58 59 bo - 52 4o 52 32 52 24 52 16 52 8 52 4 ~ 20 7 28 7 36 7 44 7 52 8 o 9-71079 71 100 71 121 7II42 7ii63 71184 20 20 20 21 21 21 IO.28 9 21 28900 2 88 79 28858 2 883 7 28816 9-77734 77763 77791 77820 77849 77877 26 27 27 28 !a8 29 10.22266 2223 7 22209 22180 22l5l 22123 io.o6656 o6663 06671 06678 06686 o66 9 3 7 7 7 7 7 7 9 9 333 7 9 332 9 9 3322 9 33i4 9 33o 7 c A 3 2 I C M Hour p.M.jHour A.M Cosine. Biff. Secant. Cotangent 'Diff.j Tangent. Cosecant. (Biff. Sine. AT I2(P 1 3 4 ^ fi 7 ( A Prop, parts of cols. < B (c 3 4 i 5 7 8 1 1 3 ii i4 4 i3 18 16 22 fi 25 7 l>i '^ 2L6] TABLE XXVII. Loo;. Sines, Tangents, and Secants. G ' A A B B C C 148' M [our A.M. lour P .M . Sine. Diir. Hoserniil. Tangent. Diff. Cotangent Secant. Di.f Cosine. M o i 2 3 4 7 52 o 5i 52 5i 44 5i 36 5i 28 4 8 o. 8 8 8 16 8 24 8 32 9.71184 71205 71226 71247 71268 o I I 10.28816 28795 28 77 4 28753 28 7 32 9.77877 7796 77935 77963 77992 o o I 1 2 10.22123 22094 22065 22037 22008 i o . 06693 0670 1 06709 067 1 6 06724 I r - os xr -IX 4o 3o 38 3 7 36 7 48 4o 48 32 48 24 48 ,6 48 8 4 I I 20 11 28 ii 36 ii 44 II 52 9.71705 7 I 7 26 71747 71767 71788 9 9 9 10 10 10.28295 28274 28253 28233 28212 9.78590 78618 7 864 7 7 86 7 5 78704 12 12 13 i3 i4 IO.2l4lO 21382 2i353 21325 2 I 296 10.06886 06892 06900 06908 069 1 6 3 3 3 4 4 9 . 9 3i,5 93108 93100 93092 93o84 35 34 33 32 3i 7 48 o 47 52 47 44 47 36 47 28 4 12 12 8 12 l6 12 24 12 3. 9.71809 71829 7 i85o 7 i8 7 o 71891 10 1 1 II 1 1 12 - - O O ON ON r^m ro C CO CO CO CO OO CN CN CS CN CN 9.78732 78760 78789 78817 78845 i5 i5 16 16 IO.2I268 21240 2121 I 2II83 2ii55 10.06923 o6 9 3i 06939 06947 o6 9 54 4 4 4 4 4 9.93077 93069 93061 93o53 9 3o46 3o 29 27 26 7 47 20 47 12 47 4 46 56 46 48 4 12 40 12 48 12 56 i3 4 13 12 9.71911 -71932 71952 71973 7 1 99-4 12 12 i3 i3 i3 10.28089 28068 28048 28027 28006 9.78874 78902 7 8 9 3o 7 8 9 5 9 78987 17 17 17 18 18 10.21 126 21098 21070 21041 2IOl3 10.06962 06970 06978 06986 o6 99 3 5 5 5 5 5 9 . 9 3o38 9 3o3o 93022 9 3oi4 93007 26 2' 22 21 I 42 43 44 45 46 47 48 4 9 7 46 4o 46 32 46 24 46 16 46 8 4 i3 20 i3 28 i3 36 i3 44 i3 52 9.72014 7203^ 72055 7 20 7 5 72096 i4 i4 i4 i5 i5 IO.27986 27966 27925 27904 9.79015 79043 79072 79100 -79128 '9 1 9 20 20 21 10.20985 20957 20928 20900 20872 10.07001 07009 0701-7 0-7024 7 o32 5 5 5 6 6 9.92999 9-299, 92983 929-6 92968 2O li l6 12 I I 7 46 o 45 52 45 44 45 36 45 28 4 i4 o i4 8 i4 16 i4 24 i4 32 9.72116 7 2l3 7 7 2l5 7 72177 72198 i5 16 16 16 17 I0.2 7 884 2 7 863 27843 27823 27802 9. 7 9i56 79 i85 792 1 3 792.41 79269 21 22 22 23 23 10.20844 208 1 5 20787 20759 2073 1 10.07040 0704 07066 07064 07071 6 6 6 6 6 9.92960 92962 92944 9 2 9 36 92929 5o 5i 3 |54 7 45 20 45 12 45 4 44 56 44 48 4 1 4 4o i4 48 i4 56 i5 4 i5 12 9. 7 22i8 72238 72259 -72299 17 18 18 18 i9 10.27782 27762 2 77 2I 2 77 OI 9.79297 79326 7 9 354 79382 794 1 o 24 24 25 25 26 10.20703 20674 20646 20618 20690 10.07079 07087 07096 07103 071 1 1 10.07119 07126 07134 07142 07! 58 Cosecant. b 7 7 7 7 9.9292. 92913 92906 9289-7 92889 10 8 6 t t i o 155 156 j! |6o 7 44 4o 44 32 44 24 44 16 44 8 44 o 4 1 5 20 i5 28 i5 36 i5 44 i5 52 16 o 9.7232C 7 234o 72360 7 238i 72401 72421 19 !9 20 20 20 21 io.2 7 68o 27660 27640 2-7619 27599 2 7 57 9 o . '7Q-43o 79466 79 4 9 5 79 5 2 3 79579 26 26 27 27 28 28 10.20662 2o534 2o5o5 20477 20449 20421 7 7 7 8 8 9.9288, 92866 92868 92860 92842 Hour P.M. Hour A. M Cosine. Diff. Secant Cotangent Diff. Tangent. Diff.[ Sine. M 1*1 o A A B B C C bf Seconds of time 1 s 2 s 3" 4' 5 s fi' 7- ( A 3 5 8 10 i3 if> 18 Prf p. parts of cols < B 4 7 ii i4 18 21 25 TABLE XXVII. [ p e e217 Log. Sines, Tangents, and Secants. G 3^ A A. B B C C 147 II i 2 3 4 HourA.M. Hour P.M. Sine. (Diff Cosecant. Tangent. Diff. Cotangent Secant. Diff, Cosine. M 7 44 o 43 52 43 44 43 36 43 28 4 16 o 16 8 16 16 16 24 16 32 9 . 72421 72441 72461 72482 7 25O2 I I 10.2-75-79 2 7 55 9 27539 2 7 5i8 27498 9.7 9 5-9 79607 79 635 79 663 79691 o 2 10.20421 2o3 9 3 20365 2o33 7 2o3o 9 io.07i5 07166 07174 07182 07190 o o o o I CN xro co co co co co 5 as>&g _ _ 10 10 10 II II II 10.26978 26959 26939 26919 26899 9 .8o4i 9 8o447 8o474 8o5o2 8o53o i4 i5 i5 16 10.19581 19553 19526 19498 19470 10.07397 07405 0741 3 07421 07429 4 4 4 4 5 9.92603 92595 92587 92579 92571 3o 29 28 27 2.6 35 36 37 38 39 7 3o 20 39 12 3 9 4 38 56 38 48 4 20 40 20 48 20 56 21 4 21 12 9.73121 7 3i6o 73 1 80 73200 12 12 12 13 i3 10.26879 26860 26840 26820 26800 9 .8o558 8o586 80614 80642 80660 16 17 17 18 18 '9 1 9 20 20 2O 10.19442 19414 19386 i 9 358 iy33 1 10.07437 07445 07454 07462 07470 5 5 5 5 9. 9 2563 92555 92546 9 2538 2.5 24 23 22 21 C ~ rs ro VT xrxrxt 5 5 6 6 10.26099 26079 26060 26041 26022 9.81666 8i6 9 3 81721 8 1 7 48 81776 7 7 8 8 9 9 10 10 ii ii io.i8334 i83o 7 18279 18252 18224 10.07765 07773 07781 07789 07798 2 2 2 3 3 9.92235 92227 922.9 922. i 92202 45 44 43 4 a 4>: 20 21 22 23 24 7 33 20 33 12 33 4 32 56 32 48 4 26 4o 26 48 26 56 27 4 27 12 9.73997 74017 7 4o36 74o55 74074 6 7 7 7 8 i o . 26oo3 2 5 9 83 25 9 64 25 9 45 25926 9.8i8o3 8i83i 8i858 81886 819.3 10.18197 18169 18142 18114 18087 10.07806 07814 07823 07831 07839 3 3 3 3 3 9-9 2 '94 92186 92177 92169 92161 4< 3<; 3l 3-7 36 35 34 33 32 3. 25 26 27 28 29 7 32 4o 32 32 32 24 32 16 3a 8 4 27 20 27 28 27 36 27 44 27 52 9.74093 74" i3 7 4 1 32 74i5i 74170 8 8 9 9 9 10 10 IO 10 II 10.25907 25887 25868 25849 2583o 9.81941 81968 8,996 82023 82o5i ii 12 12 13 i3 10.18059 i8o32 18004 17977 17949 10.07848 07856 07864 o 7 8 7 3 07881 3 4 4 4 4 4 4 4 5 5 9.92152 92144 92 1 36 92127 92119 3o 3i 32 33 M !5 36 ^7 38 ' J '9 I'- ll 43 43 44 7 32 o 3i 62 3i 44 3i 36 3i 28 4 28 o 28 8 28 16 28 24 28 32 9.74189 74208 74227 74246 74265 io.258ii 25792 25 77 3 25754 25 7 35 9.82078 82106 82i33 82161 82188 i4 i4 i5 i5 16 10.17922 17894 17867 I 7 83 9 17812 10.07889 07898 07906 079 u 07923 9.9211 . 92102 92094 92086 92077 3o 20 28 27 26 7 3i 20 3l 12 3. 4 3o 56 3o 48 4 28 4o 28 48 28 56 2.9 4 ? 9 12 9.74284 7 43o3 7 4322 7434i 7 436o II II 12 12 12 10.25716 25697 256 7 8 2565 9 2564o 9.82215 82243 82270 82298 82325 16 16 17 17 18 10.17785 17757 17730 17702 17675 10.07931 07940 0794^ 07956 o 79 65 5 5 5 5 5 9.92069 92060 92052 92044 92035 25 24 2, : 22 21 7 3o 4o 3o 32 3o 24 3o 16 3o 8 4 29 20 20 28 29 36 29 44 29 52 9.74379 743 9 b 744i7 74436 74455 l3 i3 i3 4 i4 IO. 25621 25602 25583 25564 25545 9.82.352 8 2 38o 82407 82435 82462 18 '9 '9 20 2O 10.17648 17620 17593 i 7 565 i 7 538 10.07973 07982 07990 07998 08007 6 6 6 6 6 9.92027 92018 92010 92002 91993 2O !* 17 16 Tc i3 12 1 1 10 7 6 45 46 47 48 ^2 5o 5i 52 53 54 7 3o o 29 52 29 44 29 36 29 28 4 3o o 3o 8 3o 16 3o 24 3o 32 9 74474 74493 7 45,2 7453i 745i9 i4 .5 i5 i5 16 10.25526 255o 7 25488 2546 9 2545i 9.82489 82517 82544 82571 82599 21 21 22 22 22 10.17511 i 7 483 i 7 456 17429 17401 io.o8oi5 080 2 L o8o3 2 o8o4i 08049 b 6 7 7 7 9.9,985 91976 9,968 91959 91961 7 29 20 29 12 29 4 28 56 28 48 4 3o 4o 3o 48 3o 56 3i 4 3l ,2 9-74568 7458 7 74606 74625 74644 16 16 17 17 17 17 18 18 18 '9 '9 10.25432 a54i3 253 9 4 2 53 7 5 25356 9.82626 82653 82681 82708 82735 23 23 24 24 25 10.17374 17347 17319 I?2 9? 17265 io.o8o58 08066 o8o 7 5 o8o83 08092 7 7 7 8 9.91942 91934 91925 91917 91908 55 56 5 7 58 5o 60 7 28 4o 28 32 28 24 28 16 28 8 28 o 4 3i 20 3*i 28 3r 36 3i 44 3i 52 32 9 . 74662 74681 74700 74719 74737 74756 io.25338 25319 253oo 25281 25263 25244 9.82762 82790 82817 82844 82871 82899 25 26 26 27 27 27 10.17238 17210 i 7 i83 I7i56 17129 17101 10.08100 08109 08117 08126 08 1 34 o8i43 8 8 8 8 8 8 9.91900 91891 9 i883 91874 91866 9 i85 7 4 3 2 M M PifT Secant. Cotangent Diff Tangent. Cosecant. Dirt' Sine. 28 3 A A B B C C 56- Seconds of time 1 2- 3- 4- 5- 6 7- f A 2 5 7 10 12 i4 17 Prop, parts of cols. < B ! r. I 7 2 IO 3 i4 4 17 5 21 6 24 7 TABLE XXVIJ ri'agesjg Log. Sines, Tangents, and Secants. Cl> J4 A A B B C C 14.r 51 i 3 4 He :r A.M.IIIour r.M. Sine. Diff. Cosecant. Tangent. rW'Cotangeiit Sec-ant. Diff. o o I Cosine. M 7 28 o 27 52 27 44 27 36 27 28 14 32 o 32 8 32 16 32 24 32 32 9-74756 74775 74794 7 48t2 7483 1 I I I 10.25244 25225 25206 25i88 25169 9.82899 82926 82953 82980 83oo8 o o I 2 2 3 3 4 4 i o . 17101 1 7074 17047 17020 16992 I0.o8i43 081 5 1 08160 08168 08,77 9.91857 91849 91840 9i832 91823 fio ''/ 5S 57 56 55 54 53 5 > 5i 5 6 n 8 9 7 27 20 27 12 27 4 26 56 26 48 4 3a 40 32 48 32 56 33 4 33 12 9.7485o 74868 74887 74906 74924 2 2 2 2 3 3 3 4 4 4 io.25i5o 25l32 a5n3 25094 25o 7 6 9-83o35 83o62 83o8 9 83u 7 83i44 10.16965 i6 9 38 1691 1 1 688 3 16856 10. 08 i 85 08194 08202 08211 08219 9.91815 91806 91798 91789 91781 10 1 1 12 i3 i4 7 26 4o 26 32 26 24 26 16 26 8 4 33 20 33 28 33 36 33 44 33 52 9.74943 74961 74980 74999 75017 10 25o5 7 25039 25020 25001 a4 9 83 9.83171 83 1 98 83225 83252 83 2 8o 5 5 5 6 6 10. 16829 16802 i6 77 5 16748 16720 10.08228 08237 08245 08254 08262 I 2 2 2 2 9.91772 91763 9 I 7 55 91746 9 i 7 38 5o 49 48 47 46 i5 16 17 18 !9 7 26 o 25 52 25 44 a5 36 a5 28 4 34 o 34 8 34 16 34 24 34 32 9 . 7 5o36 7 5o54 7 5o 7 3 75091 7 5i 10 5 5 5 6 6 10.24964 24946 24927 24909 24890 9.83307 83334 8336i 83388 834 1 5 7 8 8 9 10. 16693 16666 i663 9 16612 16585 10.08271 08280 08288 08297 o83o5 2 2 2 3 3 9.91729 91720 91712 91703 91695 45 44 43 42 4i 20 21 22 23 24 7 25 20 25 12 25 4 24 56 24 48 4 34 4o 34 48 ' 34 56 35 4 35 12 9.75128 75 1 47 75 1 65 75 1 84 75202 6 6 7 7 7 10.2487:* 24853 24835 24816 24798 9-83442 834 7 o 83497 835?.4 8355 1 9 9 10 10 ii 10. i6558 i653o i65o3 16476 16449 io.o83i4 o8323 o833i o834o 08349 3 3 3 3 3 9.91686 91677 91669 91660 9i65i 4o 3 3-7 34 91495 91486 91477 20 '9 ib 17 16 45 46 47 48 49 7 22 21 52 21 44 21 36 21 28 4 38 o 38 8 38 1 6 38 24 38 32 9 . 7 558 7 756o5 7 56^4 7 5642 7 566o i4 14 i4 i5 i5 i 0.2 44 i 3 24395 243 7 6 24358 2434o 9. 84 119 84 1 46 84i73 84200 84227 20 21 21 22 22 10.16881 1 5854 15827 i58oo i5 77 3 io.o853i o854o o8549 o8558 o856 7 7 7 7 7 7 9.91469 91460 9 i45i 91442 9 i433 i5 i4 i3 12 I I 5o 5i 5a 53 54 7 21 20 21 12 21 4 20 56 20 48 4 38 4o 38 48 38 56 39 4 39 12 9 . 7 56 7 8 7 56 9 6 757i4 7 5 7 33 7 5 7 5. i5 16 16 16 '7 10.24322 24304 24286 24267 24249 9.84254 84280 843o 7 84334 8436 1 23 23 23 ii 10.15746 15720 i56 9 3 i5666 i563 9 10.08575 o8584 o85 9 3 08602 086. 1 1 7 8 8 8 9.91425 91416 91407 91398 9I 38 9 10 6 55 56 57 58 5 9 60 7 20 4o 2C 32 20 24 20 1 6 20 8 20 o 4 39 20 39 28 3 9 36 39 44 3 9 5? 4o o 9. -75769 75 7 8 7 7 58o5 7 58a3 7 584. 7 585 9 '7 17 17 18 18 18 10. 2423 i 242l3 24195 24177 24 1 59 24141 9-84388 844 1 5 84442 8446 9 84496 84523 25 25 26 26 27 27 10. i 56 i 2 i5585 i5558 i553i i55o4 15477 10.08619 0862* o863 7 o8646 o8655 08664 8 8 8 8 9 9 9 . 9 i38i 91372 91 363 9i354 9i345 9 1 336 5 4 3 2 I M Hour p . M .1 Hour A -M . Cosine Diff. Secant. Colangcnt|Diff. Tangent. Cosecant. Diff. Sine. !W 134' A A B ] 3 C Seconds of time . . . 1 s 2 s 3" 4' 5 1 6' 7 s (A Prop, parts of co]s. < B (c 3 i 5 7 2 7 10 3 9 i4 4 1 1 17 5 M 7 16 24 8 C 55 TABLE XXVII. Log. Sines, Tangents, and Secants. A A B B a 144 : o.i5477 i545o 1 5424 15397 i53 7 o 0.08664 08673 08681 08690 08699' 9-84657 84684 84711 84738 84764 o.i5343 1 53 1 6 15289 0.08708 08717 08726 o8 7 34 08743 9-8479 848 1 8 84845 84872 84899 18 4o 18 32 18 24 18 16 18 9-849 84962 84979 85ooe 10.0884 o885 o885 0886! 08877 10.08886 08896 08904 08913 08922 9 .85i 9 8622 8624 852731 12 853oo! i3 i a 9.8532 7 85354 8538o 85o- 9-7639 764 1 3 7 643 7 6448 76466 o.i 454o i45i3 1 4486 i446o i4433 o.235i6 9 .8546o 9.76484 76601 76619 76637 7 6554 9.7667: 7 65 9 c 76607 7662^ 7664^ 8548- 855i4 85540 86667 9.86694 8562C 8564- o.i44o6 i438o i4353 14246 l4220 i4i 9 3 14166 85 7 8c 858o 7 8583^ 9 .8586c 86887 85i3 0914 ___ ToTom^sl 09,68 09177 9 i o.i 4007 i3 9 8< i3 9 54 1 302-3 i3oo 9.8699 8602 86o4 86073 9 . 7 683 7 685 7687 7688 7 6 9 c 7695 09186 09196 09204 Cosecant. 86100 26 86126 2 7 60 53 91566 1 5? 9.267 6 9.91348 5ol 91239 49 91230 48 91221 91212 461 9.91203 45 91 194 44 91185 43 91176 42 91 167 4 .9ii58|4d| 91 149! 3o 9ii4it38l 91.32 3 7 I __ 36 .91 i i4 35 9iio5|34 9>Q6 3 91087! 3a 9 io 7 8 3i . 9 io6 9 |3o| 91060! 9 io5i 91042 27 9 io33 26 9.91023 s! 9 1 oo 5 i 23 9 99 6 2.2 __909_8_7 9.9097820 90969! 19 9 o 9 6 9 o 9 5i 9.90933 90924 909,6 90906 90896]^ 9^0887 9 c,8 7 8 90869 90860 | 7 1 , - " 1 s 4)8 3' 4 s 5 s 6' 7 f A 2 4 7 9 1 1 i3 | Prop, parts of cols. | B (c 3 i 7 2 10 3 i3 5 17 6 20 7 23 8 j M Hour A.M. TABLE XXVII. [Page 221 Log. Sines, Tangents, and Secants. G '- A A B B C C 143 Hour P.M. Sine. Off. Cosecant. Tangent. Diff. Cotangent Secant. Diff. Cosine M 60 5? 56 i 2 3 4 6 8 .0 i . 12 i3 7 12 o I I 52 n 44 u 36 ii 28 4 48 o 48 8 48 16 48 24 48 82 9.76922 7 6 9 3 9 76957 76974 76991 o o I I I 10.28078 28061 23o43 28026 28009 9.86.26 861 53 86.79 86206 86232 i i 2 i o.i 38-74 i384 7 18821 18794 13768 i o . 092.04 092 1 3 09228 09282 0924. o o o 9.90-796 90787 90777 90768 90759 7 1 1 20 II 12 II 4 10 56 10 48 4 48 40 48 48 48 56 49 4 49 (2 9.77009 77026 77043 7706. 77078 I 2 2 2 3 10.22991 22974 22957 22989 22922 10.22905 22888 22870 22.853 22836 9.86259 86285 86812 86338 86365 ?. 3 4 4 18688 18662 i3635 10.09250 09259 09269 09278 09287 I I I I 9.90750 90741 90781 90722 907.8 55 54 53 52 5. 7 10 4o 1O 32 10 24 10 16 10 8 4 49 20 49 28 49 36 49 44 49 62 9.77095 77. 12 77i3o 77147 77 '64 3 3 3 4 4 9.86892 864 1 8 86445 864 7 > 86498 4 5 5 6 6 io.i36o8 i3582 i3555 13529 i35o2 10.09296 09806 098.5 09824 o 9 333 2 2 2 2 2 9.90704 90694 9068 5 90676 90667 5o 49 48 47 46 1 5 16 17 1 8 '9 7 10 o 9 52 9 44 9 36 9 28 4 5o o 5o 8 5o .6 5o 24 5o 82 9.77181 77 "99 77216 77>33 4 5 5 5 5 6 6 6 7 7 10.22819 22801 22784 22767 22750 9-8659.4 8655. 865 77 86608 86680 7 7 7 8 8 10.18476 1 3449 13428 13897 18870 10.09848 09852 09861 09870 09880 2 2 3 3 3 9.90657 90648 90689 90680 90620 45 44 43 4* 4i 90 21 22 9.3 24 7 9 20 9 12 8 56 8 48 4 5o 4o 5o 48 5o 56 5i 4 5l 12 9.77268 77286 77302 77819 77886 10.22782 227.5 22698 2268. 22664 9.86656 86683 86709 86 7 36 86762 9 9 10 IO 1 1 10. i 3344 i33i 7 18291 1 3264 i3 2 38 10.09889 09898 09408 094 1 7 09426 3 3 3 4 4 9.90611 90602 90592 90583 90574 4o 39 38 37 36 25 26 2 7 2.8 29 7 8 40 8 32 8 24 8 16 8 8 4 5 1 20 5i 28 5i 36 5i 44 5i 52 9 .77353 77870 7738 7 774o5 77422 7 8 8 8 10.22647 22680 226.3 22595 22578 9.86789 8681 5 86842 86868 86894 1 1 i . 12 12 i3 o CO Co Co CO CO a Co en co 1-1 ' (o co en 10.09435 o 9 445 9 454 09468 09473 4 4 4 4 5 9.90565 9o555 90546 9 o53 7 90527 35 34 33 32 3i 3o 81 39 33 34 780 7 52 7 44 7 36 7 28 4 52 o 52 8 52 16 52 24 52 32 9.77489 77456 77473 77490 775o7 9 9 9 .21 IO.2256. 22544 22527 225.0 22498 9.8692. 86947 86974 87000 87027 i3 M i5 i5 10. 18079 i3o53 13026 1 3 ooo 12978 10.09482 09491 09501 09510 09520 5 5 5 5 5 9.90518 90509 90499 90490 90480 3o 29 28 27 26 35 36 3 7 38 39 7 7 20 7 12 7 4 6 56 6 48 4 52 40 52 48 52 56 53 4 53 12 9.77524 7754i 77558 77592 10 10 1 1 u ii 10.22476 22459 22442 22425 224o8 9.87053 87079 87106 87182 87 1 58 i5 16 16 17 17 10.12947 12921 12894 12868 12842 10.09529 o 9 538 09548 09557 09566 5 6 6 6 6 9.904-71 90462 90452 90448 90434 25 24 23 22 2. 4o 43 44 7 6 4o 6 32 6 24 6 .6 6 8 4 53 20 53 28 53 36 53 44 53 52 9.77609 77626 77643 77660 77677 i . 12 12 12 13 IO.2239I 223 7 4 2235 7 22840 22323 IO.223o6 22289 22272 22256 22289 9.87185 87211 8 72 38 87264 87290 18 18 18 '9 10. I28l5 12789 12762 12786 12710 10.09576 o 9 585 09595 09604 09614 6 6 7 7 7 9.90424 904.5 90896 9 o386 20 19 18 '7 16 45 46 47 48 49 760 5 52 5 44 5 36 5 28 4 54 o 54 8 54 16 54 24 54 32 9.77694 777U 777 28 77744 77761 13 i3 i3 i4 i4 9.873,7 8 7 343 87869 87896 87422 20 20 21 21 22 10.12688 i265 7 12681 12604 12578 10.09623 09632 09642 oo65i 09661 7 7 7 7 8 9.90877 90868 908 58 90849 90889 i5 id i3 12 II 5o 5i 59 53 54 7 5 20 5 12 5 4 4 56 4 48 4 54 4o 54 48 54 56 55 4 55 12 9.77778 7779 5 778.2 77829 77 846 i4 i5 i5 i5 1 5 IO. 22222 22205 22188 2217. 22 I 54 9-87448 87475 87501 8 7 554 22 22 23 23 24 10.12559. 12525 12499 12478 12446 10.09670 09680 09689 09699 09708 8 8 8 8 8 9.90880 90820 9o3u 9o3oi 90292 10 6 55 56 57 58 r 9 60 M 7 4 4o 4 32 4 24 4 16 4 8 4 o 4 55 20 55 28 55 36 55 44 55 52 56 o 9.77862 77879 77896 779.8 77980 77946 16 16 16 16 17 Diff. 10.22.38 22.21 22104 22087 22070 22054 9 .8 7 58o 87606 8 7 633 8 7 65 9 8 7 685 87711 24 25 25 26 26 26 Diff 10.12420 12894 12867 12841 i23i5 12289 10.09718 09-72-7 09 7 3 7 09 7 46 o 97 56 09-765 9 9 9 9 9 9 Diff. 9.90282 90273 90268 90254 90244 90285 5 4 3 2 I M Hour P.M. Hour A.M. Cosine. Secant. Cotangent Tangent. Cosecant. Sine. [2(> A A B B C C 50 Seconds of time . . ! o. 3* 4. 5" 6 s 7" f (A 2 4 6 9 ii i3 i5 Prop, parts of cols. < B 3 7 10 r3 17 20 23 (c i 4 5 6 7 8 l '' l * ea231 TABLE XXVII. Log. Sines, Tangents, and Secants. G ' i7 A A B B C C 142 C .\1 lour A.M. lour P.M. Sine. Diff. Josecant. Tangent. >ft" ( Cotangent Sec-ant. Jiff. Cosine. I o 2 3 4 5 6 7 8 9 7 4 o 3 52 3 44 3 36 3 28 4 56 p 56 8 56 16 56 24 56 32 9-77946 77963 77980 77997 780 1 3 o i i i 22054 22037 22020 22003 21987 9.87711 8 77 38 8 77 64 878171 i 2 o. 1 2289 12262 12236 I22IO I2i83 o.o 97 65 o 977 5 97 84 o 979 4 o 9 8o3 o .90235 90225 90216 00206 oo, 9 7 o 8 7 6 5 3 7 3 20 3 12 3 4 2 56 2 48 4 56 40 56 48 56 56 5 7 4 5 7 12 9-78o3o 78047 7 8o63 78080 78097 i 2 2 2 2 0.21970 21953 21937 21920 21903 9.8-7843 8 79 48 j 4 12l3l 12105 12078 12052 o.o 9 8i3 051822 o 9 832 o 9 84i o 9 85i 2 2 2 2 2 .90187 910178 00168 90159 9 o 1 4 9 10 1 1 12 .3 i4 7 2 4o 2 32 2 24 2 |6 2 8 4 5 7 20 5 7 28 5 7 36 5 7 44 5 7 52 9.78113 78i3o 78147 78 1 63 78180 3 3 3 4 4 0.21887 21870 2i853 2i83 7 21820 88000 8802-7 88o53 88o 79 4 5 5 6 6 O.I2026 12000 II973 II 9 47 II921 io.o 9 86i o 9 88o o 9 88 9 o 9 8 99 7.90139 oo 1 3o 90120 901 n 90,01 5o [ 9 48 47 i5 16 i 7 18 9 ? * 2 44 36 28 4 58 o 58 8 58 16 58 24 58 32 9.78197 782,3 782.46 78263 4 4 5 5 5 io.2i8o3 21787 21770 21754 9 .88io5 88i3, 881 58 88.84 88210 7 7 8 8 0.11895 11869 II842 Il8,6 11790 10.09909 09918 09928 0993-7 o 99 47 2 3 3 3 3 9.90091 90082 90072 90063 900 5 3 45 44 43 42 20 21 22 23 24 7 20 12 o 56 o 48 4 58 4o 58 48 58 56 5 9 4 5 9 12 9.78280 78296 7 83i3 7 832 9 7 8346 5 6 6 6 7 10.21720 21704 21687 21671 21 654 9. 88236 88262 88289. 883 1 5 8834, 9 9 IO 10 IO o . i i 764 1 1738 117, i 1 1 685 11659 10.09967 09966 09976 09986 o 999 5 3 3 4 4 4 9.90043 90024 900 I L 9 ooo5 4c 3 9 38 36 25 2 7 28 29 7 o 4o 32 2^ o 16 o 8 4 5 9 20 5 9 28 5 9 36 5 9 44 5 9 52 9. 7 8362 78379 7 83 9 5 78412 78428 7 7 7 8 8 io. 21 638 21621 2i6o5 2i588 2,5 7 2 9 .8836 7 $83o3 88420 88446 884 7 2 II II 12 12 13 io. i i633 11607 n58o ii 554 1 1 528 lO.loooS iooi5 10024 4 4 4 9 .89995 8 99 85 8 997 6 8 99 6f 89956 35 34 33 32 3i 3o 3i 32 33 34 35 36 37 38 39 700 6 5 9 52 5 9 44 5 9 36 5 9 28 5 o o o 8 o 16 o 24 32 9-78445 7846, 78478 78494 7 85io 8 9 9 9 9 io.2i555 21539 21622 2i5o6 21490 9 .884 9 8 88524 8855o 885 77 886o3 i3 i4 i4 i5 IO. I l5o2 11476 1142^ 11397 io. ioo5; 1006; 1007; 10082 10092 9 .8 99 4 7 8 99 3 7 8 99 2 7 8 99 ,8 8 99 o8 2 9 2.8 2 7 26 6 59 20 5 9 12 59 / 58 56 5b 48 5 o 4o o 48 o 56 L 12 9.78527 7 8543 7 856o 7 85 7 6 7 85 9 2 10 10 IO 10 II 2i45 7 2i44o 2142^ 21408 91.88629 88655 88681 88 7 o 7 88 7 33 i5 16 16 17 '7 io. i i3 7 u 345 i;3io 1129; II267 IO. 10102 IOII2 IOI2I ioi3i ioi4i 6 6 6 6 6 9 .8 9 8 9 8 89888 89879. 89869 8 9 85 9 a5 24 23 22 2 I 4o 4i 42 43 44 6 58 4o 58 32 58 24 58 16 58 8 5 20 28 36 44 52 9. -78609 -78625 78642 7 8658 7 86 7 4 II II I0.2l3 9 l 2i3 7 5 2 1 358 2 I 342 2l320 9 .88 7 5 9 88 7 86 88812 88838 88864 17 18 18 '9 '9 10. I 124 iu8 1116 iu36 io.ioi5i 10160 10170 10180 10.10195 10205 10215 10225 10235 b 7 7 7 7 9 .8 9 84 9 8 9 84o 8 9 83o 89820 8 9 8io 2O '9 18 '7 16 45 46 4 7 48 49 6 58 o 5 7 52 5 7 44 5 7 36 5 7 28 520 2 8 2 16 2 It 2 32 9.7869, 78707 78723 78739 7 8 7 56 1 3 i3 i3 io.2i3o5 2 I 2 9 : . 2I2 77 2126 2 I 24/ 9.88890 88 9 i6 88 9 42 88 9 68 88 99 4 20 2O 20 21 21 ,0.1 I I 10 I10& iio3 11006 7 8 8 8 8 8 8 9 9 9 .8 9 8o 8979 8 97 8 8 9 77 8 97 6 ,4 .3 12 1 1 5o 5i 52 53 V 6 5 7 20 5 7 12 5 7 4 56 56 56 48 5 2 4o 2 48 2 56 3 4 3 12 9.78772 78788 788o5 78821 7 883 7 i4 i4 i4 ! l5 i5 10.21228 2I2I9 21 I 9 5 21 1 7 9 9.80020 8 9 o46 8 9 o 7 3 8 9 o 99 8 9 i25 22 22 23 '23 24 io 9 5^ 1092 1090 io8 7 10.10248 10258 10268 10278 10288 10.10298 io3o 7 io3i 7 10327 io33 7 io347 Cosecant 9 .8 97 52 8 97 42 8 97 32 89722 897.2 1C \ 1 6 55 56 5 7 58 5 9 60 6 56 40 56 32 56 24 56 16 56 8 56 o 5 3 20 3 28 3 36 3 44 3 52 4 o 9.788.53 78869 -78886 78902 78918 78934 i5 i5 16 16 16 16 10.21 4 7 2Il3 21 I 1^ 21098 21082 21066 Secant 9.89161 8 9 i 77 8 9 2o3 8 9 22 9 8 9 255 89281 Cotangent 24 24 25 25 26 26 Din" io.io84 9 1082 1079.7 1077 1074 Tangent 9 9 9 9 10 10 DhT 9.89702 8 9 6 9 3 8o683 8 9 6 7 3 8066 8 9 G5 Sine. 4 3 j. Hour I>.M jHourA.M. A A B B C C 52 Prop, parts of cols 5' 38 T TABLE XXV11. [I'age223 Log. Sines, Tangents, and Secants '" A A B B C C 141 Hour A.M. Hour I'.M Sine. Diff. Cosecant. Tai.gent. Diff. Cotangent Secant. Diff. Cosine. M o 6 56 o 55 52 55 44 55 36 55 28 5 4 o 4 8 4 16 4 24 4 32 9.78934 o 78950! 78967 I 78983 I 78999) * 10.21066 2io5o 2io33 21017 2IOO1 SO CO CO CO CO CO sO sO sO sO sO Co Co CO Co (0 CO en Co O Co enso co^j *- o I I 2 i o. 10719 10641 io6i5 IO.io347 io35 7 io36 7 io3 7 6 io386 O 9.89653 8 9 643 8 9 633 8o6 2 / 8 9 6i4 60 5 9 58 57 56 6 6 55 20 55 12 55 4 54 56 54 48 5 4 4o 4 48 4 56 5 4 5 12 9.79015 7 oo3 1 79047 79063 797V 9.79096 79111 79128 79144 79160 I 2 2 2 2 io.2o 9 85 20969 20953 20937 2092 1 9 . 894 1 1 8 9 43 7 89463 89489 8 9 5i5 2 3 3 3 4 10.10589 io563 io53 7 io5ii io485 10. io3 9 6 10406 10426 io436 2 9 . 8960^ 8 9 5 9 4 8 9 58/ 8 9 56^ 55 54 53 52 5i 10 i 12 i4 6 54 4o 54 32 54 24 54 16 54 8 5 5 20 5 28 5 36 5 44 5 52 3 3 3 3 4 10.20905 20889 20872 20856 20840 9. 8 9 54 i 8 9 56 7 8 9 5 9 3 89619 8 9 645 4 5 5 6 6 10. io45 9 io433 10407 io38i io355 10. io446 io456 10466 104-6 10486 2 2 2 2 2 XT xr XT XT XT Im XT oo CN in in in in in O O O O O CO OO CO OO CO 5o 49 48 47 46 16 18 19 20 21 22 24 54 o 53 52 53 44 53 36 53 28 5 6 o 6 8 6 16 6 24 6 32 9.79176 79192 79208 79224 79240 4 4 5 5 5 5 6 6 6 6 10.20824 20808 2.0792 20776 20760 9.89671 89607 89723 8 9 74 9 8 9 775 6 7 7 8 8 9 9 10 10 IO io.io32 9 io3o3 10277 I025l IO225 io.io4 9 6 io5o5 io5i5 io535 3 3 3 3 3 9 .8 9 5o4 8 9 4 9 5 8 9 485 8 9 4 7 5 8 9 465 45 44 43 42 4i 36 6 53 20 53 12 53 4 52 56 52 48 5 6 4o 6 48 6 56 7 4 7 12 9-79256 79272 79288 79304 79319 10.20744 20728 20712 20696 20681 9.89801 89827 8 9 853 8 9 8 79 89906 io.ioi 99 10173 10147 IOI2I ioo 9 5 10. io545 io555 io565 io5 7 5 io585 3 4 4 4 4 9 . 8 9 455 89445 8 9 435 89425 894 1 5 25 27 28 29 6 52 4o 52 32 52 24 52 16 52 8 5 7 20 7 28 7 36 7 44 7 52 9.79335 79 35. 79383 79399 7 7 7 8 io.2o665 20649 20633 20617 20601 9. 8 99 3 i 89957 8 99 83 90000 9 oo35 II II 12 12 13 10. ioo6 9 10043 10017 09991 o 99 65 io.io5 9 5 io6o5 io6i5 10625 io636 4 4 5 5 5 9.89405 8 9 3 9 5 8 9 385 8 9 3 7 5 8 9 364 35 34 33 32 3i 3o 35 36 38 39 6 52 o 5i 52 5i 44 5i 36 5 1 2.8 5 8 o 8 8 8 16 8 24 8 32 7943 1 79447 79463 79478 9.79494 795io 79526 79542 79558 8 8 8 9 9 io.2o585 2o56o 20553 2o53 7 20522 9.90061 90086 90112 9oi38 90 1 64 i3 i3 i4 i4 i5 i5 16 16 16 17 io.o 99 3 9 o 99 i4 o 9 888 o 9 862 o 9 836 10.10646 io656 10666 io6 7 6 10686 5 5 5 6 6 6 6 6 6 7 9 .8 9 354 8 9 344 8 9 334 8 9 3M 3c 27 26 6 5 1 20 5l 12 5i 4 5o 56 5o 48 5 8 40 8 48 8 56 9 4 9 12 9 10 IO IO 10 io.2o5o6 20490 2o4 7 4 2o458 20442 9.90190 90216 90242 90268 90294 10.09810 09784 o 97 58 00732 09706 io.io6 9 6 lojod 107/16 107/26 io 7 36 9.89304 89294 89284 89274 89264 25 24 23 22 21 4o 4i 42 43 44 6 5o 4o 5o 32 5o 24 5o 16 5o 8 5 9 20 9 28 9 36 9 44 9 52 9.79573 79 58 9 7 9 6o5 79621 7 9 636 II II II II 12 IO.2O42 7 2041 1 20395 2o3 7 9 2o364 9.90320 90346 903- 1 9 o3 97 90423 18 18 T 9 10.09680 09654 09629 09603 09577 10.09551 09525 00499 09473 09447 10.107/46 io 7 56 10767 10777 10787 7 7 7 7 7 XT XT oo oo oo in XT oo CN CN Oi OJ 0) 0) O O O O O OO CO CO CO CO 20 ; 8 9 17 16 45 46 47 48 49 6 5o o 4 9 52 4 9 44 49 36 49 28 5 10 o 10 8 10 16 10 24 10 32 9 .7 9 65a 79 668 79684 79699 797 1 5 12 12 12 13 i3 10.20348 2o33s 2o3i6 2o3oi 20285 Om t~~oo XT r- o CN in XT XT m m m O O O O O 20 2O 21 21 10. IO7 9 7 10807 10817 10827 io838 8 8 8 8 8 9.89203 89193 8 9I 83 89173 89162 i5 i4 i3 12 1 I 5o 5i 5 a 53 54 55 56 57 58 5 9 60 M 6 4 9 20 49 12 49 4 48 56 48 48 5 10 4o 10 48 10 56 ii 4 II 12 9.79731 79746 79762 79778 7979 3 i3 i4 i4 i4 io.2o r >6 9 20254 20238 20222 2O2O7 9.9057/8 90604 9 o63o 9 o656 90682 22 22 22 23 23 "24 24 25 25 26| 26 1 10.09422 09396 09370 o 9 344 09318 10.10848 io858 10868 10878 10888 8 9 9 9 9 sO OO 00 CO CO 00 sO SO sO sO so to Co Ix en IO SO !0 10 K> I IO 7 6 4 3 2 I 6 48 4o 48 32 48 24 48 16 48 8 48 o 5 II 20 II 28 ii 36 ii 44 I I 52 12 9.79809 79825 70840 79856 79872 79887 i5 i5 i5 i5 16 16 0.20191 20I 7 5 20l6o 20144 20128 201 l3 9 . 907/08 90734 90759 9 o 7 85 9081? oo83 7 10.09292 09266 09241 002 1 5 o 9 i8 9 OQIOO 10. io8 99 io 9 o 9 io 9 i 9 IO 9 2 9 io 9 4o io 9 5o 9 9 10 10 10 IO y. 89101 89091 89081 89071 89060 89050 lour P.M. lour A.M. Cosine. Diff. Secant. Cotan-ent|Diff.| Tangent. >osecp.nt. )iff. Sine. M 128 C 51 Seconds of" time 1 s 2* :3 S 4' 5' 6 s 7' !A 2 4 6 8 10 12 i4 B 3 6 10 ,3 16 '9 23 .C 1 3 4 5 6 8 9 r 3! age 2-24] 1 TABLE XXVII. Log. Sines, Tangents, and Secants. A A B B C C 140 M [Hour A. M.I Hour c.M. i Sine, r )iff. )secant. Tangent. I itf. (Cotangent Secant . D iff. < Cosine. M i 3 4 ~ r I 1 6 48 o 47 52 47 44 47 36 47 28 5 12 C 12 8 12 16 I> 24 12 32 >. 79887 79903 79918 79934 79950 o I I I .20113 20097 20082 20066 200 5o 9.90837 9<)863 90889 909 1 4i 90940] i o . 09 , 63 09137 09, ii 09086 09060 0.10950 10960 10970 10980 10991 o 9 .8oo5o 60 8ox>4o 59 8 9 o3o 58 89020 57 89009 56 6 47 20 47 12 47 4 46 56 > 46 48 5 12 4o < 12 48 12 56 i3 4 l3 12 7.79965 79981 79996 800 1 2 80027 I 2 2 2 2 .2oo35 20019 2000^ 19988 19973 9.90966 90992 91018 91043 91069 10.09034 09008 08982 08957 0893, 0. I ,001 IIOI I I 1022 II032 II042 S .88999 55 88989 5^ 88978 88968 88 9 58 N ! 1 ' K n > 6 46 4o 46 32 > 46 24 5 46 16 i 46 8 5 i3 20 1 3 28 i3 36 i3 44 i3 52 8oo58 80074 80089 8oio5 3 3 3 3 4 o. i 99 5 7 19942 19926 199, 1 19895 9.9,095 91 ,21 9II47 9II72 91198 10.08905 08879 o8853 08828 08802 O.I 1052 no63 11073 iio83 11094 2 : < l\ 2 2 , .88948 88937 88927 889,7 88906 i H i i. i i 6 46 o 3 45 52 7 45 44 3 45 36 ? 45 28 5 i4 o i4 8 i4 16 i4 24 i4 32 c. 80120 80, 36 8oi5i 80166 80182 4 4 4 c c 0.19880 19864 i 9 84 9 i 9 834 19818 9.91224 91250 91276 9i3oi 91327 10.08776 08750 08724 08699 08673 o.i no/ inn II 125 iu35 ni45 3 3 3 3 3 9 88896 88886 888 7 5 88865 88855 2 2 ?. 2 'j. 3 6 45 20 , 45 12 2 45 4 3 44 56 4 44 48 5 1 4 4o i4 48 i4 56 i5 4 l5 12 9.80197 802 1 3 80228 80244 80259 e 6 6 6 0.19803 19787 19772 19756 19741 9 . 9 i353 9 !^ 9 9 i43o 9i456 10.08647 9 0862 i 9 o85 9 6 io 08570 io o8544 o.i i i 56 11166) 11176 11187 11197 3 4 4 4 4 4 5 5 5 5 9.88844 88834 88824 888,3 888o3 2 2 5. 2 2 5 6 44 4o 6 44 32 7 44 24 8 44 16 9 44 8 5 1 5 20 i5 28 i5 36 i5 44 i5 52 5 16 o 16 8 16 16 16 24 16 32 9.8027^ 80290 8o3o5 8o320 8o336 6 0.19726 1971 1969 1968 1966 9.91482 91507 9 ,533 9 ,559 9 i585 i i io.o85i i i 0849 i 2 0846 12 o844 12 o84i io. i 1207 11218 11228 II23 9 11249 9 .887 9 3 88782 88772 88761 88 7 5i 3 3 3 i / i i < , o 6 44 o i 43 52 2. 43 44 3 43 36 4 43 28 9 .8o35 8o366 8o382 80397 8o4i' 10.196^ i 9 63 19618 1 960.3 19588 9.91610 9 ,636 91662 9,688 91713 1 3 io.o83- 7 i 3 o836 i 4 o833 i4 o83i i 5 0828 10,11259 11270 11280 11291 ii3oi b 5 6 6 6 6 6 6 7 7 9.8874, 88 7 3o 88720 88709 88609 5 6 43 20 6 43 i 7 43 4 !8 42 5 59 42 4 16 4" 16 48 16 56 17 4 17 12 9.80428 8o44 8o458 80489 10. 19572 i 9 55 7 19542 19527 195, i 9.91739 91765 91791 91816 91842 i5 10.0826 i 5 0823 i 6 0820 16 0818 17 o8i5 IO.Il3l2 II322 ii332 1 1 343 n353 9.88688 88678 88668 88657 88647 5 4 3 9 31 io 6 42 4 {i 42 3 42 42 2 13 42 i i4 42 ,7 2O I 7 28 17 36 17 44 17 52 9.8060^ 8o5 9 8o55< 8o565 i o . i 9496 19481 19466 19435 9- 91868 9 ,8 9 3 919,9 9,945 9'97 17 Iio.o8i3 18 08,0 i 8 0808 i 8 o8o5 1 9 1 080 '!!3 7 ^ n385 ii3 9 5 u4o 7 7 7 7 8 0.88636 88626 886,5 886o5 885 9 4 45 6 42 47 4i 4 48 4 1 3 49 4i 2 s 18 o 18 8 18 16 18 24 18 32 9 .8o5c 8o5 9 < 806 K 8o6a 8o64 \ 10. i942c i 9 3 9 c i 9 375 9- 9 9202; 9204*: 9207. 9 20 9 C 9212' 92 1 5( 92I7( 9220 9222 19 10.0800-; 20 0797 20 079 21 079 21 079 Il42" ii43- 1 1 44 ii45^ 8 8 8 8 9 9 9 9 9 9 10 10 10 IO 10 10 Dif 9.88584 885v3 88563 88552 88542 DOC: 5o 6 4i 2 5i 4i i 52 4i 53 4o 5 54 4o 4 5 1 8 4< 18 48 18 5t 19 L 19 i; 9 .8o65( 8067 > 8o68( 8070 807, ( io.i 9 34^ 1 9 32C 1 93 1 L I 9 2 9 C 1928^ io. i926c 1 92 5; I 9 23f 1922, 1920? 1919 f. Secant. _.. A ) 21 10.0787^ ) 22 0785i ) 22 0782^ i 23 0779* 7 23 0777^ 10. I > ii n ! i i n 4S 47? 4 9 < So 5 1 52: 53: 54 55 50. [57 ^IMlt 8852. 885io 88499 8848 9 55 6 4o 4 56 40 3 57 4c> 2 58 4o i 5.; 4o 60 4o 5 19 2C 19 2 19 3( 19 4^ 19 5 20 < > 91.8073 > 8074 > 8076 i 8077 i 8079 5 8o8c i 3 ,4 2 15 7 i- 2 if 7 1^ 9 9225 9227 9230 9 233 9 235 9238 Cotangei B 3 24 10.0774' ^ 24 0772 4 a4 0769^ D 2 5 O767( 5 25 0764^ i 26 0761 ( v l ~- " t'Diff.' Tangent B 1 10. I i ) i ) i i i ? L Cose ~~~c 9.00470 88468 8845 7 88447 I 88436 ! 88425 '. Sine. * C 1V1 Hour P. He >ur A.M . Cosine. L) t \ t A Seconds of time ! %2- 3 s 4 s io i3 4 5 5* 10 16 7 6 s 12 8 7' 1 3 23 9 ( A Prop, parts of cols. 1 B \ C 2 3 i 4 6 3 S'. 40' M O y 3 5 6 -7 8 9 ! 1 1 I 2 13 1 4 i5 16 17 18 '9 TABLE XXVII. P**** 3 Log. Sines, Tangents, and Secants. ** A A B B C C 139 Hour A.M. 6 4o o 39 52 39 44 3 9 36 3 9 28 Hour P.M. Sine. Diff. Cosecant. Tangent. Diff.jCotangent Secant. Diff. Cosine 31 5 20 c 20 8 20 l6 20 24 2O 32 9.80807 80822 8o83 7 8o852 8o86 7 O o I 10.19193 19.78 19.63 19148 i 9 i33 9.92.381 92407 92433 92458 92484 o o I I 2 10.07619 07593 o 7 56 7 o 7 542 o 7 5i6 io.u5 7 5 n585 1 15 9 6 11606 11617 9.88425 88^.5 884o4 883 9 4 88383 6c 3 5" 55 6 39 20 5 20 4o 39 12; 20 48 39 4; 20 56 38 56! 21 4 38 40 21 12 9.80882 80897 80912 80927 80942 I I 2 2 2 10.191 iy 19.08 19088 I90 7 3 I 9 o58 9.92510 92535 92561 92.587 926.2 2 3 3 3 4 10.07490 o 7 465 o 7 43 9 o 7 4i3 o 7 388 10.11628 1 1 638 ii64 9 11660 1 1670 I 2 9 . 88372 88362 8835. 8834o 8833o 55 54 53 52 5i 6 38 4o 38 32 38 24 38 16 38 8 5 21 20 21 28 21 36 21 44 21 52 9.8095-7 809-72 8098-7 81002 8ioi 7 2 3 3 3 3 10. .9043 19028 190.3 18998 18983 9.92.638 92663 92.689 92715 92. 7 'io 4 5 6 6 io.o 7 362 o 7 33 7 o 7 3.i o 7 285 0-7260 10. 11681 11692 II 7 02 n 7 i3 11-724 2 2 2 2 9 883i 9 883o8 88298 88287 88276 5o 49 48 47 46 6 38 o 3 7 52 3 7 44 3 7 36 3 7 28 5 22 22 8 22 l6 22 S.4 22 32 9.81032 8 1 04-7 81061 8io 7 6 81091 4 4 4 4 5 ~ 5 5 6 6 10.18968 i8 9 53 .8 9 3 9 18924 18909 9-92 7 66 9 2 79 2 9 28. 7 9 2843 9 2868 6 8 8 10.07234 07208 o 7 .83 o 7 .5 7 7 l32 10. i i 7 34 II745 n 7 56 11766 11777 3 3 3 3 3 9.88266 88255 88244 882.34 88223 45 44 43 42 4i 20 21 22 2.3 24 6 3 7 20 3 7 12 3 7 4 36 56 36 48 5 22 40 22 48 22 56 23 4 23 12 9.81106 81121 8n36 8n5i 81166 10.18894 188-79 18864 18849 1 8834 9 . 9 2.8 9 4 9 2 9 2O 9 2 9 45 92971 92996 9 9 9 10 IO I O . O 7 1 06 0-7080 o 7 o55 0-7029 0-7004 10.11788 11799 11809 11820 u83i 4 4 4 4 4 9.88212 88201 8819- 88180 88169 4o 3 3? 37 36 25 26 27 a8 29 6 36 4o 36 3 2 36 24 36 16 36 8 5 23 20 23 28 23 36 23 44 23 52 9.81 180 81195 81210 81225 81240 6 6 7 7 7 10.18820 i88o5 18790 i8 77 5 18760 9.93022 9 3o48 93o 7 3 9 3 99 93 1 24 i . 1 1 12 k I 2 io.o6 97 8 o6 9 52 0692-7 06901 o68 7 6 10. i 1842 11862 1 1 863 11874 1 1 885 4 5 5 5 5 9 .88i58 88 1 48 88i3 7 88 1 26 88 \i'j 35 34 33 32 3i 3o 11 27 26 3o 3i 32- 33 34 6 36 o 35 52 35 44 35 36 35 28 5 24 o 24 8 24 16 24 24 24 32 9.812.54 81269 81284 81299 8i3i4 9.81328 8i343 8i358 8i3 72 8 1 38 7 7 8 8 8 8 10.18746 i8 7 3i 18-7.6 18701 18686 9.93.50 9 3. 7 5 9 32.OI 9 322 7 93252 .3 i3 i4 i4 i4 io.o685o 06825 o6 799 o6 77 3 06748 10. i 1895 11906 11917 11928 ii 9 3 9 5 6 6 6 6 9.88io5 88094 88o83 8807 * 88c6i 35 36 3 7 38 3 9 6 35 20 35 12 35 4 34 56 34 48 5 24 4o 24 48 24 56 ?5 4 25 12 9 9 9 9 10 10. 18672 1 8657 18642 18628 i86i3 9-932 7 8 9 33o3 9 332 9 9 3354 9338o .5 i5 16 16 '7 1O.06 7 22 0669-7 o66 7 i 06646 06620 10. 1:949 1 1960 11971 11982 11993 8 7 7 7 9.8806 i 88o4o 88029 88018 88007 25 24 2.3 22 2 1 2O '9 18 17 1 6 4o 4i 4a 43 44 6 34 4o 34 32 34 24 34 16 34 8 5 25 20 25 28 25 36 25 44 25 52 9.8^402 8i4i 7 8i43i 8r446 81461 10 10 10 1 1 1 1 10.18598 i8583 18569 i8554 i853 9 9 . 93406 9 343, 9 345 7 93482 935o8 17 17 18 18 '9 io.o65 9 4 o656 9 o6543 o65i8 o64 9 2 10.12004 I20l5 12025 I2o36 12047 7 7 8 8 8 9.87996 8 79 85 8 797 5 8 79 64 8 79 53 45 46 47 48 49 6 34 o 33 52 33 44 33 36 33 28 5 26 o 26 8 26 1 6 26 24 26 32 9 .8i4 7 5 81490 8i5o5 8i5. 9 8 1 534 1 1 1 1 12 12 : 2 io.i8525 i85io 18495 18481 1 8466 9. 9 3533 9 355 9 9 3584 o36 . o 9 3636 '9 20 20 20 21 io.o646 7 o644< o64i6 o63 9 o o6364 10. i 2o58 12069 12080 12091 12.02 8 8 8 9 _9_ 9 9 9 10 10 IO 10 10 10 II II 9-8 7 94? 8 79 3i 87920 87909 8-7898 i5 14 [3 12 I 1 5o 5i 52 53 54 6 33 20 33 12 33 4 32 56 32 48 5 26 4o 26 48 26 56 2 7 4 2 7 12 9.8.549 8 1 563 8i5 7 8 8i5 9 2 81607 I 2 i3 i3 i3 i3 10. i 845 i i843 7 18422 18408 18393 9.93661 9 368 7 98712 9 3 7 38 9 3 7 63 21 22 22 23 23 io.o633 9 o63.3 06288 06262 0623-7 10. 12. l3 12 I 23 ' J2i34 12145 I2i56 9.87887 87877 87866 8-855 87844 1 O 9 8 7 6 -? 4 3 2 I O 55 56 '">7 58 5 9 bo 6 32 4o 32 32 32 24 32 16 32 8 32 5 2 7 20 2 7 28 2 7 36 2 7 44 2 7 52 28 o 9.81622 8 1 636 8.65i 8]665 8.680 8169,1 i4 i4 i4 i4 i5 i5 io.i83 7 8 1 8 364 18349 i8335 i832o i83o6 9.93789 9 38.4 9384o 9 3865 939' 9 3 9 i6 23 24 24 25 25 26 10.0621 i 06186 06.60 o6i35 06109 06084 10. 12167 12178 12189 12200 I22II 12222 9.87833 87822 8-811 87800 87789 87778 M Hour P.M.J Hour A.M. Cosine Diff. Secant. Cotangent Diff. Tangent. Cosecant. Dift Sine. M KU) A A B ] B t Seconds of time I s 2 s 3 R 4' 5" 6" 7* - F~ Prop, parts of cols. < B ( C 2 3 4 6 3 6 IO A 7 it 3 5 9 ,6 7 I I '9 8 13 22 C 49 page zan TABLE XXVII Log. Sines, Tangents, and Secants. 41 A A B B C C 138 Cosine. M M i 2 3 4 5 6 8 our A.M. 1 -iourp M. Sine. I Kff. Cosecant. 'angent. (T. Cotangent Secant. )iiV. 6 32 c 3i 5a 3i 44 3i 36 3 1 28 5 28 o 28 8 28 16 28 24 28-32 .81694 81709 81723 81738 81752 o c.i83o6 18291 18277 18262 18248 9.93916 93942 93967 9 3 99 3 940 1 8 o o I I 2 0.06084 o6o58 o6o33 06007 05982 0.12222 12233 12244 12255 12266 o 9 o ll .87778 60 87767 5 9 8 77 56 58 87745 5 7 8 77 34 Sc 6 3i 20 3l 12 3i 4 3o 56 3o 48 5 28 40 28 48 28 56 29 4 29 12 .81767 81781. 81796 81810 81825 I I 2 2 2 c.i8233 18219 18204 18190 18175 9.94044 94069 94096 94120 94 1 46 2 3 3 3 4 0.05956 o593i 05905 o588o o5854 0.12277 12288 12299 I23lO 12321 1 I I I 2 ). 8 77 23 55 87712 5^ 87701 53 87690 & 87679 5 I 2 i3 i4 6 3o 4o 3o 32 3o 24 3o 16 3o 8 5 29 20 29 28 29 36 29 44 29 52 .8i83 9 8i854 81868 81882 81897 2 3 3 3 3 o. 18161 18146 i8i32 18118 i8io3 9.94171 94197 94222 94248 94273 4 5 5 6 6 10.05829 o58o3 o5 77 8 o5 7 52 05727 0.12332 12343 12354 12365 12376 2 2 2 2 3 3.87668 5t 8 7 65 7 4< 8 7 646 4J 87635 4- 87624 4< i5 if 18 19 6 3o o 29 52 29 44 29 36 29 28 5 3o o 3o 8 3o 16 3o 2^ 3o 32 .81911 81926 81940 8i 9 55 81969 4 4 4 4 5 10.18089 18074 18060 i8o45 i8o3i 9- 94299 9 4324 9 435o 943 7 5 94401 6 7 ! 8 8 10.05701 o56 7 6 o565o o5625 05599 0.12387 12399 12410 12421 12432 3 3 3 3 4 9 .8 7 6i3 4 87601 4 8 7 5 9 o 4 87579 4 8 7 568 4 20 21 6 29 20 29 12 29 4 28 56 28 48 5 3o 4 3o 48 3o 56 3i 4 3l 12 9 .8i 9 83 8,998 82012 82026 82041 5 c c K 6 10. 18017 18002 17988 17974 17959 9.94426 9 4452 94477 945o 94528 8 9 9 10 10 o.o5574 o5548 o55 2 3 05497 05472 0.12443 12454 12465 12476 12487 4 4 4 4 4 9.8755 7 4 87546 3 8 7 535 3 8 7 524 3 8 7 5i3 3 2 26 28 29 6 28 4o 28 32 28 24 28 16 28 8 5 3i 20 "3 1 28 3i 36 3i 44 3i 52 9.82055 82069 82084 82098 821 12 b 6 6 7 10.17945 17931 17916 17902 17888 9 9 4554 9 45 7 9 46o 9463 9465 II 1 1 II 12 12 io.o5446 0542 c53o6 05370 o534 10.12499 I25lO I252I 12532 12543 b 5 5 5 5 9 .8 7 5oi 3 87490 3 87479 3 8 7 46S ? 87457 2 !o o k2 3 6 28 o 27 52 27 44 27 36 27 28 5 32 o 32 8 32 16 32 24 32 32 9.82I2& 82l4l 82155 8269 82184 7 8 8 8 10.1787-1 17859 1784 i 7 83 178.6 9 .9468 9470 9 4 7 3 9475 9478 i3 i3 M i4 i4 io.o53i 0529 0526 o524 O52I 10.12554 12566 12577 12588 12599 b 6 6 6 6 7 7 7 7 7 9.8744^ - 8 7 434 5 8 7 423 : 8 7 4i2 : 8 7 4o\ : 36 3 3 3 6 27 20 27 12 27 4 26 56 26 48 5 32 4f 32 48 32 5( 33 4 33 i 9.82198 82212 82226 82240 82255 8 9 9 9 9 10. 1780 1778 1777 1776 1 77 4 9 . 9 48o 9 483 9 485 9 488 9491 i5 i5 16 16 17 10.0519 o5i6 o5i4 o5u oSog IO.I26lC 12622 12633 12644 12655 9 .8 7 3 9 c : 8 7 3 7 S c 8 7 36-> : 8 7 356 : 8 7 345 : 4 4 4 4 4 6 26 4o 26" 32 26 24 26 16 26 8 5 33 2( 33 28 33 3 33 4 33 5 9.82269 82283 82297 823i 82326 10 10 10 10 10 10.1773 1771 1770 1768 1767 9 .9493 9 49" 9 4 9 8 95oi 95o3 17 17 18 18 19 io.o5o6 o5o3 o5or^ 0498 0496 10.12666 12678 12685 I270C 12712 7 8 8 8 8 ~8 9 > 9 ' 9 -9 > 9 i 10 10 1 10 ) 10 ) 10 1 10 f 11 ) II 11 1 II . Diff 9.070^4 8 7 322 8?3n 87300 87288 9-8 7 27 7 87266 87255 87243 87232 9.87221 87209 87.98 87187 87175 o 8 7 i 64 4 4 4 4 4 6 26 o 25 52 25 M 25 36 25 2fi 5 34 34 34 i 34 2 34 3 9 .8 2 34< 82354 8 2 36 82389 82396 II II II II 12 10.1766 1764 i 7 63 176. 1760 9 . 9 5o6 9508 9f 9 5i3 9 5i6 19 20 20 20 21 10.0493 0491 o488 o486 o483 ic 1272, 1273^ I2 7 4? -2 7 5- 1276* 5 5 6 25 2C 25 12 25 4 - 24 X 24 4 5 34 4 34 4 34 5 35 35 i 9.82.4^ 8242^ 8243 S 8a45: 8246- 9.8248 8249^ 8a5oc 8252' 8253- 8255 12 12 ) 12 i3 i3 10.1759 1757 i 7 56 i 7 54 i 7 53 9 . 9 5i9< 9^' 9 524 9526! 9 52 9 21 22 22 3. 22 , 23 10. < < < c ( >48i 5478 5476 3473 3470 3468 ^465 3463 3460 3458 3455 igen 10.1277^ 1279 1280; 1281: 1282? 6c 6 24 4c 24 3i 24 2^ 24 l( 24 * 24 ( 5 35 2 35 2 35 3 35 4 5 35 5 ) 36 i3 > i3 ) i4 i4 i i4 i4 T\:a to. 1751 i 7 5o 1749 1747 1746 1744 9.9531 9534 9536 9539 954i 9544 Cotaiifren 7 23 2 24 3 24 3 25 3 25 i 25 t Difl 10. < < ( < ( < . Tar IO. I20JI 1284- I285C I287C 1288 1289: Cosecant 8- 1 53 87141 87130 87119 87107 ]~Sinc. 131 A A Seconds of time 1 s B 2' 4 6 3 3 s 5 10 4 4 7 i3 6 B ,V 9 16 7 6' ii '9 8 7 s 12 22 irs C 4ff 1 _j (A Prop, parts of cols. < B f C 2 3 T TABLE XXVII. Lrs3W LOOT. Sines, Tangents, and Secants. 12 A A B B C C 137 iii Hour A.M. ,Hour P.M. Sine. ; DifF. Cosecant. Tang-ent. JDiff. Cotangent Secant. Diff. Cosine. M u 1 7: 5 3 9 u a 3 i 6 24 o 23 52 23 44 23 36 23 28 1 5 36 o 36 8 36 1 6 36 24 36 32 9.8255I 82565 8 2 5 79 82593 82607 I I 10. 17449 17435 17421 17407 i 7 3 9 3 g-95444 95469 9 54 9 5 95520 9 5545 I 1 2 10 ,o4556 o453. o45o5 o448o o4455 10. 12893 12904 12916 12927 i2 9 38 o o i i 9.871 07 87096 87085 8 7 o 7 3 87062 bo 69 58 67 561 55 54 53 62 5t G 23 20] 5 36 4o 23 12! 36 48 23 4i 36 56 22 56 37 4 22 48 37 12 9.82621 82635 82649 82663 82677 I I 2 2 2 2 3 3 3 3 10. 17379 i 7 365 i 7 35i i733 7 9.95571 9 55 9 6 95622 95647 2 3 3 3 4 4 5 5 5 6 10.04429 o43 7 8 04353 o43s 8 10. 12960 12961 12972 12984 12996 i i i 2 2 2 2 2 3 3 9 . 8 7 u5o 87039 87028 87016 87006 6 22 4o 2.2 32 22 24 22 16 22 8 5 3 7 20 3 7 28 3 7 36 3 7 44 3 7 52 9.82691 82705 82719 82 7 33 82747 lo. 17309 17295 172.81 17267 i 7 p.53 9.95698 96723 95748 95774 95799 io.o43o2 04277 04 2 5 2 04226 04201 10. i3oo7 i3oi8 i3o3o i3o4i i3o53 9.86993 86982 86970 86969 86947 5o 49 48 47 46 1 5 16 17 i8 ! 9 f> 22 21 52 21 44 21 36 21 28 5 38 o 38 8 38 1 6 38 24 38 32 9.82761 82775 82788 82802 82816 3 4 4 4 4 10.17239 1722.5 17212 17198 17184 9.95825 9585o 9 58 7 5 96901 96926 6 7 7 8 8 10.04176 04160 04126 04099 04074 10. i3o64 i3o-6 i3o8 7 13098 1 3 1 1 o 3 3 3 3 4 9 .86 9 36 86924 869 1 3 86902 86890 45 44 43 42 4r 20 21 22 2.3 2.4 6 21 20 21 12 21 4 20 56 20 48 5 38 4o 38 48 38 56 3 9 4 39 12 9.82830 82844 82858 82872 82885 5 5 5 5 6 i o . i 7 i 70 17166 17142 17128 17115 9.96962 95977 96002 96028 9 6o53 8 9 9 10 10 io.o4c>48 03998 03972 03947 IO. l3l2 I i3.33 i3i45 i3i56 y3i68 4 4 4 4 5 9.86879 86867 86855 86844 86832 4o 3 9 38 37 36 35 34 33 32 3i A] 3 1 33 J3 34 6 20 4o 2O 32 20 24 20 l6 20 8 5 39 20 3 9 28 3 9 36 39 44 3 9 52 9.82899 82913 8292.7 82941 82955 6 6 6 6 7 10. 17101 17087 I 7 o 7 3 17069 17045 96104 96129 96166 96180 u 1 1 1 1 I 2 12 10.03922 o38 9 6 03871 o3845 o382o 10. i3i 7 9 13191 l3202 i3ai4 13225 5 5 5 5 6 6 6 6 7 9.86821 86809 86798 86786 86776 6 20 19 52 19 44 19 36 19 28 5 4o o 4o 8 4o 16 4o 24 4o 32 9.82968 82982 82996 83oK 83o2.3 7 7 8 8 10. 17032 17018 17004 16990 16977 9.96206 96231 96266 96281 963o 7 i3 1 3 i4 i4 i4 i5 16 16 16 16 17 17 18 18 1 9 10.03-95 o3 7 6 9 o3 7 44 03719 o36 9 3 1 3 260 l32 7 2 i3283 9.86763 86762 86740 86728 867.7 3o 29 28 27 26 35 36 3 7 38 3 9 619 20 19 12 19 4 1 8 56 18 48 5 4o 4o 4o 48 4o 56 4i 4 4i 12 9.83o37 83o5 1 83o65 83o 7 8 83092 8 8 8 9 9 9 9 IO IO IO 10.16963 16949 16935 16922 1 6908 9.96332 9 635 7 9 6383 96408 9 6433 io.o3668 o3643 o36i 7 03692 10.13296 i33oo i33i8 i333o 1 334 1 7 7 7 8 9.86706 86694 86682 86670 86669 2.5 2.4 23 22 21 4<> 4f 43 44 6 18 4o 18 3 2 18 24 18 16 18 8 5 4 1 20 4i 28 4i 36 4i 44 4i 52 9.83io6 83 1 20 83 1 33 83^7 83i6i 10. 16894 16880 16867 16853 i683 9 9 . 96469 96484 96610 96535 96660 io.o354i o35i6 03490 o3465 o344o io.i3353 i3365 i33 7 6 1 3388 i34oo 8 8 8 8 8 9.86647 86635 8662.4 86612 86600 2O j O I O 17 16 45 46 47 48 49 6 18 o 17 52 17 44 17 36 17 28 5 42 o 42 8 42 16 42 24 42 32 9 .83i 7 4 83t88 83202 832 1 5 83229 10 II II 11 II 10. 16826 16812 16798 i6 7 85 16771 9.96686 96611 96636 96662 96687 '9 '9 20 20 21 io.o34i4 o338 9 o3364 o3338 o33i3 10. i34i i 1 3423 1 3435 1 3446 1 3458 9 9 9 9 9 9.86689 86677 86565 86554 86542 i5 i4 12 II 10 I "7 6 5ci 5( 52 53 54 6 17 20 17 12 17 4 16 56 16 48 5 42 4o 42 48 42 56 43 4 43 12 9-832.42 83256 832 7 o 83^83 II !2 12 12 12 io.i6 7 58 i6 7 44 i6 7 3o 16717 16703 9.96712 96733 9 6 7 63 96788 96814 21 22 22 22 23 io.o3288 03262 o3 2 3 7 03212 o3i86 10. i34 7 o 13482 !35o5 i35i 7 10 IO IO IO IO 9-8653o 865 18 86607 86496 86483 55 56 5 7 60 6 16 4o 16 32 16 24 16 16 16 8 16 o 5 43 20 43 28 43 36 43 44 43 52 44 o 9-833io 83324 83338 8335i 83365 833-8 Cosine. 13 i3 i3 i3 i4 i4 10.16690 16676 16662 16649 1 663 5 16622 9.96839 968154 96890 96916 96940 96966 2.3 24 24 25 25 25 io.o3i6i o3.36 o3 1 1 o o3o85 o3o6o o3o34 io.i3528 i354o 1 3552 1 3564 i35 7 5 i358 7 II II II II II 12 9 . 86472 8646o 86448 86436 86426 864 1 3 5 4 3 2 I O M M Hour p.m. Hour A.M. Diff. Secant. Cotangent Diff. Tangent. Cosecant. Diff. Sine. Seconds of time 1 S 9* 3 s 4 5 s P) s 7" p Prop, parts of cols. < B 1 r~\ 2 3 3 6 5 10 7 i3 9 16 10 19 12 22 TABLE XXVII. S' Locr. Sines, Tangents, and Secants. 4 ' r A A B B c o i; M *! Hour A.M. IFonrp.M. Sine. Diff. Cosecant. Tangent. "9^6966 96991 97016 97042 97067 iDiff. Cotangent Secant Diff. Collie. I 2 3 4 616 o 1 5 52 1 5 44 1 5 36 1 5 28 5 44 . o 44 8 44 1 6 44 24 44 32 9-833 7 8 83392 834o5 83419 83432 Q "83446 ' 8345 9 834 7 3 83486 835oo o o o I I io. 16622 16608 i65 v 5 i658i . i 6568 o ; 2 io.o3o34 03009 02984 02 9 58 02 9 33 10.13587 13599 i36u ,3623 1 3634 o 9.8641 3 86401 86389 863 77 86366 1 5 7 5* 5 6 7 8 10 i i 12 i3 14 6 1 5 20 l5 12 i5 4 1 4 56 i4 48 5 44 4o 44 48 44 56 45 4 45 12 ! 2 2 io.i6554 1 654 1 16527 i65t4 i65oo 9.97092 971.8 97i43 97168 97193 9.97219 97244 97269 97295 97320 2 3 3 3 4 10.02908 02882 02857 02832 02807 to. 136^6 1.3658 1 3670 1 368 2 i36 9 4 2 2 2 2 2 3 3 9 .86354 86342 8633o 863 1 8 863o6 55 54 53 52 5i 6 i4 4o i4 32 i4 24 i4 16 i4 8 5 45 20 45 28 45 36 45 44 45 52 9-835.3 835a 7 8354o 83554 8356 7 2 2. 3 3 3 10.16487 i646o 1 6446 i6433 io.i64i 9 16406 16392 16379 i6366 4 5 5 5 6 10.02781 02756 02 7 3l 02 7 o5 02680 I O.I 3705 :3 7 , 7 13729 i3 7 4i i3 7 53 9.86295 86283 862 7 i 86259 86247 5o 4 9 48 47 46 ID 16 1 8 '9 20 2 i 22 ?6 27 28 29 3o 3 1 3 a 33 34 3 "> 3ti I}/ 38 39 4. 4 a 43 44 45 46 47 48 4? So 5i 54 55 56 5? 58 '39 So 6 14 o i3 52 i3 44 i3 36 i3 28 5 46 o 46 8 46 1 6 46 24 46 32 9-8358. 835 9 4 836o8 836? i 83634 3 4 4 4 4 9-97345 97371 9'3 9 6 97421 __ 97447 9.97472 97497 97548 97573 6 7 8 8 ___. 9 9 IO IO 10.02655 02629 02604 02579 02553 10.13765 1 3777 i3 7 8 9 i38oo i38i2 3 3 3 4 4 9.86235 86223 86211 86200 86188 45 44 43 42. 4i 6 i3 20 1 3 12 i3 4 12 56 12 48 5 46 40 46 48 46 56 47 4 47 12 9-83648 8366 1 83674 83688 83 7 oi 4 5 5 5 5 10. (6352 16339 i6326 i63.2 16299 10.02528 O25o3 02477 02452 02427 io.i3824 i3836 i3848 i386o i38 7 2 4 4 4 5 5 9.86176 86.64 86140 86128 4o 3 9 38 37 36 6 12 4o 12 32 12 24 12 l6 12 8 5 47 20 47 28 47 36 47 44 4 7 52 9.83715 83 7 28 83 7 4i 83 7 55 83768 6 6 6 6 6 10.16285 16272 16259 16245 16232. 9.97598 97624 97649 97674 97700 1 1 1 1 1 1 12 12 10.02402 o 2 3 7 6 O235r 02326 02300 io. i 3884 i38 9 6 1.3908 13920 i3 9 3 2 5 5 5 6 6 9.86.16 86104 86092 86080 86068 35 34 33 32 3i 6 12 II 52 n 44 K 36 n 28 5 48 o 48 8 48 16 48 24 48 32 9.83781 83 79 5 838o8 83821 83834 7 7 7 7 8 i o. 16219 16205 16192 16179 16166 9.97725 97750 97776 9780 1 97826 13 i3 i3 M r4 10 022 7 5 02250 02224 02199 02174 10.13944 i3 9 56 i3 9 68 1 3 9 8o 13992 6 6 6 7 7 9.86o56 86044 86o3a 86020 86008 3o 2 9 28 27 26 6 II 20 11 12 ii 4 io 56 io 48 5 48 4o 48 48 48 56 49 4 4 9 12 9.83848 8386. 83874 8388 7 8390. 8 8 8 8 9 i o . 1 6 . 5 2 i6i3 9 16126 i6u3 16099 9.9785, 97877 97902 97927 97953 i5 i5 16 16 1 6 '7 18 18 '9 I 0.02149 O2I23 02098 02073 02047 io.i4oo4 14016 14028 i4o4<> 7 7 8 8 8 8 9 9 9 .85 99 6 85 9 84 85 97 2 85960 85 9 48 25 23 22 21 6 -o 4> 10 32 io 24 10 16 io 8 5 49 20 49 28 49 36 49 44 49 52 9.839.4 83927 83940 83954 83967 9 9 9 10 1C) io. 16086 16073 16060 i6o46 i6o33 9.97978 98003 98029 9 8o54 98079 iC.O2O22 01997 01971 01946 0192. io. 14064 14076 14088 14112 9.85936 8 5 9 24 85912 85 9 oo 85888 2O II 17 .6 6 io o 9 52 9 44 9 26 6 9 20 9 I2 - 9 4 8 56 8 48 5 5o o 5o 8 5o 16 5o 24 5o 32 9.83980 839 9 3 84006 84020 84o33 10 10 to 1 1 1 1 io. .6020 16007 i5 99 4 1 5980 1 5 9 6 7 9 . 98 i o4 98i3o 981 55 98.80 98206 '9 9 20 20 21 10.0.896 01870 01845 Ol820 01794 io. 14124 i4i36 9 9 9 10 10 9-858 7 6 85864 8585 1 8583 9 8582 7 i5 i4 i3 I 2 I I 5 5o 4o 5o 48 5o 56 5i 4 5. 12 9.84046 84059 840T3 84od5 84098 I I 1 1 12 I 2 12 IQ. i5 9 54 i5 9 4 1 5928 i5 9 .5 l5 9 O2 9.982.31 98256 98281 9 83o 7 98332 21 22 22 22 23 10.01769 0.744 01719 01693 01668 io.i4i85 14209 14221 10 IO IO II II 9 .858i5 858o3 85 779 85766 IO 7 6 6 8 4o 8 32 8 24 8 16 8 8 8 o 5 5. 20 5 1 28 5 1 36 5 1 44 5. 52 52 9 .84i 12 84i38 84 1 5 1 84 1 64 84i77 Cosine. 1 2 12 i3 i3 i3 i3 io.i588S i58 7 5 1 5862 i584 9 1 5836 1 5823 9 . 9 835 7 98383 98408 98433 9 845S 98484 23 24 24 ^ 25 IO.OI643 Ol6l7 01567 oi542 oi5i6 10.14246 14270 14282 14294 i43o 7 II 11 II 12 12 12 9 .85 7 54 85742 85 7 3o 8.5718 85706 85693 5 4 3 2 I Ti 46 M Hour P.M. Hour A . M . Diff. Secant. Cotangent Diff. Tangent. Cosecant. Diff. Sine. I*} A A B B C C Seconds of time 1- * 3" 4- 2 6" 7' f A 2 3 5 7 8 10 12 Prop- parts of cols. 53 54 6 20 12 i o 56 o 48 5 58 4o 58 48 58 56 5 9 4 59 12 9.84822 84835 84847 84860 848 7 3 io.i5i 7 8 i5i65 i5i53 i5i4o l5l2 7 9-99747 99773 99798 99823 99848 21 21 22 22 23 IO.OO25o 00227 OO2O2 00177 00l52 10. 14926 i4 9 38 i4 9 5. i4963 14976 IO 1 1 II 1 1 1 1 9 .85o 7 4 85o6a 85c>4j 85o37 85o24 6 55 56 57 58 59 60 6 o 4o 32 O 2^ o 16 o 8 O C 5 5 9 20 5 9 28 5 9 36 5 9 44 5 9 52 600 9.84885 848 9 8 84 9 1 1 84923 84936 84949 12 12 12 12 l3 i3 10. i5i i5 l5l02 i5cS 9 i5o 77 i5o64 i5o5i 9.99874 99 8 99 99924 99949 99975 IO.OOOOC 23 24 24 24 25 25 10.00126 00101 00076 oooSi 00025 00000 10.14988 1 5oo i i5oi4 i5oa6 i5o39 i5o5i 1 1 12 12 12 12 12 y. 85oi2 84 999 84986 84074 84 9 6. 84949 * iM Hour P .M Horn A .M Cosine |Diff Secant. Cotangent DiflT Tangent. Cosecant. Diff Sine. M 134' C 45 Seconds of time 1 s 2 3 3' 4 s 5 s 6 7" (A 2 3 5 p 8 10 ii Prop, parts of cols. < B 3 6 9 i3 16 '9 22 (c 2 3 5 O 8 9_ II Lat. TABLE XXXII. [Pa-sis Variation of the Sun's Altitude in one minute from noon. Declination of a different name from the Latitude. Lat n 3 4 5 6 7 8 9 10 11 II n n n a a // n i4'o 12.5 II .2 1O.2 a n ii i 2 3 4 28.1 28.1 22.4 28,1 22.4 l8. 7 28.1 22.4 18.7 16.0 28.1 22.4 l8. 7 16.0 14.0 22.4 I8. 7 l6.0 i4.o 12.5 18.7 16.0 i4-o 12.5 11 .2 i4.o 12.4 I I .2 IO.2 9-3 12.4 I I .2 10.2 9 .3 8.6 ii .1 10. I 9 .3 8.6 8.0 IO. I 9.3 8.6 8.0 7-4 c 2 3 4 A 6 7 8 9 2 2.. 4 l8. 7 l6.0 i4-o 12.4 l8. 7 16.0 i4-o 12.4 II .2 l6.0 i4-o 12.4 II. 2 10.2 i4-o 12.5 II .2 10.2 9-3 12.5 II .2 10.2 9 .3 8.6 II .2 10.2 9.3 8.6 8.0 10.2 9-3 8.6 8.0 7-5 9-3 8.6 8.0 7-5 7.0 8.6 8.0 7-5 7.0 6.6 8.0 7-5 7.0 6.6 6.2 7-4 7.0 6.6 6.2 5. 9 7.0 6.6 6.2 5. 9 56 5 6 8 9 10 ii 12. i3 i4 ii .1 10. I 9.2 8.5 7-9 10. I 9 .3 8.5 7-9 7-4 9 .3 8.6 7-9 7-4 6.9 8.6 8.0 7-4 6.9 6.5 8!o 7-4 7.0 6.5 6.2 7-4 7.0 6.5 6.2 5.8 7.0 6.6 6.2 5.8 5.5 6.6 6.2 5 .6 5.3 6.2 5. 9 5.6 5.3 5.o 5. 9 5.6 5.3 5.o 4.8 5.6 5.3 5.o 4.8 4.6 5.3 4^8 4.6 4-4 10 ii 12 i3 i4 i5 16 17 18 19 7-3 6.8 6.4 6.0 5-7 6.9 6.5 6.1 5-7 5.4 6.5 6.1 5.8 5.5 5.2 6.1 5.8 5.5 5.2 4-9 5.8 5.5 5.2 5.o 4-7 5.5 5.2 5.o 4.8 4.5 5.3 5.o 4.8 4.6 4.4 5.o 4.8 4.6 4-4 4.2 4.8 4.6 4.4 4-2 4.o 4.6 4-4 4.2 3'9 4.4 4.2 3^9 3.8 4.2 3! 9 3.8 3.6 Ie 17 18 '9 20 21 22 23 24 5.4 5.1 4.9 4.6 4-4 4*9 4-7 4.4 4.2 4-9 4-7 4.5 4.3 4 i 4-7 4.5 4.3 3^9 4.5 4.3 4^o 3 8 4.3 4.2 4.0 3.8 3-7 4.2 4.0 ft 3.6 4.0 fe 3.6 3.5 3 '.6 3.5 3.4 3.8 3.6 3.5 3.4 3.3 3.6 3.5 3.4 3.3 3 2 3.5 3.4 3.3 3.2 20 21 22 23 3.5 3.4 3.3 3.3" 3.2 3!o 2.9 3io 2.9 2.8 25 26 27 28 29 4.2 4.0 3.'5 3^6 3.4 3.9 3.8 3.6 3.5 3.3 3.8 3.6 3.5 3.4 3.2 3.5 3.4 3.3 3.2 ~37o~ 2.9 2.8 2.7 2.6 3.4 3.3 3.2 3io 3!o 2.9 2.8 2.8 3!o 2.9 2.8 2.7 3- 2.9 2.8 2.7 2.6 25 26 27 28 2 9 3o 3i 32 33 34 3.4 3.3 3!o 2.9 3.3 3.2 2.9 2.8 3.2 3!o 2.9 2.8 3!o 2.9 2.8 2-7 3.o 2.9 2.8 2.7 2.6 2.9 2.8 2.7 2.6 2.5 2.8 2.7 2.6 2.5 2.5 2.7 2.6 2.6 2.5 2.4 2.7 2.6 2.5 2.4 2.4 2.6 2.5 2.5 2.4 2.3 2.5 2.5 2.4 2.3 2.3 3o 3r 32 33 34 35 36 37 38 3 9 2.8 2.7 2.6 2.5 2.4 2.7 2.6 2.5 2.5 2.4 2.7 2.6 2.5 2.4 2.6 2.5 2.4 2.4 2.3 2.5 2.5 2.4 2.3 2.5 2.4 2.3 2.3 2.4 2.4 2.3 2.2 2.4 2.3 2.2 2.2 2.3 2.3 2.2 2.1 2.3 2.2 2.2 2.1 2.2 2.2 2.1 2.1 2.0 2.2 2.1 2. I 2.0 2.0 35 36 37 38 3 9 4o 4i 42 43 44 2.3 2.3 2.2 2.1 2.0 2.3 2.2 2.1 2.1 2.0 2.2 2.2 2.1 .0 .0 2.2 2. I 2 . I 2.0 2.2 2.1 2.O 2.0 2.1 2.1 2.0 9 2. I 2.0 .0 .0 .0 9 8 9 2.0 1.9 2.0 9 3 .7 9 '.8 7 '6 !a .7 7 .6 .6 6 4o 4i 42 43 44 45 46 47 48 49 45 46 47 48 49 2.0 9 'I 1.0 i 8 1.8 i 8 .8 .8 .7 7 .7 1-7 i .7 ,6 6 1.6 .6 6 .8 7 7 7 7 7 lie .6 .6 .6 .6 .6 .5 1.6 .6 .5 .5 .5 .5 .5 5o 52 54 56 58 .6 .6 .6 c 1.6 1.6 .5 / 4 .5 4 i.b .5 .4 .4 .4 .4 5o 52 54 56 58 .4 .3 .2 .4 .3 .2 .4 .2 I .2 I .2 .3 .3 .2 .3 .3 .2 .2 .2 .1 i .1 .1 .1 60 62 64 66- 68 7 .0 .O 0-9 0.8 0.7 .1 .0 0.9 0.9 0.8 0.7 .1 .O 0.9 0.9 0.8 0.7 I .0 0.9 0.9 0.8 0.7 3 I .1 1.0 0.9 0.8 0.8 0.7 .1 .0 0.9 0.8 0.8 0.7 .1 .0 0.9 0.8 0.8 0.7 .0 0.8 0.8 0.7 I.O i .0 0.9 0.8 0.8 0.7 .0 .0 0.9 0.8 0.7 0.7 .O .0 0.0 0.8 0.7 0.7 I .O 0. 9 0. 9 0.8 0.7 0.7 60 62 64 66 68 1* 2 4 5 6 7 8 9 10 11 r*ea40] TABLE XXXII. Vauution of the Sun's Altitude in one minute from noon. Lat. Declination of a different name from the Latitude. Lat. 12 13 14 15 a 16 17 18 n 19 3 20 21 22 23 24 n n n n n n n n n n n I 2 3 4 9.2 8.5 7-9 7-4 7.0 8.5 7-9 7-4 6.0 6.5 6.2 7 .3 6.9 6.5 6.1 5.8 6.8 6.5 6.1 5.8 5.5 6.4 6.1 5.8 5.5 5.2 6.0 5.7 5.5 5.2 5.o 5-7 5.4 5.2 4-9 4-7 5.4 1' 4-7 4.5 4-9 4-7 4-5 4.3 4.9 4.7 4.5 4.3 4.6 4-4 4.3 4.0 4 4 4 2 4 i 39 3 8 l 2 3 4 5 6 8 9 6.5 6.2 5. 9 5.6 5.3 6.2 5.8 5.6 5.3 5.o 5.8 5.5 5.3 5.o 4.8 5.5 5.3 5.o 4.8 4.6 5.2 5.o 4.8 4.6 4.4 5.o 4.8 4.6 4-4 4.2 4.8 4.6 4-4 4.2 4-5 4.4 4.2 4.0 3. 9 4.3 4.2 4.0 3. 9 3.8 4.2 4.o 3'.6 4.0 3 '.6 3.5 3.8 3. 7 3.6 3.5 3.4 3 7 3.6 3.5 3.4 3.3 5 6 8 10 ii 12 i3 i4 10 1 1 12 i3 i4 5.o 4.8 4.6 4.4 4-2 4.8 4.6 4-4 4.3 4.6 4-4 4.3 4.1 3. 9 4.4 4.2 3-9 3.8 4.2 3.9 3.8 3.7 3:9 3.8 3. 7 3.5 3. 9 3.8 3-7 3.5 3.4 3.8 3.6 3.5 3.4 3.3 3.6 3.5 3.4 3.3 3.2 3.5 3.4 3.3 3.2 2.9 2.8 2.8 2.7 3.4 3.3 3.2 3'.o 3.3 3.2 3'.o 2.9 3.2 3!o 2.9 2.8 i5 16 17 18 1 9 3*0 3.8 3-7 3.5 3. 9 3.8 3-7 3.5 3.4 3.8 3. 7 3.5 3.4 3.3 3.7 3.5 3.4 3.3 3.2 3.5 3.4 3.3 3.2 3.4 3.3 3.2 3!o 3.3 3.2 3!o 2.9 3.2 3!o 2.9 2.9 2!o 2.9 2.9 2.8 2.9 2.8 2.8 2.7 2.6 2.8 2.8 2.7 2.6 2.6 2.8 2.7 2.6 2.5 2.5 i5 16 17 18 20 21 22 23 24 3.4 3.3 3.2 3lo 3.3 3.2 3!o 2.9 3.2 3.'o 2.9 2.8 3!o 2.9 2.8 2.8 3.o 2.9 2.8 2.8 2.7 2.9 2.8 2 8 2.7 2.6 2.9 2.8 2.7 2.6 2.5 2.5 2.4 2.4 2.3 2.2 2.8 2.7 2.6 2.6 2.5 2.7 2.6 2.6 2.5 2.4 2.6 2.6 2.5 2.4 2.4 2.6 2.5 2.4 2.4 2.3 2.5 2.4 2.4 2.3 2.3 2.4 2.4 2.3 2.3 2.2 20 21 22 23 24 25 26 27 28 2.9 2.8 2 7 2.6 2.6 2.8 2.7 2.7 2.6 2.5 2.7 2.7 2.6 2.5 2.4 2.7 2.6 2.5 2.5 2.4 2.6 2.5 2.5 2.4 2.3 2.5 2.5 2.4 2.3 2.3 2.4 2.4 2.3 2.2 2.2 2.4 2.3 2.2 2.2 2. I 2.3 2.3 2.2 2.1 2. I 2.3 2.2 2. I 2.1 2.O 2.2 2. I 2.1 2.1 2.0 2.2 2.1 2.1 2.0 2.0 25 26 27 28 2 9 To" 3i 32 33 34 3o 3i 32 33 34 2.5 2.4 2.3 2.3 2.2 2.4 2.4 2.3 2.2 2.2 2.4 2.3 2.2 2.2 2. I 2.3 2.3 2 .2 2.1 2 . I 2.3 2.2 2.2 2.1 2.O 2.2 2.2 2.1 2.1 2.0 2.2 2.1 2 I 2.0 2.0 2.1 2.1 2.0 2.0 2. I 2.0 2.0 9 9 2.0 2.0 9 9 9 2.O 2.O 9 3 2.0 1.9 1.0 1.8 T 8 1.0 1.8 1.8 i 8 35 36 37 38 39 4o 4i 42 43 44 2.2 2.1 2.1 2.0 2.0 2.O i .g 9 1.0 1.8 .8 .8 .8 .8 .8 .7 1-7 35 36 37 38 39 .0 2.0 2.0 1.9 I . O .8 8 1.8 i 8 .8 .7 7 .7 i 6 1.6 i 6 9 ,1 .8 7 7 1.9 1-9 1.8 1.8 1.7 i-7 1.8 .8 1.8 1-7 1.6 1.6 7 7 .6 .6 .5 .5 .5 .4 1.6 1.6 .8 .8 .7 '.6 1.8 i-7 1.6 1.6 7 7 .'6 '.6 .6 .6 .5 1-7 1.6 1.6 .6 .6 .6 .5 .5 .6 .6 .5 .5 .5 !:i 4o 4i _42 44 45 46 47 48 49 .6 6 .6 6 1.6 !l .5 .5 1*5 .5 4 .5 4 .4 .4 .4 .4 .4 .4 1*3 1 A 45 46 47 48 49 5 5 r 4 / 4 4 .4 .3 .3 3 3 .5 .4 .5 .4 iil 1.4 .4 .4 1:3 .4 .3 .4 .3 .3 .3 .3 .3 .3 .3 I .2 I .2 5o 52 54 56 58 4 .3 2 .4 .3 i!3 I 2 .3 .3 .2 1.3 I 2 .3 .2 2 .3 .2 I .3 .2 .3 .2 . I .2 .2 I .2 I . I I i I .2 I .1 j j 5o 52 54 56 58 .2 I .1 i I . I I . I .1 I . I I . I . I .0 I .O I .O . i 1 .1 .O I .O .0 I .0 .O .0 .0 I .O I .0 60 62 64 66 68 70 I .0 0.9 0-9 0.8 0.7 0.7 I .0 0.9 0.9 0.8 0.7 0.7 I .0 0.9 0.9 0.8 0.7 o-7 I .0 0.9 0.9 0.8 0.7 0.6 15 I 0.9 0.8 0.8 0.7 0.6 I .O 0.9 0.8 0.8 0.7 0.6 I .0 0.9 0.8 0.8 0.7 0.6 0. 9 0. 9 0.8 0.8 0.7 0.6 0.9 0.9 0.8 0.8 0.7 0. 9 0.9 0.8 o-7 0.7 0.9 0.9 0.8 0.7 0-9 0. 9 0.8 0.7 0.9 0.8 0.8 60 62 64 66 68 70 12 13 14 16 17 18 19 20 21 22 23 24 TABLE XXXII. [Page 241 Variation of the Sun's Altitude in one minute from noon. Lat. i 2 3 4 Declination of the same name as the Latitude. Lat. 1 // 2 ii 3 4 5 6 7 8 9 10 11 " " n u n n 28.1 i 28.1 2.4 8.0 8.7 2.4 28.0 6.0 8.6 2.3 7-9 i4.o 16.0 18.6 22.3 27.8 12.4 ,3.9 i5 o i8.5 22.2 l\ 9 5.8 8.5 10. I n. i 12.3 3.8 i5.8 i 2 3 4 5 6 8 9 22.4 l8. 7 16.0 i4.o 12.4 2- ; 5.0 22.4 18.6 16.0 i3. 9 28.0 22.3 18.6 i5. 9 11:1 8.5 27.8 22.2 27.7 27.7 22. I 2 7 .6 18.4 22.0 27.4 5 6 8 9 10 u 12 i3 i4 n. i 10. I 9.2 8.5 7-9 12.4 1 1 .1 10. I 9.2 8.5 13.0 12.3 ii . i 10.0 9 .2 i5.8 i3.8 2.3 ii .0 0.0 18.5 i5.8 i3.8 12.2 10.9 22.1 18.4 fe 12. I 27.6 22.0 18.3 i5.6 i3.6 27.4 Is'.l 27.3 21.7 18.0 27.1 21.6 26.9 10 ii 12 i3 i4 i5 16 17 18 '9 7 .3 6.8 6.4 6.0 5-7 7.8 7-3 6.8 6.4 6.0 8.4 7.8 7.2 6.8 6.3 9.1 8.4 7.8 7.2 6.7 6.3 5. 9 5.6 5.3 5.o 9-9 9.1 8.3 7-7 7-2 10. 9 0.0 8.3 7-6 12. I 10.8 9.8 8. 9 8.2 i3.5 12.0 10.7 9-7 8,9 ib.4 i3.4 11.9 10.6 9.6 17.9 i5.3 i3.3 u. 8 10.6 IT 8.0 7-4 6.8 21.4 l5*.2 13.2 11.7 26.7 21.3 17.6 i5.o i5 16 i? 18 1 9 20 21 22 23 24 5.4 4^9 4.6 4-4 5-7 5.4 5.i 4.8 4.6 6.0 5.6 5.3 5.o 4.8 6.7 6.3 5^2 e'.6 6.2 5.8 5.5 7.6 7.0 6.6 6.1 5.8 8.1 7 .5 7.0 6.5 6.1 8.8 8.1 7-5 6.9 6.4 io.5 9 .5 8.6 11.6 10.4 0.4 8.5 7.8 20 21 22 23 24 25 26 27 28 4.2 4.0 ft 3.5 4-4 4.2 4.0 3.8 3.7 4.6 4.3 4!o 3.8 4-7 4.5 4.3 3*9 5.o 4-7 4-5 4.3 5.2 4-9 4-7 4.4 4-2 5.4 A Q 4-6 4.4 5-7 5.4 4'.8 4.6 6.0 5.7 5.3 5.o 4-7 6.4 6.0 5.6 5.3 5.o 6.8 6.3 1:1 5.2 7-2 6-7 6.2 5.8 5.5 25 26 2 29 3o 3i 32 33 34 3.4 3.3 3!o 2.9 3^4 3.2 3!o 3.6 3.5 3.3 3.2 3. 7 3.6 3.4 3.3 3.2 3*.5 3.4 3.2 4.0 3.8 3.7 3.5 3.3 4.2 4.0 3.8 3.6 3.4 4.3 3. 9 3l<5 4.5 4.3 1 4.7 4.4 4.2 4.0 3.8 4-9 4.6 4.4 4.2 3. 9 4^8 4-6 4-3 3o 3i 32 33 34 35 36 37 38 3 9 35 36 37 38 3 9 2.8 2.7 2.6 2.5 2.4 -2.3 2.3 2.2 2.1 2.O 2.9 2.8 2.7 2.6 2.5 3.o 2.8 l'.5 3.o 2.0 2.8 2.7 2.6 3!o 2. 9 2.8 2.7 3.2 2.0 2.8 2.7 3.3 3.2 3.o 2 -9 2.8 3.4 3.3 3!o 2.9 3.5 3.4 3.2 3.o 2.9 2.8 2.7 2.6 2.5 2.4 3.6 3.5 3.3 3.2 3.o 3.7 3.6 3.4 3.2 !i 3.5 3.3 3.2 O " 00 XT xr XT XT xr XT 2.4 2.3 2.2 2.1 2.1 2.4 2.4 2.3 .2 2.5 2.4 2.3 2.2 2.1 2.6 2.5 2.4 2.3 2.2 2.6 2.5 2.4 2.3 2.2 2.7 2.6 2.5 2.4 2.3 2.7 2.6 2.5 2.4 2.3 2.9 2.8 2.6 2.5 2.4 3.o 2.8 2.7 2.6 2.5 3,o 2.9 2.8 2.7 2.5 4o 4i 42 43 44 45 46 47 f 48 49 2.O 1.8 1.8 I -7 2.O 9 9 .8 .7 .O .0 9 .8 .8 2.1 2.0 9 'I 2.1 .O .0 I 2.2 2.1 2.0 1.0 i 8 2.2 2.1 2.0 2.O 1.9 2.2 2.2 2.1 2.0 2.3 2.2 2.1 2.0 1-9 2.3 2.2 2.1 2.1 2.0 2.4 2.3 2.2 2.. I 2.O 2.4 2.3 2.2 2.1 2. I 45 46 47 48 49 5o 52 54 56 58 1.6 '.6 .4 .*5 7 .6 .5 / .8 .6 .5 / 1.8 1.6 1.8 .8 7 .4 1.9 1-7 I:! .6 ,5 9 .8 .6 ,5 2.0 .8 7 5o 52 54 56 58 I .2 .2 .3 .3 .3 i.3 i.3 .3 I.J .4 .4 .4 60 62 64 66 68 70 I .1 1.0 I .O 0-9 0.8 0.7 .O .0 0.9 0.8 0.7 .2 .1 .0 0-9 0.8 0.7 .2 .1 1.0 -9 0.8 0.7 .2 .O o. 9 0.8 0.7 1.2 I .1 I .0 0.9 0.8 0.7 1.2 I .1 I .0 0-9 0.8 0.7 .2 .1 .0 0.9 0.8 0.7 1.2 I.I 1.0 0-9 0.8 0.8 .2 .0 0. 9 0.8 0.8 .3 .2 .0 0.9 0.0 0.8 ,3 .2 .1 .0 0.9 0.8 60 62 64 66 68 70 1 2 3 4 5 6 7 8 9 10 11 ^242j TABLE XXXII. Variation of the Sun's Altitude in one minute from noon. Lat. Declination of the same name as the Latitude. Lat. 12 13 14 15 16 17 18 19 20 21 22 23 24 // // n /' n 7 '.3 7.8 8.4 9.1 n ii ii 6*0 6.3 6.7 7.2 n 5-. 7 6.0 6.3 6.7 u n n '/ I 2 3 4 9.2 10. I ii . i 12.3 i3.8 8.5 9.2 IO.O II. 12.2 7-9 8.5 9.2 IO.O 10.9 7.3 7.8 8.4 9.1 9.9 6.4 6.8 7.2 7.8 8.3 6.0 6.4 6.8 7.2 7-7 5.4 5.6 5. 9 6.3 1? 5.3 5.6 5. 9 4.6 4.8 5.o 5.3 5.5 4-4 4.6 4.8 5.o 5.2 1 2 3 4 5 6 8 9 i5. 7 i8.3 21.9 2 7 .3 i3. 7 i5.6 18.2 21.7 27.1 12. I i3.6 i5.5 18.0 21.6 10.9 12. I i3.5 i5.4 17.9 9.8 10.8 12.0 i3.4 i5.3 9.0 9.8 10.7 11.9 i3.3 15.2 17.6 21 .1 26.2 8.3 8.9 10.6 n. 8 13.2 i5.o i 7 .5 20.9 26.0 7-6 8.2 8.9 9.6 10.6 7 '.6 8.1 8.8 9 .5 6.6 7.0 7-5 8.1 8-7 9 .5 10.4 ii. 5 12.8 14.6 6.2 6.6 O . O 5.8 6.1 6.5 6-9 7-4 5.5 5.8 6.1 6.4 6.8 " 7 .3 7.8 8.4 9.2 IO.O 5 6 7 8 9 10 u 12 i3 26.9 21.4 26.7 17.8 21.3 2C.5 11.7 14^9 17.3 20.7 io.5 u. 6 i3.o i4.8 17.1 8.6 9-4 io.3 12.7 7-9 8.5 9 .3 10. I II .2 10 1 1 12 i3 i4 i5 16 18 '9 26.5 21 .1 I 7 .5 14.9 26.2 20.9 i 7 .3 26.0 20.7 2 5. 7 25.7 20.4 25.4 16.9 2O. 2 25.1 i4-4 16.7 20. o 24.8 12.5 i4.3 i6.5 19.7 24.5 u .1 12.4 Id'.l , 9 .5 i5 16 17 18 J y 20 21 22 23 24 i3.o n. 5 io.3 9-3 8.4 i4.8 12.8 u. 3 10. I 9.2 17.1 14.6 12.7 II .2 IO.O 20.4 16.9 i4.4 12.5 n. i 25.4 20.2 l6. 7 i4-3 12.4 25.1 20. o 16.5 24.8 19.7 i6.3 24.5 i 9 .5 24.2 To. 2 15.9 i3.5 11.7 io.3 24.2 20 21 22 23 24 25 26 27 28 29 7-7 e!e 6.2 5.7 8.3 7-6 7.0 6.5 6.1 9 .0 8.2 7.5 7.0 6.4 9.9 8.9 8.1 7-4 6.9 10.9 9.8 8.8 8.0 7-3 12.2 10.8 9 .6 8-7 7-9 7.2 6.7 6.2 5. 7 5.3 i3. 9 12. I 10.6 9 .5 8.6 7.8 ^5 6.1 5.6 16.1 i3. 7 u. o io.5 9-4 23.8 18.9 i5.6 i3.3 n. 5 23.5 18.6 i5.4 23.1 18.3 22.7 18.0 25 26 27 28 29 CO CO CO CO CO -fcs CO S3 O 5.4 4^8 4.5 4.3 5. 7 5.3 5.o 4.7 4-4 6.0 5.6 5.2 4.9 4.6 6.4 5. 9 5.5 4.S 6.8 6.3 5.8 5.4 8.4 7-7 7.0 6.4 5. 9 9.2 8.3 7.5 6.9 6.3 10. I 9.0 8.1 7.4 6.8 u. 3 IO.O 8.9 8.0 7.3 12.8 II. I 9.8 8.7 7-8 14.9 12.6 10.9 0.6 8.6 3o 3i 32 33 34 35 36 37 38 39 35 36 3 7 38 3 9 4.0 3.8 3.6 3.4 3.3 4.2 4.0 3.8 3.6 3.4 4.4 3^5 4.5 4.3 4.0 3.8 3.6 4-7 4.5 4.2 4.o 3.8 5.o 4-7 4.4 3^ 5.2 4.6 4.3 4.o 5.5 4^8 4.5 4.2 5.8 5.4 5.o 4-7 4.4 6.2 5-7 5.3 4. 9 4.6 6.6 6.1 5.6 5.2 4.8 6.5 6.0 5.5 7-7 7.0 6.4 5.8 5.4 4o 4i 42 43 44 3!o 2.9 2.7 2.6 3.2 2.9 2.8 2.7 3.3 3.2 3.o 2.9 2.7 2.6" 2.5 2.4 2.3 2.2 3.4 3.3 3!o 2.8 3.6 3.4 3.2 3.0 2.9 3. 7 3.5 3.3 3!o 2.7 2.6 2.4 2.3 3.8 3.6 3.4 3.2 4.0 1:1 3.3 3.2 4.1 a 3 :? 3.5 3.3 4.3 4.o 3.8 3.6 3.4 4.5 4.2 4.o 3-7 3.5 4.7 4.4 3 .6 5.Q. 4.6 4.3 4.0 3.8 4o 4i 42 43 44 45 46 47 48 49 2.5 2.4 2.3 2.2 2.1 2.6 2.4 2.3 2.2 . 2.1 2.7 2.6 2.4 2.3 2.2 2.8 2.6 2.5 2.4 2.3 2.9 2.8 2.6 2.5 2.4 3.o 2.8 2.7 2.6 2.4 2.0 2.8 2.6 2.5 3.2 3.o 2.9 1:1 2.4 2.2 2 .O 3.3 !:i 2.6 3.4 3.2 3.o 2.9 2.7 3.5 3.3 3'.o 2.8 45 46 47 48 49 5o 52 54 56 r tf 2.0 1.8 2.0 9 2.1 2.1 2.2 2.0 i 8 2.2 2.0 I 8 2.3 2.1 2.3 2.1 2.4 2.1 2.5 2.2 2.6 2.3 2 . I 2.6 2.4 2. I 5o 52 54 56 58 1.5 .6 .4 1.6 1.6 1.6 7 i .y 1 -7 i .5 i .y .'e .8 .6 .8 6 1.9 1-7 1-9 1-7 60 62 64 66 68 ?o 3~ i 3 ~i~3~ -7- / -7- 4 5 .5 .5 60 62 64 66 68 70 o ^ 3 3 .3 .3 4 .2 2 I .2 I .C 0.9 0.8 .0 0.9 0.8 i .0 0.9 0.8 I .0 0.9 0.8 I .0 0.9 0.8 .0 0.9 0.8 I .0 0.9 0.8 I .0 0. 9 0.8 .0 0.9 0.8 0. 9 0.8 21 .1 o 9 0.8 .1 .0 0.8 I .1 I .0 0. 9 12 13 14 J5 16 17 18 19 20 22 23 24 TABLE XXXIII. To reduce the numbers of Table XXXII to other given intervals of time from noon. Time from Noon. s. 0' 1' 2' 3' 4' 5' & 7' 8' 9> 10' 11' 12' S. 0.0 .0 4.0 9.0 16.0 25.0 36.o 49.0 64.o 81.0 IOO.O 121 .0 i44.o o i 0.0 .0 4- 1 9.1 16. i 25.2 36.2 49.2 64-3 8i.3 ioo.3 121 .4 )44.4 i 2 0.0 . I 4- 1 9.2 i6.3 25.3 36.4 49-5 64.5 81.6 100.7 121.7 )44.8 2 3 0.0 . I 4-2 9 .3 16.4 25.5 36.6 49.7 64.8 81.9 101 .0 122.1 i45.2 3 4 0.0 . I 4.3 9-4 i6.5 25. 7 36.8 4 9 . 9 65.i 82.2 101 .3 122.5 i45.6 4 5 0.0 .2 4.3 9.D 16.7 25.8 3 7 .o 50.2 65.3 82.5 101 .7 122.9 i46.o 5 6 0.0 .2 4-4 9.6 16.8 26.0 3 7 .2 5o.4 65.6 82.8 IO2 .O 123.2 i46.4 6 7 0.0 .2 4.5 9-7 16.9 26.2 3 7 -4 5o.6 65. 9 83.i 102.3 123.6 i46.8 7 8 0.0 .3 4.6 9-8 17.1 26.4 3 7 .6 5o.o 66.1 83.4 102.7 124.0 l4 7 -2 8 9 0.0 .3 4.6 9.9 17.2 26.5 3 7 .8 5i i 66.4 83. 7 io3.o 124.3 147.6 9 10 o.o 4 4-7 10. i7-4 26.7 38.o 5i.4 66.7 84.0 io3.4 124.7 i48.o 10 1 1 0.0 4 4-8 10. I i 7 .5 26. 9 38.2 5i.6 67.0 84.3 io3.7 125. 1 i48.4 ii 12 0.0 .4 4.8 10.2 17.6 27.0 38.4 5i.8 67.2 84.6 io4-o 125.4 i48.8 12 i3 0.0 .5 4.9 io.3 17.8 27.2 38.6 52.1 6 7 .5 84.9 io4.4 125.8 l4 9 -2 i3 i4 0. .5 5.o io.5 17.9 27.4 38.9 52.3 67.8 85.3 104.7 126.2 149.7 i4 1 5 0. .6 5. i 10.6 18.1 27.6 3 9 .i 52.6 68.1 85.6 io5.i 126.6 iSo.i i5 16 0. .6 5. i 10.7 18.2 27.7 3 9 .3 52.8 68.3 85. 9 io5.4 126.9 i5o.5 16 17 o. .6 5.2 10.8 i8.3 27. 9 3 9 .5 53.o 68.6 86.2 io5.7 127.3 i5o. 9 17 18 0. .7 5.3 10.9 i8.5 28.1 39-7 53.3 68.8 86.5 106.1 127.7 i5i.3 18 19 0. .7 5.4 II. 18.6 28.3 39.9 53.5 69.2 86.8 106.4 128.1 i5i. 7 19 20 0. ,8 5.4 1 1 .1 18.8 28.4 4o.i 53.8 69.4 87.1 106.8 128.4 I52.I 20 21 o. .8 5.5 II. 2 18.9 28.6 4o.3 54.0 60-7 87.4 107.1 128.8 i5a.5 21 22 o. 9 5.6 ii. 3 19.1 28.8 4o.5 54-3 70.0 87-7 107.5 129.2 1 5 2 . 9 22 2.3 o. 9 5-7 n. 4 19.2 29.0 40.7 54.5 70.3 88.0 107.8 129.6 i53.3 23 75 0.2 0.2 2.0 2.0 5.8 5.8 1 1. 6 11.7 19.4 19.5 29.2 29.3 4i.o 4l.2 54.fi 55.o 70.6 70.8 88.4 88.7 108.2 io8.5 i3o.o i3o.3 i53.8 i54.2 25 0.2 2.1 5.9 11.8 19.7 2 9 .5 4i.4 55.3 71.1 89.0 108.9 i3o.7 i54.6 20 28 O.2 O.2 2. I 2.2 6.0 6.1 11.9 12. i 9 .8 20. 29.7 29.9 4i.6 4i.8 55.5 55.8 7i.4 71.7 8 9 .3 8 9 .6 109.2 109.6 i3i!5 i55.o i55.4 27 28 29 0.2 2 .2 6.2 12. 1 20.1 3o.i 42.0 56.o 72.0 89-9 109.9 i3i. 9 i55.8 20 3o O.2 2 .2 6.2 12.2 20.2 3o.a 42.2 56.2 72.2 90.2 no. 2 132.2 i56.a 3o 3r 0.3 2.3 6.3 12.4 2O.4 3o.4 42.5 56.5 7 2.5 00.6 no. 6 i32.6 i56. 7 3i JJ CO CO CO -n.CK Co s. o.3 o.3 o.3 o.3 2.4 2.4 2.5 2.5 6.4 6.5 6.6 6.7 12.5 12.6 12.7 12.8 20.6 20.7 20. 9 21 .O 3o.6 3o.8 3i.o 3l.2 42.7 42.9 43.i 43.3 56.8 5 7 .o 5 7 .3 5 7 .5 72.8 7 3.i 7 3.4 7 3. 7 9-9 9 1.2 91.5 91.8 III .0 in. 3 111.7 112. i33.o i33.4 i33.8 i34.2 i5 7 .i i5 7 .5 i5 7 -9 i58.3 32 33 34 35 36~ 3 7 38 3 9 4o 4i o!4 0.4 0.4 0.4 o.5 i'.6 2.7 2.7 2.8 2.8 6^8 6.9 7.0 7.2 i3.o i3] 2 i3.3 i3.4 i3.6 21 .2 21.3 21.5 21.6 21.8 21. 9 ~3i.4 3i.5 3i. 7 3i. 9 32.1 32.3 43.6 43.8 44.o 44-2 44-4 44-7 5 7 .8 58.o 58.3 58.5 58.8 59.0 74.0 74.3 74-5 74.8 7 5.i 7 5.4 92.2 92.5 92.8 9 3.i 9 3.4 9 3.8 112. 4 II2.7 ii3.i ii3.4 ii3.8 ii4.i i34.6 i34-9 i35.3 i35. 7 i36.i i36.5 i58.8 159.2 159.6 160.0 160.4 160.9 36 .3 7 38 3 9 40 42 43 44 45 46 /_ o.5 o.5 o.5 0.6 0.6 o 6 2.9 3.o 3 2 " 7 .3 7-4 7.5 7.6 7-7 7 7 i3. 7 i3.8 i3. 9 14.2 i4.3 22. I 22.2 22.4 22.6 22.7 22. 9 32.5 32. 7 32. 9 33.i 33.3 33,4 44-9 45.i 45.3 45.6 45.8 46.o 5 9 .3 5 9 .5 5 9 .8 60. i 6o.3 60.6 75-7 76.0 7 6.3 76.6 76.9 77.1 9 4.i 9 4-4 94-7 9 5.i 9 5.4 95.7 ii4-5 ii4-8 Il5.2 ii5.6 ii5. 9 ii6.3 1 137-7 i38.i i38.5 i38.8 161 .3 161 .7 162.1 162.6 i63.o i63.4 42 43 44 45 46 4" 48" 49 5o 5i 52 <;^ 0.7 o 7 o 7 0.8 o 8 3^3 3.4 3.4 3.5 3 5 7-9 8.0 8.1 8.2 8,3 i4-6 i4-7 14.8 i5.o "alTo" 23.2 23.4 23.5 23. 7 23.8 "3T6" 33.8 34.o 34.2 34-4 34.6 ^6.2 46.5 46.7 46. 9 47-2 47.4 6i.'i 61.4 61.6 6i. 9 62.1 77.4 77-7 78.0 7 8.3 78.6 78.9 9 6.o 9 6.4 96.7 97-4 97-7 116.6 llf .17-4 117.7 118.1 118.4 l3 9 .2 139.6 i4o.o i4o.4 i4o.8 i4i 2 i63.8 i64-3 164.7 1 65.1 i65.6 166.0 48 5i 52 53 > xrm o r-co c i Uo m m in in u "oT8~ 0.8 0.9 0.9 0,9 I O 3! 7 3.7 3.8 3 o 8.4 8.5 8.6 8.7 8.8 8.0 l5.2 i5.3 i5.5 i5.6 i5. 7 i5. 9 24.0 24.2 24.3 24.5 24.7 34.8 35.0 35.2 35.4 35.6 35.8 47-6 47-8 48.1 48.3 48.5 48.8 62.4 62.7 62.9 63.2 63.5 63. 7 79.2 79 .5 79- 8 80. i 8o.4 80.7 9 8.o 9 8.3 98-7 99.0 99.3 99-7 118.8 119.2 119.5 119.9 120.3 120.6 i4,i -6 l42.0 142.4 i4a.8 143.2 143.6 166.4 166.8 167.3 167.7 168.1 168.6 54 55 56 57 58 5 9 -'y 0' 1' 2' 3' y 5' i - & 7' . 8' 9' 10 -^ 11' - i .^ TABLE LI. TABLE LII. [1^329 To change mean solar time into To change sideral t : me nto mean sideral time. solar time. Solar Hours. Add. Solar Min- utes. Add. Solar Sec- onds. Add. Sideral llours. Subtract. Sider,.] Min- utes. Subtract Sider; 1 Sec- onds. Subtract M. S. s. S, M. s. S. S. I o 9.9 I 0.2 I 0.0 I 9.8 I 0.2 I O.O 2 o 19.7 2 o.3 2 0.0 2 o 19.7 2 o.3 2 0.0 3 o 29.6 3 o.5 3 0.0 3 29.5 3 o.5 3 0.0 4 o 39.4 4 0.7 4 0.0 4 3 9 .3 4 0.7 4 0.0 D o 49.3 5 0.8 5 0.0 5 o 49.1 5 0.8 5 O.O 6 o 69. i 6 I .0 6 o.o 6 o 59.0 6 I .0 6 0.0 7 9.0 7 I .2 7 0.0 7 8.8 7 1 .1 7 0.0 8 18.9 8 i.3 8 0.0 8 18.6 8 .3 8 0.0 9 28.7 9 i.5 9 0.0 9 28.5 9 .5 o 0.0 10 38.6 10 1.6 10 0.0 10 38.3 10 .6 10 0.0 1 1 48.4 ii 1.8 1 1 0.0 ii 48.i 1 1 .8 1 1 o.o J2 58.3 12 2.0 12 0.0 12 58.o 12 2.0 12 o.o i3 2 8.1 i3 2. 1 i3 o.o i3 2 7 .8 i3 2. I i3 o.o i4 2 18.0 i4 2.3 i4 0.0 i4 2 17.6 i4 2.3 i4 o.o i5 2 27.8 i5 2.5 i5 0.0 i5 2 27.4 i5 2.5 i5 o.o 16 2 3 7 . 7 16 2.6 16 0.0 1.6 2 3 7 .3 16 2.6 16 0.0 i? 2 47-6 17 2.8 17 0.0 17 2 47.1 17 2.8 !7 0.0 18 2 5 7 .4 18 3.o 18 0.0 18 a 56.9 18 2.9 id o.o '9 3 7 .3 *9 3.i '9 o. '9 3 6.8 '9 3.i 1 9 0. 20 3 17.1 20 3.3 20 o. 20 3 16.6 20 3.3 2-0 o. 21 3 27.0 2J 3.5 21 o. 21 3 26.4 21 3.4 21 o. 22 3 36,8 22 3.6 22 o. 22 3 36.2 22 3.6 22 o . 23 3 46. 7 23 3.8 23 0. 23 3 46.1 2J 3.8 23 o. 24 3 56.6 24 3. 9 24 0. 24 3 55.9 24 3. 9 24 o. 25 4.i 25 0. 25 4-i 25 c 26 4.3 26 0. 26 4-3 26 0. 27 4-4 2 7 0. 27 4-4 27 o. 28 4.6 28 o. 28 4.6 28 0. 29 4.8 29 o. 29 4.8 29 o. 3o 4-9 3o 0. 3o 4-9 3o 0. 3i 5.i 3i 0. 3i 5.i 3i i o. 32 5.3 32 0. 32 5.2 32 ! 0. 33 5.4 33 0. 33 5.4 33 0. 34 . 5.6 34 o. 34 5.6 34 0. 35 5.8 35 o. 35 3.7 35 o. 36 5. 9 36 0. 36 5. 9 36 O.I 37 6.1 3 7 0. 3 7 6.1 3 7 o. 38 6.2 38 0. 38 6.2 38 > 39 6.4 3 9 o. 39 6.4 3 9 0. 4o 6.6 4o o. 4o 6.6 4o o. 4i 6.7 4i 0. 4i 6.7 4i 0. 42 6.9 42 0. 42 6.9 42 o. 43 7-1 43 0. 43 7.0 43 0. 44 7-2 44 o. 44 7.2 44 0. 45 7-4 45 o. 45 7-4 45 n 46 7.6 46 o. 46 7 .5 46 i 47 7-7 47 o. 47 7-7 47 o. 48 7-9 48 o. 48 7-9 48 o. 49 8.1 49 0. 49 8.0 49 o. DO 8.2 5o 0. bo 8.2 5o o. 5i 8.4 5i 0. 5i 8.4 5i 0. 52 8.5 52 o. 52 8.5 52 o. 53 8.7 53 o. 53 8.7 53 o. 54 8.9 54 o. 54 8.8 54 o. 55 9.0 55 0. 55 9.0 55 0.2 56 9.2 56 o. 56 9.2 56 0.3 5 7 9-4 5 7 o. 5? 9 .3 57 O.2 58 9 .5 58 o . 5? 9.5 58 0.2 5 9 9-7 5 9 o. 5 9 9 'Z 59 2 60 9-9 60 ' 60, 9.8 60 0.2 76 MIDDLE LATITUDE SAILING BY GUNTER. 1st. The extent from the distance 215, to the departure 167, on the lint; of numbers, will reach Irom the radius 90, to the course 50 58' on the line of sines. 2dly. The extent from radius 90, to the complement of the course 39 02' on the line of sines, will reach from the distance 215, to the difference of latitude 135.4, oil the hue oi numbers. 3dly. The extent from the complement of the middle latitude 41 37', to the radius 90, on the line of sines, will reach from the departure 107, to the difference of longitude 251.5, on the line of numbers. BY INSPECTION. As in Case V. Plane Sailing, find the course by seeking in Table II. till against the distance, in its column, is found the given departure in one of the following columns, adjoining to which, in the other column, will be the difference of latitude, which if greater than the departure, the course will be at the top, but if less the course will be found at the bottom. Then take the middle latitude as a course, and find the departure in the column of difference of latitude, against which, in the distance column, will be found the difference of longitude. Thus the distance 215, and the departure 167, ar* found nearly to correspond to a course of 51 degrees, and a difference of latitude of 135.3 ; then with the middle latitude 48, as a course, I enter the table, and seek for the departure 1(57, in the latitude column ; the distance corresponding 250 is the difference of longitude nearly. In all the preceding examples, we have used the middle latitude, without any correction, in computing the difference of longitude ; but when absolute accuracy is required, this latitude must be corrected. We have given in the following table the value of this correction in the most common cases. It requires no particular explana- jon : one example will serve to show its use. Suppose, therefore, tne two latitudes *,o be 40 and 60. Here the middle latitude is 50, and the difference of latitude 20 ; the tabular correction corresponding to these numbers is 57' ; adding this to 50, we get the corrected middle latitude 50 57', which is to be used instead of 50, when great accuracy is required. We have inserted in the notes at the bottom of the pages, in the preceding examples, the values of this correction, but have not introduced it into the calculations, because it is generally unnecessary on account of its smallness. TABLE. This Table contains the correction, in minutes, to be added to the Middle Latitude to obtain the corrected Middle Latitude. MID. LAT. 15 18 21 DIFFERENCE OF LATITUDE. Mm. LAT. 1 2 3 i 2 4 5 6 / 7 6 5 5 5 4 7 8 9 f 15 13 12 10 12 / 26 23 21 14 i 36 32 29 27 25 24 ~25~ 26 28 31 33 35 37 40 43 47 52 58 16 18 59 52 47 44 41 40 41 43 46 51 55 58 62 67 72 20 72 64 58 ~54~ 50 49 50 53 57 63 68 72 / / 1 1 1 i 3 3 2 2 2 2 ~2~ 2 2 i 5 4 4 3 3 3 i 9 8 7 ~7~ 6 6 i 12 10 9 9 8 8 i 18 16 15 14 13 12 13 13 14 47 41 37 35 32 32 32 34 36 40 43 46 ~49~ 52 57 62 68 76 o 15 18 21 24 30 35 11 10 10 ~io~ 11 11 20 18 18 18 19 20 24 30 36 40 45 50 3 3 4 5 5 5 6 6 7 8 8 9 40 45 50 55 58 60 ~62~ 64 (56 55 58 60 1 2 2 3 3 3 4 4 4 5 5 5 6 6 a 8 8 9 ~9~ 10 11 ~12~ 13 14 10 11 11 12 13 14 13 14 14 15 16 18 19 21 23 16 17 18 ~19~ 20 22 22 24 26 27 29 32 ~34~ 38 42 62 64 66 2 2 2 2 2 3 3 3 4 4 4 5 7 7 8 77 83 90 99 110 124 68 70 72 6 6 7 8 9 10 15 16 18 24 26 29 79 88 98 68 70 72 This Table is to be entered at the top with the difference of the two latitudes, anil at the side with the middle latitude ; under the former, and opposite to the latter, is correction, in minutes, to be added to the middle latitude, to obtain the correc' middle latitude. J LOGARITHMS. IN order to abbreviate the tedious operations of multiplication and division wich large numbers, a series of numbers, called Logarithms, was invented by Lord Napie;, Baron of March inston in Scotland, and published in Edinburgh in 1614; by means of which the operation of multiplication may be performed by addition, and division by subtrac- tion ; numbers may be involved to any power by simple multiplication, anct me root of any power extracted by simple division. In Table XXVI. are given the logarithms of all numbers from 1 to 9999 ; to each one must be prefixed an index, with a period or dot to separate it from the otner part, as in decimal fractions; the numbers from 1 to 100 are published in that table with their indices ; but from 100 to 9999 the index is left out for the sake of brevity ; but it may be supplied by this general rule, viz. The index of the logarithm of any integer or mixed number is always one less than the number of integral places in the natural number. Thus the index of the logarithm of any number (integral or mixed), betweer ?0 and 100, is 1 ; from 100 to 1000, it is 2 ; from 1000 to 10000 is 3, &c. ; the method of finding the logaritli:s from this table will be evident from the following examples. To fnd the, logarithm of any number less than 100. RULE. Enter the first page of the table, and opposite the given number will be found the logarithm with its index prefixed. Tims opposite 71 is 1.85126, which is its logarithm. To find the logarithm of any number between 100 and 1000. RULE. Find the given number in the left-hand column of the table of logarithms, and immediately under in the next column is a number, to which must be prefixed the number 2 as an index (because the number consists of three places of figures) and you will have the sought logarithm. Thus, if the logarithm of 149 was required ; this number being found in the left- hand column, against it, in the column marked at the top (or bottom), is foifud 17319 to which prefixing the index 2, we have the logarithm of 149=: 2. 17319. To find the logarithm of any number between 1000 and 10000. RULE. Find the three left-hand figures of the given number, in the left-hand column of the table of logarithms, opposite to which, in the column that is marked at the top (or bottom) with the fourth figure, is to be found the sought logarithm; to which must lie prefixed the index 3, because the number contains four places of figures. Thus, if the logarithm of 1495 was required; opposite to 149, and in the columr marked 5 at the top (or bottom), is 17464, to which prefix the index 3, and we have the sought logarithm, 3.17464. To find the logarithm of any number above 10000. KVLE. Find the three first figures of the given number in the left-hand column of Jie table, und the fourth figure at the top or bottom, and take out the corresponding number as in tne preceding rule ; take also the difference between this logarithm and .he next greater, and multiply it by the given number exclusive of the four first figures; rross off at the right hand of the product as many figures as you had figures of the /i ven number to multiply by; then add the remaining left-hand figures of this product to the logarithm taken from the table, and to the sum prefix an index equal to one less LOGARITHMS 29 than the immber of integral figures in the given number, and you will have the sought logarithm. To facilitate the calculation of these proportional parts, several small tables are placed in the margin, which give the correction corresponding to the difference D and to thejifth figure of the proposed number. The use of these tables will be seen in the following examples. Thus, if the logarithm of 14957 was required ; opposite to 149, and under 5, is 17464 . the difference between this and the next greater number, 17493, is 29, the difference D : this multiplied by 7 (the last figure of the given number) gives 203; crossing off the right-hand figure leaves 20.3 or 20 to be added to 17464, which makes 17484 ; to this prefixing the index 4, we have the sought logarithm, 4.17484. This correction, 20 may also be found by inspection in the small table in the margin, marked at the top with D =n29, and opposite to the fifth figure of the number, namely 7, at the side ; the corresponding number is the correction, 20. Again, if the logarithm of 1495738 was required ; the logarithm corresponding to 149 at the left, and 5 at the top, is, as in the last example, 17464 ; the difference between this and the next greater is 29 ; multiplying this by 738 (which is equal to the given number, excluding the four first figures) gives 21402; crossing off the three right-hand figures of this product (because the number 738 consists of three figures), we have the sorrection 21 to be added to 17464 ; and the index to be prefixed is 6, because the given number consists of 7 places of figures ; therefore the sought logarithm is 6.17485. This correction, 21, may be found as above, by means of the marginal table, marked at the top with D :=: 29, and at the side 7.38 or 7 nearly, to which corresponds 21, as before. To find the logarithm of any mixed decimal number. RULE. Find the logarithm of the number, as if it was an integer, by the last rule, to which prefix the index of the integral part of the given number. Thus, if the logarithm of the mixed decimal 149.5738 was required; find the logarithm of 1495738, without noticing the decimal point; this, in the last example, was found to be 17485 ; to this we must prefix the index 2, corresponding to the integral Dart 149 ; the logarithm sought will therefore be 2.17485. To find the logarithm of any decimal fraction less than unity. The index of the logarithm of any number less than unity is negative ; but to avoid the mixture of positive and negative quantities, it is common to borrow 10 or 100 in the index, which must afterwards be neglected in summing them with other indices thus, instead of writing the index 1, it is usually written -[- 9, or -|- 99 ; but in general it is sufficient to borrow 10 in the index ; and it is what we shall do in the rest of this work. In this way we may find the logarithm of any decimal fraction by the following rule. RULE. Find the logarithm of a fraction as if it was a whole number; see how many ciphers precede the first figure of the decimal fraction, subtract that number from 9, and the remainder will be the index of the given fraction. Thus the logarithm of 0,0391 is 8.59218; the logarithm of 0.25 is 9.39794; th*> logarithm of 0.0000025 is 4.39794, &c. To find the logarithm of a vulgar fraction. RULE. Subtract the logarithm of the denominator from the logarithm of the numerator (borrowing 10 in the index when the denominator is the greatest); the remainder will be the logarithm of the fraction sought. EXAMPLE 1. Required the logarithm of f . From log. of 3 0.47712 Take log. of 8 0.90309 Remainder, log. of f or .375 9.57403 EXAMPLE II. Required the logarithm of 3J> or From log. of 13 l. Take log. of 4 0.60206 Remainder, log. of 3| or 3.25.. . 0.51188 To find the number corresponding to any logarithm. RULE. In the column marked at the top (and bottom) of the table, seek for the nexi less logarithm, neglecting the index; note the number against it, and carry you L-./f the three othei figures; if you wish for greater accuracy, you must take the difference, D, between this tabular logarithm and the next greater, also the difference, rf, between that least tabular logarithm and the given one ; to the latter difference, i/, annex two or more ciphers at the right baud, and divide it by the former difference, D, and place the quotient* to the right hand of the four figures already found, and you will have the number sought, expressed in a mixed decimal, the integral part of which will consist of a number of figures (at the left hand) equal to the index of the logarithm increased by unity.f Thus, if the number corresponding to the logarithm 1.52634 was required, we find 520.34 in the column marked at the top or bottom, and opposite to it is 336; now, the index being 1, the sought number must consist of two integral places; therefore it ' If the given logarithm was 2.32838, we find that 32838 stands in the column marked at the top or bottom, directly opposite to 213, which is the number sought. because, the index being 2, the number must consist of three places of figures. If the number corresponding to the logarithm 2.57345 was required, we must look in the column 0; and we find in it, against the number 374, the logarithm 57287 ; and, guiding the eye along that line, we find the given logarithm, 5/345, in the column marked 5; therefore the mixed number sought is 3745; and, since the index is 2. the integral part must consist of 3 places; therefore the number sought is 374.5. If the index be 1, the number will be 37.45; and if the index be 0, the number will be 3.745. If the index be 8, corresponding to a number less than unity, the answer will be 0.03745, &c. Again, if the number corresponding to the logaritlm 5.57811 was required, look in the column 0, and find in it, against 378, and under 5, the logarithm 57807, the difference between this and the next greater logarithm, 57818, being I f, and the difference between 57807 and the given number, 57811, being 4 ; to this 4 affix two ciphers, which make 400, and d'vnle it by 11 ; the quotient is 36 nearly ; this number, being connected with the former four figures, makes 378536, which is the number required, since, the index being 5, the number must consist of six places of figures. To show, at one view, the indices corresponding to mixed and decimal numbers, we have given the following table. Mixed number. Logarithms. 40943.0 Log. 4.6J218 4094.3 Log. 3.61218 409.43 Log. 2.61218 40.943 Log. 1.61218 4.0943 Log. 0.61218 Decimal number. Logarithms. 0.40943 Log. 9.61218 0.040943 Log. 8.61218 0.0040943 ..Log. 7.61213 0.00040943 Log. 6.61218 0.000040943 Log. 5.61*18 MULTIPLICATION BY LOGARITHMS. H.ULE. Add the logarithms of the two numbers to be multiplied, and the sum will be the logarithm of their product. EXAMPLE I. Multiply 25 by 35. 25 Log. 1.39794 35 Log. 1.54407 Product, 875 Log. 2.94201 EXAMPLE II. Multiply 22.4 by 1.8. 22.4 Log. 1.35025 1.8 Log. 0.25527 Product, 40.32 Log. 1.60552 * This quotient must consist of as many places of figures as there were ciphers annexed, conformable to the rules of the division of decimals. Thus, if the divisor was 40, and the number to which two ciphers were annexed was 2, making 2.00, the quotient must not be estimated as 5, but as 05, and theJ two figures must be placed to the right of the four figures before found. t If the index corresponds to a fraction less than unity, you must place as many ciphers to the left of that number as are equal to the index subtracted from 9, the decimal point being placed to the Jeft of uiese ciphers ; in this manner you will obtain the sought number. We may find the fifth figure of the required number by means of the marginal tables, by entering the table corresponding at the top to the proposed value of D, and in the right-hand column with d; thff eorresponding number is the fifth figure o<" the required natural number. LOGARITjIIVia. 31 EXAMPLE III. Multiply 3.26 by 0.0025. 3.26.' Log. 0.51322 0.0025 Log. 7.39794 Product, 0.00815 Log. 7.91116 EXAMPLE IV. Multiply 0.25 by 0.003. 0.25 Log. 9.3971M 0.003 Log. 7.4771',! Product, 0.00075 Log. 6.87506 In the hist example, the sum of the two indices is 16; but since 10 was borrowed in each number, we have neglected 10 hi the sum ; and the remainder, (5, hein" less than the other 10, is evidently the index of the logarithm of a fraction less than unity DIVISION BY LOGARITHMS. RULE. From the logarithm of the dividend subtract the logarithm of the tlie remainder will be the logarithm of the quotient. divisor EXAMPLE 1. Divide 875 by 25. 875 Log. 2.94201 25 Log. 1.39794 Quotient, a5 . .Log. 1.54407 EXAMPLE II. Divide 40.32 by 22.4. 40.32 Log. 1.60552 22.4 Log. 1.35025 Quotient, 1.8 Log. 0.25527 EXAMPLE 111. Divide 0.008 15 by 0.0025. 0.00815 Log. 0.0025 Log. Quotient, 3.26 Log. 0.5 1 323 7.91116 7.39794 EXAMPLE IV. Divide 0.00075 by 0.025. 0.00075 Log. 0.025 Log. Quotient, 0.03 Log. 8.47712 6.87506 8.39794 In Example III. both the divisor and dividend are fractions less than unity, and the divisor is the least ; consequently the quotient is greater than unity. In Example IV. both fractions are less than unity ; and, since the divisor is the greatest, its logarithm is greater than that of the dividend ; for this reason it is necessary to borrow 10 in the index before making the subtraction ; hence the quotient is less than unity. INVOLUTION BY LOGARITHMS. RULE. Multiply the logarithm of the number given, by the index of the power to which the quantity is to be raised ; the product will be the logarithm of the power sought. But in raising the powers of any decimal fraction, it must be observed, that the first significant figure of the power must be put as many places below the place of units as the -index of its logarithm wants of 10 multiplied by the index of the power EXAMPLE I. Required the square of 18. 18 Log. 1.25527 Answer, 324 .'. Log. 2.51054 EXAMPLE II. Required the cube of 13. 13 Log. 1.11394 Answer, 2197 Log. 3.34182 EXAMPLE III. Required the square of 6 4. 6.4 Log. 0.80658 2 Answer, 40.96 Log. 1.61236 EXAMPLE IV. Required the cube of 0.25. 0.25 Log. 9.39794 3 Answer, 0.015625 Log. 28.19382 In the last example, the index 28 wants 2 of 30 (the product of 10 by the power 3); therefore the fin* significant figure of the answer, viz. 1, is placed two figures distant the nl-ve of unit* LOGARITHMS EVOLUTION BY LOGARITHMS. RULE. Divide the logarithm of the number bp the index of the power ; the quotient will be the logarithm of the root sought. Bat if the power whose root is to be extracted is a decimal fraction less than unity, prefix to the index of its logarithm a figure less by one than the index of the ppwer,* and divide the whole by the index of the power ; the quotient will be the logarithm of the root sought. EXAMPLE I. Wht is the square root of 324 ? ?J4 Log. 2 ) 2.51055 Answer, 18 Log. 1.25527 EXAMPLE II. Required the cube root of 2197. 2197.. Log. 3)3.34383 Answer, 13 Log. 1.11394 EXAMPLE III. Required the square root of 40.96. 40.96 Log. 2 ) 1.61236 Answer, 6.4 Log. 0.80618 EXAMPLE IV. Required the cube root of 0.015625. 0.015625 Log. 8.19382 Prefix 2 to the index 3 ) 28. 19382 Answer, 0.25 Log. 9.39794 TO WORK THE RULE OF THREE BY LOGARITHMS. When three numbers are given to find a fourth proportional, in arithmetic, we make a statement, and say, As the first number is to the second, so is the third to the fourth ; and by multiplying the second and third together, and dividing the product by the first, we obtain the fourth number sought. To obtain the same result by logarithms, we must add the logarithms of the second and third numbers together, and from the sum subtract the logarithm of the Jirst number; the remainder will be the logarithm of the sought fourth number. EXAMPLE I. If 6 yards of cloth cost 5 dollars, what will 20 yards cost ? As 6. Log. 0.77815 Is to 5 Log. 0.69897 So is 20 Log. 1.30103 Sum of 2d and 3d 2.00000 Subtract the first. . .- 0.77815 To 16.67 Log. 1.22185 The answer, therefore, is 16 dollars and lVu> or 16 dollars and 67 cents. EXAMPLE II. II a ship sails 20 miles in 7 hours, how much will she sail in 21 hours at the same rate ? As 7 Log. 0.84510 Is to 20 Log. 1.30103 So is 21 Log. 1.32222 Sum of 2d and 3d 2.62325 Subtract the first 0.84510 To 60 Log. 1.77815 The answer is 60 miles. TO CALCULATE COMPOUND INTEREST BY LOGARITHMS. To 100 dollars add its interest for one year ; find the logarithm of this sum, and reject 2 in the index ; then multiply it by the number of years and parts of a year for which the interest is to be calculated ; to the product add the logarithm of the sum put at interest ; the sum of these two logarithms will be the logarithm of the amount of the given sum for the given time. * In tliis rule it is supposed that 10 is borrowed in finding the index to the decimal according U the ritte, pige 29. LOGARITHMS. 38 EXAMPLE. Inquired the amount of the principal and interest of 355 dollars, fet at 6 per cent compound interest, for 7 years. Adding 6 to 100 gives 106 ; whose logarithm, rejecting 2 in the index, is 0.02531 Multiplied by 7 Product 0.17717 Principal, 355 dollars Log. 2.55023 Sum gives the logarithm of 533.83 Log. 2.72740 Therefore the amount of principal and interest is 533 dollars and 83 cents. To Jind the logarithm of the sine, tangent, or secant, corresponding to any number of degrees and minutes, by Table XXVII. The given number of degrees must be found at the bottom of the page when between 45 and 135, otherwise at the top ; the minutes being found in the column marked M, which stands on the side of the page on which the degrees are marked ; thus, if the degrees are lefts than 45, the minutes are to be found in the left-hand column, &c.: and it must be noted that if the degrees are found at the top, the names of hour, sine, cosine, tangent, &c., must also be found at th'e top ; and if the degi-ees are found at the bottom, the names sine, cosine, &,c.,must also be found at the bottom. Then opposite to the number of the minutes will be found the log. sine, log. secant, &c. in the columns marked sine, secant, &c. respectively. EXAMPLE I. Required the log. sine of 28 37'. Find 28 at the top of the page, directly below which, in the left-hand column, find 37' ; aguinst which, in the column marked sine, is 9.68029, the log. sine of the given number of degrees ; and in the same manner the tangents, &c. are found. EXAMPLE II. Required the log. secant of 126 20 / . Find 126 at the bottom of the page, directly above which, in the left-hand column, find 20' ; against which, in the column marked secant, is 10.22732 re- quired. To find the logarithm of the sine, cosine, Sfc.for degrees, minutes, and seconds, by Table XXVII. Find the numbers corresponding to the even minutes next above and below the given degrees and minutes, and take their difference, D ; then say, As 60" is to the number of seconds in the proposed number, so is that difference, D, to a correction, d, to be applied to the number corresponding to the least number of degrees and minutes ; additive if it is the least of the two numbers taken from the table, otherwise subtractive. EXAMPLE III. Required the log. sine of 24 16' 38". Sine of 24 16' Log. 9.61382 Sine of 24 17 Log. 9.61411 Difference D 29 Then, as 60" : 38" ::29 : 18, which, being added to the number corresponding to 24 16', gives 9.61400, the log. sine of 24 16' 38". EXAMPLE IV. Required the log. secant of 105 20> 16". Secant of 105 20 7 Log. 10.57768 Secant of 105 21 Log. 10.57723 Difference .D 46 Then, as 60" : 16" : 46 : 12, which, being subtracted from the number corre- sponding to 105 20', gives 10.57756, the log. secant of 105 2(X 16". If the given seconds be , , parts may be taken of the differ , , or, or any other even parts of a minute, the like rence of the logarithms, and added or subtracted as above, which may be frequently done by inspection. These proportional parts may also be found very nearly by means of the three columns of differences for seconds, ^ven, for the first time, in the ninth edition of this work The first cohmm of differences, which is to be used with the two columns marked A, A, is placed betwee these columns. The secuiid column of differences, whica is to bo used with the two columns B, B, is placed between these two columns. In like manner, the third column of differences, between the columns C, C, is to be used with them. The correction of the tabular logarithms in any of the columns A, B, C, for any number of seconds, is found by entering the left-hand Column of the table, marked S'*at the top, and finding the number of seconds ; opposite to this, in the column of differences, will be found the corresponding correction. Thus, in the table, page 215, which contains the log. sines, tangents, &c., for 30, the corrections corresponding to 25", are 9 for the columns A, A, 12 for the columns B, B, 3 for the columns C, C ; so that, if it were required to find the sine, tangent, or secant of 30 12' 25", we must add these corrections respectively to the numbers corresponding to 30 12' ; thus, COL. A. COL. B. COL. C Logs, for 30 12' .... Sine 9.70159 Tangent ---- 9.76493 Secant ____ 10.06335 Corrections for 25" in S' -f- 9 +12 -f- 3 Logs, for 30 12' 25" .... 9.70168 9.76505 1006338 these corrections being all added, because the logarithms increase in proceeding from 30 12' to 30 13'. Instead of taking out the logarithms for 30 12', and adding the correction for 25", we may take out the logarithms for 30 13', and subtract the correction for 60" 25'', or 35", found in the margin S' ; thus, Logs, for 30 13' .... Sine 9.70180 Tangent ____ 9.76522 Secant ____ 10.06342 ~ 4 Corr. for 35" in col. S', or 25" in col. G' .... Logs, for 30 12' 25" .... 9.7_0167 9.76505 10.06338 The corrections are in this case subtracted, because the logaiithms decrease in proceeding backward 35" from 30 13', to attain 30 12' 25". The tangents and secants, in this example, are the same by both methods; the sines differ by one unit, in the last decimal place, and this will frequently happen, because the difference of the logarithms for 1', sometimes differ one or two units from the mean values which are used in the three columns of differences. The error arising from this cause is generally diminished by using the smallest angle * S', when the seconds of the pro- posed angle are smaller than 30" ; or the greatest angle G', when the number of seconds are greater than 30". Thus, in the above example, where the angle S' 30 12', and the angle G' =30 13', it is best to use the angle S' when the given ar.gle is less than 30 12' 30", but the angle G' when it exceeds 30 12' 30". Thus, if it be required to find the sine of 30 12' 51", it is best to use the angle G' =30 13', and find the correction by entering the margin marked S', with the difference 60" 51" 9", opposite to which, in the column of differences, is 3, to be subtracted from log. sine of 30 13' = 9.70180, to get the log. sine of 30 12' 51" = 9.70177. To save the trouble of subtracting the seconds from 60", we may use the rfght-hand margin, marked G', and the correction may then be found by the following rules : RULE 1. When the smallest angle S' is used, find the seconds in the column S', and take out the corresponding correction, which is to be applied to the logarithm corresponding to S' ; by adding, if the log. of G' be greater than the log. of S'; otherwise, by subtracting. RULE 2. When the greater angle G' is used, find the seconds in the column G', and take out the corresponding correction, which is to 'be applied to the logarithm corresponding to G' ; by adding, if the log. of S' be greater than the lo^. of G' ; otherwise, by subtracting; so that, in all cases, the required logarithm may fall be- tween the two logarithms corresponding to the angles S' and G'. The correctness of these rules will evidently appear by comparing them with the preceding examples ; and by the inverse process we may find the angle coi respond- ing to a given logarithm, as in the next article. We have given at the bottom of the page, in this table, a small table for finding the proportional parts for the odd seconds of time, corresponding to the column of Hours A. M. or P. M. ; to facilitate the process of finding the log. sine, cosine, &c* corresponding to the nearest second of time in the column of hours, or, on the con- trary, to find the nearest second of time corresponding to any given log. sine, cosine. &c. Thus, in the preceding examples, where the angle S'zz=30 12', and the * If we neglect the seconds in any proposed angle whose sine. &c. is required, we get the angle denoted above by S', and this angle increased by I', is represented by G' ; so that the proposed angle falls between S' and G' ; S' being a smaller, and G' a greater angle than that whuse log. sine, &c., is required ; the letters S ' and G', accented for minutes, being used because they are easily remembered as the \nitiais of smaller and greater LOGARITHMS s hl the column of Hours P.M., are ;; and if we wish to find the log. sine, cosine, &r corresponding to any intermediate time, as, for example, 4" l m 39% which differs 3- from tl.e angle S' we must find the tabular logarithm corresponding to S', and applv the correction for 3% given hy the table at the bottom of the page, as in the following examples : Logs, for S' - 4" 1- 36' Sine 9.70159 Tangent 9.76493 Secant m0633J Correction for -f- 3 s -|_ 8 _|_ n 13 Logs, for ..... 4" 1" 39 s Sine 9.70167 Tangent 9.76504 Secant 1O06338 Nearly the same results are obtained by using the angle G', in the manner we nave before explained : Logs, for G' 4" l m 44 s Sine 9.70180 Tangent 9.76522 Secant 10.06342 Correction for 5 s 13 _ 18 _ 5 Logs. for. ... 4 h 1 39 s Sine 9.70167 Tangent 9.76504 Secant 10.06337 These corrections must be applied by addition or subtraction, according to the directions given above, so as to make the required logarithm fall between those which correspond to the times S' and G'. the table at the bottom of the page, it is found to correspond to 3 s ; adding this to the time S' z=4 h l m 36% we get 4 h l m 39* for the required time. We may proceed in the same manner with the logarithms in the columns B, C ; using the numbers corresponding, marked 15, C, respectively, in the table at the bottom of the page. To Jind the degrees, minutes, and seconds, corresponding to any given logarithm sine, cosine, $c. by Table XXVII. Find the two nearest numbers to the given log. sine, cosine, &c., in the column marked sine, cosine, &c., respectively, one being greater, and the other less, and take their difference, D; take also the difference, d, between the given logarithm and the logarithm corresponding to the smallest number of degrees and minutes ; then say, As the first found difference is to the second found difference, so is 60" to a number of seconds to be annexed to the smallest number of degrees and minutes before found. The three columns of differences may also be used, by an inverse operation to that which we have explained in the preceding article. EXAMPLE V. Find the degrees, minutes, and seconds (less than 90), corresponding to the log. sine 9.61400. Next less log. S' z=24 16' 9.61382 Log. of smallest angle S'=24 16' is 9.61382 Greater G' = 24 17 9.61411 Given log 9.61400 D = 29 c?_ 18 Then say, As 29 : 18 : : 60" : 38", nearly ; which, annexed to 24 16', give 24 16' 38", answering to lo