a to 00 o >- VV o rl IN Henry Senger "**% ^ n PAGES OF TABLES FROM RAYMOND'S PLANE SURVEYING Copyright, 1896, by AMERICAN BOOK COMPANY TV? 3 IN MEMORIAM \i ' " r \ TABLES. V. TABLES. TABLE I. 361 CORRECTION TO ONE HUNDRED UNITS MEASUR^ ALOF& THE!,; '\1 SLOPES GIVEN. UNITS RISE IN 100. CORRESPONDING VERTICAL ANGLE. CORRECTION. 1.02 o35' 0.005 2.01 i 09' O.O2O 3-03 i 44' 0.046 4.02 2 1 8' 0.081 5.01 2 52' 0.125 6.00 3 26' 0.179 7.00 4 oo' 0.244 8.02 4 35' 0.320 9.01 5 09' 0.404 10.01 5 43' 0.497 20.01 11 19' 1.617 30.00 1 6 42' 4.218 40.00 21 48 7.151 50.00 26 34' 10.559 TABLE II.i CORRECTION COEFFICIENT FOR TEMPERATURE AND HYGROMETRIC CONDITIONS. This correction is used when no hygrometric observations have been made. To the difference in altitude found in Table III. for the given barometer readings is added algebraically the product of that difference and the correction below given, according to the formula, Diff. Alt. = (Diff. by Table III.) (1 + c). SUM O. T.2 CORR. COEFF.3 SUM O. T. CORR. COEFF. SUM 0. T. CORR. COEFF. - 0.1024 70 0.0273 140 0.0471 10 0.0915 80 0.0166 150 0.0575 20 0.0806 90 0.0058 160 0.0677 30 0.0698 100 0.0049 170 0.0779 40 0.0592 no 0.0156 1 80 0.0879 50 0.0486 120 0.0262 60 0.0380 I 3 0.0368 1 Computed from Tables I. and IV., Appendix 10, " U. S. Coast Survey Report " for 1881. J Sum of Observed Temperatures. 8 Correction Coefficient. 362 APPENDIX. TABLE III. 1 BAROMETRIC ELEVATIONS. Giving altitudes above arbitrary sea level (barometer reading 30 inches) for various barometer readings B. To determine difference of elevation of two points having barometer readings B and B v take from the table the altitudes corresponding to B and B v and correct their difference by Table II. The corrected difference is the quantity required. B. A. DlFF. FOR .01. B. A. DlFF. FOR .01. B. A. DlFF. FOR .01. Inch en. Feet. Feet. Inches. Feet. Feet. Inches. Feet. Feet. II. O 27,336 24.6 14.0 20,765 -19-5 17.0 15,476 l6.O II. I 27,090 24.4 14.1 20,570 19-3 17.1 !53'6 IS-9 II. 2 26,846 24.2 14.2 20,377 19.1 I 7 .2 '5, '57 J s 15.8 "3 11.4 26,604 26,364 24.0 23.8 14-3 14.4 20,186 i #997 18.9 18.8 17-3 17.4 14,999 14,842 '5-7 15.6 "5 26,126 23.6 14-5 19,809 18.6 17-5 14,686 15.5 H.6- 25,890 23-4 I 4 .6 19,623 18.6 I 7 .6 H,53i '5-4 11.7 25,656 23.2 14.7 19,437 18.5 17.7 '4,377 '5-4 u. 8 25,424 23.0 14.8 19,252 18.4 I 7 .8 14,223 11.9 25,194 22.8 14.9 19,068 18.2 17.9 14,070 !=;. 2 I2.O 24,966 22.6 I 5 .0 18,886 18.1 18.0 13,918 J 15.1 12. 1 24,740 22-4 '5- 1 18,705 18.0 18.1 '3,767 IS.O 12.2 24,516 22.2 15.2 18,525 17.9 18.2 13,617 D 14.9 12.3 24,294 22.1 '5-3 18,346 / .7 17.8 18.3 13,468 14.9 12.4 24,073 21.9 15-4 18,168 17.6 18.4 '3,3'9 14.7 I2. 5 23,854 21.7 15-5 17,992 17. c 18.5 I3,i7 2 14.7 12.6 23,637 / 21.6 15.6 17,817 / J 17.4 18.6 13,025 14.6 I2. 7 23,421 21.4 15-7 17.643 18.7 12,879 14.6 12.8 23,207 21.2 15.8 17,470 17.2 18.8 '2,733 14.4 12.9 22,995 21. 15-9 17,298 17.1 18.9 12,589 14.4 13.0 22,785 2O.9 16.0 17,127 16.9 19.0 '2,445 '3-' 22,576 20.8 16.1 16,958 16.9 19.1 12,302 14.2 13.2 22,368 20. 6 1 6.2 16,789 16.8 19.2 12,160 14.2 13-4 22,162 21,958 20.4 20. i 16.3 16.4 16,621 16.7 16.6 19-3 16.4 12,018 11,877 14.1 14.0 '3-5 2I ,757 20. o 16.5 16,288 16.4 19-5 ",737 13.9 13.6 '3-7 2 ',557 21,358 19.9 19.8 16.6 16.7 16,124 15,961 16.3 16.3 19.6 19.7 ",598 ",459 O s '3-9 13.8 13.8 21,160 -7 ** 19.8 16.8 15,798 * w * 3 16.2 19.8 11,321 vJ 17.7 13-9 20,962 19.7 16.9 15,636 16.0 19.9 11,184 J 1 17.7 14.0 20,765 7 / 17.0 15,476 20. o 11,047 o / 1 Taken from Appendix 10, " U. S. Coast and Geodetic Survey Report " for 1881, TABLES. 363 TABLE III. (continued). B. A. DlFF. FOR .01. B. A. DlFF. FOR .01. B. A. DJFF. FOR .01. Inches. Feet. Feet. Inches. Feet. Feet. Inches. Feet. Feet. 20.0 11,047 -13.6 23-7 6,423 u-5 27.4 2,470 0.9 2O. I 20. 2 20.3 10,911 10,776 10,642 * J" v 13-5 13-4 23-8 23-9 24.0 6,308 6,194 6,080 11.4 11.4 27.5 2 7 .6 27.7 2,371 2,272 2,173 y.y 9.9 9-9 Q 8 20.4 10,508 13-3 24.1 5,967 11.3 27.8 2,075 y. u 9.8 20.5 20. 6 io,375 10,242 13-3 13.2 24.2 24-3 5,854 5,741 "3 II. 2 27.9 28.0 '.977 ,880 9-7 9.7 20.7 10,110 o 24.4 5,629 II. I 28.1 ,783 9.7 20.8 9,979 13 I 24-5 5.518 I I.I 28.2 ,686 / 9.7 20.9 9,848 13.0 2 4 .6 5,407 II. I 28.3 ,589 y / 9.6 21.0 21. 1 9,718 9,589 12.9 12.9 24.7 24.8 5,296 5,186 II. O IO.9 28.4 28.5 ,493 ,397 9.6 g.c 21.2 21.3 9,460 9-332 12.8 12.8 24.9 25.0 5,077* 4,968 IO.9 IO.9 28.6 28.7 ,302 ,207 -7 J 9-5 9. c 21.4 9,204 12.7 25-1 4,859 10.8 28.8 ,112 s D 9.4 21.5 9,077 12.6 25.2 4,751 10.8 28.9 ,018 9.4 21.6 8,951 12.6 25-3 4,643 10.8 29.0 924 9.4 21.7 21.8 8,825 8,700 12.5 12.5 25-4 25-5 4,535 4,428 10.7 10.7 29.1 29.2 830 736 9.4 9-3 21.9 8,575 12.4 25.6 4,321 10.6 29-3 643 9-3 22.0 8,451 12.4 25-7 4,215 10.6 294 550 9.2 22.1 8,327 12.3 25.8 4,109 10.1; 29-5 458 9.2 22.2 8,204 12.2 25-9 4,004 J IO. C 29.6 366 9.2 22.3 8,082 12.2 26.0 3,899 IV. ^ 10.1; 29.7 274 y m Q.2 22.4 7,960 12.2 26.1 3,794 v J 10.4 29.8 182 3r 9.1 22.5 7,838 12. 1 26.2 3,690 10.4 29.9 9 1 9.1 22.6 7,717 12.0 26.3 3,586 * v .*f- IO.3 30.0 oo 9.1 22.7 7,597 12. 26.4 3,483 IO.T 30.1 -91 Q.O 22.8 7,477 II.9 26.5 3,38o AW. ^ IO-3 30.2 181 ^/^ 9-O 22.9 7,358 II.9 26.6 3,277 IO.2 30.3 271 9.0 23.0 7,239 ii. 8 26.7 3,175 10.2 3-4 361 9-0 23.1 7,121 ii. 7 26.8 3,073 IO. I 30.5 45 l 8.9 23.2 7,004 / II. 7 26.9 2,972 IO. I 30.6 540 8.9 23-3 6,887 / II.7 27.0 2,871 IO. I 3-7 629 <7 8.8 23-4 6,770 / ii. 6 27.1 2,770 IO.O 30.8 717 8.8 23-5 6,654 1 1. 6 27.2 2,670 IO.O 30-9 805 -8.8 23-6 6,538 II. C 27-3 2,570 IO.O 31.0 -893 23-7 6,423 J 27.4 2,470 \\ 364 u'* APPENDIX. TABLE IV. POLAR DISTANCE OF POLARIS. For January 1 of years named. 1894 1897 1900 1903 1906 1909 1912 1915 1918 1921 1 1543' 1 14.50' 1 13.55' 1 12.62' i 11.68' i 10.75' i 09.82' i 08.88' i 07.97' i 07.03' sin polar distance Sin of azimuth at elongation = . : cosine latitude Latitude = altitude of Polaris at culmination polar distance refraction correc- tion given below. LATITUDE. CORRECTION, MINUTES. LATITUDE. CORRECTION, MINUTES. 20 30 40 2.60 l.6 5 I.I3 50 60 0.80 0-55 TABLE V. 1 AMOUNT AND VARIATION OF THE MAGNETIC NEEDLE FROM ITS MEAN DAILY POSITION. The letters E and W indicate which side of the mean position the needle points. LOCAL MEAN TIME ; MORNING HOURS. 6 h 7 h 8 h 9 h 10* nh I2 h December, January, February : Latitude 37 to 49 / o 7 E r i i E l i o F l 2 2 E / T C F / n T W 1 T 8 W Latitude 25 to 37 ...... o i W o i E i o E 2 O E 1.5 XL, 2 2 F T T F n e \V March, April, May : Latitude 37 to 49 26E Q 8 E A A F a c F T f\ F o 8 \V Latitude 25 to 37 .... i 6 E 28 E F oo ^ 2 6 E T T F n f\ \V T n "W June, July, August : Latitude 37 to 49 Latitude 25 to 37 .... 4.0 E 2 A E 5-6 E 4 o E DO -^ 5-7 E A 2 F 4-5 E 2 O F 1.7 E r> c F 1.6 E T f\ W 4.1 VV r> 8 W September, October, November: Latitude 37 to 49 .... i 8 E 2 6 F 4" s 3 T F 2 C. E T n F T e F o o W Latitude 25 to 37 . . . 2 I E 2 6 E 2 I E n 6 F 1.5 & n n \V *\ W SEASON AND POSITION IN LATITUDE. LOCAL MEAN TIME; AFTERNOON HOURS. o h I* 2* 3 h 4 h 5 h 6* December, January, February : Latitude 37 to 49 Latitude 25 to 37 . / 1.8 W 0.5 W 3.8 W 1.9 W 4.1 W 2.8 W 3-3 W 2.1 W / 2.9 W 1.5 W 4.8 W 2.6 W 5.6 W 3.2 W 4.0 W 2.3 W / 2.8 W 1.8 W 4.6 W 2.8 W 5.6 W 3.1 W 3.4 W 1.9 W 1 2.1 W 1.6 W 3-8 W 2.4 W 4.6 W 2.4 W 2.3 W 1.2 W / 1.3 W i.oW 2.5 W 1.6 W 3.0 W i.5 W 1.2 W 0.7 W / 0.7 W 0.4 W 1.4 W 0.9 W 1.4 W 0.8 W 0.6 W 0.4 W / 0.2 W o.i W 0.7 W 0.5 W 0.6 W 0.4 W o.i W 0.2 W March, April, May: Latitude 37 to 49 .... Latitude 25 to 37 . June, July, August : Latitude 37 to 49 .... Latitude 2^ to 37 September, October, November : Latitude 37 to 49 . . . . . . Latitude 25 to 37 1 From " Manual of Instructions " issued by the U. S. Land Office to Surveyors General. IS/ TABLES. TABLE VI ?> I. VI 365 APPROXIMATE LOCAL MEAN TIMES (COUNTING FROM NOON 24 HOURS) OF THE ELONGATIONS AND CULMINATIONS OF POLARIS IN THE YEAR 1897 FOR LATITUDE 40 N. ; LONGITUDE 6 h W. FROM GREENWICH. DATE. EAST ELONGATION. WEST UPPER ELONGATION. CULMINATION. LOWER CULMINATION. h. rn. h. m. Jan. i o 38.2 12 27.8 6 33-6 18 31-6 15 23 39-0 II 32.5 5 38.6 !7 36.3 Feb. i 22 31-8 10 25-4 i 4 31.2 16 29.2 '5 21 36.6 9 30-2 3 35-9 15 33-9 Mar. i 20 41.4 8 34-9 2 40.7 H 38.7 15 19 46.3 7 39-8 I 45-7 13 43-7 Apr. i 18 39-3 6 32-8 O 38-6 12 36.7 May l \ 16 i -44-3 5 4 37-8 35-o 23 22 39-7 36.8 U. 10 1 4L5 15 15 46.6 3 40.1 21 41.9 9 43-9 June i H 39-9 2 33-4 2O 35-3 8 37-3 15 13 45- I 38.5 19 40.4 7 42.4 July i 12 42.4 35-9 18 37-8 6 39-8 15 II 47-5 23 37- * 17 42.9 5 44-9 Aug. i 10 41.0 22 30.6 16 3 6 -4 4 38.4 '5 9 46.! 21 35-7 15 41-5 3 43-5 Sept. i 8 39-5 2O 29.1 H 34-9 2 36.9 15 7 44.6 19 34-2 13 40.0 I 42.0 Oct. i 6 41.8 18 3i-4 12 37-2 39-2 15 5 46.8 1 7 36.4- II 42.2 2 3 40-3 Nov. i 4 40.0 16 29.6 10 35-4 22 33-4 15 3 44.8 15 34-4 9 40.2 21 38-2 Dec. i 2 41.8 H 3M 8 37-2 2O 35-2 15 1 46-5 !3 36-1 7 41.9 19 39-9 To refer to any calendar day other than the first and fifteenth of each month, subtract 3.94 for every day between it and the preceding tabular day, or add 3.94 m for every day between it and the succeeding tabular day. To refer the tabular times to any year subsequent to the year 1897, add 0.25 m (nearly) for every additional year (after 1900, 0.2 m ). Also, For the second year after a leap year, add, 0.9 m . For the third year after a leap year, add, 1.7 m . For leap year before March 1, add, 2.6 m . For leap year on and after March 1, subtract, 1.2 m . For the first year after a leap year the table is correct, except for the regu- lar annual change. To refer the tabular times to other longitudes than six hours, add when east, and subtract when west of six hours, 0. 16 m for each hour. To refer to any other than the tabular latitude between the limits of 25 and 50 north, add to the time of west elongation 0.13 m for every degree south of latitude 40, and subtract from the time of west elongation 0.18 m for every degree north of 40. Reverse these signs for corrections to the times of east elongation. For latitudes as high as 60, diminish the times of west elongation and increase the times of east elongation by 0.23 m for every degree north of latitude 40. 1 Computed from information contained in the " Manual of Instructions " issued by the General Land Office. The information was furnished by the U. S. Coast and Geodetic Survey. 366 APPENDIX. TABLE VII. 1 REFRACTION CORRECTIONS TO DECLINATION OF TEIE SUN. The hour angle is the time either side of noon. LATI- TUDE. HOUR ANGLE. DECLINATIONS. + 20 +i5 D + 10 +5 -5 10 -15 2CP o ' b. 25 oo O o 05 o 10 '5 21 o 27 o 33 o 40 o 48 o 57 2 o 08 o 14 o 19 o 25 o 31 o 38 o 46 o 54 i 5 3 12 o 18 o 24 o 30 o 37 o 44 o 53 i 04 i 18 4 o 23 o 29 o 35 o 45 o 53 i 03 i 16 i 3i i 52 5 o 49 o 59 I 10 i 24 i 52 2 07 2 44 3 46 5 43 27 30 o o 08 o 13 o 18 o 24 o 30 o 36 o 44 o 52 I 02 2 O II o 16 22 o 28 o 34 o 41 o 49 I OO I IO 3 o 17 22 o 28 o 35 o 42 o 50 I 00 I II I 26 4 o 28 o 35 o 42 o 50 I OO I II i 26 1 43 2 09 5 o 54 I 05 i 18 i 34 i 54 2 24 3 ii 4 38 8 15 30 oo O IO 15 21 o 27 o 33 o 40 o 48 o 57 I 08 2 o 14 o 19 o 25 o 31 o 38 o 46 o 54 i 05 i 18 3 20 o 26 o 32 o 39 o 47 55 i 06 i 19 i 36 4 o 32 o 39 o 46 o 52 i 06 i 19 i 35 i 57 2 29 5 I 00 I 10 I 24 i 52 2 07 2 44 3 4 6 5 43 13 O6 32 3 o o 13 o 18 o 24 o 30 o 36 o 44 o 52 I 02 I H 2 o 17 22 o 28 o 35 o 42 o 50 I 00 III I 26 3 o 23 o 29 o 35 o 43 o 5i I 01 I 13 I 28 i 47 4 o 35 o 43 o 5i I 01 I 13 I 27 I 46 2 I 3 2 54 5 i 03 i '5 1 3 1 i 53 2 2O 3 5 4 25 7 36 35 o 15 O 21 o 27 o 33 o 40 o 48 o 57 i 08 I 21 2 20 o 25 o 32 o 38 o 46 55 i 5 i 18 i 35 3 o 26 o 33 o 39 o 47 o 56 i 07 I 21 i 38 2 OO 4 o 39 o 47 o 56 i 07 I 20 i 36 i 59 2 32 3 25 5 i 07 I 20 i 38 2 OO 2 34 3 29 5 H 10 16 1 Computed from formula C=57"cot in which 6 is the declination, plus when north, and minus when south; and N an auxiliary angle found by tan N= cot cos t, in which is the latitude of the place, and t the angle between the meridian of the place and the meridian through the sun at the given time, called the " hour angle." The formulae are from Chauvenet's " Spherical and Practical Astronomy," vol. I., p. 171. The table was computed by Mr. Edward W. Arms, C.E., for Messrs. W. & L. E. Gurley, of Troy, N.Y., and is here used by their permission. TABLES. 367 TABLE VII. (continued). LATI- TUDE. HOUR ANGLE. DECLINATIONS. +20> -MS + I0 c +5 00 -5 10 -15 20 3 o ' h. , .. 37 3 o 18 o 24 o 30 o 36 o 44 o 52 i 02 i 14 I 2 9 2 O 22 o 28 o 35 o 42 o 50 I 00 I 12 i 26 i 45 3 o 29 o 36 o 43 o 52 i 02 I 14 I 29 i 49 2 16 4 o 43 5 1 I OI I 13 i 27 i 49 2 I 4 2 54 4 05 5 I II i 26 i 44 2 10 2 49 3 55 6 15 H 58 40 oo 21 o 27 o 33 o 40 o 48 o 57 i 08 I 21 i 03 2 o 25 o 32 o 39 o 46 o 52 i 06 i 19 i 35 i 57 3 33 o 40 o 48 57 I 08 I 21 1 38 2 O2 2 36 4 o 47 o 55 i 06 i 19 1 36 I 5 8 2 30 3 21 4 59 5 i 15 1 5 1 2 2O 3 05 4 25 7 34 25 18 42 3 o 24 o 30 o 36 o 44 o 52 i 02 i 14 i 29 i 49 2 o 28 o 35 o 39 o 50 I 00 I 12 i 26 1 45 2 II 3 o 36 o 43 o 52 I 02 I 13 I 29 i 49 2 17 2 59 4 o 50 I OO i ii I 26 i 44 2 IO 2 49 3 55 6 16 5 i 16 1 36 i 58 2 30 3 22 C OO 9 24 45 o 27 o 33 o 40 48 o 57 I 08 I 21 i 39 2 02 2 o 32 o 39 o 46 o 52 i 06 I 19 i 35 i 57 2 29 3 o 40 o 47 o 56 I 07 I 21 1 38 2 00 2 34 3 29 4 o 54 i 04 I 16 i 33 i 54 2 24 3 ii 438 8 15 5 i 23 i 41 2 5 2 41 3 40 5 40 12 02 47 30 o o 30 o 36 o 44 o 52 I 02 i 14 I 29 i 49 2 18 2 o 35 o 42 o 50 I OO I 12 i 26 1 45 2 01 2 5 1 3 o 43 5 1 I 01 I 13 I 28 i 47 2 15 2 5 6 408 4 o 56 i 09 I 23 I 40 2 05 2 40 3 39 5 37 ii 18 5 i 27 i 46 2 12 2 52 4 oi 6 30 16 19 50 oo o 33 o 40 o 48 o 57 I 08 I 21 i 39 2 O2 236 2 o 38 o 46 o 55 i 06 i 18 1 35 i 57 2 28 3 19 3 o 47 o 56 i 06 i 19 i 36 2 29 2 3 1 3 23 5 02 4 I 02 I 14 i 29 i 48 2 16 258 4 18 6 59 19 47 5 I 30 i 5 1 2 19 3 4 4 22 7 28 24 10 5 2 3 o 36 o 44 o 52 I 02 I 14 i 29 i 49 2 18 3 05 2 o 43 o 50 o 59 I II I 26 i 42 2 23 2 49 3 55 3 o 50 I 00 i ii I 26 1 45 2 II 2 51 2 5 8 6 22 4 1 5 i 18 i 35 2 10 2 28 3 19 4 53 8 4 2 5 1 34 i 56 2 27 3 16 4 47 852 55 o o 40 o 48 57 i 08 I 21 i 39 2 02 2 36 3 33 2 3 46 o 55 fli i 05 i 19 i 18 i 35 !3 i 56 2 30 2 30 3 21 3 J 5 4 58 4 47 9 19 4 I IO I 23 i 42 2 06 2 43 3 44 5 49 12 41 5 i 37 2 01 2 34 3 28 5 15 10 18 368 APPENDIX. TABLE VIII. 1 MAGNETIC DECLINATION. Formulas giving approximately the magnetic declination at the places named arid for any time within the limits of the period of observation. The places are di- vided into three groups, as follows: GROUP I. Magnetic stations on the eastern coast of the United States and in- clusive of the region of the Appalachian range, with some additional stations in Newfoundland and other foreign localities. GROUP II. Magnetic stations mainly in the central part of the United States between the Appalachian and Rocky Mountain ranges, with additions in British North America, Canada, the West Indies, and Central America. GROUP III. Magnetic stations on the Pacific coast and Rocky Mountain re- gion ; also in Mexico and Alaska and in some foreign countries. D stands for declination, + indicating west, and east declination ; m stands for t 1850.0 or for the difference in time, expressed in years and fraction of a year, for any time t and the middle of the century ; a * indicates uncertainty. 6 fc NAME OF STATION AND STATE. LATI- TUDE. WEST LONGI- TUDE. THE MAGNETIC DECLINATION EXPRESSED AS A FUNCTION OF TlME. GROUP I. ' ' i Saint Johns, New- 47 34-4 5241.9 D= + 21.94 + 8.89 sin(i.o5 7/1 + 63.4)* foundland. 2 Quebec, Canada. 46 48.4 7 1 H-5 D= + i4.66 + 3.035111(1.4 m+ 4.6) + 0.61 sin (4.0 TO + 0.3) 3 Charlottetown,P.E.I. 4614 6327 D= + i5-95 + 7-78sin(i.2 7^ + 49.8) 4 Montreal, Canada. 45 30-5 73 34-6 D= + u.88 + 4.i7sin(i.5 m 18.5) + 0.363111(4.9 TO+I9) 5 Eastport, Me. 4454-4 66 59.2 D= + i5.i8 + 3.79sm(i.25TO + 3i.i)* 6 Bangor, Me. 4448.2 68 46.9 D= + i3.86+ 3.55 sin(i.3o TO + 8.6) 7 Halifax, Nova Scotia. 44 39-6 6335-3 D= + i6.i8 + 4.53sin(i.o 7/1+46.1)* 8 Burlington, Vt. 4428.5 73 12.0 D= + 10.81 + 3.65 sin (i. 30771 20.5) + o.i8sin(7.o 771+132) 9 Hanover, N. H. 4342.3 7217.1 D=+ 9.80 + 4.o2sin(i.4 771 14.1)* ro| Portland, Me. 43 38.8 70 1 6.6 D= + 11.40 + 3.28 sin(i.3o TO+ 2.7) ii Rutland, Vt. 43 3 6 -5 7255-5 D= + 10.03 + 3.82sin(i.5 791-24.3) 1 2 Portsmouth, N. H. 43 04-3 7042.5 D= + io.7i + 3.36 sin (i. 44 m- 7.4) 1 3 Chesterfield, N. H. 4253-5 7224 D=+ 9.60+ 3.84 sin (1.35 m 1 6.1)* 14 Xewburyport, Mass. 14248.9 7049.2 D= + 10.07 + 3.02 sin ( i. 35 m i.o) 15 Williamstown, Mass. 16 Albany, N. Y. 4242.8 42 39-2 73 13-4 7345-8 D = + 8.84+ D=+ 8.17 + 3.i3sin(i.4 77114.0)* 3.02 sin (1.44 m 8.3) 17 Salem, Mass. 423^9 7 52.5 D= + 9.98 + 3.85 sin (i. 4 TO- 5.1)* 18 Oxford, N. Y. 42 26.5 75 40.5 D=+ 6.19 + 3.24 sin(i.35 m 18.9) 1 9, Cambridge, Mass. 42 22.9 7107.7 D=+ 9.54 + 2.69 8111(1.30 TO+ 7.0) o.i8sin(3.2 7/1 + 44) 20 Boston, Mass. 4221.5 7 1 3-9 D=+ 9.48 + 2.94 sin (i. 3 TO+ 3.7) 21 Provincetown, Mass. 4203.1 7011.3 D=+ 9.67 + 3.o4sin(i-3 TO+II.O)* 22 Providence, R. I. 41 50.2 71 23.8 n=+ 9.10+ 2.99 sin (i. 45 TO- 3.4) + 0.26 sin ( 7 TO + 84) 23 Hartford, Conn. 4i 45-9 72 40.4 ])=+ 8.06+ 2.90 sin(i.25 7/1 26.4) 24!New Haven, Conn. 41 18.5 7255-7 D=+ 7.78 + 3.11 sin(i.4ow 22.1) 25! Nan tucket, Mass. 41 17.0 70 06.0 D=+ 8.61 + 2.83 sin(i. 35 TO+ 19.7) 26 Cold Spring Harbor, Long Island, N. Y. 4052 7328 D = + 7.19 + 2?52sin(i.35 TO 11.4) 27 New York City, N. Y. 4042.7 7400.4 D=+ 7.04+ 2.77 sin(i.3o m 18.1) + o.i4sin(6.3 7/1 + 64) 1 From Appendix 7, " U. S. Coast and Geodetic Survey Keport " for 1888. TABLES. 369 6 NAME OF STATION LATI- WEST THE MAGNETIC DECLINATION fc AND STATE. TUDE. LONGI- TUDE. EXPRESSED AS A FUNCTION OF TlME. O ' 00 28 Bethlehem, Pa. 40 36.4 75 22.9 D= + 5.40+ 3.13 sinCi.cc 711-38.3) 2<> Huntingdon, Pa. 4031 7802 D= + 3.76+ 2.93 sin(i.48 774-35.2) 30 New Brunswick, N.J. 40 29.9 74 26.8 L>= + 5.11+ 2.94 sin (1.30 7>i+ 4.2) 31 Jamesburg, N. J. 40 21 7427 D= + 6.03+ 2.94 sin (1.40771 22.4) 32 Harrisburg, Pa. 40 15.9 76 52.9 D= + 2.93+ 2.98 sin (i. 50 77i+ 0.2) 53 Hatboro, Pa. 40 12 7507 D = + 5.17+ 3.16 sin (1.54 771 16.7) + o.22sin( 4 .i 774 + 157) 34 Philadelphia, Pa. 39 56.9 7509.0 D -+ 5-3 6 + 3- I 7 sin ( I -5ra-26.i) + 0.195^(4.0 771+146) 35 Chambersburg, Pa. 3955 7740 D=+ 2.79+ 3.10 sin(i.55 774-30.6) + 0.20 sin (4.6 771+124) 30 Baltimore, Md. 39 17-8 76 37.0 D= + 3.20+ 2.57 sin(i.45 7)t-2i. 2) 37 Washington, D. C. 38 53-3 7700.6 D=+ 2.73+ 2.57 sin (1.45 774-21.6) + o.i4sin(i2 774 + 27) 38 39 Cape Henlopen, Del. Williamsburg, Va. 3846.7 37 16.2 75 5- 76 42.4 D=+ 4.01+ 3.22 sin (i. 35 771-25.2) D=+ 2.33+ 2.56sin(i.5 774-38.1) 40 Cape Henry, Va. 41 iNewbern, N. C. 3655-6 35 6 7600.4 :Dm+ 2.42+ 2.25 sin(i.477?4 30.6) 7702 |D= + 0.63+ 2.56 sin(i.45 m 18.2)* 42 Milledgeville, Ga. 33 04.2 8312 iD= 3.10+ 2.53 sin(i.4om 61.9)* 43 Charleston, S. C. 3246.6 7955.8 D= 1.82+ 2.75 sin (i. 40 m 12.1)* 44 Savannah, Ga. 32 04.9 81 05.5 D= 2.13+ 2.55 sin{ i. 40 7/140.5)* 45 Paris, France. 48 50.2 2 20.2E D= + 6.479 + i6.oo2 sin (0.765 m + 1 1 8 46'.5 + [0.85 0.35 sin (0.6974)] sin [(4.04 + 0.005474 + .000035 w' 2 )n] 46 St. George's, Ber- muda 3223 6442 D=+ 6.95+0.0145 774 + 0.000567742* 47 R io de Janeiro, Brazil -2254.8 4309.5 D=+ 2.19 + 9.91 sin(o.8o 774 10.4)* GROUP II. i York Factory, Brit- ish North America 5 6 59-9 92 26 D = + 7.34 + 1 6.03 sin ( i. io 774 -97.9) 2 Fort Albany, British North America. 5222 8238 0=1 + 15.78+ 6.95 sin (1.20774 99.6) * 3 f Duluth, Minn., and (Superior City, Wis. 46 45-5 46 39-9 92 04.5 1 92 04.2 / D= 7.70+ 2.41 sin(i.4 m 120.0)* 4 Sault Ste. Marie, Mich. 46 29.9 8420.1 D=+ 1.54+ 2.70 sin (i. 45 771-58.5) 5 Pierrepont Manor, N.Y. 4344-5 76 03.0 D=+ 5.95+ 3.78sin(i.4 774-22.2) 6 Toronto, Canada. 43 39-4 79 23-5 D=+ 3.60+ 2.82sin(i.4 77444.7) + 0.09 sin (9.3 774+136) + 0.08 sin (19 771 + 247) 7 Grand Haven, Mich. 435- 2 86 12.6 D= 4-95+ 0.0380774 + 0.00120 7?4 2 8 Milwaukee, Wis. 43 02.5 87 54-2 D= 4.12+ 3.60 sin (1.45 m 64.5)* 9 Buffalo, N. Y. 4252.8 78 53-5 D=+ 3.66+ 3.478^(1.4 774-27.8) 10 Detroit, Mich. 42 2O.O 83 03.0 D= 0.97+ 2.2isin(i.5 774 15.3) ii Ypsilanti, Mich. 42 H 8338 D= 1.20+ 3.40 sin (i. 40 m 4.1) 12 Erie, Pa. 42 07.8 8005.4 D = + 2.17+ 2.69810(1.5 111-27.3) 13 Chicago, 111. 41 50.0 87 36.8 D=- 3.77+ 2.48 sin( i. 45 774 -62.5) 14 Michigan City, Ind. 41 434 86 54.4 D= 3.23+ 2.42 sin (1.4 m 48.0) 15 Cleveland, O. 41 30.4 8141.5 D=+ 0.47+ 2.39 sin (1.30 m 14.8) 1 6 Omaha, Neb. 4i 15-7 95 5 6 -5 D=- 9.30+ 3.34 sin (i. 30 774 -54.7) 1 7 Beaver, Pa. 4044 8020 D=+ 1.41+ 2.72 sin( i. 40 m 39.6) R'M'D SURY. 24 370 APPENDIX. NAME OF STATION LATI- WEST THE MAGNETIC DECLINATION AND STATE. TUDE. LONGI- TUDE. EXPRESSED AS A FUNCTION OF TlME. 18 Pittsburg, Pa. O ' 40 27.6 O ' 8000.8 O O O D= + 1.85+ 2.45 sin (1.45 m 28.4) 1 9 Denver, Col. 3945-3 104 59-5 D 15.30+ o.oi i 771+0.0005 w' 2 20 Marietta, O. 3925 81 28 D=+ 0.02+ 2.89 sin (1.4 771-40.5) 21 Athens, 0. 39 19 8202 D= 1.51+ 2.63sin(i.4 771 24.7) 22 Cincinnati, O. 39 08.4 8425.3 D=- 2.59+ 2.43 sin (i. 42 771-37.9) 23 Saint Louis, Mo. 38 38.0 90 12.2 D=r 5.91+ 3.00 sin (1.40771 51.1)* 24 Nashville, Tenn. 36 08.9 86 48.2 D =- 3-57+ 3-33 s in ( I- 35 Wl ~ 68.5)* 25 Florence, Ala. 3447- 2 8741-5 D= 4.25+ 2.33sin(i.3 771 52.8) 26 Mobile, Ala. 3041.4 8802.5 D= 4.38+ 2.69801(1.45771 76.4) Pensacola, Fla. 30 20. 8 87 18.3 D= 4.40+ 3. 1 6 sin (1.4 771 59.4) 27 New Orleans, La. 2957- 2 9003.9 D= 5.20+ 2.98 sin (1.40 77?. 69.8) 28 San Antonio, Tex. 29 25.4 98 29.3 D-_ 7.40+ 2.88 sin (i. 35 77i -8 1. 8)* 29 Key West, Fla. 24 33-5 8 1 48.5 I)=- 4.31+ 2.86 sin(i. 30771-23.9) 3 Havana, Cuba. 23 09.3 8221.5 D=- 4.25+ 2.74 sin (i. 25 7 -23.3)* 31 Kingston, Port Royal, Jamaica. 1755-9 76 5- 6 D= 3.81+ 2.39 sin (i. 10 77i 10.6) 32 Barbados, Caribbee Islands. !305.7 59 37-3 T)= 1.38+ 2. 84 sin ( 1. 1 o 771+09.4) 33 Panama, Colombia. 857-i 79 32-2 D= 5.66+ 2.22 sin(i. 10 771 27.8) GROUP III. j Acapulco, Mexico. 16 50.5 99 52-3 D= 4.48+ 4.41 sin ( i. o 771 85.7)* 2 Vera Cruz, Mexico. 19 11.9 9608.8 D=- 5.09+ 4-22sin(i.2 771 63.4)* 3 City of Mexico, Mex. 19 26.0 9911.6 1)= 5.34+ 3. 28 sin ( i. o 771 87.9)* 4 San Bias, Mex. 21 32.5 105 18.4 D= 5.21+ 4.265111(1.15771 96.5) 5 San Lucas, Lower Cal. 2253-3 109 54.7 D= 5.94+ 3.68sin(i.2o TO 116.8)* 6 Magdalena Bay, Lower Cal. 2438.4 11208.9 D= 6.33+ 4.17 sin(i. 15 m 119.2)* -7 Cerros Island, Lower / Cal. 2804 115 12 D= 7.40+ 4.61 sin (1.05 77i 107.0) 8 El Paso, Tex. 3i 45-5 1 06 27.0 D= 9.08+ 3.40 sin (1.3 771108.4) 9 San Diego, Cal. 3242.1 "7 H-3 D= 10.32 + 3.00 sin(i.io m 126.5) 10 Santa Barbara, Cal. 34 24-2 11943.0 0^-11.52+ 3. 32 sin( 1. 10 771 123.1) ii Monterey, Cal. 3636-1 121 53.6 D= 13.25+ 2. 83 sin (i. 10 ?7i 144.0) 12 San Francisco, Cal. 37 47-5 122 27.3 D=- 13.94+ 2.65 sin( 1.05 m- 135.5) 3 Cape Mendocino, (y al. 40 26.3 12424.3 D 15.25+ 2.45 sin ( 1. 10 m 128.0)* H Salt Lake City, Utah. 40 46. i IH53-8 D= 12.40 + 4.25sin(i.4 771121.6)* IS Vancouver, Wash. 45 37-5 12239.7 D=-i7.93+ 3.12 sin(i.35 m- 134.1)* 1 6 Walla Walla, Wash. 4604 Il8 22 0^-17.80+ 3.3osin(i.3 771-129.0)* r 7 Cape Disappointment, Wash. 46 16.7 12402.8 D=- 19.39+ 2.54 sin(i. 25 m- 158.7) 18 Seattle, Wash. 47 35-9 122 2O.O D= 19.19+ 3.i4siii(i.4 771136.1)* 19 Port Townsend, Wash. 48 07.0 122 44.9 D=- 18.84+ 3.00 sin (i. 45m -i 22.1) 20 Neah Bay, Wash. 4821.8 12438.0 D= 19.83+ 2.91 sin(i.4O 77i 141.6) 21 Nootka, Vancouver Isl. 49 35-5 12637.5 D 21.25+ 2.74 sin(i. 30 77i 152.0)* 22 Captain's and Iliuliuk Harbors. 53 52.6 16631.5 D= 18.01 + i.82sin(i.3 77169.6)* 2 3 Sitka, Alaska. 5702.9 135 19-7 0^-25.79+ 3.30 sin(i.30 TO- 104.2) 2 4 St. Paul, Kadiak Island. 5748.0 152 21.3 D- -22.21+ 5. i8sin(i.35 771-72.5) 2 5 Port Mulgrave, Alaska. 59 33-7 1 39 45 -9 I>= -24.03+ 7.77 sin( i. 30 771- 85.8) 26 Port Etches, Alaska. 60 20.7 14637.6 D=- 23.71+ 7.89 sin (i. 35 7?i -80.9) 27 Port Clarence, Alaska. 65 16 1 66 50 D=- 18.98+ 7.99sin(i.3 771-68.4)* 28 Chamisso Isl., Alaska. 6613 161 49 D= -23.62+ 7.648^(1.3 771-64.0)* 29 Petropaulovsk, Siberia. 53 oi 2OI 17 D-- 3.35+ 2.97sin(i.3 771+12.2) TABLES. 371 TABLE IX. ANGULAR CONVERGENCES AND DISTANCES BETWEEN MERIDIANS. 1. Angular convergence of meridians per mile of easting or westing. 2. Distance betweep meridians converging by one minute. LATI- TUDE. ANGULAR CON- VERGENCE PER MILE. MINUTES. DISTANCE FOR CONVERGENCE OF 1'. FEET. LATI- TUDE. ANGULAR CON- VERGENCE PER MILE. MINUTES. DISTANCE FOR CONVERGENCE OFl'. FEET. I 0.015 348733 31 0.521 10140 2 .030 I743H 32 542 9751 3 .045 116150 33 .563 9382 4 .061 87052 34 .585 9034 5 .076 69578 35 .607 8703 6 .091 57917 36 .630 8387 7 .107 49578 37 .653 8087 8 .122 43337 38 .677 7801 9 137 38436 39 .702 7527 10 '53 34525 40 .727 7265 ii .169 31320 4i 753 7<>i3 12 .184 28642 42 .780 6770 13 .200 26371 43 .808 6537 H .216 24419 44 .836 6313 15 .232 22723 45 .866 6097 16 .24 9 21234 46 897 5888 17 .265 19916 47 .929 5686 18 .282 18740 48 .962 5491 '9 .299 17685 49 .998 5301 20 .316 16731 5 .032 5118 21 333 15864 5i .069 4940 22 350 !573 52 .108 4766 23 .368 H348 53 .149 4597 24 .386 13680 54 .191 4433 25 .404 13062 55 .236 4271 26 423 12488 56 .283 4"5 2 7 .442 "955 57 333 3962 28 .461 "457 58 385 38i3 2 9 .480 10990 59 .440 3666 30 .500 10552 60 499 3523 372 APPENDIX. TABLE X. 1 LENGTH OF ONE MINUTE OF LATITUDE ANTD ONE MINUTE OF LON- GITUDE TO THE NEAREST WHOLE FOOT. LATI- TUDE. 1' LATITUDE. FEET. 1' LONGITUDE. FEET. LATI- TUDE. 1' LATITUDE. FEET. 1' LONGITUDE. FEET. o I 6046 6086 o 31 6062 5222 2 6046 6083 32 6063 5^7 3 6046 6079 33 6064 5110 4 6046 6072 34 6065 5052 5 6046 6064 35 6066 4992 6 6047 6054 36 6067 4930 7 6047 6042 37 6068 4867 8 6047 6028 38 6069 4803 9 6047 6013 39 6070 4737 10 6048 5995 40 6071 4670 ii 6048 5976 4i 6072 4601 12 6049 5955 42 6074 4531 13 6049 5932 43 6075 4459 H 6050 5908 44 6076 4386 15 6050 5881 45 6077 4312 16 6051 5853 46 6078 4236 *7 6051 5823 47 6079 4159 18 6052 579i 48 6080 4081 19 6052 5758 49 6081 4001 20 6053 5722 50 6082 3921 21 6054 5685 5i 6083 3839 22 6055 5647 52 6084 375 6 2 3 6055 5606 53 6085 367 1 2 4 6056 5564 54 6086 3586 25 6057 5520 55 6087 3499 26 6058 5475 56 6088 3412 27 6059 5427 57 6089 3323 28 6059 5379 58 6090 3234 29 6060 5328 59 6091 3H3 30 6061 5276 60 6092 305 ! 1 Abbreviated from the Smithsonian Geographical Tables. TABLES. 373 TABLE XI. TRIGONOMETRIC FUNCTIONS AND FORMULAS. SOLUTION OF TRIANGLES. By definition, if R = 1, ED sine a. OD = cosine a. DA = versed sine . HF ' = coversed sine a. BA = tangent a. FC = cotangent . OB = secant . OC = cosecant . If R is other than 1, it follows from the above definitions and the propor- tionality of similar figures, that 1. ED = R sin a. 2. OD = Rcosa. 3. DA = R versin a. 4. HF = R co versin a. G c 5. BA = R tan a. 6. FC = Rcota. 7. OB = R sec . 8. OC = R cosec a. from which also in any right triangle of angles and (3, if o be the side opposite the angle a, a the side adjacent thereto, and h the hypotenuse, 9. sin a = - = cos ft. h 10. cos a = - = sin ft. h 11. Hence, 17. 18. 19. 12. cot a = - = tan ft. sin a cos /? a = h cos a = h sin /?. . cos a sin /? = a tan a = a cot ft. a = -?- = -?-. tan a cot ft 13. sec a = - = cosec ft. 14. cosec a = - = sec B. o 15. vers a = ~ rt = covers ft. h 16. covers a = ~ = vers /?. 20. a = o cot a = o tan ft. a a o = cot tan ( h = a sec a = a cosec 21. 1 h = A sec a cosec /3 ^ = o cosec a = o sec y 22. ^ = "ft = A cosec a sec ft 374 APPENDIX. 23. o = VA 2 -a 2 24. a = V^ 2 - o 2 = V(ft -f o) (h - o). Oblique triangles may be solved by some one of the following formulas : \* -"' LX yJA^A,- " GIVEN. I SOUGHT. . FORMULAS. /E 27. A,B,a, 28. A, a, b, 29. C, a, 6, 30. 81. 32. 33. 34. a, 6, c, 35. 36. A,B,C t a, C, o, c, 5, C, c, i (>4 4 5), ^,B, c, Area, -4, Area, Area, sin yl r a ifri (4 i R^ sin A "in R sm ^4 -, .0, ieo ^ 4 4^ R" a c ^ a sin C. sin ^4 J(^ + -B)=90- JC tan ^ (^4 B) a ~~ tan A (^4 + B) a + b '_" & ^l ( d+? sin 2 (^4 -B) Area = ^ a& sin C. If s = J (a 4 & 4 c), tan? 4 J0-&)0-<0 A 2 Vs^ a)(s - 6)(s c) vt-is yi &c Area = Vs(s a) (s 6) (# c) . \ rca _ fl2 sin 5 sin C 2 sin 4 \ TABLES. 375 From the definitions of the trigonometric functions, the geometrical properties of right triangles and in some cases algebraic transformations, it may be shown that if A is any angle and B any other angle, 37. sin 2 A + cos 2 A = 1. 38. sin A = = Vl cos 2 A = tan A cos A cosec A = 2 sin | A cos \A = vers A cot \ A = Vi vers 2 A = V|(l -cos 2 A). 39. cos A = = VI - sin' 2 A = cot A sin A sec A = 1 -vers A = = cos 2 \A- sin 2 i .4 = 40. tan A =sinA 1 cos A cot ^4 = Vsec 2 .4 -1 VI - cos 2 4 sin 2 A cos 2 A cos ^4 1 + cos 2 1 - cos 2 ^4 _ vers 2 .4 sin 2 A sin 2 ^4 = cot i ^4 (sec A -1). 41. cot.4 = cos = __ = Vcosec 2 .4 - 1 sm A tan A sin 2 .4 sin 2 ^ 1 + cos 2 .4 1 cos 2 A vers 2 ^4 sin 2 A sec A 1 42. vers .4 = 1 -cos A = sin A tan $ ^4 = 2 sin 2 i .4 = cos A (sec ^4 - 1) . 43. sin (A J5) = sin A cos 5 sin B cos ^4 . 44. cos (A B) = cos A cos 5 T sin ^4 sin 5. Az -- i * ' A uua ..-a /vers 46. sin 2 ^4 =2 sin .4 cos 47. COS 2 48. cos 2 ,4 = 2 cos 2 .4 -I = cos 2 .4 -sin 2 y4 = l- 49. tanM = **" '* = cosec .4 - cot A = 1 ~ cos A 1 + sec .4 sin A 50. tan 2 .4 = 2tan ^ . 1 -tan 2 M 51. cot | 4= sin ^ = l + sA = 1_ vers A sin A cosec ^4 cot A 376 APPENDIX. 52. cot 2 A = 53. vers * A = cot 2 .4 -1 2 cot ,4 vers ^4 1 cos A - vers J. 2 4- V2(l + co 54. vers 2 ^4 = 2 sin 2 A. 55. sin ^4 + sin = 2 sin \ (A + B) cos %(A - B). 56. sin ^4 - sin B = 2 cos (.4 + JB) sin (4 - 5) 57. cos A + cos = 2 cos J (4 + B) cos J (4 - 5) 58. cos B - cos 4 = 2 sin } (4 + B) sin J (.4 - ) 59. sin 2 A - sin 2 = cos 2 !? - cos 2 ,4 = sin (A + 5 60. cos 2 4 - sin 2 B = cos (4 + B) cos (.4 - 5). 61. 62. tan A - cos y4 cos B cos ^4 cos x> sn - B). TABLE XII. LENGTHS OF CIRCULAR ARCS OF RADIUS 1, AND VARIOUS CIRCULAR MEASURES. No. DEGREES. MINUTES. SECONDS. No. DEGREES. MINUTES. SECONDS. i 0174533 .0002909 .0000048 6 .1047198 .0017453 .0000291 2 .0349066 .0005818 .0000097 7 .1221730 .0020362 .0000339 3 0523599 .0008727 .0000145 8 .1396263 .0023271 .0000388 4 .0698132 .0011636 .0000194 9 .1570796 .0026180 .0000436 5 .0872665 0014544 .0000242 10 - 1 745329 .0029089 .0000485 Degrees in arc of length equal to radius, 57. 295 780. Degrees in arc of length equal to TT, 180. 000 000. Circumference = 2 TIT = 360. 000 000. Area = Trr 2 . '. I = length of circular arc d number of degrees in same r = radius of same c = chord of same m = middle ordinate 180 r - L . 18 Q. d IT Area of sector = | Ir. Area of sector = Trr 2 . 360 Approximate area of segment = f cm. TABLES. 377 TABLE XIII. LINEAR TRANSFORMATIONS. 1. Gunter's Chains to Feet. CHAINS. O.O O.OI .02 .03 .04 05 .06 .07 .08 .09 0.0 .66 1.32 I. 9 8 2.64 3.30 3.96 4.62 5.28 5-94 .1 6.60 7.26 7.92 8.58 9.24 9.90 10.56 11.22 11.88 12.54 .2 13.20 13-86 14.52 I5.I8 15.84 16.50 17.16 17.82 18.48 19.14 3 19.80 20.46 21.12 21.78 22.44 23.10 23.76 24.42 25.08 25-74 4 26.40 27.06 27.72 28.38 29.04 29.70 30-36 31.02 31-68 32.34 5 33-00 33-66 34-32 34.98 35.64 36-30 36.96 37.62 38.28 38.94 .6 39.60 40.26 40.92 41.58 42.24 42.90 43-56 44.22 44.88 45-54 7 46.20 46.86 47-5 2 48.18 48.84 49.5 50.16 50.82 51.48 52.14 .8 52.80 53-46 54.12 54.78 55-44 56.10 56.76 57-42 58.08 58.74 9 59-40 60.06 60.72 61.38 62.04 62.70 63-36 64.02 64.68 65-34 0.0 I.O 2.O 3-0 4.0 5-0 6.0 7.0 8.0 9.0 o.o 66 I 3 2 198 264 330 396 462 528 594 10.0 660 726 792 858 924 990 1056 1122 1188 1254 20.0 1320 1386 1452 1518 1584 1650 1716 1782 1848 1914 30.0 1980 2046 2112 2178 2244 2310 2376 2442 2508 2574 40.0 2640 2706 2772 2838 2904 297 3036 3102 3168 3234 5O.O 3300 3366 3432 3498 3564 3630 3696 3762 3828 3894 6O.O 3960 4026 4092 4158 4224 4290 4356 4422 4488 4554 7O.O 4620 4686 4752 4818 4884 495 5016 5082 5H8 5214 80.0 5280 5346 5412 5478 5544 5610 5676 5742 5808 5874 378 APPENDIX. * 3?o 00 PO . 1-1 M PO Tf g 00 OO OO 00 00 ON co POQNO POONO POQNO PO O M PO ^" to NO t"* ON O "* vOOO NOO -I M co Tt- to NO 00 ONO OOOOOOOOOOOOOOOO ON w co to r^ ON. M co >o t^ ^O N tOO\vO M VO M d M co 4 to NO i>- ON d NO NO NO NO NO NO NO NO r^* NO M OO Tj- 00 -H PO t^ ON >-> fO 06 d F- oo O M co "S t> oo ^ O < POrfiONO t^OO O !-! MMMMMMMMCOCO OO O ~ roiO ONVO vOOO O ON N O 1-1 POTftoNO i>oo O MMMMMMMMPO H- POtnt^ONi-i POiot^. (M OO to M 00 if) ** OO t^>. ON O M O S ^ 5' - M - 5ooo 8 o H M PO >-O NO t^ oo oo oo oo oo oo M TJ- NO 00 O M 10VDOO ONI-" rO vO CJOO ^M t^ vO fOONvO fOON 1-1 M PO to 00 00 00 00 M ^ NO 00 t^ 00 ON ^ ^-S ro u"i vO OO O ^^ *^ 1 O *O OO M 4 NO' 00 O M 4NOOO ON ON^O Tl-i-i fOto N fOLrjvO MOO Tt-Q OO rj-i-ioo vOCO O 1-1 ON M COO t^ W Tf^O O ** N ^- >-i I^rf fOONNO t^OO O PO ON to PO ON NO M PO to d M _ ^ M" ^ NO" oo" o" 10 t^. OO d M 4 NOOO ON O MOO u" MOO O <-* M Po4tot^OO ^ MMMMMMMMM M TfNOOO O M Tj-NO q q q 5 ? q^ M 4 NO oc5 d M CO 10 o o 2 4 NO 06 M COIOVOOO ON" M NO MOO TJ-QNO COON I i^Mco4toNoodoN 8 3& 8 8 S dodo^do^dp^ TABLES. 379 3. Feet to Meters. Vwf I 2 3 4 5 6 7 8 9 iVEET. Meters. Meters. Meters. Meters. Meters. Meters. Meters. Meters. Meters. Meters. O.OOO 0.305 0.610 0.914 I.2I9 1.524 1.829 2.134 | 2.438 2-743 10 3.048 3-353 3.658 3.962 4.267 4-572 4.877 5.182 5.486 5-791 20 6.036 6.401 6.706 7-010 7-3I5 7.620 7.925 8.229 8-534 8.839 30 9.144 9-449 9-753 10.058 10.363 10.668 10.972 11.277 11.582 11.887 40 12.192 12.496 12.801 13.106 13.411 13.716 14.020 H.325 14.630 H-935 50 I5- 2 39 15-544 15.849 16.154 16.459 16.763 17.068 17-373 17.678 17-983 60 18.287 18.592 18.897 19.202 I9-507 19.811 20.116 20.421 20.726 21.031 7 21-335 2 1 .640 21-945 22.250 22-555 22.859 23.164 23.469 23-774 24.079 80 24.383 24.688 24.993 25.298 25.602 25.907 26.212 26.517 26.822 27.126 90 27-43I 27.736 28.041 28.346 28.651 28.955 29.260 29.565 29.870 3- I 74 100 30.479 30.784 31.089 31-394 31.698 32.003 32.308 32.613 32.918 33-222 4. Meters to Feet. \f T-T-T o I 2 3 4 5 6 7 8 9 METEKS. Feet. Feet. Feet. Feet. Feet. Feet. Feet. Feet. Feet. Feet. O.OO 3.28 6.56 9.84 I3-I2 16.40 19.69 22.97 26.25 29-53 10 32-81 36.09 39-37 42.65 45-93 49-21 52.49 55-78 59.06 62.34 2O 65.62 68.90 72.18 7546 78.74 82.02 85.30 88.58 91.87 95-'5 3 98.43 101.71 104.99 108.27 "1-55 114.83 118.11 121.39 124.67 127.96 40 131.24 I34-52 i37-8o 141.08 144.36 147.64 150.92 154.20 157-48 160.76 50 164.04 167.33 170.61 173.89 177.17 180.45 183.73 187.01 190.29 193-57 60 196.85 200.13 203.42 206.70 209.98 213.26 216.54 219.82 223.10 226.38 7 229.66 232.94 236.22 239-5 * 242.79 246.07 249-35 252.63 255-9I 259.19 80 262.47 265.75 269.03 272.31 275.60 278.88 282.16 285.44 288.72 292.00 90 295.28 298-56 391-84 305.12 308.40 311.69 3H.97 318.25 321.53 324-81 IOO 328.09 331-37 334-65 337-93 341.21 344-49 347.78 351.06 354-34 357-62 i statute mile = 1.6093 kilometers I kilometer = 0.6214 statute miles "*.?, >"' TABLE XIV. DISTANCES AND DIFFERENCES OF ELEVATION. CO al angles. The values for other readings are obtained by multiplying the quantities under o undreds of units; thus, if the reading is 204, multiply by 2.04. Use a slide rule. Com- st, second Geological Survey of Pennsylvania. |5ju " " *! ! *? ro A rr P PEND1 O vo H \o t-s. fxCO OO [X ON t^cd co co ON CO oT roro 5- 00 CO CO CO CO l-l f~ 01 00 CO CO CO CO ro 00 vd o s 6 CO O 6 6 ? I^*j ON ON ON ON ON 00 CO i ^ii^ CO 1 iiii i ON ON ON ON 55 ON 10 ro M ON io io io -r ON ON ON ON i 1111 ON 5 101010.010 5 si?2 8 vO M fs. N O H H N * vO v6 vo vO vO it VO 01 t^ vO vo t^ t^ vO v6 VO VC3 ro vo vO vO vO t^ o CO N s 6 VO 6 6 io ro oi o co t;u io vo io io * - trt^ co ro fri C4 co H ON Mil CO ON VO J JJ ON ON ON ON 1 vO ^" OJ O O O O C^ t^ t^ 1^ ON O> ON ON ^Q ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON 00 3w <; j * 2 ^^ vg *?&? SN ON M vO 04 10 M tx m< % ro5- Ifl H 10 oo .... in 6 o 6 o 6 > ~ co" co 00" co" co - 0- ON ON ON ON O 'oo tx io ro ON CO 00 00 00 ON ON ON ON ON CO o oo vo io ON t^vo vO vo I O^O^ONO^ o SB ^ 2 M 1 c) ^8 ro QH fi pi tvi oi oi * oi oi oi oi 1 otnl ! H^ !- * K Jf^ co rx roco * CO ON ON O 2 ei 10 i 8 6 6 6 6 t:~ ONONCOCO'OO ro N w O co N itii i P.VO'NOVO' ^^i 10 NO 8- o 6 ON o 6 g 6 ? GW 06 co co oo oo iJ -4J 01 01 01 01 01 ss ggggg o. CO ON ON ON ON OO t^vO IO ! ON ON ON ON M 1 M 8 8" ON * NO NO t^ t^ 00 ON "dN^6 6 mi & i 'ON'ON'ON'ON o ig ;; "ON o o~ ? ? e? O vO 0) CO ro ro * -1- ? ?--- CO CO ^ ON IO CO ON ON O CO CO CO 00 00 ro 0) H O 8:8^8; 0_ 00 ON g ^- 10 lOvO CO CO CO 00 00 t^vO 10 CO CO " 6 " 6 8 6 K3 ON ON ON ON ON ON ON ON ON ON 1 VO VO XO ^ > *-!* ? g 0) M O ON CO c5 CO t-vO 10 HORIZONTAL '. For stadia readings of 100 units at various vertic the proper vertical angle by the stadia reading in h puted by Mr. Arthur Winslow while assistant geologi % Qy io io io 10 io >-' ^ K fi. P. P. 2. % ^gNCOCO^> c^ g IO IO IOVO vo OT- ro VO vO vO vO ^ ON ON CJN ON ON ON ON o' vO vo vo VO vo vo vo vo i VO vo vO vO vO 10 10 10 ON vo g 6 6 6 8 6 10 * |j|3KSSg. 00 o?8,S;3 s- roco ^- O vO tt"? $ H vO N 00 t^ txCO CO ? S^S" 0? o o o 8 S 1 6 10 00 CO CO CO CO ON ON ON ON ON 1 CO CO CO OO CO* g CO 00 CO CO gggg ! an CO CO^ t--, t-xvO^ ^ 10 ?% o ON 10 M t>. Hi 0) 01 ? %t-^ - vO t^ t^OO ON ON O O 11 3 ^roro? ? o 6 8 6 10 SS&rSYg Si => 8;8;gg8; - 1111 g 1111 ON ro ro N N ON ON ON ON 8^8:8:8; - ON ON ON ON % Ill CO ON ON % t*J t* Q *O W FX. CO iS o o M M w ir ro 5- TJ- io * v?^ ~ ro ON to H ON ON O H vo 01 00 - O V to 10VO vO ON g 6 8 s 6 ,. 88888 || 8 8 8 8 8 8 8 8888 8888 8 8 Soil I %%%% I Ull 00 ON g 00 CO ^ t^ ON ON ON ON - - 01 --vOCO o 01 -<*-vO 00 0) -4-NOCO * 0) -*VO CO ro ro ro ro * :.-l, "*T K vS 8 I? ii ii TABLES. 381 . ^-oo rot^NNO MinON^-oo ro t** w NO O 1> MMOwroro-----nninNONO tx t>. o& . . o NO ro ON >n U- COW M ro ro ro ro ( td r^ t^t^. ti. ^"**!" .coroco ! ro ro tr jj-oorop.M^NO^NO in ^ U c.2 ro ro ro ro oo m M 3O rOOO I ro ro ro i m\o * ON^OO 1 !? 8^30?^ loo ? ^5-% 8NS80- O> O\ +1 m o oo m H c.2 **'?'?'? wo 8,8,8.8. 8. NO NO NO t^ g^g. g.^ H?; M N ro ro 8,% gf.! sq 8N8N8NSN 8N8N8NON N N < OO OO C3> ON ON ON ON cr5"cr?r oo m tM oo QW J^-c? ro O r^ * M M O O co co co co o O t^ oo t^ sts SN ON ON SN . . t- 00 rO {g > -a-inmNO ;^~ co co co co co M> ^ N N N 4 M 2 8*0 3" ^ N N M O t^ m N t^NO \O NO 3333 SNO^R. ctctctci S^SS^^ 3353 ,8 ctcTcTcT S ft J? ro 6 6 . . N IS. N OO fO (e > ON o o o w g.g ^SN^ScS ONVO ro M O I m o m H t< t^oooo o 5 O^ONONO^ JnS>^4: Z2.Z S; :> roro^m., 5g o o o o o s ON ON ON ON - co co SS3S ^ 00 * tt ON o" O ON ON in in 4- 4-! * ON ON ON ONJ ON| m M \o M M M (M ON C> ON ON 8*0,^3 ^iiSii^i^ii^^S^io^SS 3 3333 O m t- t^ ON ON ON ON 8888 tKtnw O 00 t- tX t^ t^> NO 3333 $ JJ R J. Tr' " " 382 APPENDIX. > tj > m m^m m 3- gj* 5 m^m S AAA* m ssss j cTo^M LC K CO 6 vO 6 6 6 6 " M t* 8S&J?5 JO fcffjsi ON -* .ON,; ON ? ON. ON. ON moo moo ONOO oo r-^ oo moo N VC vO 10 10 BIS 4. Jt rt Jt tt " * *.'* ^ tt tt tt tt R KKKK m KKKK * |q vf vdvfvdNd vO N Itll 8 i SR:g0 ft 8 6 vO 6 ON 6 oo d vS 6 M go M P.; > IOOO W 1OCO vS IOOO H . s 00 00 00 ON ON S;8^ I? P) 10 ON P4 ? oo H . r-x 3- $, co 5 IN r^ (Ni tx N CO <* ON C>CO '06 CO CO CO CO 1 CO CO CO CO CO 10 I CO CO CO CO R^SJ 6666 OO OO 00 OO VO ON mvO O oo moo <* 6666 oo co oo oo 9 6 6 6 ON ON 1 * J'lSSet aof.^ ON ON ON ON a N vC ON M 1000 pa m m m . 34 oo moo . 10 10 . . ON eJN ON ON : ro ro 6 vO 6 6 6 K 6 O CM O5 CO CO CO CO CO " CO CO CO CO CO CO oo oo oo oo t- moo < 0000 t^ t^ I P. (^ t^OO ""volo to cS co ON m t^Q 1 . 00 ON ON O O pi oo moo j . OO M IOOO 3?;^^ ON 10 ONO CV CO t^ p) t^ m ON ONOO OO eg c eg eg 3 CO eg 6 - o rf 6 6 6 m 00 00 00 OO 00 00000000 CO OO 00 OO 00 00 00000000 O ST isl" 8 "^ en ^Tt 1 ? s ^vSvg 8. t^ &? 00 cS . ON 10 M 00 tg 00 C cS 10 ON mvo 00 00 00 00 PI t^ moo P) PJ P) N 00000000 O CO 6 6 6 ON 6 e* d H CO CO 00 CO CO p) rn m m m m S10 w tx H H oo oo oo oo s ON ONOO 00 N pi cS pi 00 OO OO OO eg eg ^^N^vo 1 o 5sj jjrfvg^ S c^oo^octocr t^ M 1 H ioomt-M vO .00 M VO O .OO W vO O IO ON m m m m m O vo PI t^ ONOO 00 t^ 4- co 8" 6 - 6 a 6 ON 6 * 6 -4- vO CO 4- 10 10 10 N 00 -I- O co 10 10 10 10 m m m m P) 00 * 10 Tj- Tf ^ ^ 10 10 10 10 w t^ m ON m <-a 10 10 10 10 00 OO 0000 en CO 1O 1O IO to OO OO 00 OO c p. vO Z IIII m m m m vd vd vo vd oo oo oo oo S r^ o 6 S 6 vO "^ 00 00 00 OO 00 a .NO 00 S sirs* 8 ScTU'S , fc **T I am 10 O 6 H H II II II TABLES XV, XVI. COMMON LOGARITHMS OF NUMBERS. LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. EDITED BY C. W. CROCKETT. 3*3 NOTE. THE well-known tables of Gauss, Hoiiel, Becker, and Albrecht have been taken as the standards, and the figures compared with the more extensive tables, the doubtful cases being recomputed. 384 EXPLANATION OF THE TABLES INTRODUCTORY. 1. When we have a number with six or more decimal places, and we wish to use only five : (a) If the sixth and following figures of the decimal are less than 5 in the sixth place, they are dropped; thus, 0.46437 4999 is called 0.46437. () If the sixth and following figures of the decimal are greater than 5 in the sixth place, the fifth place is increased by unity and the sixth and following places are dropped; thus, 0.46437 5001 is called 0.46438. (c) If the sixth figure of the decimal is 5, and if it is followed only by zeros, make the fifth figure the nearest even figure ; thus, 0.46437 500 is called 0.46438, while 0.46438 500 is also called 0.46438. The number is thus increased when the fifth figure is odd, and decreased when it is even, the two operations tending to neutralize each other in a series of computations, and hence to diminish the resultant error. 2. Hence any number obtained according to Art. i may be in error by half a unit in the fifth decimal place. 3. When the last figure of a number in these tables is 5, the number printed is too large, the 5 having been obtained according to Art. i (b \ ; if the 5 is without the minus sign, the number printed is too small, the figures following the 5 having been dropped according to Art. i ( and logo.373 =1.57171; Iog373 = 4-57 I 7 I > an d ^0.0373 = 2.57171. Hence the position of the decimal point affects the characteristic alone, the mantissa being always the same for the same sequence of figures. For this reason the common system of logarithms is used in practice. 10. The characteristic is found as follows : M'hen t/ie number is greater t/iiin i, the characteristic is positive, and is one less than the num- ber of digit* to the left of the decimal point ; when the number is less than i, the characteristic is negative, and is one more than the number of zeros between the decimal point and the first significant figure. 11. To avoid the use of negative characteristics we add io to the characteristic and write io after the mantissa, i.e. adding and subtract- ing the same quantity, io. Thus log o. 2 = 1.30103 would be written 388 EXPLANATION OF THE TABLES. 9.30103 10. The 10 is often omitted for brevity when there is no danger of confusion, but its existence must not be forgotten. Such logarithms are called augmented logarithms. In this case the characteristic of the logarithm of a pure decimal is 9 diminished by the number of ciphers to the left of the first significant figure. Thus the characteristic of log 0.004 is 9 2, or 7, and that of log 0.94 is 9 o, or 9. 12. The arithmetical complement of the logarithm (written colog) of a number is the logarithm of its reciprocal, and is found by subtract- ing each figure of the logarithm from 9, commencing at the left, except the last significant figure on the right, which is subtracted from 10. For log = log x 10 log x 10 ; OC thus, if log*= 2.46403, colog^= 7.53597 10 ; if \ogx = 8.43000 10, colog x = 1.57000. TABLE XV. 13. Page 397 contains the logarithms of numbers from i to 100, to five decimal places. Pages 398-415 contain the mantissas of the logarithms of numbers from 1000 to 10009, to five decimal places. Pages 416,417, contain the mantissas of the logarithms of numbers from TOOOO to 11009, to seven decimal places. NOTE. The mantissas of the logarithms of numbers, except those of the integral powers of 10, are incommensurable, the mantissas in the tables being found as shown in Art. I. To find the Logarithm of a Number. 14. The characteristic is found by the rules in Arts. 10 and u, and the mantissa from the tables, as shown in Arts. 15, 16, 17, 18. 15. When the number has four figures. Find on pages 398415 the first three figures in the column marked JV f and the fourth at the top of one of the other columns. The last three figures of the mantissa are found in this column on the horizontal line through the first three figures of the given number in column N. The first two figures of the mantissa are those under L in the same line with the number, or else those nearest above it, unless the last three figures of the mantissa as given in the tables are preceded by a *, when the first two figures are found under L in the first line below the number. Thus (page 398), log 1136 = 3.05538; log 1137 = 3.05576; log 1138 -3.05614; log 1370 = 3.13672; log 1371 = 3.13704; log 1372 = 3.13735 ; log 1380 = 3.13988 ; log 1381 = 3.14019 ; log 1382 = 3.14051. EXPLANATION OF THE TABLES. 389 16. When, the number has less than four figures, annex ciphers on the right and proceed as in Art. 15. Thus, log 1.13 = 0.05308; log 12.8= 1.10721 ; log 130= 2.11394; log 15 = 1.17609; log 16 = 1.20412 ; log 17 =1.23045. 17. When the number has more than four figures, as 11.4672. Since the mantissa is independent of the position of the decimal point, point off the first four figures and find the mantissa of log 1146.72. This will be between the mantissas of log 1146 and log 1147. Hence find from the tables the mantissas corresponding to 1146 and 1147; multiply the difference between them (called the tabular difference) by .72, and add the product (called the correction) to log 11.46; the result will be the logarithm required. Mantissa of log 1146 = 05918 log 11.46 = 1.05918 Mantissa of log 1147 = 05956 correction = 38 x .72 = 27.36 Tabular difference = 38 /. log 11.4672 = 1.05945 36 or = 1.05945 NOTE. Since any mantissa in the tables may be in error by half a unit in the fifth decimal place (Art. 2), no advantage is gained by using the sixth place in the interpolated logarithm. Thus, according to Art. I, we drop the .36, and call log 1 1. 4672 = 1.05945. NOTE. The marginal tables should be used in multiplying the tabular difference to rind the correction (Art. 4). NOTE. It is assumed that the change in the mantissa is proportional to that in the number, as the latter increases from 1146 to 1147. An increase of I in the num- ber causes an increase of 38 in the mantissa; hence an increase of .72 in the number will cause an increase of 38 X .72 in the mantissa. NOTE. We could also find the mantissa of log 11.4672 by subtracting the prod- uct of the tabular difference by .28 (or i.oo .72) from the mantissa corresponding to 1147; that is, the required mantissa is 05956 (38 x .28) =05956 10.64 05945 as before. 18. The general rule is : Find the mantissa corresponding to the first four figures of the number; multiply the tabular difference by the fifth and following figures treated as a decimal ; and add the product to the mantissa just found. The tabular difference is the difference between the mantissas corre- sponding to the two numbers in the tables, between which the given number lies. log 1.62163 = 0.20995 ; log 0.38024 = 1.58006 ; ^0.0852763 = 2.93083; ^189.524=2.27767; Iogo. 3 86o2 = i.5866i ; ^0.0085938 = 3.93419; log 19983.4 = 4.30067 ; ^3.98743 = 0.60070; logo. 090046 =2.95446. 390 EXPLANATION OF THE TABLES. NOTE. Page 397 is used when the number contains less than three figures, the number being found in the column N, and the logarithm in the column headed Log. The characteristic is given for whole numbers, and must be changed for decimals. NOTE. When a number is composed of three figures, find on pages 398-415 the number in the column N, and the mantissa corresponding in the column L. o. To find the Number corresponding to a Given Logarithm. 19. From the tables we find the sequence of figures corresponding to the given mantissa, as shown in Arts. 20, 21, and 22, the position of the decimal point being determined by the characteristic (Arts. 10, n). 20. When the given mantissa can be found in the tables. Find on pages 398-415 the first two figures of the mantissa under L in the column headed L. o. The last three figures of the mantissa are then sought for in the columns headed o, i, 2, 9, in the same line with the first two figures, or in one of the lines just below, or in the line next above (where they would be preceded by a *). The first three figures of the required number will be found in the column headed N, in the same horizontal line with the last three figures of the mantissa, and the fourth figure of the number at the top of the column in which the last three figures of the mantissa are found. Thus (page 398), 0.06221 log 1.154 ; 0.06558 = log 1.163 > 0.06893 = lg 1.172 ; 0.07004 log 1.175 ; 0.07188 log 1.180; 0.08063 = log 1.204. 21. When the given mantissa can not be found in the tables. If we wish to find the number whose logarithm is 2.16531, we enter the tables with 16531, and find that it lies between 16524 and 16554, so that the given mantissa corresponds to a number between 1463 and 1464. Also 16531 exceeds 16524 by 7, and this difference, divided by the tabular difference 30, gives .23"- as the amount by which the required number exceeds 1463. Hence 2.16531 = log I46.323---, which we call 146.32, according to Art. i, the incompleteness of the tables making the sixth figure uncertain. NOTE. The marginal tables should be used in dividing the difference between the given mantissa and the one next less in the tables by the tabular difference. 22. The general rule is : Find the number corresponding to the mantissa in the tables next less than the given mantissa ; divide the excess of the given mantissa over the one found in the tables by the tabular difference; and annex the quotient to the first four figures already found. The tabular difference is the difference between the two mantissas in the tables, between which the given mantissa lies. I.i66oo = log 0.14656 ; 0.18002 = log 1.5136 ; 2.18200 = log 152.06 ; 1.19000 = log 15.488 ; 4.19680 = log 15773 ; 1.20020 = log 15.856. 23. For the use of the numbers S', T\ S", T", see Arts. 35-38. EXPLANATION OF THE TABLES. 391 TABLE XVI. 24. This table (pages 420-464) contains the logarithms, to five deci- mal places, of the trigonometric sines, cosines, tangents, and cotangents of angles from o to 90, for each minute. The logarithms in the columns headed Z. Sin, L. Tan, and L. Cos, are augmented, and should be diminished by 10 (Art. n), while those in the columns headed L. Cot are correctly given. 25. Since sec^ = , and cosec.# = - , the logarithms of the cos.* secant and cosecant of an angle are the arithmetical complements of those of the cosine and sine respectively (Art. 12). To find the Logarithmic Functions of an Angle Less than 90. 26. When the angle is less than 45, the degrees are found at the top of the page, and the minutes on the left. The numbers in the same horizontal line with the minutes of the angle are the logarithmic functions indicated by the notation at the top of the columns. Thus (page 428), log sin 8 4' = 9.14714 10, log tan 8 4' = 9.15145 10, log cot 8 4' = 0.84855, log cos 8 4' = 9.99568 10. 27. When the angle is greater than 45, the degrees are found at the bottom of the page, and the minutes on the right. The numbers in the same horizontal line with the minutes of the angle are the logarithmic functions indicated by the notation at the bottom of the columns. Thus (page 428), log sin 81 25' 9.99511 10, log tan 81 25' = 0.82120, log cot 81 25'= 9.17880 10, log cos 81 25' = 9.17391 10. 28. When the angle is given to decimals of a minute. In finding log sin 30 8 '.48, for example, we see that it will lie between the logarithmic sines of 30 8' and 30 9', that is, between 9.70072 and 9.70093, their difference 21 being the change in the logarithmic sine caused by a change of i f in the angle. Hence, to find the correction to log sin 30 8' that would give log sin 30 8'.48 we multiply 21 by .48 (Art. 4). The product 10.08 added to log sin 30 8', since log sin 30 9' is greater than log sin 30 8', gives log sin 30 8 '.48 = 9.70082 (Art. i). Similarly, log tan 30 8'.48 = 9.76391, log cot 30 8'.48 = 0.23609, log cos 30 8'.48 = 9.93691, the correction being subtracted in the last two cases, since the cotangent and the cosine decrease as the angle increases. 392 EXPLANATION OF THE TABLES. 29. The general rule is : Find the function corresponding to the given degrees and minutes; multiply the tabular difference by the decimals of a minute ; add the product to the function corresponding to the given degrees and minutes when finding the logarithmic sine or tangent, and subtract it when finding the logarithmic cosine or cotangent. The tabular differences are given in the columns headed d. and c. d., the latter containing the common difference for the L. Tan and Z. Cot columns. The difference to be used is that between the functions cor- responding to the two angles between which the given angle lies. For 30 39'.38 : log sin = 9.70747 ; log cos = 9.93462 ; log tan = 9.77285 ; log cot = 0.22715. For 59 43 '.46: log sin = 9.93632 ; log cos = 9.70257 ; log tan = 0.233 75 ; log cot = 9,76625. 30. When the angle is given to seconds, the correction may be found by multiplying the tabular difference by the number of seconds, and dividing the product by 60. To find the Acute Angle corresponding to a Given Logarithmic Function. 31. The column headed Z. Sin is marked L. Cos at the bottom, while that headed L. Cos is marked L. Sin at the bottom ; hence, if a logarith- mic sine or cosine were given, we should expect to find it in one of these two columns. Similarly, we should expect to find a given logarithmic tangent or cotangent in one of the two columns headed L. Tan and L. Cot. 32. When the function can be found in the tables. If a logarithmic sine is given, find it in one of the two columns marked L. Sin and L. Cos ; if found in the column headed Z. Sin, the degrees are taken from the top, and the minutes from the left of the page ; if in the column headed Z. Cos but marked Z. Sin at the bottom, the degrees are taken from the bottom, and the minutes from the right of the page. Thus, 9.70115 = log sin 30 10'; 9.93457 = log sin 59 20'; 9.93724 = log cos 30 4'; 9.70590 = log cos 59 28'; 9.76406 = log tan 30 9'; 0.23130 = log tan 59 35' ; 0.23420 = log cot 30 15' ; 9.76870 = log 358 402 156 312 340 368 396 424 479 507 535 562 6 17.4- 16.8 358 403 157 59 618 645 673 700 728 756 783 811 838 7 20.3 19.6 403 158 866 893 921 948 976 *oo3 ="058 "085 *II2 g 23.2 22.4 159 20 140 167 194 222 249 276 303 330 358 385 9 26 I 25.2 (357 404 160 412 439 466 493 520 548 575 602 629 656 9*7 9(1 |V>7 404 161 683 710 737 763 790 817 844 871 898 925 357 40? 162 952 978 *oo5 *O32 *o^9 +085 *II2 *i39 *i6 S 1 2 7 2.0 356 405 163 21 219 245 272 299 325 352 378 405 4S8 2 5 4 5-2 35 6 406 164 484 5H S37 564 S90 617 643 669 696 722 3 8.1 7.0 : 35<5 406 165 748 7/5 801 827 8S4 880 9 06 932 9S8 98S 4 356 406 1 66 22 Oil 037 063 089 "5 141 I6 7 194 220 246 6 16.2 ic.6 356 355 407 407 167 1 68 272 531 298 SS7 324 S83 350 608 376 634 401 660 427 686 453 712 479 737 505 763 7 18.9 18.2 821.6 20.8 ; 408 169 789 840 866 891 917 943 968 994 *oi9 9 =4 3 23.4 1 355 1 4o8 170 23 045 070 096 121 M7 172 198 223 249 274 355 408 171 300 325 3 So 376 401 426 4S2 477 502 528 25 354 4<>5 172 553| 578 603 629 654 679 74 729 7S4 779 I 2-5 354 409 173 805] 830 8.S5 880 905 93 955 980 2 5 354 410 174 24 055 080 105 130 155 180 204 229 2S4 279 3 7-5 354 410 175 34 3 2 9 3 S3 378 403 428 452 477 S02 527 4 |354 411 176 55 1 S76 601 625 650 674 699 724 748 773 5 I2 -5 '353 411 177 797 822 846 871 8 9 S 920 944 969 993 *oi8 7 15.0 17. r 353 4" 178 25042 066 091 115 139 164 1 88 212 237 261 8 2O. O 353 412 179 285 310 334 358 382 406 43 1 455 479 503 9 22-5 353 412 180 527 551 575 600 624 648 672 696 720 744 353 +3 181 768 792 816 840 864 888 912 9^5 9S9 98s 24 23 332 4i3 182 26007 031 OSS 079 IO2 126 ISO 198 221 I 2.4 2.3 352 414 183 245 269 293 3i6 340 364 387 411 435 4S8 2 4.8 4.6 352 4i4 184 482 505 529 576 600 623 647 670 694 3 7 2 6. 9 SS 2 4i5 1*5 717 764 788 8n 8^4 858 881 90S 928 4 9.0 9.2 351 4i5 1 86 975 998 *O2I *45 *o68 *O9I *II 4 *l6i 5 I2.O II.5 35i 4i5 187 27184 207 231 2S4 277 300 323 346 370 393 6 144 13.8 rA i& T jlx 416 416 1 88 189 416 439 646 669 462 692 485 715 508 738 554 784 577 807 600 830 62J. 852 8 19.2 18.4 9 21.6 2O.7 350 417 I9O . 875 898 921 944 967 989 *OI2 *035 "058 *o8i 350 4i7 191 28 103 126 149 171 194 217 240 262 285 307 22 21 35 418 192 330 i 353 37 S 398 421 443 466 488 S" S33 I 2. 2 2.1 350 418 193 556 578 601 623 646 668 691 713 735 758 2 4.4 4.2 350 419 194 780 803 825 847 870 892 914 937 9S9 981 3 6.6 6.3 1 419 195 29 003 026 048 070 092 115 137 159 181 203 4 8.8 8.4 349 420 196 226 248 270 292 336 358 38o 403 42S 5 n. o 10.5 34,' 34^ 348 420 421 421 197 198 199 2OO 4471 667 i 8851 469 688 907 491 710 929 513 732 95 * 535 754 973 557 776 994 579 798 *oi6 601 820 "038 623 842 *o6o 276 645 863 *o8i 298] to 9 13.2 12.6 15.4 14.7 17.6 16.8 19.8 18.9 : 422 12^ 146 1 68 190 211 233 255 N. L. 1 23 4 5678 9 P. P. S.' T.' S." T." g // f n I' 6-46 373 373 o 2'= 120" 4-68557 557 o2S'=i6So" 4.68557 2 373 373 o 3 = 1 80 557 557 o 29 = 1 740 557 559 15 372 373 o 4 = 240 557 558 o 30 = 1 800 557 559 20 372 373 o 25 =1500 557 558 o 31 =1860 557 559 o 26=1560 557 558 o 32 = 1920 557 559 o 27=1620 557 55 s o 33=1980 557 559 o 28=1680 557 558 o 34 =2040 557 400 N, L, 1 234 5 6 7 8 9 P, P, 200 20 1 202 203 2O4 205 206 207 208 209 210 211 212 2I 3 2I 4 215 216 2I 7 218 219 22O 221 222 223 224 22 5 226 22 7 228 229 230 231 232 233 234 235 236 237 238 239 24O 241 242 243 244 2 45 246 247 248 249 25O 30103 125 146 1 68 190 211 233 255 47 1 685 899 *II2 323 534 744 952 1 60 276 298 i 2 3 4 5 i 6 i I \ 9 i 2 3 4 8 9 2 3 4 6 I 9 2 3 4 I 8 9 i 2 3 4 9 22 21 2.2 2.1 4.4 4-2 6.6 6.3 8.8 8.4 i.o 10.5 3.2 12.6 5-4 14-7 7.6 16.8 9.8 18.9 20 2.O 4.0 6.0 8.0 IO.O I2.O 14.0 16.0 1 8.0 19 1.0 3-8 5-7 7-6 9-5 11.4 13-3 15.2 17.1 320 535 750 963 3i 175 387 597 806 32015 34i 557 771 984 197 408 618 827 035 363 578 792 *oo6 218 429 639 848 056 384 600 814 *027 239 450 660 869 077 406 621 835 *o 4 8 260 47 1 68 1 890 098 428 643 856 *o6g 281 492 702 911 118 449 664 878 *O9i 302 5'3 723 93i 139 492 707 920 *i33 345 555 765 973 181 5H 728 942 *i54 366 576 785 994 201 222 243 263 284 305 325 346 366 387 408 428 634 838 33041 244 445 646 846 34044 449 654 858 062 264 465 666 866 064 469 675 879 082 284 486 686 885 084 490 695 899 IO2 34 56 706 905 IO4 5 10 7i5 919 122 325 526 726 925 124 53i 736 940 H3 345 546 746 945 H3 552 756 960 163 365 566 766 965 163 572 777 980 183 385 586 786 985 -T83 593 797 *OOI 203 405 606 806 *oo5 203 6l 3 818 *O2I 22 4 425 626 826 *025 223 242 262 282 301 321 34i 361 38o 400 420 439 635 830 35 2 5 218 411 603 793 984 459 655 850 044 238 43 622 813 *oo3 479 674 869 064 257 449 641 832 *O2I 498 694 889 083 2 7 6 468 660 8 5 I *O4O 5 I8 713 908 102 295 488 679 870 *059 537 733 928 122 315 57 698 889 "=078 557 753 947 141 334 526 717 908 *o 97 577 772 967 1 60 353 545 736 927 *n6 596 792 986 1 80 372 564 755 946 *i35 616 811 "005 199 392 583 774 965 *i 54 36i73 192 211 229 248 267 286 305 324 342 18 361 549 736 922 37 107 291 475 658 840 380 568 754 940 125 310 493 676 858 399 586 773 959 144 328 I" 694 876 418 605 791 977 162 346 530 712 894 436 624 810 996 181 365 548 73 1 912 455 642 829 *oi4 199 383 566 749 93i 474 66 1 847 *033 218 401 585 767 949 493 680 866 *5 l 236 420 603 785 967 5 11 698 884 *070 254 438 621 803 985 530 717 903 *o88 273 457 639 822 *oo3 1.8 3-6 5-4 7-2 9.0 10.8 12.6 14.4 16.2 17 1.7 3-4 is 8.5 IO.2 II.9 I 3 .6 l S-3 38021 039 057 75 093 112 130 148 i 66 184 202 382 5 6l 739 917 39094 270 445 620 220 399 578 757 934 in 287 463 637 238 417 596 775 952 129 305 480 655 256 435 614 792 97 146 322 498 672 274 453 632 810 987 164 340 5*5 690 292 471 650 828 *00 5 182 358 533 707 310 489 668 846 *O23 199 375 550 724 328 57 686 863 *O4i 217 393 568 742 346 525 703 88 1 *058 235 410 585 759 364 543 721 899 *076 252 428 602 777 794 811 829 846 863 88 1 898 9i5 933 95 N. L, 1 3 4 5 6 7 8 9 P, P, S.' T.' 2' 6.46 373 373 3 373 373 o 3'= i 04=2 S." T." So" 4.68557 557 40 557 558 30 557 558 o 2 o 2 o 3 &=21 7 = 22 S." T." 60" 4.68 557 559 20 557 559 80 557 559 20 372 373 25 372 373 05-3 8 = 22 o 33 = 1980 557 559 o 34 = 2040 557 559 o 35 = 2100 557 559 o 36 = 2160 557 559 o 39-2340 557 559 o 40 = 2400 557 559 o 41 = 2460 556 560 o 42 = 2520 556 560 401 N, L, i 1 2 3 4 5 6 7 8 9 P.P. 250 2 5 1 252 2 53 254 2 55 256 257 258 259 26O 261 262 263 264 265 266 267 268 269 27O 271 272 273 274 275 276 277 278 279 28O 281 282 283 284 2 8 8 i 287 288 289 290 291 292 293 294 295 296 297 298 299 300 39794 811 829 846 863 881 898 9*5 933 95 2 3 4 6 8 9 i 2 3 4 1 8 9 i 2 3 4 5 6 9 i 2 3 4 I I 9 2 3 4 8 9 18 1.8 3-6 54 7-2 9.0 10.8 12.6 14.4 16.2 17 i-7 34 6^8 10.2 II.9 13-6 15-3 16 1.6 64 8.0 9.6 II. 2 12.8 14.4 15 3- 4-5 6.0 7-5 10.5 I2.O 1.4 2.8 4.2 5-6 7.0 8.4 9-8 II. 2 12.6 967 40140 312 483 654 824 993 41 162 33 985 157 329 500 671 841 *OIO 179 347 *OO2 175 346 5 l8 688 858 196 363 192 364 535 705 * 8?5 212 3 80 *<>37 209 552 722 892 *o6i 229 397 226 398 569 739 909 +078 246 414 243 586 756 ! 926 ! 263 43 *o88 261 432 603 773 943 *iu 280 447 *io6 278 449 620 790 960 *I28 296 464 "123 637 807 976 481 497 5H 53i 547 564 581 597 614 631 647 664 830 996 42 160 325 488 975 43^6 68 1 847- *OI2 66 7 830 99 i 697 *02 3 193 357 521 684 846 7H 880 210 -374 537 700 862 *O24 73 1 896 *062 226 390 553 716 878 747 243 406 570 732 ^894 764 929 *095 259 423 586 749 9" 780 946 *ui 275 439 602 765 927 *o88 797 963 *I2 7 292 455 619 781 * 943 814 979 *i44 308 472 635 797 959 *I20 152 165 185 20 1 217 233 249 265 281 297 457 616 775 933 44091 248 404 560 473 632 791 949 107 264 420 576 329 489 648 807 965 122 2 7 9 436 592 345 55 664 823 981 138 295 45 i 607 361 521 680 838 996 154 3 11 467 623 377 537 696 854 *OI2 I 7 326 483 638 393 553 712 870 *028 185 342 498 654 409 569 727 886 20 1 358 425 584 743 902 217 373 529 685 441 600 759 917 *75 232 389 545 700 716 73i I 747 762 778 793 809 824 840 855 871 45 2 5 17.9 332 484 637 788 939 46090 886 040 194 347 500 652 803 954 105 902 056 209 362 515 667 818 969 120 917 -071 225 378 530 682 834 984 135 932 086 240 393 545 697 849 *ooo 150 948 IO2 255 408 5 6l 712 864 65 963 117 271 423 576 728 879 "=030 180 979 286 439 59i 743 * 894 - 195 994 148 301 454 606 758 909 *o6o 210 *OIO 163 469 621 773 * 92 - 225 240 255 270 285 300 315 33 345 359 374 389 538 835 982 47 129 276 422 567 404 553 702 850 997 144 290 436 582 419 568 7 l6 864 *OI2 159 305 451 596 434 583 879 *026 465 611 449 598 746 * 894 1 88 334 480 625 464 613 761 909 *o 5 6 202 349 494 640 479 627 776 923 "=070 217 363 59 654 494 642 790 * 938 232 378 524 669 509 657 805 953 *IOO 246 392 538 683 523 672 820 967 *U 4 261 407 553 698 712 727 j 741 756 ; 770 7^4 ! 799 813 828 842 N. L. 1 23 4 567 8 9 P. P, S.' T.' 2' 6.46 373 373 3 373 373 S." T." o 4'= 240" 4-68557 558 o 5 = 300 557 558 < o S." T." 15' =2700" 4.68556 560 = 2760 556 560 4.7 = 2820 556 560 l8 = 2880 556 560 19 = 2940 556 560 50 = 3000 556 561 25 372 373 26 372 373 27 372 374 30 372 374 041= 2460 556 560 o 42 2520 556 560 o 43 = 2580 556 560 o 44 = 2640 556 560 o 45 = 2700 556 560 o O t o < R'M'D SURV. 26 402 N, L. 1 2 3 4 5 6 7 8 | 9 pTp! | 300 301 302 303 34 305 306 307 308 39 310 3 11 312 3U 3H 315 316 317 3i8 319 320 321 322 3 2 3 324 325 326 327 328 329 330 33i 332 333 334 335 336 337 338 339 34O 34i 342 343 344 345 346 347 348 349 350 47712 727 74i 756 770 784 799 813 828 842 i 2 3 4 I 8 9 i 2 3 4 I 9 2 3 4 i 9 i 2 3 4 I 9 15 -S 3-o 4-5 6.0 7-5 9.0 10.5 I2.O 13-5 14 1.4 2.8 4.2 5-6 7.0 8.4 9.8 II. 2 12.6 13 i-3 2.6 3-9 5.2 6-5 7-8 9-i 10.4 11.7 12 1.2 2.4 3-6 4.8 6.0 7-2 8.4 9-6 10.8 857 48001 144 287 43 572 7'4 855 996 871 oi5 159 302 444 586 728 869 *OIO 885 029 1 73 3i6 458 601 742 883 *O24 900 044 187 330 473 615 756 *038 914 058 202 344 487 629 770 911 *O52 929 073 216 359 5 QI 643 785 926 *o66 943 087 230 373 5'5 657 799 940 *o8o 958 IOI 244 387 530 671 813 954 *094 972 116 259 401 544 686 827 968 *io8 986 130 273 416 558 700 841 982 *I22 49136 '50 164 178 192 206 220 234 248 262 276 415 554 693 831 969 50 106 243 379 290 429 568 707 845 982 120 256 393 34 443 582 721 859 996 !33 270 406 3i8 457 596 734 872 *OIO 147 284 420 332 47 1 610 748 886 *024 161 297 433 346 485 624 762 900 "037 174 3" 447 360 499 638 776 914 *o5i 1 88 325 461 374 I 13 651 790 927 *o65 202 338 474 388 III 803 941 *079 215 III 4O2 541 679 8l 7 955 *O92 229 365 501 5i5 529 542 556 569 583 596 610 623 637 651 786 920 5'55 322 455 587 720 664 799 934 068 202 335 468 601 733 678 813 947 081 215 348 481 614 746 691 826 961 095 228 362 495 627 759 705 840 974 108 242 375 508 640 772 718 853 987 121 $ 521 654 7 86 732 866 *OOI 135 268 402 534 667 799 745 880 *oi4 148 282 415 548 680 812 759 893 *028 162 295 428 561 693 825 772 907 *O4i 175 308 441 574 706 838 851 865 878 891 904 917 930 943 957 ! 97 983 52114 244 375 54 634 763 892 53020 996 127 257 388 517 647 776 905 033 *oo9 140 270 401 530 660 789 917 046 *022 153 28 4 414 543 673 802 930 058 "035 1 66 297 427 556 686 8i5 943 071 *048 179 310 440 569 699 827 956 084 *o6i 192 323 453 582 711 840 969 097 "075 205 336 466 595 724 853 982 no *o88 218 349 479 608 737 866 994 122 *IOI 231 362 492 621 750 879 *oo7 J 35 148 161 173 1 86 199 212 224 237 250 263 275 403 529 656 782 908 54033 158 283 288 415 542 668 794 920 045 170 295 301 428 555 68 1 807 933 058 183 307 3H 441 567 694 820 945 070 195 320 326 453 580 706 832 958 083 208 332 339 466 593 719 845 97 095 220 345 352 479 605 732 857 983 1 08 233 357 364 491 618 744 870 995 1 20 245 37 377 54 631 *oo8 133 382 390 r 7 643 769 895 *020 H5 270 394 407 419 432 444 456 469 481 494 506 518 N, L, 1 2 3 4 5 6 7 8 9 P, P, S.' TV 3' 646 373 373 4 373 373 S." T." o 5'= 300" 4-68557 558 o 6 = 360 557 558 o 54' =3 o 55 = 3 S." T." 240" 4.68 556 561 300 556 561 360 556 561 420 555 561 480 555 562 540 555 562 30 372 374 35 37 2 374 o 50 = 3000 556 561 051= 3060 556 561 o 52 = 3120 556 561 o 53 = 3 I 8o 556 561 o 54 = 3240 556 561 o 56-3 57 = 3 o 58 = 3 o 59 = 3 403 t N. L, 1 23 4 5 J 6 7 8 | 9 P.P. 35O 351 35 2 353 354 355 356 357 35* 359 360 361 362 363 364 365 366 367 368 369 37O 37i 372 373 374 9 377 |378 379 380 38i 382 383 384 385 386 387 388 389 39O 39i 392 393 394 395 396 397 398 399 4OO 54407 419 432 444 456 469 481 494 506 518 i 2 3 4 I I 9 i 2 3 4 g I 9 2 3 4 9 i 2 3 4 I I 9 13 i-3 2.6 3-9 11 7-8 9-i 10.4 11.7 12 1.2 2.4 3-6 4.8 6.0 7-2 8.4 9.6 10.8 11 i.i 2.2 3-3 4-4 8 11 9-9 10 I.O 2.0 3-o 4.0 5-o 6.0 7.0 8.0 9.0 53i 654 777 900 55 02 3 H5 267 388 j 509! 543 667 790 9U 35 157 279 400 522 555 ^ 925 047 169 291 4i3 534 g 814 937 060 182 303 425 54 6 58o 704 827 949 072 194 315 437 558 593 716 839 962 084 206 328 449 570 605 728 851 974 096 218 340 461 582 617 74i 864 986 108 230 352 473 594 6^0 753 8)6 998 121 242 364 6^2 765 888 *OII 133 ^55 376 497 618 630 642 654 666 678 691 703 715 727 739 75 1 871 991 56 no 229 348 467 f85 703 763 883 "003 122 2 4 I 360 478 597 714 775 895 *oi5 J 34 253 372 490 608 726 787 907 *O27 146 265 384 502 620 738 799 919 *038 158 277 396 I 14 632 750 811 93i *5 170 289 407 526 644 761 823 943 *062 182 301 419 538 656 773 835 955 *074 194 312 431 549 667 785 847 967 *o86 205 324 443 f 679 797 859 979 *og8 217 336 455 573 691 808 820 832 844 855 867 879 891 902 914 926 937 57054 171 287 403 5i9 634 749 864 978" 949 066 183 299 415 530 646 761 875 961 078 194 3I 2 426 542 657 772 88 7 972 089 206 322 438 553 669 784 898 984 IOI 217 334 449 565 680 795 910 996 "3 229 345 461 576 692 807 921 *oo8 124 241 357 473 588 703 818 933 *oi9 136 252 368 484 600 715 830 944 *3 I 148 264 380 496 611 726 841 955 *043 ' 5 ? 276 392 57 623 738 T 967 990 *ooi *'3 *O24 *Q35 *47 "058 *07O *o8i 58092 206 320 433 546 659 771 883 995 104 218 33i 444 557 670 782 894 *oo6 "5 229 343 456 569 68 1 794 906 *oi7 127 240 354 467 580 692 805 917 *028 138 252 365 478 591 704 816 928 *O4O 149 263 377 490 602 7i5 827 939 *5 I 161 274 388 5 01 614 726 838 95 *062 172 286 399 Si 2 625 737 850 961 *073 184 297 410 524 636 749 861 973 *o8 4 195 309 422 647 760 872 984 *095 59 106 1 1 8 129 140 I5 1 162 173 184 J 95 207 218 329 439 550 660 770 879 988 60097 229 340 45 561 671 780 890 999 1 08 240 35i 461 572 682 791 901 *OIO 119 T 362 472 583 693 802 912 *O2I I 3 262 373 483 594 704 813 923 +032 141 273 384 494 605 715 824 934 *043 152 284 395 506 616 726 835 945 *054 163 295 406 5^7 627 737 846 956 "063 173 306 417 528 638 748 857 966 +076 184 3i8 428 539 649 759 868 977 *o86 J 95 206 217 j 228 239 249 260 271 282 293 304 N, L, 1 2 3 | 4 56789 P. P. S.' T.' 3' 6.46 373 373 4 373 373 o 5'- 2 06='^ S." T." oo" 4-68557 558 6o 557 558 20 557 55 s o i'=3< 2 = 3 S." T." 36o" 4-68555 562 720 555 562 jSo 555 562 HO 555 563 P 555 5 6 3 ?6o 555 563 320 555 563 35 372 374 39 372 374 40 372 375 o 7 - A o 58 = 3480 555 562 o 59 = 3540 555 5 62 i o = 3600 555 562 i i = 3660 555 562 4-3: 5 =3< 6 = 3 < 7 =4< N, | L. | 1 2 3 4 5 6 7 8 9 P.P. 400 401 402 403 404 405 406 407 408 409 4IO 411 412 413 414 415 416 417 418 419 42O 421 422 423 424 425 426 427 428 429 430 43i 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 60 206 217 228 239 249 260 271 282 293 304 i 2 3 4 9 - 2 3 4 6 8 9 2 3 4 6 8 9 11 i.i 2.2 3-3 44 1:1 U 9.9 10 1.0 2.O 3-0 4.0 5- 6.0 7-o 8.0 9.0 9 0.9 1.8 2 i 3.6 4-5 % 3H 423 53i 638 746 853 959 61066 172 325 433 54i 649 756 863 97 077 183 336 444 552 660 767 874 981 087 194 347 455 563 670 778 885 991 098 204 358 466 574 681 788 895 *OO2 109 215 369 477 584 692 799 906 *oi3 119 225 379 487 595 703 810 917 *O23 130 236 390 498 606 7i3 821 927 *034 140 247 401 59 617 724 831 938 *045 151 257 412 520 627 735 842 949 *055 162 268 278 289 300 310 321 33 1 342 352 363 374 384 490 595 700 805 909 62014 118 221 395 500 606 711 815 920 024 128 232 405 511 616 721 826 930 034 138 242 416 52i 627 73i 836 941 045 149 252 426 532 637 742 847 951 055 J 59 263 437 542 648 752 857 962 066 170 273 448 553 658 97J 076 1 80 284 458 5 6 3 669 IP 982 086 190 294 469 574 679 784 888 993 097 201 304 479 584 690 794 899 *oo3 107 211 3H 325 335 346 356 366 377 387 397 408 418 428 531 634 737 839 941 63043 144 246 439 & 747 849 95i 053 155 256 449 552 651 757 859 961 063 165 266 459 562 665 767 870 972 073 175 276 469 572 675 778 880 982 083 185 286 480 583 685 788 890 992 094 '95 296 490 593 696 798 900 *OO2 I0 4 205 306 500 603 706 808 910 *OI2 II 4 215 3'7 511 613 716 818 921 *O22 124 225 327 521 624 726 829 93i *Q33 134 236 337 347 357 367 377 387 397 407 4i7 428 438 448 548 649 749 849 949 64048 H7 246 345 458 558 659 759 859 959 058 157 256 468 568 669 969 068 167 266 478 579 679 779 879 979 078 '77 276 488 589 689 789 889 988 088 187 286 498 599 699 799 899 998 098 197 296 508 60 9 709 80 9 909 *oo8 108 207 306 5^8 619 719 819 919 *oi8 ii8 217 316 I 28 629 729 829 929 *028 128 227 326 538 639 739 839 939 "=038 137 237 335 355 365 375 385 39? 404 414 424 434 444 542 640 738 836 933 65031 128 225 454 552 650 748 846 943 040 137 234 464 562 660 758 856 953 050 H7 244 473 572 670 768 865 963 060 ! 57 254 483 582 680 777 875 972 070 167 263 493 59i 689 787 885 982 079 176 273 503 60 1 699 797 895 992 089 1 86 283 5 J 3 611 709 807 904 *002 99 I 9 6 292 523 621 719 816 914 *OII 1 08 205 302 532 631 729 826 924 *02I 118 215 312 321 33i 34i 350 360 369 379 389 398 408 N, L, 1 2 3 4 5 6 7 8 9 P. P, S.' T.' 4' 6.46373 373 5 373 373 o o 6'= 3 7=4 S." T." 60" 4-68557 558 20 557 558 80 557 558 9'= 4i 10 = 42 S." T." 40" 4-68555 563 oo 554 563 60 554 564 20 554 564 80 554 564 40 554 564 oo 554 564 40 372 375 42 37 2 375 43 37 1 375 44 37i 375 45 37i 375 8= 4 1142 i 6 = 3960 555 563 i 7 = 4020 555 563 i 8 = 4080 555 563 i 9=4140 555 563 12 -43 13 = 43 14=44 15=45 405 N, L, | 2 | 3 4 5 6 7 | 8 9 P. P, 450 45i 452 453 454 455 45 6 457 458 459 460 461 462 463 464 465 466 467 468 469 470 47i 472 473 474 475 476 477 478 479 48O 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 65321 33i 34i 35 360 369 379 389 398 408 i 2 3 4 I I 9 i 2 3 4 i ? 9 i 2 3 4 1 I 9 10 I.O 2.0 3- 4.0 5-o 6.0 7.0 8.0 9.0 9 0.9 1.8 ii 4.5 5-4 6-3 7- 2 8.1 8 0.8 1.6 2.4 3-2 4.0 4.8 5.6 6.4 7.2 418 5H 610 706 801 896 992 66087 181 427 523 619 715 811 906 *OOI 096 191 437 533 629 725 820 916 *OII 106 200 447 543 639 734 830 925 *O2O "5 2IO 45 6 $ 744 839 935 *3 124 219 466 562 658 753 849 944 *039 134 229 475 57i 667 763 858 954 *049 H3 238 485 f< 677 772 868 963 "058 ! 53 247 495 591 686 782 877 973 *o68 162 257 54 600 696 982 *77 172 266 276 285 295 304 3*4 323 332 342 35i 36i 370 464 558 652 745 839 93 2 67025 117 380 474 567 661 751 848 941 034 127 389 483 577 6 r 764 857 95 043 136 398 492 586 680 773 867 960 052 H5 408 502 596 689 783 876 969 062 154 417 5" 605 699 792 885 978 T 164 427 52i 614 708 801 894 987 080 !73 436 530 624 717 811 904 997 089 182 445 539 633 727 820 9i3 *oo6 099 191 455 % 736 829 922 * OI 5 108 201 210 219 228 237 247 256 265 274 284 293 3 02 394 486 578 669 761 852 943 68034 124 3" 403 495 587 679 77 86 1 95 2 043 321 413 54 596 688 779 870 961 052 330 422 5'4 605 697 788 879 97 061 339 43 1 523 614 706 797 888 979 070 348 440 532 624 7 J S 806 897 988 079 357 449 54i 633 724 8.5 906 997 088 367 459 550 642 733 825 916 *oo6 097 376 468 560 651 742 834 925 *Ei 385 477 569 660 752 843 934 *O24 !I 5 133 142 I 5 l 160 169 178 187 196 205 215 305 395 485 574 664 753 842 93i 224 3H 404 494 583 673 762 851 940 233 323 413 502 592 68 1 771 860 949 242 332 422 5" 601 690 780 869 958 251 34i 43i 520 610 699 789 878 966 260 350 440 529 619 708 797 886 975 269 359 449 538 628 717 806 895 984 278 368 458 547 637 726 8i 5 904 993 287 377 467 556 646 735 824 9U *OO2 296 386 476 565 655 744 833 922 *OII 69020 028 037 046 055 064 073 082 090 099 1 08 197 285 373 461 548 636 723 810 117 205 294 38i 469 557 644 732 819 126 214 302 390 478 566 653 740 827 135 223 3ii 399 487 574 662 749 836 144 232 320 408 496 583 671 75 8 845 152 241 329 4i7 504 592 679 767 854 161 249 338 425 5J3 601 688 775 862 170 258 346 434 522 609 697 784 871 I 79 267 355 443 $ 705 793 880 1 88 276 364 452 539 627 7H 80 1 888 897 906 914 923 932 940 949 958 966 975 N. L, 1 2 3 4 5 6 7 8 9 P. P, S.' T.' 4' 6.46 373 373 5 373 373 o 7'= A o 8 = A S." T." ^20" 4-68557 558 ^80 557 558 40 557 55 8 i8' = 46 19 =47 S." T." So" 4-68554 565 40 554 5 6 5 oo 554 565 60 553 566 20 553 566 80 553 566 40 553 566 45 37i 375 48 37 1 375 49 37 1 37 6 50 37 1 376 o 9=1 ' >o =4% Ji =48 >2 =49 23 =49 24 =50 i 15 =4500 554 564 i 16 =456 554 565 i 17 =4620 554 565 i 18 =4680 554 565 406 N, L, 1 2 3 | 4 5 | 6 7 | 8 9 P.P. 500 5 01 502 503 54 505 506 507 508 509 510 5 11 512 5U 5H 5I I 5i6 Si? 518 5 J 9 52O 52i 522 523 524 525 526 527 528 529 53O 53i 532 533 534 $ 537 538 539 54O 54i 542 543 544 545 546 547 548 549 55O 69897 906 914 923 932 940 949 958 966 975 i 2 3 4 9 i 2 3 4 8 9 I 2 3 4 I 9 9 0.9 1.8 2.7 3-6 4-5 5-4 6-3 7-2 8.1 8 0.8 1.6 2.4 3-2 4.0 4.8 5-6 6.4 7.2 7 0.7 1.4 2.1 2.8 3-5 4.2 4-9 5-6 6-3 984 70070 157 243 329 4i5 5 01 586 672 992 079 165 252 338 424 59 595 680 *OOI 088 !74 260 346 432 5'8 603 689 *OIO 096 183 269 355 441 526 612 697 *oi8 105 191 278 364 449 535 621 706 *O27 114 2OO 286 372 458 544 629 714 *036 122 2O9 295 381 467 ill 723 * 044 131 217 303 389 475 561 646 73' *o 53 140 226 312 398 484 569 655 740 *062 148 234 321 406 492 578 663 749 757 766 774 783 791 800 808 817 825 834 842 927 71 OI2 096 181 265 349 433 517 851 935 020 105 189 273 357 441 525 859 944 029 113 198 282 366 45 533 868 952 037 122 206 290 374 458 542 876 961 046 130 214 299 383 466 550 885 969 054 139 223 37 39i 475 559 893 978 063 147 231 315 399 483 567 902 986 071 J 55 240 324 408 492 575 910 995 079 164 248 332 416 ?oo 584 919 *oo3 088 172 257 34i 425 508 592 600 609 617 625 634 642 650 659 667 675 684 767 850 933 72016 099 181 263 346 692 775 858 941 024 107 t 9 272 354 700 784 867 95 032 "5 198 280 362 709 792 875 958 041 123 206 288 370 & 883 966 049 132 214 296 378 725 809 892 973 057 140 222 304 387 734 817 900 983 066 148 230 3i3 395 742 908 991 074 156 239 321 403 75 834 917 999 082 165 247 329 411 759 842 925 *oo8 090 173 2 55 337 419 428 436 444 452 460 469 477 45 493 501 59 754 83 1 916 997 73 78 159 518 599 681 762 843 925 *oo6 086 167 526 607 689 770 852 933 *oi4 094 175 534 616 697 779 860 941 *O22 102 183 542 624 705 787 868 949 *O3O in 191 55 632 7i3 791 876 957 *o 3 8 119 199 558 640 722 803 884 965 "046 127 207 567 '648 730 811 892 973 *054 135 215 573 656 738 819 900 981 *062 143 223 583 665 746 827 908 989 *O7O 151 231 239 247 255 263 272 280 288 296 304 312 320 400 480 560 640 719 799 878 957 328 408 488 568 648 727 807 886 965 336 416 496 576 656 735 815 894 973 344 424 504 584 664 743 823 902 981 352 432 5*3 592 672 75 1 830 910 989 360 440 520 600 679 759 838 918 997 368 448 528 608 687 767 846 926 *oo5 376 456 536 616 695 771 854 933 *oi3 384 464 544 624 703 783 862 941 *O2O 392 472 SS 2 632 711 791 870 949 *028 74036 044 052 060 068 076 084 092 099 107 N. L. 1 2 3 4 5 6 7 8 9 P. P. S.' TV 5' 6.46 373 373 6 373 373 o 8'= 4 09=5 S." T." .80" 4-68557 558 40 557 558 00 557 558 o 26'= 5 27 = 5 S." T." 1 60" 4.68 553 567 220 553 567 280 553 567 340 553 567 400 553 567 460 552 568 520 552 568 5 37i 376 55 37i 376 O IO = 6 28-5 i 23 = 4980 553 566 i 24 = 5040 553 566 i 25 = 5100 553 566 i 26 = 5160 553 567 29-5 30 = 5 3i =5 32-5 407 1 " L, 1 ! 2 3 4 5 6 78 9 P.P. 550 551 552 553 554 555 556 557 558 559 560 561 5 ? 563 564 565 566 567 568 569 570 57 1 572 573 574 ' 575 576 577 578 579 58O 581 582 583 584 1% 586 587 588 589 59O 591 592 593 594 595 596 597 598 599 6OO 74036 044 0^2 060 Q68 076 084 092 099 107 i 2 3 4 5 6 7 8 9 I 3 4 9 8 0.8 1.6 2.4 3-2 4.0 4-8 5-6 6.4 7-2 7 -7 1.4 2.1 2.8 3-5 4.2 4-9 I' 6 6-3 "5 194 273 35i 429 57 586 663 74i 123 202 280 359 437 515 593 671 749 131 2IO 288 367 445 523 60 1 679 757 U9 218 296 374 453 53i 609 687 764 47 225 304 382 461 539 617 695 772 153 2 33 312 390 468 547 624 702 780 162 241 320 398 476 554 632 710 788 170 249 327 406 484 562 640 ll l 796 178 257 335 414 492 570 648 g 1 86 265 343 421 500 578 656 733 811 819 827 834 842 850 858 865 873 88 1 889 896 974 755i 128 205 282 358 435 5" 904 981 059 136 213 289 366 442 5*9 912 989 066 H3 220 297 374 45 526 920 997 074 IS* 228 305 38i 458 534 927 *oo5 082 '59 236 312 389 465 542 935 *OI2 089 1 66 243 320 397 473 549 943 *020 097 174 25 1 328 404 481 557 95 *028 105 182 259 335 412 488 565 641 958 *035 "3 189 266 343 420 496 572 966 *043 1 20 197 274 35 i 427 504 580 587 i 595 603 610 618 626 633 648 656 664 740 815 891 967 76042 118 193 268 671 747 823 899 974 050 1*5 200 275 679 751 831 906 982 057 133 208 283 686 762 838 914 989 065 140 215 290 694 77 846 921 ^97 072 148 223 298 702 778 853 929 *oo5 080 155 230 305 709 937 *OI2 08 7 163 238 313 717 944 *O2O 095 I 7 245 320 724 800 876 952 *O27 103 178 253 328 732 808 884 959 *035 no *5 260 335 343 I 35 358 365 373 380 388 395 403 410 418 492 567 641 716 790 864 938 77012 425 500 574 649 723 797 871 945 019 433 507 582 656 730 805 879 953 026 440 515 589 664 738 812 886 960 034 448 522 597 671 745 819 893 967 041 455 530 604 678 753 827 901 975 048 4 62 537 612 686 760 834 908 982 056 47 I 45 619 693 768 842 916 989 063 477 552 626 701 775 849 923 997 070 483 559 634 708 782 856 930 *OO4 078 085 093 IOO 107 "5 122 | 129 !37 144 151 159 232 305 379 452 525 597 670 743 1 66 240 313 386 459 S3 2 60? 677 750 173 247 320 393 466 539 612 685 757 181 254 327 401 474 546 619 692 764 1 88 262 335 408 481 554 627 699 772 195 269 342 4i5 488 561 634 706 779 203 276 349 422 495 568 641 7H 786 2IO 283 357 430 53 576 648 721 793 217 291 364 437 5 10 583 656 728 801 22? 2 9 8 371 444 517 590 663 735 808 815 822 830 837 844 851 859 866 873 880 N. L, | 1 23 4 5 6 7 8 9 P . P. S.' T.' 6' 6.46 373 373 S." T." o 9'= 540" 4.68 557 558 o 10 = 600 557 558 i3 1 3 5'= 57 S." T." oo" 4.68 552 569 60 552 569 20 552 569 80 552 569 40 55 r 569 oo 551 570 55 37 1 37 6 5 6 37i 376 57 37i 377 5 8 37 1 377 59 370 377 60 370 377 o-57 7 = 58 8 = 58 9 = 59 o = 60 i 31 = 5460 552 568 i 32 = 5520 552 568 i 33 = 558o 552 568 i 34 = 5640 552 568 i 35 = 5700 552 569 i 3 i 3 1 3 i 4 408 1 N> L, 1 2 3 4 5 | 6 7 8 9 P.P. GOO 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 65O 77815 822 830 837 844 851 859 866 873 880 2 3 4 8 9 i 2 3 4 6 I 9 i 2 3 4 5 6 8 9 8 0.8 1.6 2.4 3-2 4.0 4.8 5-6 6.4 7.2 7 0.7 1.4 2.1 2.8 3-5 4.2 4-9 5.6 6-3 6 0.6 1.2 1.8 2.4 3-0 3-6 4.2 4.8 5-4 887 960 78032 104 176 247 3 J 9 390 462 895 967 039 in 183 254 326 398 469 902 974 046 118 190 262 333 405 476 909 981 053 125 197 269 340 412 483 916 988 06 1 132 204 276 347 419 490 924 996 068 140 211 283 355 426 497 93 i *oo3 075 147 219 290 362 433 504 938 *OIO 082 '54 226 297 369 440 5 12 945 *oi7 089 161 233 305 376 447 S 1 9 952 *025 097 1 68 240 312 383 455 526 533 540 547 554 561 5<>9 576 583 590 597 604 6 75 746 817 888 958 79029 099 169 611 682 753 824 895 965 036 106 176 618 689 760 831 902 972 043 "3 183 625 696 767 838 909 979 050 120 I 9 633 704 774 845 916 986 057 127 197 640 711 781 852 923 993 064 134 204 647 718 789 859 930 *ooo 071 141 211 654 725 796 866 937 *oo7 078 148 218 661 732 803 873 944 *oi4 085 155 225 668 739 810 880 95 i *O2I 092 162 232 239 246 253 260 267 274 28l 288 295 302 309 379 449 518 588 657 727 796 865 3i6 386 45 6 5 2 5 5?5 604 734 803 872 323 393 463 '532 602 671 741 810 879 330 400 47 539 609 678 748 817 886 337 407 477 546 616 685 754 824 893 344 414 484 553 623 692 761 831 900 351 4 2I 49 i 560 630 699 768 837 906 358 428 498 f7 637 706 775 844 9i3 365 435 505 574 644 7i3 782 851 920 372 442 5" 58i 650 720 789 858 927 934 941 948 955 962 969 975 982 989 996 80003 072 140 209 277 346 414 482 55 010 079 H7 216 284 353 421 489 557 017 085 154 223 291 359 428 496 564 024 092 161 229 298 366 434 502 570 030 099 1 68 236 35 373 441 509 577 037 106 175 243 312 380 448 516 584 044 "3 182 250 3i8 387 451 523 59i 95 1 1 20 1 88 257 325 393 462 530 598 058 127 J 95 264 332 400 468 536 604 065 134 202 271 339 407 475 543 611 618 625 632 638 645 652 659 665 672 679 686 754 821 889 95 6 81 023 090 158 224 693 760 828 895 963 030 097 164 231 699 767 835 902 969 037 104 171 238 706 774 841 909 976 043 ii i 178 243 7^3 781 848 916 983 050 117 184 251 720 787 855 922 990 057 124 191 258 726 794 862 929 996 064 131 198 265 733 80 r 868 936 *00 3 070 137 204 271 740 808 875 943 *OIO 077 144 211 2 7 8 747 814 882 949 *oi7 084 1 S 1 218 28! 291 298 305 3" 3i8 325 33i 338 345 35i N, L, 1 2 3 4 5 6 7 8 9 P, P, S.' T.' 6 6.46 373 373 7 373 373 S." T." o io'= 600" 4.68 557 558 011= 660 557 558 44 ' = 62 45 = 6 3 S." T." 40" 4.68 551 571 00 55 1 57 1 60 55i 57i 20 550 572 80 550 572 40 55 572 60 370 377 63 37 377 6 4 37 37 8 6 5 37 378 40 =6000 551 570 41 =6060 551 570 42 =6120 551 570 43 =6180 551 570 44 =6240 531 571 46 =63 47 = 6 4 48 =64 49 =65 409 N. L, I 23 4 5 6 7 8 Q P , P, 650 651 652 653 654 i III 659 66O 661 662 663 664 s 667 668 669 67O 671 672 673 674 675 676 677 678 679 680 681 682 G3 5 680 687 688 689 690 691 692 693 694 |695 696 697 698 699 7OO 81 291 298 305 311 348 325 33i 338 345 35 1 i 2 3 4 1 8 9 i 2 3 4 8 9 7 0.7 1.4 2.1 2.8 3-5 4.2 4-9 5-6 6-3 6 0.6 1.2 1.8 2-4 3-o 3-6 4.2 4.8 54 358 425 49 i 558 624 690 757 823 889 365 43i 498 564 63 I 697 763 829 895 37i 438 505 57i 637 704 77 836 902 378 445 5" 1 7S 644 710 776 842 908 385 45i 518 584 651 717 783 849 9i5 39i 458 525 59i 657 723 790 856 921 398 465 53i 598 664 730 796 862 928 405 47i 538 604 671 737 803 869 935 411 478 544 611 677 743 809 875 941 418 485 55i 617 684 750 816 882 948 954 961 968 974 981 987 994 *ooo *oo7 *oi4 82020 086 151 217 282 347 413 478 543 027 092 I 5 8 223 289 354 419 484 549 033 099 164 230 2 g 360 426 491 556 040 105 171 236 302 367 432 497 562 046 112 I 7 8 243 308 373 439 54 569 053 119 184 249 315 380 445 5 10 575 060 125 191 256 321 387 452 5'7 582 066 132 197 263 328 393 458 523 588 073 138 204 269 334 400 465 530 595 079 145 210 276 34i 406 47i 536 601 607 614 620 627 633 640 646 653 659 666 672 737 802 866 930 995 83059 123 187 251 3 1 ! 378 442 506 569 632 696 759 822 679 743 808 872 937 *OOI 065 129 93 685 750 814 879 943 *oo8 072 136 200 692 756 821 885 95 *oi4 078 142 206 698 763 827 892 956 *O2O 085 149 213 705 769 834 898 963 *O27 091 155 219 711 776 840 905 969 "033 097 161 225 718 $ 911 975 *040 104 1 68 232 724 789 853 918 982 *o 4 6 no 174 238 730 795 860 924 988 *0 5 2 117 181 245 257 264 270 2 7 6 283 289 296 302 308 321 383 448 5'2 575 639 702 765 828 327 39i 455 518 582 645 708 77i 835 334 398 461 525 588 651 778 841 340 404 467 531 594 658 721 784 847 347 410 474 537 601 664 727 790 853 353 4i7 480 544 607 670 734 797 860 359 423 487 550 613 677 740 803 866 366 429 493 556 620 683 9 872 372 436 499 563 626 689 1% 879 885 891 897 904 910 916 923 929 935 942 948 84011 073 136 198 261 323 386 448 954 017 080 142 205 267 330 392 454 960 023 cS6 148 211 273 336 398 460 967 029 092 155 217 280 342 404 466 973 036 098 161 223 286 348 410 473 979 042 105 167 230 292 354 417 479 985 048 in 173 236 298 36i 423 4*3 992 055 117 1 80 242 305 367 429 491 998 06 1 123 1 86 248 3" 373 435 497 *004 067 130 192 251 317 379 442 54 5!o 516 522 i 528 535 54i 547 553 559 5 6 6 1 N. L. 1 2 3 4 5 6789 P . P, S.' T.' 6' 6.46373 373 7 373 373 S." T." io'= 600" 4.68 557 558 ii = 660 557 558 12 = 720 557 55 S 5 5 5 l':=66 2-67 T." 60" 4-68550 573 20 550 573 80 550 573 40 55 573 oo 549 574 60 549 574 20 549 574 6 5 37 378 69 370 378 7 37 379 o 3-67 I 48 = 6480 550 572 i 49 = 6540 550 572 i 50 = 6600 550 572 i 51 =6660 550 573 54 = 6* 55 = 65 56 = 65 i 57 = 7C 410 N. L, 1 23456 7 8 | 9 P. P. 7OO 701 702 703 704 3 $ 709 7IO 711 712 7U 714 7i5 716 717 718 719 720 721 722 723 724 7 2 5 726 727 728 729 730 73i 732 733 734 735 736 737 738 739 74O 74i 742 743 744 745 746 747 748 749 750 84 510 516 522 528 535 54i 547 553 615 677 739 800 862 924 985 046 107 559 566 i 2 3 4 5 6 8 9 i 2 3 4 i 8 9 i 2 3 4 6 8 9 7 0.7 1.4 2.1 2.8 3-5 4-2 4.9 5-6 0-3 6 0.6 1.2 1.8 2.4 3i6 4-2 4 .8 5-4 5 o-5 I.O i-5 2.O 2-5 3-o 3-5 4.0 4-5 572 634 696 757 819 880 942 85 003 065 578 640 702 763 825 887 948 009 071 584 646 708 770 831 893 954 016 077 590 652 714 776 837 899 960 022 08 3 597 658 720 782 844 905 967 028 089 603 Is 788 850 911 973 034 095 609 671 733 794 856 917 979 040 IOI 621 683 741 807 868 930 991 052 114 628 689 75i 813 874 936 997 058 1 20 126 132 138 144 '5 156 163 169 i?5 181 187 248 309 37 43i 491 552 612 673 193 254 315 376 437 497 558 618 679 199 260 321 382 443 503 564 625 685 205 266 327 3 88 449 509 570 631 691 211 2 7 2 333 394 455 5'6 576 637 697 217 278 339 400 461 522 582 643 73 224 285 345 406 467 528 588 649 709 230 291 352 412 473 534 594 655 715 236 297 358 418 479 540 600 66 1 721 242 303 364 425 485 546 606 667 727 733 739 745 75i 757 763 769 775 781 788 794 854 914 974 86034 094 153 213 273 800 860 920 980 040 IOO 159 219 279 806 866 926 986 046 1 06 165 225 285 812 872 932 992 052 112 171 231 291 818 878 938 998 058 118 177 237 297 824 884 944 *OO4 064 124 183 243 303 830 890 9?o *OIO 070 130 189 249 308 836 896 956 *oi6 076 136 195 255 3H 842 902 962 *O22 082 141 201 26l 320 848 908 968 *028 088 J 47 207 267 326 332 338 344 35 356 362 368 374 380 386 392 45i 5io 57 629 688 747 806 864 398 457 516 576 631 694 753 812 870 404 463 522 581 641 700 759 817 876 410 469 528 587 646 75 764 823 882 41^ 475 534 593 652 711 770 829 888 421 481 540 599 658 717 776 835 894 427 487 546 605 664 723 782 841 900 433 493 552 611 670 729 788 847 906 439 499 558 617 676 735 794 853 911 445 54 564 623 682 741 800 859 917 923 929 93? 941 947 953 958 964 970 976 982 87 040 099 '57 216 274 332 390 448 988 046 105 163 221 280 338 396 454 994 052 in 169 227 286 344 402 460 999 058 116 175 233 291 349 408 466 *oo5 064 122 181 239 297 355 4U 47i *OII 070 128 186 245 303 36i 419 477 *oi7 075 134 192 251 309 367 421 483 *02 3 08 1 I4O 198 2 5 6 3'3 373 43i 489 *O29 087 146 204 262 320 379 437 495 *035 093 IS* 210 268 326 384 442 5 00 506 512 518 5 2 3 529 535 54i 547 SS 2 558 N. L. 1 234 5 6 7 8 9 P. P. | S.' TV 7' 6.46373 373 8 373 373 ] O 1 S." T." i'= 660" 4.68 557 558 2 = 720 557 558 3= 780 557 558 i 2 2 59'= 7 = 7 S." T." 140" 4.68 549 575 200 549 575 260 549 575 320 548 576 380 548 576 440 548 576 500 548 577 70 370 379 7 1 37 379 72 369 379 74 369 379 75 369 380 ] 1 -7 i 56 = 6960 549 574 i 57 = 7020 549 574 i 58 = 7080 549 575 i 59 = 7140 549 575 2 2-7 2 3 = 7 2 4 = 7 2 5 = 7 411 N, L, 1 2 3 4 5 6 7 | 8 i 9 P, P, 75O 75 1 75 2 753 754 755 756 757 758 759 760 761 762 763 764 765 766 768 769 77O 771 772 773 774 775 776 777 778 779 78O 781 782 783 784 7oO 787 7 88 789 79O 791 79 1 793 794 795 796 797 798 799 8OO 87 506 512 518 523 529 535 541 547 552 558 616 6/4 73 1 789 846 904 961 *oi8 076 6 i j 0.6 2 1.2 3 1-8 4 2.4 5 3-0 6 3.6 7 4.2 8 4.8 9 5-4 5 i 0.5 2 I.O 3 1-5 4 2.0 5 2.5 6 3-0 7 3-5 8 4.0 9 4-5 622 679 737 795 852 910 967 88024 570 628 685 743 800 858 915 973 576 633 691 749 806 864 921 978 036 639 697 754 812 869 927 984 041 587 045 703 760 818 875 933 990 047 593 651 708 766 823 88 1 938 996 053 599 656 7H 772 829 887 944 *OOI 058 604 662 720 777 835 892 * 95 064 610 668 726 783 841 898 955 OI 3 070 08 1 087 093 098 104 no 116 121 127 133 138 195 252 39 366 423 480 536 593 144 20 1 258 315 372 429 485 542 598 150 207 264 321 377 434 491 547 604 156 213 270 326 383 440 497 553 610 161 218 275 332 389 446 52 559 615 167 224 281 338 395 508 564 621 '73 230 287 343 400 457 513 57 627 I 7 8 235 292 349 406 463 576 632 184 241 298 355 412 468 525 581 638 190 247 304 360 474 53 643 649 651 660 666 672 677 683 689 694 700 762 818 874 930 986 89 042 098 '54 7" 767 824 880 936 992 048 104 717 773 829 941 997 053 109 165 722 779 835 891 * 94 l 059 170 728 784 840 897 953 734 790 846 902 958 739 795 852 908 964 745 80 1 857 913 969 75* 807 863 919 975 756 812 868 925 981 *37 092 148 204 064 120 I 7 6 070 126 182 076 187 08 1 137 193 087 '43 198 209 215 221 226 232 237 243 248 254 260 265 321 376 432 487 542 597 653 708 763 271 326 383 437 492 548 603 658 713 2 7 6 332 387 443 498 553 609 664 719 282 337 393 448 504 559 614 669 724 287 343 398 454 59 564 620 675 730 293 348 404 459 515 570 625 680 735 298 354 409 465 520 575 631 686 304 360 415 47 526 581 636 691 746 365 421 476 586 642 697 752 315 426 481 537 592 647 702 757 768 774 779 7^5 790 796 801 807 812 818 873 927 982 90037 091 146 200 251 823 878 933 988 042 097 260 829 883 938 993 048 IO2 157 211 266 834 889 944 998 053 108 162 217 271 840 894 949 059 168 222 2 7 6 900 955 064 119 173 227 282 851 905 960 069 124 179 233 287 856 911 966 *O2O 075 129 184 238 293 862 916 971 *026 080 135 189 244 298 867 922 977 *0 3 I 086 140 195 249 304 358 309 3H 320 325 33i 336 342 347 352 N. L. | 1 2 3 4 56789 P. P. S.' T.' 7' 6.46 373 373 8 373 373 o 12'= 7 o 13 = 7 S." T." 20" 4-68557 558 80 557 558 40 557 55 s 2 2 2 I 8' = 76 9 =77 S." T." 80" 4-68547 578 40 547 578 oo 547 578 60 547 579 20 547 579 80 547 579 40 546 579 75 369 380 80 369 380 o 14 = o =78 1=78 2=79 3 =79 4=80 2 5 =75 548 577 2 6=7560 548 577 2 7=7620 548 577 2 8=7680 547 578 2 I 2 I 2 I 2 I 412 N, L, | 1 2 | 3 4 5 6 7 | 8 9 P 1 p 1 800 80 1 802 803 804 805 806 807 808 809 8IO 811 812 813 814 815 816 8i 7 818 819 82O 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841. 842 843 844 84S- 846 847 848 849 850 90309 3H 320 325 33i 336 390 445 499 553 607 660 714 768 822 342 347 35 2 358 i 2 3 4 I 9 i 2 3 4 6 8 9 6 0.6 1.2 1.8 2-4 3-0 3-6 4.2 4-8 5-4 5 o-5 I.O i-5 2.0 2-5 3-o 3-5 4.0 4-5 363 417 472 526 580 634 687 74i 795 369 423 477 f5 639 693 747 800 374 428 482 536 590 644 698 752 806 380 434 488 542 596 650 73 757 811 385 439 493 547 60 1 655 709 763 816 396 45 54 558 612 666 720 773 827 401 455 509 f3 617 671 725 779 832 407 461 5i5 569 623 677 73 784 838 412 466 520 574 628 682 736 789 843 849 854 859 865 870 875 881 886 89. 897 902 956 91009 062 116 169 222 328 907 961 014 068 121 174 228 28l 334 9i3 966 020 073 126 1 80 233 286 339 918 972 025 078 132 185 238 291 344 924 977 030 084 137 190 243 297 350 929 982 036 089 142 196 249 302 355 934 988 041 094 148 20 1 254 37 360 940 993 046 100 '53 206 259 312 365 945 998 052 105 158 212 265 318 371 95 *oo4 57 I IO 164 217 270 323 376 38l 387 392 397 403 408 4i3 418 424 429 434 487 540 593 645 698 75i 803 855 440 492 545 S<& 651 703 756 808 86 1 445 498 55i 603 656 709 761 814 866 45 503 556 609 66 1 714 766 819 871 455 508 561 614 666 719 772 824 876 461 5H 566 619 672 7 2 4 777 829 882 466 5*9 572 624 677 730 782 834 887 47 1 524 577 630 682 735 787 840 892 477 529 582 635 687 740 793 845 897 482 535 587 640 693 745 798 850 903 908 9i3 918 924 929 934 939 944 950 955 960 92 OI2 065 117 I6 9 221 273 324 376 965 018 070 122 174 226 2 7 8 330 381 971 023 075 127 179 231 283 335 387 976 028 080 132 184 236 288 340 392 981 033 085 :g 241 293 345 397 986 038 091 H3 195 247 298 35 402 991 044 096 148 200 252 304 355 407 997 049 IOI 153 205 257 309 36i 412 *002 5 4 106 158 210 262 3H 366 418 *oo7 059 in 163 215 267 319 37i 423 428 433 438 443 449 454 459 464 469 474 480 531 583 634 686 737 788 840 891 485 III 639 691 742 793 845 896 49 542 593 645 696 747 799 850 901 495 547 598 650 701 752 804 906 500 552 603 6 55 706 758 809 860 911 55 557 660 711 763 814 865 916 5' 1 562 614 665 # 819 870 921 5<6 567 619 670. 72,2 773 824 875 927 521 572 624 6 75 727 778 829 88 1 932 526 578 629 68 1 732 783 834 886 937 942 947 952 957 962 967 973 978 983 988 N, L. 1 2 3 4 5 6 7 8 9 P P, S.' TV 8' 6.46 373 373 9 373 373 S." T." o 13'= 780" 4-68557 558 o 14 = 840 557 558 o 15 = 9oo 557 558 2 ] 2 1 2 ] 2 2 ; 2 : 2 : 6'= 8 7-8: S.' 60" 4.68 54* >2o 54^ >8o 54* HO 54< po 54= ^o 54! ;2Q 54 ' T." ) 580 > 580 i 581 i 581 , 582 ; 582 , 582 80 369 380 81 369 381 82 368 381 85 368 381 8 = 82 213 = 7980 547 579 2 14 8040 546 579 2 15 = 8100 546 580 2 16 = 8160 546 580 9-8. JO r=& >I = 8. 22 = 8 413 N. L, 1 2 3 4 5 6 7 8 9 P , P, 850 S;i ,S 5 2 853 854 855 850 857 Ss3 859 860 861 862 863 864 865 866 867 868 869 87O 871 872 873 874 875 876 877 878 879 88O 88 1 882 883 884 885 ! 886 887 888 889 89O 891 892 893 894 895 896 897 ! 898 i 899 9OO 92942 947 952 957 962 967 973 978 983 988 o 3 4 8 9 i 2 3 4 I 9 i 2 3 4 6 9 6 0.6 1.2 1.8 2.4 3-o 3-6 4.2 4.8 5-4 5 0-5 I.O -S 2.0 2-5 3-o 3-5 4.0 4-5 4 0.4 0.8 1.2 1.6 2.0 2.4 2.8 $ 993 9344 095 146 197 247 298 349 399 998 049 100 151 202 252 303 354 404 "003 054 105 156 207 258 308 359 409 *oo8 059 no 161 212 263 313 34 052 099 147 194 242 289 336 961 *oo9 057 104 '5 2 199 246 294 34i 966 *oi4 06 1 109 156 204 251 298 346 971 *oi9 066 114 161 209 256 33 350 976 *023 071 118 1 66 213 261 308 355 980 *028 076 123 171 218 265 313 360 985 "033 080 128 7S 223 270 317 363 990 *o 3 8 085 ' 227 275 322 369 995 *O42 090 137 183 232 280 327 374 379 384 388 393 398 402 407 412 417 421 426 473 520 567 614 661 708 m 431 478 525 572 619 666 7*3 759 435 483 530 577 624 670 717 764 811 440 487 534 58i 628 675 722 769 816 445 492 539 586 633 680 727 774 820 45 497 544 59i 638 683 73i 778 823 454 5l 548 595 642 689 736 783 830 459 506 553 600 647 694 74i 788 834 464 5" 558 603 652 699 745 792 839 468 5^5 562 609 656 703 75 797 844 8 4 8 453 858 862 867 872 876 881 886 890 8 9 3 942 988 9703? 08 1 128 174 220 267 900 946 993 039 086 132 179 223 271 904 95 * 997 044 090 137 183 230 276 909 95 6 *OO2 049 095 142 1 88 234 280 914 960 *oo7 053 IOO 146 192 239 285 918 963 *OII 058 104 151 197 243 290 923 97 *oi6 063 109 155 202 248 294 928 974 *02I 067 114 1 60 206 253 299 932 979 *O25 072 118 163 211 257 34 937 984 "030 077 "3 169 216 262 308 313 3i7 322 327 331 336 340 345 350 354 359 405 45i 497 543 589 635 681 727 772 364 410 456 502 548 594 640 685 73i 368 414 460 506 552 598 644 690 736 373 419 463 5" % 649 693 740 377 424 470 5^6 562 607 653 699 745 382 428 474 520 566 612 658 704 749 387 433 479 523 57i 617 663 708 754 39i 437 483 529 575 621 667 7'3 759 396 442 488 626 672 717 763 400 447 493 539 f5 630 676 722 768 777 782 786 791 795 800 804 809 813 N, L. 1 2 3 4 5 6 7 | 8 9 P . P. S.' T.' 9' 6.46373 373 10 373 373 S." T." o 15'= 900-' 4.68 557 558 o 16 = 960 557 558 2 34' =92 2 35 = 93 S." T." 40" 4-68543 587 oo 543 5 8 7 60 543 587 20 542 588 80 542 588 40 542 588 90 368 383 9i 368 383 92 367 383 94 367 383 95 367 384 2 30 = 9000 544 585 2 31 = 9060 544 585 2 32 =9120 543 586 2 33 = 9i8o 543 586 2 34 = 9240 543 587 2 36-93 2 37 = 94 2 38 = 94 2 39 = 95 415 N. L. 1234 5 | 6 7 8 9 P , P, I ! 950 951 95 2 953 954 955 956 957 958 959 96O 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 3 989 99O 991 992 993 994 995 996 997 998 999 1000 97772 818 864 909 95? 98000 046 091 *37 182 777 782 786 79 j 795 800 804 809 813 I 2 3 4 I 8 9 i 2 3 4 I I 9 5 o-5 I.O i-5 2.0 2-5 3.0 3-5 4.0 4-5 4 0.4 0.8 1.2 1.6 2.0 2-4 2.8 3-2 3.6 823 868 914 959 005 050 096 141 1 86 827 873 918 964 009 055 100 146 191 832 877 923 968 014 059 105 150 195 836 882 928 973 019 064 109 155 200 841 886 932 978 023 068 114 159 204 845 891 937 982 028 73 118 164 209 850 896 941 987 032 078 123 1 68 214 855 900 946 991 037 082 I2 7 173 218 859 90S 95 996 041 087 132 177 223 227 272 3* 363 408 498 543 588 632 677 232 277 322 367 412 457 502 547 592 637 236 241 245 250 254 259 263 268 281 327 372 4^7 462 57 552 597 641 286 331 376 421 466 5 11 & 646 290 426 47* 516 56' 605 650 295 340 385 43 475 520 f5 610 655 299 345 390 435 480 525 570 614 659 304 349 394 439 484 529 574 619 664 308 354 399 444 489 534 579 623 668 3 1 3 358 403 448 493 538 583 673 682 686 691 695 700 74 709 7U 717 722 767 811 856 900. 945 989 99034 078 "123" 726 III 860 905 949 994 038 083 73J 776 820 865 909 954 998 043 087 735 780 825 869 914 958 *oo3 047 092 740 784 829 874 918 963 *oo7 052 096 744 789 834 878 923 967 *OI2 056 100 749 793 838 883 927 972 *oi6 061 103 753 798 843 887 932 976 *O2I 065 109 g 847 892 936 981 *02 5 069 114 762 807 851 896 941 985 *O29 074 118 127 131 136 140 H5 149 154 158 162 167 211 255 3 00 344 388 432 476 520 171 216 260 34 348 392 436 480 524 176 220 264 308 352 396 441 484 528 180 224 269 313 357 401 445 489 533 185 229 273 3i7 36i 405 449 493 537 189 233 277 322 366 410 454 498 542 193 238 282 326 370 414 458 502 546 I 9 8 242 286 330 374 419 463 506 550 2O2 247 291 335 379 423 467 5" 555 207 251 295 339 383 427 47 r 515 559 564 568 572 577 58i 585 590 594 599 603 607 651 695 739 782 826 870 913 957 612 656 699 743 787 830 874 917 961 616 660 74 747 791 835 878 922 965 621 664 708 752 795 839 883 926 970 625 669 712 756 800 843 887 93 974 629 673 717 760 804 848 891 935 978 634 677 721 765 808 852 896 939 983 638 682 726 769 813 856 900 944 987 642 686 73 774 817 861 904 948 991 647 691 734 778 822 865 909 952 996 00000 004 009 013 017 022 026 030 035 039 N, L, I 2 3 4 5 | 6 7 8 | 9 P, P. S.' T.' 9' 6.46 373 373 10 373 373 o 15'= c o 16 = c S " T " >oo" 4-68557 558 60 557 558 >20 557 558 2 4 I'= <> 2 42 = 9 S." T." 660" 4.68542 589 720 541 590 780 541 590 840 541 590 900 541 591 960 541 591 >020 540 592 95 367 384 98 367 384 99 367 385 100 366 385 o 17 = ic 2 t \Z - 9 W = 5 t5 = ^ 16= S \1 =ic 2 38 =9480 542 588 2 39 =9540 542 588 2 40 =9600 542 589 2 4 I =9660 542 589 2 i 2 < 2 < 2 , 416 N, L, I 2 3 4 5 6 7 8 | 9 IOOO 1001 1 002 1003 1004 1005 1006 1007 1008 1009 IOIO ion 1012 1013 1014 1015 1016 1017 1018 1019 IO2O IO2I IO22 1023 IO24 1025 IO26 1027 IO28 1029 IO3O 1031 1032 I0 33 1034 I0 35 1036 I0 37 1038 1039 IO4O 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 ooooooo 0434 0869 1303 J 737 2171 2605 3039 3473 ! 3907 4341 8677 ooi 3009 7337 002 1 66 1 5980 003 0295 4605 8912 4775 9111 3442 777 2093 6411 0726 5 36 9342 5208 9544 3875 8202 2525 6843 "57 5467 9772 5642 9977 4308 8635 2957 7275 1588 5898 *0203 6076 *O4ii 4741 9067 3389 7706 2019 6328 *o6 33 6510 *o844 5'74 9499 3821 8138 245 i 6 759 *io63 6943 *i277 5607 9932 4253 8569 2882 7190 *I 49 3 7377 *i7io 6039 *036 4 4685 9001 3313 7620 *I92 4 7810 *2i43 6472 *0796 5116 9432 3744 8051 *2354 8244 *2 57 6 6905 *I228 5548 9863 4174 8481 *2 7 8 4 0043214 3 6 44 4074 454 4933 5363 5793 6223 6652 7082 75 * 2 005 1805 6094 006 0380 4660 8937 007 3210 7478 008 1 742 7941 2234 6523 0808 5088 9365 3637 7904 2168 8371 2663 6952 1236 55i6 9792 4064 8331 2594 8800 3092 738o 1664 5944 *02I9 4490 8757 3020 9229 3521 7809 2092 6372 *o6 47 49J7 9184 3446 9659 395 8238 2521 6799 *io 74 5344 9610 3872 *oo88 4379 8666 2949 7227 *i5oi 577i *oo37 4298 *S 1 7 4808 9094 3377 7655 *i928 6198 ="0463 4724 *0947 5237 9523 3805 8082 *2355 6624 "=0889 5i5 *i 37 6 5666 995 * 4233 8510 *2 7 82 705 1 *i 3 i6 5576 6002 6427 6853 7279 7704 8130 8556 8981 9407 9832 0090257 459 8756 oio 3000 7 2 39 on 1474 574 993 i 0124154 0683 4934 9181 3424 7662 1897 6127 *0354 4576 1108 5359 9605 3848 8086 2320 6550 *0776 4998 1533 5784 *oo30 4272 8510 2743 6 973 "1198 5420 1959 6208 *Q454 4696 8933 3166 7396 *I62I 5842 2384 6633 *o878 5120 9357 3590 7818 *2043 6264 2809 7058 *i33 5544 9780 4013 8241 *2 4 6 5 6685 3234 7483 *I 7 2 7 5967 *O2O4 4436 8664 *2887 7107 3659 7907 *2I5I 6391 *o627 4859 9086 * 3310 7529 4084 8332 * 2 575 6815 *io5o 5282 959 *3732 795i 8372 8794 9215 9637 *oo59 *048o *090i *i323 *i744 *2i65 013 2587 6797 014 1003 5205 9403 015 3598 7788 016 1974 6i55 3008 7218 1424 5625 9823 4017 8206 2392 6 573 3429 7 6 39 1844 6045 *02 43 443 6 8625 2810 6991 3850 8059 2264 6465 *o662 4855 9044 3229 7409 4271 8480 2685 6885 *I082 5274 9462 3647 7827 4692 8901 3105 7305 *i5oi 5 6 93 9881 4065 8245 5"3 9321 3525 * 772? *I92O 6112 *0300 4483 8663 5534 9742 3945 8144 *234O 6531 *o7i8 4901 9080 5955 *0l62 4365 8564 *2759 6950 *"37 5319 9498 6376 *o 5 8 3 4785 8984 * 3 i 7 8 7369 *!555 5737 9916 0! 7333 Q75 1 1168 1586 2003 2421 2838 3256 3673 4090 457 8677 0182843 7005 019 1163 53!7 9467 0203613 7755 4924 9094 3259 7421 1578 5732 9882 4027 8169 5342 95" 3676 7837 1994 6147 *o2g6 4442 8583 5759 9927 4092 8253 2410 6562 *o7ii 4856 8997 6176 *0344 4508 8669 2825 6977 *II26 5270 9411 6593 *076i 4925 9084 3240 7392 *I540 5684 9824 7010 *ii77 534i 9500 3 6 5 6 7807 *i 95 5 6099 *0238 7427 *i594 5757 9916 4071 8222 *2 3 6 9 6513 *o652 7844 *2OIO 6173 *0 33 2 4486 8637 *2 7 8 4 6927 *io66 8260 *2427 6589 *o 74 7 4902 9052 * 3 i 9 8 734i "1479 02 1 1893 2307 2720 3134 3547 3961 4374 4787 5201 5 6l 4 IM, L, 1 2 3 4 5 6 7 8 9 S." T." S." T." 2 46' = 9960" 4.68541 591 2 51' = 10260" 4.68540 593 2 47 = 10020 540 592 2 52 = 10320 539 594 2 48 = 10080 540 592 2 53 = 10380 539 594 2 49 = 10140 540 592 2 54 = 10440 539 595 2 50 = 10200 540 593 2 55 = 10500 539 595 417 N. L, 1 2 | 3 | 4 5 J^ 6 7 8 9 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 IO6O 1061 1062 1064 ! 1065 I066 1067 1068 1069 IO7O 1071 i 1072 1073 1074 1075 1076 1077 1078 1079 IO8O 1081 1082 i Io8 3 i 1084 i 1085 i 1086 | 1087 1088 1089 IO9O i 1091 1 1092 I0 93 1094 1095 1096 1 1097 1098 1099 1100 021 1893 2307 : 2720 3^34 3547 396i 4374 4787 5201 5614 6027 0220157 4284 8406 02 3 2525 6639 024 0750 4857 8960 6440 0570 4696 8818 2936 7050 1161 5267 937 6854 0983 5 I0 9 9230 3348 7462 1572 5678 978o 7267 1396 5521 9642 3759 7873 1982 6088 7680 1808 5933 +0054 4171 8284 2393 6498 *o6oo 8093 2221 6345 *0 4 66 4582 8695 2804 6909 *IOIO 8506 2634 6758 4994 9106 32H 73 1 9 "1419 8919 3046 7170 "1289 5405 95'7 3625 * 7729 9332 3459 7582 1701 9928 4036 ^8139 9745 3871 7994 *2II3 6228 *0339 4446 * 8549 025 3059 3468 3878 4288; 4697 5 I0 7 5516 5926 6335 6744 7*54 026 1245 5333 9416 027 3496 7572 028 1644 57 J 3 9777 75 6 3 1654 574i 9824 3904 7979 2051 6119 *oi83 7972 2063 6150 4312 8387 2458 6526 "=0590 8382 8791 2472 2881 6558 6967 47*9 5 I2 7 8794 9201 2865 3272 6932 j 7339 *O996 *I402 9200 3289 7375 * I 457 5535 9609 3679 7745 *i8o8 9609 3698 7783 "1865 5942 *ooi6 4086 8152 *22I4 *ooi8 4107 8192 6350 *0 4 23 4492 8558 *2620 ="0427 455 8600 *268o 6757 "0830 4899 ^8964 4924 9008 *3o88 7165 "1237 5306 937 1 *3432 029 3838 4244 4649 5055 546i 5867 6272 6678 7084 7489 7895 030 1948 5997 031 0043 4085 8123 032 2157 6188 033 0214 8300 2353 6402 0447 4489 8526 2560 6590 0617 8706 2758 6807 0851 4893 8930 2963 6993 1019 9111 7211 1256 5296 9333 3367 7396 1422 95 l6 3568 7616 1660 5700 9737 377 7799 1824 9922 3973 8020 2064 6104 4173 8201 2226 4378 8425 2468 6508 4576 8604 2629 4783 8830 2872 6912 4979 9007 3031 *ii 3 8 5188 9234 3277 7315 *I 35 5382 9409 3433 *'543 5592 9638 3681 * 77 * 9 5785 9812 3835 4238 4640 5042 5444 5846 6248 6650 7052 7453 7855 8257 034 2273 6285 035 02 93 4297 8298 036 2295 6289 037 0279 8659 2674 6686 0693 4698 8698 2695 6688 0678 9060 375 7087 1094 5098 9098 394 7087 1076 9462 3477 7487 1495 5498 9498 3494 7486 H75 9864 3878 7888 1895 5898 9898 3893 7885 1874 4279 8289 2296 6298 4293 8284 2272 4680 8690 2696 6698 4692 8683 2671 *io68 5081 9091 3096 ^7098 5091 9082 3070 *I 47 5482 9491 3497 7498 *I496 948i 3468 5884 9892 3897 ^7898 5890 9880 3867 4265 4663 5062 5460 5858 6257 6655 7053 7451 7849 8248 038 2226 6202 0390173 4141 8106 040 2066 6023 9977 8646 2624 6599 0570 4538 8502 2462 ^6419 9044 3022 6996 0967 4934 8898 2858 6814 *o 7 6 7 9442 3419 7393 1364 533i 9294 3254 7210 *Il62 9839 3817 7791 1761 5727 9690 3650 7605 *i557 4214 8188 2158 6124 *oo86 4045 8001 *o6 35 4612 8585 2554 6520 4441 8396 *2347 5009 8982 295 * 6917 *o8 7 8 4837 ^8791 *i 43 i 5407 9379 3348 7313 *I2 74 5232 * 9187 5804 9776 3745 ^7709 5628 9582 *3532 041 3927 4322 4716 5111 j 5506 5900 6295 6690 7084 | 7479 N. L, 1 2 3 ! 4 5 6 7 8 9 S." T." S." T." 2 55' = 10500" 4-68539 595 3o' = io8oo" 4-68538 597 2 56 = 10560 539 595 3 i = 10860 537 598 2 57 = 10620 538 596 32= 10920 537 598 2 58 = 10680 538 596 33= 10980 537 599 2 59 =10740 538 597 3 4 =11040 537 599 R .M L> SL'KV. 2< 418 / M, S'. T', Sec. S", T". o I 2 3 4 I 9 IO ii 12 J 3 14 15 16 12 19 2O 21 22 23 24 s 3 29 30 3i 32 33 34 Si 11 39 4O 4i 42 43 44 45 46 47 48 49 5O 5i 52 53 54 P 11 59 60 1 80 6., 353 *6 412 10800 4- 538 68 597 181 182 183 184 185 186 187 1 88 189 353 352 352 352 352 35i 35i 35 * 35 1 4i3 413 414 414 415 415 415 416 416 10860 10920 10980 11040 moo 11160 1 1 220 11280 11340 537 537 537 537 537 536 536 53 * 536 598 598 599 599 599 600 600 60 1 60 1 190 350 417 11400 535 602 191 192 193 194 195 196 197 198 199 350 35 350 350 349 349 349 349 348 417 418 418 419 419 420 420 421 421 11460 11520 11580 11640 11700 11760 11820 11880 11940 535 535 535 534 534 534 534 533 533 602 603 603 604 604 605 605 606 606 200 348 422 I2OOO 533 607 20 1 202 203 204 205 206 207 208 209 348 348 347 347 347 347 346 346 346 422 423 423 424 424 425 425 426 426 I2O6O 1 21 2O I2I80 12240 I23OO 12360 I242O 12480 12540 533 532 532 532 S3 2 53i 53i 53i 53i 607 608 608 609 609 610 610 611 611 2IO 346 427 12600 530 612 211 212 213 214 215 216 217 218 219 345 345 345 343 344 344 344 344 343 427 428 428 429 429 43 43 43i 43i 12660 12720 12780 12840 I29OO 12960 13020 13080 I3I40 530 530 530 529 529 529 529 528 528 612 6^3 613 614 614 615 615 616 616 22O 343 432 I32OO 528 617 221 222 223 224 225 226 227 228 229 "230" 343 342 342 342 342 341 341 341 340 432 433 434 434 435 435 436 436 437 13260 13320 13380 13440 I3 5 00 13560 13620 13680 13740 528 527 527 5 2 7 526 526 526 526 525 617 618 618 619 620 620 621 621 622 340 437 13800 525 622 231 232 233 234 235 236 237 238 239 340 340 339 339 339 338 338 338 338 438 439 439 440 440 441 441 442 443 13860 13920 13980 14040 I4IOO 14160 I422O 14280 14340 525 525 524 524 524 523 523 523 522 623 623 624 625 625 626 626 627 628 240 337 443 14400 522 | 628 / M, S', T'. Sec. S", T", O 240 6. 337 *6 443 14400 4- 522 58 628 2 3 4 1 8 9 241 242 243 244 2 45 246 247 248 249 337 337 336 336 336 336 335 335 335 444 444 445 446 446 447 447 448 449 14460 14520 14580 14640 14700 14760 14820 14880 14940 522 522 521 521 521 520 520 520 520 629 629 630 631 63i 632 632 633 634 10 250 334 449 15000 5i9 634 ii 12 13 14 :i J 7 18 19 2 5 * 252 253 254 2 55 256 257 258 259 334 334 333 333 333 332 332 332 332 45 45 45i 452 452 453 454 454 455 15060 15120 15180 15240 15300 15360 15420 15480 15540 519 Si9 518 518 518 5^7 517 5 J 7 516 635 & 637 637 638 638 639 640 20 260 33i 456 15600 516 640 21 22 23 24 2 2 29 261 262 263 264 265 266 267 268 269 33 i 33i 330 330 330 329 329 329 328 456 457 457 458 459 459 460 461 461 15660 15720 15780 15840 15900 15960 16020 16080 16140 5i6 5i5 5i5 5i3 5H 5H 5H 5i3 5i3 641 642 642 643 644 644 . 645 646 646 30 270 328 462 16200 5 J 3 647 3i 32 33 34 ! 38 39 271 272 2 73 274 275 276 277 278 279 328 327 327 327 326 326 326 325 325 463 463 464 465 465 466 467 467 468 16260 16320 16380 16440 16500 16560 16620 16680 16740 5 12 512 S" 5" 5 11 5" 5'o 5io 5 10 648 648 649 650 650 651 652 652 653 4O 280 32-5 469 16800 59 654 4i 42 43 44 4 46 47 48 49 281 282 283 284 285 286 287 288 289 324 324 324 323 323 323 322 322 321 469 47 471 472 472 473 474 474 475 16860 16920 16980 17040 17100 17160 17220 17280 17340 59 59 508 508 508 57 57 57 506 654 655 656 656 657 658 659 659 660 50 290 321 47 6 17400 506 66 1 5i 52 53 54 P P 59 291 292 293 294 295 296 297 298 299 321 320 320 320 3i9 3'9 3*9 3i8 3i8 477 477 478 479 479 480 481 482 482 17460 17520 17580 17640 17700 17760 17820 17880 17940 506 505 505 503 54 54 53 503 503 66 1 662 663 664 664 665 666 666 667 60 300 3 J 7 483 18000 502 668 411) TABLE XVI. THE LOGARITHMS OF THE TRIGONOMETRIC FUNCTIONS FOR EACH MINUTE. Formulas for the Use of the Auxiliaries S and T. 1. When a is in the first five degrees of the quadrant: log sin a = log a' -j- S.' log a' = log sin a + cpl 5.' log tan a = log a' + T.' log cot a = cpl log tan a. log sin a = log a" -f S." log tan a = log a" + T. 1 ' log cot a = cpl log tan a. = log tan a + cpl T.' cpl log cot a 4- cpl T: log a" = log sin a -f cpl 5." = log tan a + cpl T." = cpl log cot a + cpl T.' 1 2. When a is in the last five degrees of the quadrant : log cos a = log(90 a) ' -f S.' log cot a = log(90 a)' -f T.' log tan a = cpl log cot a. log cos a = log(90 - a)" -f S." log cot a = log(90 a)' 7 -f T." log tan a = cpl log cot a. a = 90 log(90 a)' = log cos a + cpl S. 1 = log cot a + cpl T. ' = cpl log tan a + cpl T.' log(90- a) "= log cos a + cpl S." = log cot a + cpl T." = cpl log tan a + cpl T." (90 - a). 420 It / L, Sin, d. Cpl. S', Cpl, T', L, Tan, c, d, L, Cot, L, Cos, O o.ooooo 6O 60 I2O 1 80 240 3 00 3 60 420 4 80 540 I 2 3 4 i 9 6.46 373 6.76476 6.94 085 7.06579 7.16270 7.24 188 7.30 882 7.36 682 7.41 797 30103 17609 12494 9691 79 i8 66 94 5800 5"5 3-53627 3-53 627 3-53 627 3-53 627 3-53627 3-53 627 3-53 627 3-53627 3-53627 3-53 627 3-53627 3-53 627 3-53 627 3-53627 3-53627 3-53 627 3-5362 7 3-53627 646 373 6.76476 6.94085 7.06579 7.16 270 7.24 188 7.30 882 7.36 682 7.41 797 30103 17609 12494 9691 7918 6694 5800 5 JI 5 3-53 627 3-23 5 2 4 3.05915 2.93421 2.8^? 730 2.75812 2.69 118 2.63 318 2.58 203 o.oo ooo o.oo ooo o.oo ooo o.oo ooo o.oo ooo o.oo ooo o.oo ooo o.oo ooo o.oo ooo 59 58 57 56 55 54 53 52 5 1 600 IO 746 373 3-53 627 3-53 627 7-46 373 2.53627 o.oo ooo 5O 660 7 20 7 80 8 4 9 00 960 IO2O I080 1140 ii 12 13 H 15 16 \l 19 7-50 5 12 7.54291 7-57767 7.60 985 7.63 982 7.66784 7.69417 7.71 900 7.74 248 3779 3476 3218 2997 2802 2633 2483 2348 3-53 627 3-53627 3-53 627 3-53 628 3-53628 3-53628 3-53628 3-53628 3-53 628 3-53627 3-53627 3-53 627 3-53627 3-53627 3-53 627 3-53627 3-53627 3-53627 7-5 5 12 7.54291 7-57767 7.60 986 7.63 982 7-66 785 7.69418 7.71 900 7-74 248 3779 347 6 3219 2996 2803 2633 2482 2348 2228 2.49488 2-45 79 2.42 233 2.39014 2.36018 2.33215 2.30 582 2.28 100 2.25 752 o.oo ooo o.oo ooo o.oo ooo o.ooooo o.oo ooo o.oo ooo 9-99 999 9.99 999 9-99 999 49 48 47 46 45 44 43 42 4i 1200 20 7-76475 3-53 628 3-53627 7.76476 2119 2.23 524 9-99 999 4O 1260 1320 1380 1440 1500 1560 l62O 1680 1740 21 22 23 24 1 27 28 29 7-78 594 7.80615 7-82 545 7-84 393 7.86 166 7.87 870 7.89 509 7.91 088 7.92 612 2021 1930 l8 4 8 1773 1704 1639 1579 1524 3.53628 3-53 628 3-53 628 3-53 628 3-53 628 3-53 628 3-53 628 3-53 628 3-53 628 3-53 627 3-53627 3-53627 3-53 627 3-53627 3-53 627 3-53626 3.53626 3-53 626 778 595 7.80615 7.82 540 7-84 394 7.86 167 7.87871 7.89510 7.91 089 7.92613 2O2O I93 1 1848 J 773 1704 1639 X 579 i5 2 4 1473 2.21 405 2.19385 2.17454 2.15 606 2.13833 2.12 129 2.IO49O 2.O8 911 2.07 387 9-99 999 9-99 999 9.99 999 9-99 999 9-99 999 9-99 999 9-99 999 9-99 999 9-99 998 39 38 37 36 35 34 33 32 3i I800 30 7-94 084 3-53 628 3-53 626 7.94 086 1424 2.05 914 9-99 998 30 1860 1920 1980 2040 2100 2l6o 222O 2280 2340 3 1 3 2 33 34 H 37 38 39 7-95 5 8 7.96 887 7.98 223 7.99 520 8.00 779 8.02 002 8.03 192 8.04 350 8.05 478 1379 1336 1297 1259 I22 3 II9O 1158 1128 3-53 628 3-53 628 3-53 628 3-53628 3-53628 3-53628 3.53628 3.53628 3.53 628 3-53 626 3-53 626 3-53626 3.53 626 3.53626 3-53 626 3-53 626 3-53626 3.53 626 7-95 5 10 7.96 889 7.98 225 7-995 2 2 8.00 781 8. 02 004 803 194 8-04 353 8.05 481 1379 1336 1297 259 223 190 159 128 2.04 490 2.03 1 1 1 2.01 775 2.00 478 1.99 219 1.97996 1.96806 1.95647 1.94519 9-99 998 9-99 998 9-99 998 9.99 998 9-99 998 9-99 998 9-99 997 9-99 997 9-99 997 29 28 27 26 25 24 23 22 21 2400 40 8.06 578 3-53 628 3-53625 8.06581 072 I.934I9 9-99 997 2O 2460 2520 2580 2640 2700 2760 2820 2880 2940 4i 42 43 44 3 47 48 49 8.07 650 8.08 696 8.09 718 8.10717 8. 1 1 693 8.12647 8.13581 8.14495 8.15 39i 1046 IO22 999 976 954 934 914 896 877 3.53 628 3-53 628 3-53 629 3-53 629 3-53 629 3-53 629 3-53 629 3-53 629 3-53 629 3-53 625 3-53625 3-53625 3-53625 3-53 625 3-53 625 3-53 625 3-53 625 3-53 624 8.07 653 8.08 700 8.09 722 8.10720 8. 1 1 696 8.12651 8-13585 8.14500 8.15 395 047 022 998 976 955 934 915 895 878 L92347 I.9I 300 I.9O 278 1.89280 1.88304 1.87349 1.86415 1.85 500 1.84 605 9-99 997 9-99 997 9-99 997 9.99 996 9-99 996 9-99 996 9-99 996 9.99 996 9.99 996 19 18 J 7 16 15 H 13 12 II 3000 50 8.16268 /7 860 3-53 629 3-53 624 8.16273 070 860 1.83727 9.99 995 IO 3060 3120 3180 3240 3300 3360 3420 3480 354 5 1 5 2 53 54 11 H 59 8.17 128 8.17971 8.18798 8.19 610 8.20407 8.21 189 8.21 958 8.22713 8.23456 843 827 812 797 782 769 755 743 TiO 3-53 629 3-53 629 3-53 629 3-53 629 3-53 629 3-53 629 3-53 629 3-53 629 3-53 630 3-53 624 3-53 624 3-53 624 3-53 624 3-53 624 3-53 624 3-53623 3-53 623 3-53 623 8.I7I33 8.17976 8.18 804 8.19616 8.20413 8.21 195 8.21 964 8.22 720 8.23 462 843 828 812 797 782 769 756 742 1.82867 I.82O24 1.81 196 1.80384 1.79587 1.78805 1.78036 1.77280 1.76538 9.99 995 9-99 995 9-99 995 9-99 995 9-99 994 9-99 994 9-99 994 9-99 994 9-99 994 9 8 7 6 5 4 3 2 3600 60 8.24 1 86 /J^ 3-53 630 3-53 623 8.24 192 7JV 1.75 808 9-99 993 L, Cos. d, L, Cot, c. d, L, Tan, L, Sin, / 89 C 421 // I L. 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SS- 2 54-8 54.4 69.5 69 o 68.5 68.0 83 4 82.8 82.2 81.6 97-3 96.6 95 9 95.2 24 8-97 363 J j4 133 8-97 556 !r 1.02444 9-99 807 36 8 in. 2 110.4 109.6 108.8 2^ 8.97 496 8.97 691 o o 1.02309 9.99 806 35 26 8.97 629 J 33 8.97 823 *34 1.02 175 9.99 804 34 27 28 8.97 762 8.97 894 132 8-97 959 8.98 092 A 34 133 I.0204I i.oi 908 9.99 803 9.99 802 33 32 i 2 135 134 133 132 *3-5 13-4 13-3 13-2 27.0 26.8 26.6 26.4 -9 8.98 026 132 8.98 225 1 33 'i 775 9.99 So i 3 40.5 40.2 39.9 39.6 30 8.98 157 1 j 1 8.98 358 i.oi 642 9.99800 30 4 54- 53-6 S3- 2 52.8 67.5 67.0 66 5 66.0 3 1 8.98 288 I 3 l 8.98 490 J 2 i.oi 510 9.99 798 29 6 81.0 80.4 79 8 79-2 32 53 8.98419 8.98 549 130 8.98 622 8.98 753 132 i.oi 378 i.oi 247 9.99 797 9.99 796 28 27 7 8 9 94-5 93-8 93 i 92-4 108.0 107.2 106 4 105.6 121.5 120.6 119.7 118.8 34 8.98 679 130 8.98 884 I 3 l i.oi 116 9-99 795 26 35 8.98 808 129 8.99015 I 3 l 1.00985 9-99 793 25 131 13O 129 128 36 8.98937 129 8.99 145 130 1.00853 9-99 792 24 i 13.1 13.0 12.9 12.8 >7 8.99 066 129 8-99 2 75 130 1.00723 9-99 79 1 2 S 3 39.3 39.0 38.7 38.4 38 39 8.99 194 8.99 322 125 128 8.99 403 8-99 534 130 129 128 1.00595 i .00 466 9-99 790 9.99 788 22 21 4 52.4 52.0 51.6 51 2 65.5 65.0 64.5 64.0 78.6 78.0 77.4 76.8 40 8.99 430 8.99 662 i. oo 338 9-99 787 20 z 91.7 91.0 90.3 89.6 4 1 8-99577 127 S-9979I 9 1.00209 9.99 786 10 42 8.99 704 127 8.99919 128 1.00081 9-99 7 8 5 18 43 8.99 830 126 9.00 046 0-99 954 9-99 783 17 127 126 123 124 44 8.99 956 1 20 9.00 174 I2O 0.99 826 9-99 782 16 i 12.7 12.6 12.5 12.4 45 46 9.00 082 9.00 207 125 9.00301 9.00427 127 1-6 0.99 699 0.99573 9-99 781 9 99 780 15 14 3 4 25.4 25.2 25.0 24.8 38.1 37.8 375 372 50.8 50.4 50 o 49 6 47 4 s 9.00 332 9.00456 124 9.00553 9.00679 I2O 126 0.99 447 0.99 321 9-99 778 9-99 777 12 7 63 5 63 o 62 5 62 o 76.2 75.6 75 o 74.4 88.9 83.2 87.5 868 49 9.00581 I2 3 9.00 805 I2O 0-99 195 9-99 77 6 II 8 101.6 100.8 loo o 99.2 50 9.00 704 *-3 9.00 930 I2 5 0.99 070 9-99 7/5 IO 9 5i 9.00 828 124 9.01 053 125 0.98 945 9-99 773 9 123 12^ I'M 12O 52 9.00951 I2 3 9.01 179 124 0.98 821 9.99 772 8 12 3 12.2 12. 1 12 O 53 9.01 074 I2 :> 9.01 303 124 0.98 697 9 99 77 1 7 2 24.6 24.4 24.2 24.0 54 55 9.01 196 9.01 318 122 122 9.01 427 901 55 124 123 0.98 573 0.98 430 9-99 769 9-99 7 68 6 S 3 4 5 36.9 36.6 36.3 36.0 49-2 48.3 484 48.0 61.5 61.0 60 5 60.0 5- 9.01 440 9.01 673 I2 3 0.98 327 9.99 767 4 6 73-8 73-2 72.6 72.0 9.01 561 121 9.01 796 123 0.98 204 9-99 7 6 5 3 98.4 97-6 96.8 96.0 5^ 9.01 682 121 9.01 918 122 0.98 082 9-99 7 6 4 2 110.7 109.8 108.9 108.0 59 9.01 803 121 9.02 040 122 0.97 960 9-99 7 6 3 I 60 9.01 923 9-O2 102 0.97 838 9-99 7 61 O 1 L. Cos. I d, L, Cot, c.d. L. Tan. L. Sin., P. P. 84 C 426 t L. Sin. d. L. Tan. c.d. L. Cot. L. Cos. P. P. o 9.01 923 9.02 162 0.97 838 9-99 761 60 2 3 4 i 8 9 9.02 043 9.02 163 9.02 283 9.02 402 9.02 520 9.02 639 9.02 757 9.02 874 9.02 992 120 1 2O 119 118 119 118 117 118 9.02 283 9.02 404 9-02 525 9.02 645 9.02 766 9.02 885 9.03 005 9.03124 9.03 242 121 121 120 121 1 2O 119 118 I IQ 0.97 717 0.97 596 0-97475 0-97 355 0.97 234 0.97115 0.96 995 0.96 876 0.96 758 9-99 760 9-99 759 9-99 757 9-99 756 9-99 755 9-99 753 9-99 752 9-99 75 J 9.99 749 59 58 57 56 55 54 53 5 2 i 2 3 4 5 6 121 12O 119 118 12. 1 12. Il.g II. 8 24.2 24.0 23.8 23.6 36.3 36.0 35.7 35.4 48.4 48.0 47.6 47.2 60.5 60.0 59.5 59.0 72.6 72.O 7I-4 70.8 IO 9.03 109 1 V 9.03 361 i ly 118 0.96 639 9.99 748 50 7 8 84.7 84.0 83.3 82.6 96.8 96.0 95 2 94.4 ii 12 13 15 16 18 19 9.03 226 9-03 342 9-03 458 9-03 574 9.03 690 9.03 805 9.03 920 9.04 034 9.04 149 117 116 116 116 116 MS "5 114 "5 9-3 479 9-03 597 9.03 714 9.03 832 9.03 948 9.04 065 9.04 181 9.04 297 9.04413 118 117 118 116 117 116 116 116 0.96 521 0.96 403 0.96 286 0.96 1 68 0.96052 0-95 935 0.95 819 o-95 73 o-95 587 9-99 747 9-99 745 9.99 744 9.99 742 9-99 74i 9.99 740 9-99 738 9-99 737 9-99 736 49 48 47 46 45 44 43 42 9 i 2 3 4 108.9 108.0 107.1 106.2 117 116 115 114 11.7 ii. 6 11.5 11.4 23.4 23.2 23.0 22.8 35.1 34.8 34.5 34.2 46.8 46.4 46.0 45.6 58.5 58.0 57.5 57-o 20 9,04 262 1 l j 9.04 528 X1 5 0.95 472 9-99 734 4O 6 70.2 69.6 69.0 68.4 21 22 23 24 3 11 29 9.04376 9.04 490 9.04 603 9.04715 9.04 828 9.04 940 9.05 052 9.05 164 9.05 275 114 114 113 112 "3 112 112 112 III 9.04 643 9.04 758 9.04 873 9.04 987 9.05 101 9.05 214 9.05 328 9.05 441 9-05 553 11 5 "5 "5 114 114 "3 114 112 -95 357 0.95 242 0.95 127 0.95 013 0.94 899 0.94 786 0.94 672 0-94 559 0.94 447 9-99 733 9.99731 9-99 73 9.99 728 9-99 727 9.99 726 9-99 7 2 4 9-99 723 9-99 72i 37 36 35 34 33 3 2 3 1 9 i 2 3 93.6 92.8 92.0 91.2 105.3 I0 4-4 103.5 102.6 113 112 111 11O II-3 II. 2 II. I II. 22.6 22-4 22.2 22. 33-9 33-6 33-3 33-Q 30 9.05 386 9.05 666 JI 3 o-94 334 9-99 720 3O 4 5 45.2 44.8 44.4 440 56.5 56.0 55.5 55.0 32 33 34 11 H 39 9-05 497 9.05 607 9.05 717 9.05 827 9-05 937 9.06 046 9.06 155 9.06 264 9.06 372 IIO IIO IIO IIO 109 IO9 109 1 08 9.05 778 9.05 890 9.06 002 9.06113 9.06 224 9-o6 335 9.06 445 9.06556 9.06 666 112 112 III III III IIO III IIO 0.94 222 0.94 1 10 0.93 998 0.93 887 0.93 776 0.93 665 0-93 555 0.93 444 0-93 334 9.99718 9.99717 9-99 7 l6 9-99 7H 9-99 7 J 3 9.99711 9-99 7 10 9-99 7 8 9.99 707 29 28 27 26 25 24 23 22 21 6 9 2 67.8 67.2 66.6 66.0 79.1 78.4 77.7 77.0 90.4 89.6 88.8 88.0 101.7 100.8 99-9 99-o 1O9 IOS 1O7 1O6 10.9 10.8, 10.7 10.6 121. 8 21.6 21-4 21.2 4O 9.06481 iuy Tn o 9.06 775 IO9 0.93 225 9-99 75 20 3 32.7 32.4 32.1 31.8 41 42 43 44 45 46 47 48 49 9.06 589 9.06 696 9.06 804 9.06 911 9.07 018 9.07 124 9.07 231 9-07 337 9.07 442 107 1 08 107 107 1 06 107 1 06 I0 5 106 9.06 885 9.06 994 9.07 103 9.07 211 9.07 320 9.07 428 9.07 536 9.07 643 9.07751 109 109 108 109 108 108 107 108 0.93 115 0.93 006 0.92 897 0.92 789 0.92 680 0.92 572 0.92 464 0.92357 0.92 249 9-99 74 9.99 702 9-99 7 01 9-99 699 9.99 698 9-99 696 9.99 695 9-99 693 9.99 692 19 18 16 15 12 II 6 7 8 9 43.6 43.2 42.3 42.4 54-5 54-o 53-5 53- 65.4 64 8 64.2 63.6 76.3 75.6 74.9 74 2 87.2 864 85.6 84.8 98.1 97.2 96.3 95.4 1O5 1O4 1O3 50 9.07 548 IOC 9.07 858 107 1 06 0.92 142 9.99 690 10 2 2I.O 20 .8 20. 6 5 2 53 54 55 56 H 59 9-07 653 9.07 758 9.07 863 9.07 968 9.08072 9.08 176 9.08 280 9.08 383 9.08 486 1(J J I0 5 I0 5 I0 5 104 104 104 103 103 9.07 964 9.08071 9.08177 9.08 283 9.08 389 9.08 495 9.08 600 9.08 705 9.08 810 107 1 06 106 106 1 06 I0 5 I0 5 0.92 036 0.91 929 0.91 823 0.91 717 0.91 611 0.91 505 0.91 400 0.91 295 0.91 190 9.99 689 9.99 687 9.99 686 9.99 684 9.99 683 9.99 681- 9.99 680 9-99 678 9-99 677 9 8 7 6 5 4 3 2 I 3 31-5 31-2 3-9 4 42.0 41.6 41.2 5 52.5 52.o 51.5 6 63.0 62.4 61.8 7 73-5 72-8 72.1 8 84.0 83.2 82.4 9 94-5 93-6 92.7 60 9-o8 589 j 9.08914 0.91 086 9-99 675 O L. Cos. d. L. Cot. c.d. L. Tan. L. Sin. ; P. P. 83' 427 j L, Sin, d. L. Tan, c.d. L. Cot, L, Cos. p. p, o 9.08 589 9.08914 0.91 086 9.99 075 60 I 9.08 692 103 9.09019 IO 5 0.90 981 9.99 674 S9 2 9.08 795 I0 3 9-09 123 104 0.90 877 9.99 672 58 105 104 103 3 9.08 897 IO2 9.09 227 0.90 773 9-99 670 57 i 10.5 10.4 10.3 4 9.08 999 9-09 330 J 0.90 670 9.99 669 56 2 21.0 20.8 20.6 5 9.09 101 9-09 434 104 0.90 566 9-99 667 55 3 31.5 31.2 30.9 6 9.09 202 9-09 537 I0 3 0.90 463 9.99 666 54 4 42.O 41.6 41.2 7 9.09 304 IO2 9.09 640 103 0.90 360 9-99 664 53 5 52.5 52.0 51.5 8 9.09 405 9.09 742 0.90 258 9-99 663 S2 6 63.0 62.4 6l.8 9 IO ii 9-09 5 6 100 101 9-09 845 IO 3 IO2 IO2 0.90 155 9.99661 51 50 49 8 9 73-5 72.8 72.1 84.0 83.2 82.4 94-5 93-6 92.7 9.09606 9.09 947 0.90053 9-99 659 9.09 707 9.10049 0.89951 9.99 658 12 9.09 807 9.10 150 0.89 850 9-99 656 48 13 9.09 907 9.10 252 0.89 748 9-99 655 47 M 9.10006 99 9-10353 IOI 0.89 647 9-99 653 46 102 101 99 15 9.10 106 9.10454 0.89 546 9.99651 45 I IO.2 IO.I 9.9 16 9.10205 99 9-10555 0.89 445 9-99 650 44 2 2O.4 2O.2 19.8 17 9.10304 99 9.10 656 [ 0.89344 9-99 648 43 3 30.6 30.3 29.7 18 9.10402 95 9-10 756 ; JJ | 0.89 244 9.99 647 42 4 40.8 40.4 39.6 19 9.10 501 99 9.10856 ; ;| 0.89 144 9-99 645 5 1 51.0 50.5 49.5 20 9.10599 9 9.10956 IOO 0.89 044 9-99 643 4O 6 i 61.2 60.6 59.4 21 9.10697 _0 9.11 056 0.88 944 9.99 642 39 7 71.4 70.7 69.3 S T A %r\ 8 nn i 22 23 9.10795 9.10893 95 98 9-n 155 9.11 254 99 99 0.88 845 0.88 746 9.99 640 9-99 638 38 37 9 91.8 90.9 89.1 24 9.10990 9V 9-n 353 99 0.88 647 9-99 637 36 25 9.11 087 9; 9.11 452 99 0.88548 9-99 635 35 26 9.11 184 9/ > 0.88449 9-99 633 34 98 97 96 2 7 9.11 281 97 9.11649 ; 0.88351 9-99 632 33 i 9.8 9.7 9.6 28 9-II377 9.11 747 08 a882 53 9-99 630 32 2 19.6 19.4 19.2 29 9.11 474 97 06 9.11845 98 0.88155 9-99 629 3 29.4 29.1 28.8 30 32 33 9.11 570 9 96 li 9-ii943 95 97 98 97 0.88057 9-99 627 3O 29 28 27 4 6 8 39.2 38.8 38.4 49.0 48.5 48.0 58.8 58.2 57.6 68.6 67.9 67.2 78.J. 77.6 76.8 9.11 666 9.11 761 9.11857 9.12 040 9.12 138 9.12235 0.87 960 0.87 862 0.87 765 9.99 625 9-99 624 9.99 622 34 9.11952 95 9.12332 97 0.87668 9.99 620 26 9 88.2 87.3 86.4 35 9.12047 95 9.12428 y" 0.87572 9.99 618 25 36 9.12 142 95 9.12525 9/0.87475 9.99617 24 37 9.12 236 94 9.12 621 ? 0.87379 9.99615 23 QC CM QO 38 9-12331 95 9.12717 y" 0.87283 9.99613 22 39 9.12425 94 9.12813 > 0.87187 9.99 612 21 I 9-5 9-4 9.3 40 42 43 9.12519 94 93 94 93 9.12909 v" 95 95 95 0.87091 9.99 610 20 19 18 17 2 3 4 I9.O 15.5 I5.O 28.5 28.2 27.9 38.0 37.6 37.2 47-5 47-o 46-5 57.0 56.4 55.8 9.12 612 9.12 706 9.12799 9.13004 9.13099 9-13 194 0.86 996 0.86 901 0.86 806 9.99 608 9-99 607 9-99 605 44 9.12892 93 9.13289 ' 0.86711 9-99 603 16 M 66.5 65.8 65.1 45 9.12985 93 9-13384 9:> 0.86616 9.99 601 15 g 76.0 75.2 74.4 46 9.13078 93 9-13478 1- 0.86522 9.99 600 H 9 85.5 84.6 83.7 47 9.13 171 93 9-13573 9^ 0.86427 9-99 598 13 48 9.13263 92 9.13667 94 0.86 333 9-99 596 12 49 9-13355 9 2 9.13761 94 o.sr, 239 9-99 595 II no qi an 50 9-13447 92 9- i 3 854 93 0.86 146 9-99 593 10 5' 5 2 53 9.13539 9.13630 9.13722 9 2 92 9.13948 9.14041 9.14134 94 93 93 0.86052 0.85 959 0.85 866 9.99591 9.99 589 9-99 588 9 8 7 2 1 18.4 1 8.2 18.0 3 27.6 27.3 27.0 4 ! 36.8 36.4 36.0 54 55 9-13813 9.13904 9i 9.14227 9.14320 yj 93 0-85 773 0.85 680 9-99 586 9-99 584 6 5 5 46.0 45.5 45.0 6 55.2 54.6 54.0 5 6 9.I3994 9 9.14412 92 0.85588 9-99 582 4 7 ! 64.4 63.7 63.0 57 9.14085 9 1 9.14504 92 0.85496 9-99 581 3 8 73.6 72.8 72.0 58 9-I4I75 9 9.14597 93 0.85 403 9-99 579 2 9 82.8 81.9 81.0 59 9.14 266 9 1 9.14688 9* 0.85312 9-99 577 I 60 9-H 35 6 9.14 780 i " 0.85 220 9-99 575 O L, Cos. d, L. Cot, c,d, L, Tan, L, Sin, ' P, P. 82' 428 ' L. Sin. d. L. Tan. c.d. L. Cot. L. Cos. pTpi | 9-I4356 80 9.14780 0.85 220 9-99 575 60 I 9- i 4 445 oy 9.14872 92 0.85 128 9-99 574 59 2 9.H535 90 8r 9.14963 9 1 0.85 037 9-99 572 S8 92 91 90 3 9.14624 9 9-I5054 9 1 0.84 946 9-99 57 57 i 9.2 9.1 9.0 4 I 9.14714 9.14803 9.14891 V u 89 88 0_ 9-15 H5 9.15 236 9.15 327 y 1 91 91 0.84 855 0.84 764 0.84 673 9-99 568 9-99 5 66 9-99 565 56 55 54 2 3 4 18.4 18.2 18.0 27.6 27.3 27.0 36.8 36.4 36.0 7 9.14980 59 o n 9.I54I7 9 0.84 583 9.99 563 5S 5 46.0 45.5 45.0 8 9 9.15069 9-15 1 S7 09 88 88 9.15 508 9.15 598 9 1 90 0.84 492 0.84 402 9-99 561 9-99 559 52 5 1 6 55-2 54-6 54-0 64.4 63.7 63.0 10 9-15245 88 9.15 688 yu 80 0.84312 9-99 557 50 8 73.6 72.8 72.0 ii 9-15333 88 9-15777 oy 0.84 223 9-99 556 49 9 12 9.15421 o- 9.15867 yu o n 0.84 133 9.99 554 48 13 9.15 508 8 7 00 9.I5956 9 0.84 044 9-99 552 47 H 9-15 596 c- 9.16046 90 o ft 0-83 954 9-99 55 46 89 88 15 9.15 683 5 7 87 9-16135 59 80 0.83 865 9.99 548 45 i 8.9 8.8 16 9.15770 / 0- 9.16224 oy 00 0.83 776 9.99 546 44 2 17.8 17.6 17 9.15857 57 o,_ 9.16312 o.n 0.83 688 9-99 545 43 3 26.7 26.4 18 9.15944 8 7 86 9.16401 59 CO 0-83 599 9-99 543 42 4 35-6 35-2 19 9.16030 86 9.16489 CO 0.83511 9-99 54i 5 44-5 44-0 20 9.16 116 87 9.16577 88 0.83 423 9-99 539 40 6 53-4 5 2 .8 21 22 23 9.16 203 9.16 289 9.16374 / 86 85 CA 9.16 665 9-16753 9.16841 88 88 Of. 0-83 335 0.83 247 0.83 159 9.99 537 9-99 535 9-99 533 39 38 37 8 9 71.2 70.4 80. i 79.2 24 9.16460 o r 9.16928 8 7 00 0.83 072 9-99 532 36 25 26 9.16545 9.16 631 S 5 86 9.17016 9.17103 87 0.82 984 0.82 897 9-99 530 9-99 528 35 S4 87 86 85 27 9.16 716 ^ Se 9.17 190 87 O,- 0.82810 9-99 526 33 i 8.7 8.6 8.5 28 29 9.16 801 9.16886 8 5 85 9.17277 9.17363 8 7 86 8-7 0.82 723 0.82 637 9-99 524 9.99 522 3 2 2 3 17.4 17.2 17.0 26.1 25.8 25.5 3O 9.16 970 ~ 4 9.17450 7 0.82 550 9-99 520 SO 4 34.8 34.4 34.0 32 33 9.17 139 9.17223 84 84 84 9.17536 9.17 622 9.17708 86 86 86 0.82 464 0.82 378 0.82 292 9.99518 9-99 5 1 7 9-99 5 '5 27 6 8 43-5 43- 4 2 -5 52.2 51.6 51.0 60.9 60.2 59.5 69.6 68.8 68.0 34 9.17307 8/1 9.17 794 86 0.82 206 9-99 5 1 3 26 9 78.3 77.4 76.5 35 9-I739I 4 8-> 9.17880 Cr 0.82 1 20 9.99511 25 36 9.17474 8 3 8/1 9.17965 8 5 Qf. 0.82 035 9-99 59 24 % 9.17558 9.17641 4 83 0-> 9.18051 9.18 136 || 0.8 1 949 0.8 1 864 9-99 57 9-99 55 23 22 84 83 39 9.17724 8 3 9.18 221 II 0.81 779 9-99 53 21 i 8.4 8.3 4O 9.17807 ^ 9.18 306 5 5 0.81 694 9-99 5 01 20 I6.o 16.6 42 43 9.17890 9.17973 9.18055 83 82 82 9.18391 9.18475 9.18 560 84 85 8/1 0.81 609 0.8 1 525 0.8 1 440 9.99 499 9.99 497 9-99 495 19 18 4 6 33-6 33-2 42.0 41.5 50.4 49.8 44 9.18 137 S-. 9.18 644 4 0.81 356 9.99 494 16 7 58.8 58.1 45 46 9.18220 9.18 302 83 82 Or 9.18728 9.I88I2 84 84 o . 0.81 272 0.81 1 88 9.99 492 9-99 490 '5 H 8 9 67.2 66.4 75-6 74-7 47 9.18383 9.18896 84 0.81 104 9.99 488 13 48 9.18465 02 Q 9.18979 83 0.8 1 021 9.99 486 12 49 9.18547 o2 CT 9.19063 84 0.80937 9.99 484 II 82 81 80 5O 9.18628 fi 9.19 146 3 0.80 854 9.99482 10 T Q ~ C T C n 52 53 54 9.18709 9.18 790 9.18871 9.18952 00 00 00 C 9.19229 9.I93I2 9.19395 9.19478 83 83 83 0, 0.80 771 0.80 688 0.80 605 0.80 522 9.99 480 9.99 478 9-99 476 9.99 474 9 8 7 6 2 3 4 16.4 16.2 16.0 24.6 24.3 24.0 32.8 32.4 32.0 41.0 40.5 40.0 55 9-19033 80 9.19561 8* 0.80 439 9.99472 5 6 49 2 48.6 48.0 S 6 9.19113 Q n 9.19 643 8-7 0.80357 9.99 470 4 7 57 4 56.7 56.0 57 9.19 193 0_ 9.19725 0.80 275 9.99 468 3 8 6 64.8 64.0 58 9.19273 o 9.19807 o2 0_ 0.80 193 9.99 466 2 9 73.8 72.9 72.0 59 9-19353 80 9.19889 82 0.80 1 1 1 9.99 464 I 60 9-19433 9.I997I 0.80 029 9.99 462 O L. Cos. | d. L. Cot. c.d. L. Tan. L. Sin. ; P. P. sr 429 f L. Sin. d. L. Tan, c,d. L, Cot. L. Cos. p. p. o I 2 3 4 I 9 IO ii 12 13 14 !i 17 18 19 20 21 22 23 24 s 27 28 29 30 3i 3 2 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 ? H 59 60 9-19433 80 79 80 79 79 79 79 79 78 78 79 78 78 77 78 78 77 77 77 77 77 77 76 77 76 76 76 76 75 76 75 76 75 75 75 74 75 75 74 74 74 74 74 74 73 74 73 73 73 73 73 73 72 . 73 7 2 72 73 7 1 72 7 2 9^9971 9.20053 9-20 134 9.20 216 9.20 297 9-20 378 9.20459 9.20 540 9.20621 9.20 701 82 81 82 81 81 81 81 81 80 81 80 80 80 80 80 79 80 79 79 79 79 79 78 79 7f 78 78 78 78 78 77 78 77 77 77 77 77 76 77 76 76 77 76 76 M 75 76 75 75 75 75 75 74 75 74 75 74 74 74 0.80 029 9-99 462 60 59 58 57 56 55 54 53 52 5i 5O 49 48 47 46 45 44 43 42 4i 4O 39 38 37 36 35 34 33 32 3i 3O 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 H 13 12 II 10 7 6 5 4 3 2 I 2 3 4 6 8 9 i 2 3 4 Q I 2 3 4 6 9 2 3 4 i 9 82 81 80 8.2 8.1 8.0 16.4 16.2 16.0 24.6 24.3 24.0 32.8 32.4 32.0 41.0 40.5 40.0 49.2 48.6 48.0 57-4 5 6 -7 5 6 - 65.6 64.8 64.0 73.8 72.9 72.0 79 78 77 7-9 7-8 7-7 15.8 15.6 - 15.4 23.7 23.4 23.! 31.6 31.2 30.8 39-5 39-0 38-5 47.4 46.8 46.2 55-3 54-6 53-9 63.2 62.4 61.6 71.1 70.2 69.3 76 75 74 7- 6 7-5 7-4 15.2 15.0 14.8 22.8 22.5 22.2 30.4 30.0 29.6 38.0 37.5 37.0 45-6 45.0 44.4 53-2 52-5 5i-8 60.8 60.0 59.2 68.4 67.5 66.6 73 72 71 7-3 7-2 7-1 14.6 14.4 14.2 21.9 21.6 21.3 29.2 28.8 28.4 36.5 36.0 35.5 43.8 43.2 42.6 51.1 50.4 49.7 58.4 57.6 56.8 65.7 64.8 63.9 9-195*3 9.19592 9.19672 9-19 75 1 9.19830 9.19909 9.19988 9.20067 9.20 145 o-79 947 0.79 866 0.79 784 0.79 703 0.79 622 o-79 54i 0.79 460 o-79 379 0.79 299 9-99 46o 9-99458 9-99 45 6 9-99 454 9-99452 9.99 450 9.99 448 9.99 446 9-99 444 9.20 223 9.20 782 0.79 218 9-99 442 9.20 302 9.20 380 9.20458 9-20535 9.20613 9.20 691 9.20 768 9.20 845 9.20922 9.20 862 9.20 942 9.21 022 9.21 102 9-21 l82 9.21 26l 9.21 341 9.21 420 9-21 499 0.79 138 0.79 058 0.78978 0.78 898 0.78818 0.78 739 0.78 659 0.78 580 0.78501 9-99 440 9-99 438 9-99 43 6 9-99 434 9-99 432 9-99 429 9-99 427 9-99425 9-99 423 9.20999 9-2i 578 0.78 422 9.99421 9.21 076 9.21 153 9,21 229 9.21 306 9.21 382 9.21 458 9-2i 534 9.21 610 9.21 685 9.21657 9.21 736 9.21 814 9-21 893 9.21971 9.22 049 9.22127 9.22 205 9.22 283 0.78 343 0.78 264 0.78 186 0.78 107 0.78029 0.77951 o-77 873 o-77 795 0.77717 9.99419 9.99417 9.99415 9-994I3 9.99411 9.99 409 9-99 407 9-99 404 9-99 402 9.21 761 9.22361 0.77 639 9.99 400 9.21 836 9.21 912 9.21 987 9.22 062 9-22 137 9-22 211 9-22 286 9.22 361 9-22435 9-22 438 9-22 516 9.22 593 9.22 670 9-22 747 9.22 824 9.22 901 9.22977 9.23054 9-23 13 9.23 206 9.23 283 9-23 359 9-23 431 9.23510 9-23 586 9.23 661 9-23 737 9.23 812 0.77 562 o-77 484 0.77 407 0-77 330 0.77 253 o-77 J 7 6 0.77 099 0.77023 0.76 946 9-99 398 9-99 396 9-99 394 9-99 392 9-99 390 9-99 388 9-99 385 9-99 383 9-99 381 9-22 509 0.76 870 9-99 379 9-22 583 9.22657 9.22731 9.22 SO^ 9.22 878 9.22952 9.23 02 5 9.23 098 9.23171 0.76 794 0.76717 0.76 641 0.76 565 0.76 490 0.76414 0.76 339 0.76 263 0.76 1 88 9-99 377 9-99 375 9-99 372 9-99 37 9-99 368 9-99 366 9-99 364 9-99 362 9-99 359 o 2 3 o i 3 333 79 78 77 13.2 13.0 12.8 39-5 39-o 38.5 65.8 65.0 64.2 333 76 75 74 12.7 12.5 12.3 38-0 37-5 37- 63.3 62.5 61.7 9.23 244 9-23 887 0.76113 9-99 357 9-233I7 9-23 390 9.23 462 9-23 53? 9.23 607 9-23 679 9-23 752 9.23823 9.23 895 9.23 962. 9.24037 9.24112 9.24 1 86 9.24 261 9-24 335 9.24410 9.24484 9.24 558 0.76038 0.75 963 0.75 888 0.75 814 o-75 739 0.75 66 5 0-75 590 0.75516 0.75 442 9-99 355 9-99 353 9-99 35 1 9-99 348 9-99 346 9-99 344 9-99 342 9-99 340 9-99 337 9-23 967 9.24632 0.75 368 9-99 335 L, Cos. d. L. Cot. 1 c. d. L. Tan. L. Sin, t p. P. 80 430 10 ', L. Sin. d. L, Tan. c. d.| L. Cot. L. Cos. d. p. p. 9.23 967 9.24 632 74. 0.75 368 9-99 335 2 6O I 2 9.24 039 9.24 no 7i 9.24 706 9.24 779 73 0.75 294 0.75 221 9-99 333 9-99 33i 2 59 58 74 73 72 3 9.24 181 71 9-24853 74 0.75 147 9-99 328 2 57 i 7-4 7-3 7-2 4 9-24 253 9.24 926 10 0.75 074 9.99 326 2 56 2 14.8 14.6 14.4 S 9-24 324 7 1 9.25 ooo 74 77 0.75 ooo 9-99 324 2 55 3 22.2 21.9 21.6 6 9-24 395 X 1 9-25 073 1 J 0.74927 9.99 322 54 4 29.6 29.2 28.8 I 9.24 466 9-24 536 70 9.25 146 9.25 219 73 73 0.74 854 0.74 781 9-99 319 9-993I7 3 2 2 53 52 i 37.0 36.5 36.0. 44.4 43.8 43.2 9 10 9.24 607 7 1 70 71 9.25 292 73 73 72 0.74 708 9-993I5 2 3 5O 51.8 5I.I 50.4 59-2 58-4 57-6 66 6 65 7 64 8 9.24 677 9.25 365 0.74 635 9.99313 n 9.24 748 9-25437 /* 0.74 563 9.99310 2 49 12 13 9.24818 9.24 888 / u 7 9.25510 9.25 582 73 72 0.74490 0.74418 9.99 308 9.99 306 2 48 47 71 70 69 H IS 9.24 958 9.25 028 7 70 9-25 655 9-25 727 72 0-74 345 0.74 273 9.99 304 9.99 301 3 2 46 45 2 7.1 7.0 6.9 14.2 14.0 13.8 16 17 18 19 2O 9.25 098 9.25 168 9-25 237 9-25 37 70 69 7 69 69 9.25 799 9.25 871 9-25 943 9.26015 72 72 72 72 0.74 201 0.74 129 0.74057 0.73 985 9-99 299 9.99 297 9-99 294 9.99 292 2 3 2 2 2 44 43 42 4O 3 4 I I 21.3 2I.O 2O-7 28.4 28.0 27.6 35-5 35- 34-5 42.6 42.0 41.4 49.7 49.0 48.3 56.8 56.0 55.2 9.25 376 9.26 086 0.73914 9-99 290 21 22 9.25 445 9-255I4 69 60 9.26 158 9.26 229 7 1 0.73 842 0.73 771 9.99 288 9-99 285 3 39 38 9 63.9 63.0 62.1 23 9-25 583 uy 6q 9.26 301 72 71 o-73 699 9-99 283 2 37 68 67 66 24 11 9.25 652 9.25 721 9.25 790 6 9 69 9.26 372 9.26443 9.26514 71 7 1 0.73^628 -73 557 0.73 486 9.99 281 9-99 278 9.99 276 3 2 36 35 34 2 6.8 6.7 6.6 13.6 13.4 13.2 27 28 29 9.25 858 9.25 927 9-25 995 6 9 68 68 9.26 585 9.26 655 9.26 726 7 1 7 71 0.73415 0-73 345 0.73 274 9-99 274 9.99 271 9-99 269 3 2 2 33 32 3 4 20.4 20. i 19.8 27.2 26.8 26.4 34-0 33-5 33-0 AO 8 4.O 2 "3Q 6 30 9.26 063 68 9.26 797 / * 7O 0.73 203 9-99 267 2 3O 7 47.6 46.9 46.2 31 9.26 131 68 9.26 867 o.73 133 9-99 264 2 29 8 54-4 53-6 52.8 32 9.26 199 68 9.26937 0.73 063 9.99 262 28 9 61.2 60.3 59.4 33 9.26 267 68 9.27 008 7 1 0.72992 "9.99 260 27 S4 9.26 335 68 9.27 078 7" 0.72 922 9.99 257 2 26 65 3 ii 9.26 403 9.26 470 67 68 9.27 148 9.27 218 7 70 7O 0.72 852 0.72 782 9-99 255 9.99 252 3 2 25 24 I 6.5 0.3 2 I7O 06 37 38 9-26 538 9.26 605 67 9.27 288 9-27 357 /*' 69 7O 0.72 712 0.72 643 9.99 250 9-99 248 2 2 23 22 3 19-5 -9 4 26.0 1.2 39 9.26 672 67 9.27427 69 0.72 573 9-99 245 2 21 5 32.5 i-5 40 9.26 739 67 9.27 496 7O 0.72 504 9.99 243 2 20 6 39.0 1.8 42 9.26 806 9.26873 67 9.27 566 9.27 635 69 0.72434 0.72 365 9-99 241 9-99 238 3 2 19 18 7 45-5 2.1 8 52.0 2.4 43 9.26 940 67 9.27 704 60 0.72 296 9.99 236 3 17 9 58-5 2.7 44 9.27 007 66 9-27 773 60 0.72 227 9-99 233 2 Ib 45 9.27073 67 9.27 842 6Q 0.72 158 9-99 231 2 15 46 9.27 140 66 9.27911 fio 0.72 089 9.99 229 14 333 47 9.27 206 67 9.27 980 uy 60 0.72 020 9.99 226 , 2 13 74 73 72 48 9.27 273 66 9.28049 68 0.71 951 9-99 224 12 49 5O 9-27 339 66 66 9.28 117 69 68 0.71 883 9.99 221 2 2 II 10 i 2 12-3 12.2 I2.O 37- 36.5 36-0 617 60 8 60 o 9.27 405 9.28 1 86 0.71 814 9-99 219 Si 9.27471 66 9.28 254 60 0.71 746 9.99217 J 9 3 52 9-27537 6c 9-28 323 68 0.71 677 9-99 214 2 8 53 9.27 602 5 66 9.28391 68 0.71 609 9.99 212 3 7 3333 54 9.27 668 66 9.28 459 68 0.71 541 9-99 209 2 6 71 70 69 68 55 5 6 11 9-27 734 9-27 799 9.27 864 9.27 930 65 65 66 9.28527 9.28 595 9.28 662 9.28 730 68 67 68 AC 0.71 473 0.71 405 0.71 338 0.71 270 9-99 207 9-99 204 9.99 202 9.99 200 3 2 2 5 4 3 2 n.8 11.7 11.5 ii. 3 2 35-5 35- 34-5 34-o 3 59-2 58-3 57-5 56.7 59 9-27 995 6c 9.28 798 67 0.71 202 999 197 2 I 60 9.28 060 J 9.28 865 0-71 135 9-99 195 O L. Cos. d. L. Cot. c. d. L. Tan. L. Sin. d. ' P. P. 79 C ir 431 i L, Sin. d. L, Tan. c, d. L. Cot, L, Cos. d, p, p. 9.28 060 6s 9.28 865 68 0.71 135 9-99 195 3 60 I 9.28 125 9-28933 0.71 067 9-99 192 j 59 2 9.28 190 ,5 9.29 ooo 6-7 0.71 ooo 9-99 190 58 68 67 66 3 9.28 254 6s 9.29067 7 67 0.70933 9-99 187 3 57 i 6.8 6.7 6.6 4 9.28319 6 5 9.29 134 w / 67 0.70 866 9-99 183 56 2 13.6 13.4 13.2 j 9.28 384 ft/i 9.29 201 07 6*7 0.70 799 9.99 182 55 3 20-4 20.1 19.8 6 9.28 448 4 AA 9.29 268 7 0.70 732 9.99 1 80 54 4 27.2 26.8 26.4 8 9 IO ii 9.28512 9-28577 9.28641 A 5 64 64 64 9-29 335 9.29 402 9.29 468 67 66 67 66 0.70 665 0.70 598 0.70 532 9.99 177 9-99 175 9-99 172 2 3 2 3 53 5 2 5 1 50 49 I 7 9 34-o 33-5 33-o 40.8 40.2 39.6 47.6 46.9 46.2 54.4 53.6 52.8 61.2 60.3 59.4 9.28 705 9-29 535 0.70 465 9-99 17 9.28 769 9.29 601 0.70 399 9.99 167 12 9.28 833 9.28 896 63 9.29 668 9-29 734 66 66 0.70332 0.70 266 9.99 165 9.99 162 3 48 47 65 64 63 14 9.28 960 4 9.29 800 0.70 200 9.99 1 60 46 i 6.5 6.4 6.3 ! 15 9.29 024 AT 9.29 866 AA 0.70 134 9^99 I57/ 3 45* 2 13.0 12.8 12.6 16 9.29 087 3 9-29 932 0.70 068 9-99 155 44 3 19.5 19.2 18.9 18 19 20 9.29 150 9.29214 9.29 277 ?N ON ON ON C o Co Co 4* O- 9.29 998 9.30 064 9.30 130 66 66 65 66 0.70 002 0.69 936 0.69 870 9-99 IS 2 9-99 15 9.99 147 3 2 3 2 43 42 40 4 6 7 8 26.0 25.6 25.2 32.5 32.0 31.5 39.0 38.4 37.8 45.5 44.8 44.1 S2 O S I 2 ^O J. 9.29 340 9.30 195 0.69 805 9-99 145 21 22 9.29 403 9.29 466 63 9.30 261 9.30 326 65 Ar 0.69 739 0.69 674 9.99 142 9.99 140 2 39 38 9 58.5 57.6 56.7 23 9.29 529 62 9-30 39i 5 fifi 0.69 609 9-99 137 2 37 62 fii an 24 s 27 28 29 30 9.29591 9.29 654 9.29716 9.29 779 9.29 841 9.29 903 63 62 63 62 62 63 9.30457 9-30522 9.30 587 9.30652 9.30717 9.30 782 3N ON ON ON ON ON ON < n 41. en Cn U> Cn <-n < 0.69 543 0.69 478 0.69413 0.69 348 0.69 283 0.69 218 9-99 135 9-99 132 9-99 130 9-99 127 9.99 124 9.99 122 3 2 3 3 2 3 2 36 35 34 33 32 30 i 2 3 4 6 7 6.2 6.1 6.0 12.4 12.2 I2.O 18.6 18.3 18.0 24.8 24.4 24.0 31.0 30.5 30.0 37.2 36.6 36.0 43.4 42.7 42.0 9.29 966 9.30 846 0.69 154 9.99119 3 1 9.30 028 62 9.30911 -J 64 0.69 089 9.99117 29 8 49.6 48.8 48.0 32 9.30090 61 9-30 975 6s 0.69 023 9.99114 2 28 9 55.8 54.9 54.0 | 33 9.30151 9.31 040 **3 0.68 960 9.99112 27 34 9.30213 62 9.31 104 4 0.68 896 9-99 109 3 26 59 3 P 9-30 275 9-30 336 61 62 9.31 1 68 9-31 233 65 6A 0.68 832 0.68 767 9.99 106 -9.99 104^ 3 2 25 i 1 5-9 0.3 4 I f f fi 06 37 38 39 9-30 398 9-30459 9.30521 61 62 9.31 297 9-3i 361 9-3i 425 64 64 64 0.68 703 0.68 639 0.68575 9.99 101 9-99 099 9-99 096 2 3 a 23 22 21 3M7-7 0-9 4 23.6 1.2 S 2Q.S I.S 40 9.30 582 61 9.31 489 0.68 511 9.99093 2 20 6 1 35.4 1.8 4i 9-3 643 61 9-31 552 6/i 0.68 448 9.99091 19 7 41.3 2.1 42 9.30 704 61 9.31 616 4 0.68 384 9.99 088 3 18 8 47.2 2.4 43 9.30 765 61 9.31 679 f)A 0.68 321 9.99 086 17 9 1 53-i 2.7 44 9.30 826 61 9-3i 743 67 0.68 257 9.99 083 16 45 46 9.30 887 9-30 947 60 61 9.31 806 9.31 870 u o 64 A.-> 0.68 194 0.68 130 9.99 080 9-99078 2 M 333 47 9.31 008 60 9-3 1 933 63 0.68 067 9-99 075 13 67 66 65 48 9.31 068 61 9-3i 996 f* 0.68 004 9.99072 12 o 49 9.31 129 60 9.32 059 P 6l 0.67 941 9-99 070 II i 1 1. 2 II.O IO.8 5O 51 9.31 189 61 9.32 122 63 0.67 878 9-99 067 3 IO Q 2 3 33-5 33-0 32-5 55-8 55-o 54-2 9.31 250 9.32 185 0.67815 9-99 064 52 9.31 310 f 9.32 248 .3 0.67 752 9.99 062 8 53 9-3i 37 fo 9.32311 62 0.67 689 9-99 059 7 333 54 9-3i 430 ^ 9-32 373 6? 0.67 627 9-99 056 6 64 63 62 55 9.31 490 9-32436 U J A? 0.67 564 9-99 054 5 o 56 9-3 1 549 59 9.32 498 A- 0.67 502 9.99051 3 4 i 10.7 10.5 10.3 11 9.31 609 9.31 669 60 9.32 561 9.32623 03 62 0.67 439 0.67 377 9-99 048 9-99 046 2 3 2 2 3 32.0 31.5 31.0 53.3 52-5 5J-7 59 9.31 728 59 60 9.32 685 62 0.67315 9 99 043 3 7. I 60 9.31 788 ; 9.32747 ; 0.67253 9-99 040 L, Cos. d, L. Cot. c. d. L. Tan. L. Sin. d. ' P. P. 78 C 432 12' / L. Sin. d. L. Tan. c. d, L. Cot. L. Cos. d. p. p. o 9.31 788 CQ 9-32 747 61 0.67 253 9.99 040 2 6O I 2 9-3 1 847 9.31 907 jy 60 9.32 810 9.32 872 62 0.67 190 0.67 128 9.99 038 9-99 035 3 a 59 58 63 62 61 3 9.31 966 59 9-32933 62 0.67 067 9.99032 6 2 57 i 6.3 6.2 6.1 4 9-32025 59 9-32 995 62 0.67 005 9-99 030 a. 56 2 12.6 12.4 12.2 5 9-32 084 59 9.33057 62 0.66 943 9.99027 7 55 3 18.9 18.6 18.3 6 9-32 H3 59 9-33 "9 61 0.66 88 1 9.99 024 2 54 4 25.2 24.8 24.4 8 9.32 202 9.32 261 59 59 9-33 1 80 9-33 242 62 fir 0.66 820 0.66 758 9.99022 9.99019 3 53 52 I 31.5 31.0 30.5 37-8 37-2 36-6 9 10 9-32319 59 9-33 303 62 61 0.66 697 9.99016 3 3 2 5 1 50 I 44.1 43.4 42.7 50.4 49.6 48.8 cfi n r c 8 c A n 9.32 378 9-33 365 0.66 635 9.99013 ii 12 13 9-32437 9.32495 9-32553 On On O oo oo ^ 9-33426 9.33487 9-33 548 61 61 fiT 0.66 574 0.66 513 0.66 452 9.99011 9.99 008 9.99 005 3 3 49 48 47 j"'/ jj"" Di-y 60 59 9.32612 39 c8 9-33 609 0.66 391 9.99 002 3 46 i 6.0 5.9 " 15 9.32 670 IS 9-33 6 7 fir 0.66 330 9.99 ooo 45 2 I2.O II. 8 16 9.32 728 5 5 _0 9-33 73 1 0.66 269 9.98 997 44 3 18.0 17.7 17 18 19 9.32 786 9.32 844 9.32 902 T On On O^ X) 00 00 O 9-33 792 9-33853 9-339I3 61 60 61 0.66 208 0.66 147 0.66087 9.98 994 9.98991 9.98 989 3 3 2 -1 43 42 4 24.0 23.6 5 3o.o 29.5 6 36.0 35.4 20 9.32 960 J^ 9-33 974 60 0.66 026 9.98 986 -3 40 8 48.0 47.2 21 9.33018 - 9-34 034 61 0.65 966 9.98 983 a 39 9 54.0 53.1 22 9-33075 X 9-34095 60 0.65 905 9.98 980 2 38 23 9-33 !33 9.34I55 60 0.65 845 9.98 978 37 58 57 24 9-33 190 57 9.34215 61 0.65 785 9-98 975 36 2 5 9-33 248 5 9.34 276 fin 0.65 724 9.98972 35 1 5-8 5-7 26 9-33 35 57 9-34 33 6 fin 0.65 664 9.98 969 34 2 11.6 11.4 27 28 29 9-33 3 fi 2 9-33420 9-33477 58 57 9-34 396 9-34 45 6 9-34 5 l6 60 60 fin 0.65 604 0.65 544 0.65 484 9-98 967 9.98 964 9.98961 3 3 7 33 3 2 3 17-4 I7- 1 4 23.2 22.8 5 29.0 28.5 6 ^4.8 34.2 30 9-33 534 9-3457 6 CQ 0.65 424 9.98958 7 3O 7 40.6 39.9 3 2 9-33591 9-33 6 47 56 9-34 635 9-34 695 60 fin 0.65 365 0.65 305 9-98955 9.98953 2 29 28 8 46.4 45.6 9 52-2 51.3 33 9.33 704 57 9-34755 0.65 245 9.98950 27 34 9-33 7 61 57 9-34 814 59 fin 0.65 1 86 9.98 947 3 26 56 55 3 35 36 9.338i8 9-33 874 56 9-34 874 9-34 933 59 0.65 126 0.65 067 9.98 944 9.98 941 3 2 5 24 i 2 5-6 5-5 0.3 112 IIO 06 11 9-33931 9-33 987 57 56 9-34992 9-3505I 59 60 0.65 008 0.64 949 9.98 938 9.98 936 2 23 22 3 16.8 16.5 0.9 22-4 22.O 1.2 39 9-34 043 C7 9-35 l11 CQ 0.64 889 9.98933 -J 21 c 28.O 27.5 1.5 4O 9.34 loo ^6 9-35 J 7 CQ 0.64 830 9.98 930 a 2O 6 33.6 33.0 1.8 4 1 9-34 156 * 9-35 229 jy 0.64771 9.98927 19 7 39.2 38.5 2.1 42 9.34212 cfi 9.35 288 59 0.64 712 9.98924 3 18 8 44.8 44.0 2.4 43 9-34 268 5 9-35 347 59 0.64 653 9.98921 1 7 9 50.4 49.5 2.7 44 9.34 324 9-35 45 5 0.64 595 9.98919 16 45 9.34 380 3 9-35 464 0.64 536 9.98916 15 _ 46 9-34 436 5 9-35 523 59 0.64 477 9.98913 14 333 47 9-34 49 1 55 rfi 9-35 58i 58 0.64419 9.98910 3 13 62 61 60 48 49 9-34 547 9-34 602 5 55 5fi 9-35 6 40 9-35 698 59 58 CQ 0.64 360 0.64 302 9.98 907 9.98 904 3 3 -2 12 II o i IO.3 IO.2 IO.O 50 51 9-34 658 w 55 cfi 9-35 757 58 c8 0.64 243 9.98 901 3 2 IO 9 2 3 51.7 50.8 50.0 9-34 7 J 3 9-35 815 0.64 185 9.98 898 5 2 9-34 7 6 9 5 9-35 873 8 0.64 127 9.98 896 8 53 9-34 824 55 9-35 93 1 5 5 0.64 069 9.98 893 7 333 54 9-34 879 55 9-35 989 5 0.64011 9.98 890 6 59 58 57 i 9-34 934 9-34 989 9-35 44 9-35 99 n On On On O i On On On O 9.36047 9.36 105 9.36 163 9.36 221 58 58 11 0-63953 0.63 895 0.63 837 0.63 779 9.98887 9.98 884 9.98 88 1 9.98 878 3 3 3 5 4 3 2 i 2 3 9-8 9.7 9-5 29.5 29.0 28.5 49.2 48.3 47-5 59 9-35 154 33 9.36 2 79 5 C.7 0.63 721 9.98875 i I 60 9-35 209 9.36 336 J/ 0.63 664 9.98 872 L. Cos. d. L, Cot. c. d. L.Tan. L. Sin. d. 1 p.p. 77' 13 433 / L, Sin, d, L, Tan, c. d. L, Cot, L, Cos, d, p, p. 9.35 209 9-36 336 , 8 0.63664 9.98 872 6O I 9-35 263 JT- 9-36 394 -Q 0.63 606 9.98 809 59 58 57 56 2 55 9.36452 5 s 0.63 548 9.98 867 58 3 9.35 373 55 9-36 59 57 0.63491 9.98 864 3 57 i 5.8 5.7 5.6 4 6 9.35 427 9-35 48i 9-35 536 54 55 9.36 566 9-36 624 9.36 681 5V 58 57 0-63 434 0.63 376 0.63 319 9.98 861 9.98 858 9-98 855 3 3 3 56 55 54 2 II.6 II.4 II. 2 3 17.4 17.1 1 6.8 4 23.2 22.8 22.4 5 29 o 28 c 28 o I 9 9-35 590 ^ 9-35 644 9-35 698 54 9-36 738 9-36 795 9.36852 57 57 C7 0.63 262 0.63 205 0.63 148 9-98 852 9.98 849 9.98 846 3 3 53 5 2 6 34.8 34.2 33.6 7 40.6 39.9 39.2 8 46.4 45.6 44.8 10 9.35 752 * 9.36 909 C7 0.63 09 1 9.98 843 -3 50 9 52-2 51.3 50.4 ii 9-35 806 J* 9.36 966 0.63 034 9.98 840 49 12 9-35 860 54 9-37 02 3 57 0.62 977 9.98837 3 48 55 54 53 3 9-35 9H JT 9-37 8o 57 0.62 920 9-98834 3 47 15 16 9.35 968 9.36022 ^7 9.36075 53 9-37 137 9-37 193 9-37 250 56 57 0.62 863 0.62 807 0.62 750 9.98831 9.98 828 9-98 825 3 3 3 46 45 44 1 5-5 5-4 5-3 2 n.o 10.8 10.6 3 16.5 16.2 15.9 4 22.O 21.6 21.2 18 9.36129 J7 9.36 182 ?> 9-37 306 9-37 363 s 0.62 694 0.62 637 9.98 822 9.98819 3 43 42 5 27.5 27.0 26.5 6 33.0 32.4 31.8 1 '9 9.36 236 * 9.37419 5 C7 0.62 581 9.98816 3 41 7 38-5 37-8 37- 1 20 9-36289 ^ 9-37476 J/ 0.62 524 9-98813 40 8 44-0 43-2 42.4 21 9.36 342 ^ 9-37 S3 2 ^ 0.62 468 9.98 810 39 9 49-5 48.6 47.7 22 9-36 395 JJ 9-37 588 cfi 0.62 412 9.98 807 o 38 23 9.36 449 J* 9-37 644 5 0.62 356 9.98 804 3 37 52 51 24 9.36 502 ;: 9-37 7 5 0.62 300 9.98 80 1 3 36 I $ 2 K I 2 5 26 9.36555 H 9.36608 ^ 9-37 756 9.37812 56 0.62 244 0.62 1 88 9.98 798 9-98 795 3 3 35 34 2 10.4 10.2 3 i5- 6 l S-3 27 9.36660 ^~ 9.37868 > 0.62 132 9.98 792 33 4 20. 8 20.4 28 9-36713 ^ 9-37 924 cfi 0.62 076 9.98 789 J 32 5 26.0 25.5 29 9.36766 JJ 9-37 98o 5 c c 0.62 020 9.98 786 3 6 31.2 30.6 3O 9-36819 ^ 9-38035 JJ 0.61 965 9.98 785 30 7 36.4 35-7 32 9-36871 J 9.36924 i 9-38091 9-38 H7 56 0.61 909 0.61 853 9.98 780 9-98 777 3 29 28 8 41.6 40.8 9 ! 46.8 45.9 33 9.36976 ?? 9.38 202 55 0.61 798 9.98 774 3 2 7 34 9-37 28 ^ 9-38 257 55 0.6 1 743 9.98 771 3 26 4 3 35 9-37 081 g 9.383I3 0.6 1 687 9.98 768 J 25 i 0.4 0.3 36 9-37 J 33 : 9.38 368 55 0.61 632 9.98 765 I 24 2 0.8 0.6 37 9-37 185 5* 9.38423 55 ef\ 0.61 577 9.98 762 ^ 23 3 1-2 -9 38 9-37 237 5 2 9-38479 5 0.61 521 9.98759 I 22 4 1.6 1.2 39 9.37 289 5 2 9-38 534 55 re 0.61 466 9-98 756 3 21 5 "5 40 9-37 34i 2 9.38 589 JJ ce 0.61 411 9-98 753 , 2O 6 2.4 1.8 1 A fl n \ 4 1 9-37 393 9.38 644 0.61 356 9.98 750 19 Q 1 ? r, A 42 43 9-37 445 9-37 497 5 2 52 9.38 699 9-38 754 55 55 0.61 301 0.61 246 9-98 746 I 9.98 743 ~ 18 5 3-2 2.4 9 3-6 2.7 AA e ._ 5 2 978 808 54 n 08 7/io i ft 45 46 9.37600 5' 9-37652 ^ 9.38 863 9.38918 55 55 0.61 137 0.61 082 9.90 740 9-98 737 9-98 734 3 3 15 14 4433 47 9.377 3 -, 9.38 972 54 0.61 028 9-98 73 1 3 13 55 54 58 57 48 9-37755 J, 9.39027 55 r r 0.60 973 9.98 728 ^ 12 3 6.9 6.8 9.7 9.5 49 9-378o6 * 9-39 082 JJ 0.60918 9.98 725 I II 1 20.6 20.2 29.0 28.5 50 9-37858 ^ T 9-39 136 C4. 0.60 864 9.98 722 j -\ 10 34.4 33.8 48.3 47.5 52 9-37 909 9.37960 51 9-39 190 9-39 245 55 0.60 810 0.60 755 9.98719 9-98 7'5 4 9 8 3| 4 8.i47-2 53 9.38011 5 1 9.39 299 54 0.60 701 9.98712 3 7 333 54 9.38 062 5 1 9-39 353 54 0.60 647 9-98 79 3 6 \a 55 54 55 9.38 113 5 1 9-39 407 54 0.60 593 9.98 706 3 5 56 9.38 164 5 1 9.39 461 54 0.60 539 9.98 703 4 9.3 9.2 9.0 11 9-38215 9.38 266 5 1 9-39 5 J 5 9-39 569 54 54 0.60 485 0.60431 9.98 700 9.98 697 3 3 3 2 28.0 27.5 27.0 46.7 45.8 45.0 59 9-38317 5 1 C J 9-39 623 54 0.60 377 9.98 694 I 6O 9-38 368 9-39 677 "^ 0.60 323 9.98 690 o L. Cos. d, L, Cot, c, d, L. Tan, L. Sin. d, 1 P, P, 76 C 434 14 C ; L. Sin. | d. L, Tan. |c. d. L. Cot. L. Cos. d. p. p. i 2 3 4 I * 10 ii 12 13 H 18 19 20 21 22 23 2 4 25 26 27 28 29 30 3i 32 33 34 35 36 11 39 4O 42 43 44 45 46 47 48 49 50 5i 52 53 54 57 58 59 6O 9.38 368 5 5 1 5 5 5 5 1 5 5 5 5 5 5 50 49 5 50 49 50 49 49 5 49 49 49 49 49 49 49 49 49 49 49 48 49 48 49 48 48 48 48 48 48 47 48 47 48 47 48 47 47 47 48 9-39 677 54 53 54 53 54 54 53 53 54 53 53 53 53 53 53 52 53 53 52 53 53 52 52 53 52 52 52 52 S 2 52 5i 5 2 5i 52 5i 5i 5i 5 1 5i 5 1 5 1 5 1 5i 5i 5 0.60 323 9.98 690 3 3 3 3 4 3 3 3 3 4 3 3 3 3 4 3 3 3 4 3 3 3 4 3 3 3 4 3 3 3 4 3 3 4 3 3 3 4 3 3 4 3 3 4 3 3 4 3 3 4 3 3 4 3 3 4 3 4 60 59 58 57 56 55 54 53 5 2 50 49 48 47 46 45 44 43 42 4O 39 38 37 36 35 34 33 32 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 J 3 12 II 10 9 8 7 6 5 4 3 2 I O , ( ; < i 2 3 4 6 8 9 i 2 4 I I 9 [ 2 3 \ 3 ' ) i I 2 2 3 ; 4 4 I I 2 2 3 3 4 i 2 3 4 5 9 54 53 5-4 5-3 10.8 10.6 16.2 15.9 21.6 21.2 27.0 26.5 32.4 31.8 37-8 37-i . 43.2 42.4 48.6 47.7 52 51 50 5-2 5-i 5-o 0.4 IO.2 IO.O 5-6 I5.3 IS- 0.8 20.4 20.0 6.0 25.5 25.0 1.2 30.6 30.0 6-4 35-7 35-o 1.6 40.8 40.0 6.8 45.9 45.0 49 48 47 4-9 4-8 4-7 9.8 9.6 9.4 4.7 14.4 14.1 9.6 19.2 18.8 4.5 24.0 23.5 9.4 28.8 28.2 4-3 33-6 32-9 9.2 38.4 37.6 4.1 43.2 42.3 4 3 0.4 0.3 0.8 0.6 1.2 0.9 1.6 1.2 2.0 1.5 2.4 1.8 2.8 2.1 3-2 2.4 3-6 2.7 9.38418 9.38 469 9.38519 9-3857 9.38 620 9.38 670 9.38721 9-38 77i 9.38821 9-39731 9-39 785 9-39 838 9-39 892 9-39 945 9-39 999 9.40052 9.40 1 06 9.40 159 0.60 269 0.60 215 0.60 162 0.60 1 08 0.60 055 0.60001 0.59 948 0-59 894 0-59 841 9.98 687 9.98 684 9.98 681 9.98 678 9.98 675 9.98671 9.98 668 9.98 665 9.98 662 9.38871 9.40212 0.59 788 9.98 659 9.38921 9.38971 9.39021 9.39071 9-39 121 9-39 17 9-39 220 9.39 270 9.39319 9.40 266 9.40319 9.40 372 9.40 425 9.40 478 9.40 531 9.40 584 9-40 636 9.40 689 0-59 734 0.59 68 1 0.59 628 0-59 575 0.59 522 0.59 469 0.59416 0.59 364 o-59 3 1 1 9.98 656 9.98 652 9.98 649 9.98 646 9.98 643 9.98 640 9.98 636 9-98 633 9.98 630 9-39 369 9.40 742 0.59 258 9.98 627 9.39418 9-39 467 9.39517 9-39 566 9.39615 9-39 664 9-39 7 1 3 9-39 762 9.39811 9-40 795 9.40 847 9.40 900 9-40952 9.41 005 9.41 057 9.41 109 9.41 161 9.41 214 0.59 205 0-59 i53 0.59 100 0.59 048 0-58995 0.58 943 0.58 891 0.58 839 0.58 786 9-98 623 9.98 620 9.98 617 9.98 614 9.98610 9.98 607 9.98 604 9.98 601 9-98 597 9.39 860 9.41 266 0.58 734 9-98 594 9-39 99 9-39 958 9.40 006 9.40055 9.40 103 9.40152 9.40 200 9.40 249 9.40 297 9.41 318 9.41 370 9.41 422 9.41 474 9.41 526 9.41 578 9.41 629 9.41 681 9-41 733 0.58 682 0.58 630 0.58578 0.58 526 0.58474 0.58422 0.58371 0.58319 0.58 267 9.98 591 9.98 588 9-98 584 9.98 581 9-98578 9-98 574 9.98571 9.98568 9.98 565 9.40 346 9.41 784 0.58216 9.98561 940 394 9.40 442 9.40 490 9-40 S3 8 9.40 586 9.40 634 9.40 682 9.40 730 9.40 778 9.41 836 9.41 887 9-41 939 9.41 990 9.42 041 9-42 093 9.42 144 9.42 195 9.42 246 0.58 164 0.58 113 0.58061 0.58010 0-57959 0.57 907 0.57856 0.57805 0-57 754 9-98 558 9.9855 1 9.98 548 9-98 545 9.98 541 9-98 538 9.98 535 9-98 53 1 4444 54 53 52 51 6.8 6.6 6.5 6.4 1 20.2 19.9 19.5 I9.I .33-833- 1 32-53I-9 ^47.246.445.544.6 3333 54 53 52 51 9.0 8.8 8.7 8.5 1 27.0 26.5 26.0 25.5 3 45.0 44.2 43.3 42.5 9.40 825 9.42 297 0-57 73 0.57652 0.57 60 1 0-5755 0-57499 0.57 448 0-57 397 -57 347 0.57 296 -57 245 9.98 528 9.40 873 9.40921 9.40 968 9.41 016 9.41 063 9.41 in 9.41 158 9.41 205 9.41 252 9.42 348 9-42 399 9-42 45 9.42 501 942552 9.42 603 9.42 653 9.42 704 9-42 755 9.98 525 9.98521 9.98518 9-98515 9.98511 9.98 508 9-98 55 9.98 501 9.98 498 9.41 300 9.42 805 -57 195 9.98 494 L. Cos. d. L. Cot. c. d. L.Tan. L. Sin. | d. ' P. P. 75' 15' 435 1 L. Sin. d. L. Tan. c. d. L. Cot. L. Cos. d. p.p. o I 2 3 4 i \ 9 10 ii 12 13 14 15 16 :i 19 20 21 22 23 24 3 27 28 29 30 3 1 32 33 34 35 36 3 39 4O 4i 42 43 44 45 46 47 48 49 50 5 1 52 53 54 55 56 11 59 6O 9.41 300 47 47 47 47 47 47 46 47 47 46 47 46 47 46 47 46 46 47 46 46 46 46 46 46 45 46 46 46 45 46 45 46 45 46 45 45 46 45 45 45 45 45 45 45 44 45 45 45 44 45 44 45 44 45 44 44 44 45 44 44 9.42 805 5 1 50 5 1 50 50 5i 50 50 5 50 50 50 50 50 5 49 50 50 49 50 49 5 49 50 49 49 49 5 49 49 49 49 49 49 49 48 49 49 48 49 49 48 49 48 48 49 48 48 48 49 48 48 48 48 48 48 47 48 48 48 o*57 '95 9.98 494 3 3 4 3 4 3 3 4 4 3 4 3 3 4 3 4 3 4 3 4 3 4 3 3 4 3 4 3 4 3 4 3 4 4 3 4 3 4 3 4 3 4 3 4 4 3 4 3 4 3 4 4 3 4 3 4 4 3 4 6O -8 D 8 57 56 55 54 53 52 5 1 5O 49 48 47 46 45 44 43 42 41 4O 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 2O 19 18 1 7 16 15 14 '3 12 II 10 9 8 7 6 5 4 3 2 O 2 3 4 6 8 9 i 2 3 4 5 6 8 9 k < i i 2 2 J J 4 4 i i 2 2 3 . ; A i 2 3 I I ) i 2 3 4 j 9 51 50 49 5.1 5.0 4.9 O.2 IO.O 9.8 5.3 15.0 14.7 0.4 20.0 19.6 5-5 25.0 24.5 0.6 30.0 29.4 5-7 35- 34-3 0.8 40.0 39.2 5.9 45.0 44.1 48 47 46 4.8 4.7 4.6 9.6 9.4 9.2 4.4 14.1 13.8 9.2 18.8 18.4 40 23.5 23.0 8.8 28.2 27.6 3.6 32.9 32.2 8.4 37.6 36.8 3.2 42.3 41.4 45 44 4-5 44 9.0 8.8 13-5 13-2 18.0 17.6 22.5 22.O 27.0 26.4 31.5 30.8 36.0 35.2 40.5 39.6 4 3 0.4 0.3 0.8 0.6 1.2 0.9 1.6 1.2 2.0 1.5 2,4 1.8 2.8 2.1 3.2 2.4 3.6 2.7 9-4i 347 941 394 9.41 441 9.41 488 9-4i 535 9.41 582 9.41 628 9.41 675 9.41 722 9.42 856 9.42 906 942957 943 007 94357 943 108 943 158 943 2 8 943 258 0.57 144 0.57094 0.57 43 0-56993 0.50 943 0.50892 0.56 842 0.56 792 0.56 742 9.98491 9.98 488 9.98484 9.98 481 9.98477 9.98474 9.98471 9.98 467 9.98 464 9.41 768 943 38 0.56692 9.98460 9.41 815 9.41 861 9.41 908 9-41 954 9.42001 9.42 047 9.42 093 9.42 140 9.42 186 943 358 943 408 943 458 943 5 8 943 558 943607 943 657 943 77 943 75 6 0.56 642 0.56 592 0.56 542 0.56492 0.56 442 0.56 393 0-56 343 0.56 293 0.56 244 9.98457 9.98453 9.98 450 9.98 447 9-98 443 9.98 440 9.98436 9.98433 9.98429 9.42 232 943 806 0.56 194 9.98 426 9.42 278 9.42 324 9.42 370 9.42416 9.42 461 9.42 507 9-42 553 9-42 599 9.42 644 943 855 943 905 943 954 9.44004 944053 9.44 1 02 9-44I5 1 9.44 2OI 9.44 250 0.56 145 0.56 095 0.56 046 0-55 996 o-55 947 0.55 898 0-55 849 0-55 799 0-55 75 9.98422 9.98419 9.98415 9.98412 9.98 409 9.98 405 9.98 402 9.98 398 9-98 39! 9.42 690 944 299 o-55 7 01 9.98 391 9-42 735 9.42 781 9.42 826 9.42 872 9.42917 9.42 962 9-43 o<38 9-43 053 9-43 098 9-44 348 9-44 397 944 446 944 493 944 544 944 592 9.44 641 944 690 9-44 738 0-55 652 0-55 603 0-55 554 -55 55 0.55 456 0.55 408 o-55 359 0.553JO 0.55 262 9.98 388 9.98 384 998381 9.98377 9.98 373 9.98 370 9.98 366 9-98 363 9.98 359 9-43 H3 944 787 0-55213 998356 9-43 1 88 9-43 233 9-43 278 9-43 323 9-43 367 9.43412 9-43457 9-43 5 2 9.43 546 944 836 9.44 884 9-44 933 9.44981 945 o 2 9 945 78 9.45 126 945 J 74 945 222 0.55 164 0.55 1 16 0.55 067 0-55 OI 9 0.54971 0.54 922 0.54 874 0.54 826 0.54 778 9.98352 9 98 349 9.98 345 9.98 342 9-9^ 338 9-98 334 9-98 33i 9.98 327 9.98 324 4444 50 49 48 47 D 6.2 6.1 6.0 '5.9 18.818.4 18.017.6 ,,31.2 30.6 30.0 29.4 ^43.842.942.041.1 3333 51 50 49 48 | 8.5 8.3 8.2 8.0 \ 25.5 25.0 24.5 24.0 742.541.740.840.0 9-43 59i 945 271 0.54 729 9-98 320 943 6 35 943 680 943 724 943 769 943813 943 857 943 901 943 946 943 990 945 319 945 367 945 4i5 945 463 9455" 945 559 945 6o6 945 6 54 945 72 0.54681 0-54 633 0-54 585 0-54537 0.54489 0.54441 0-54 394 0.54 346 0.54 298 9-983 1 7 9-983I3 9.98 309 9.98 306 9.98 302 9.98 299 9.98 295 9.98 291 9.98 288 944 034 945 75 0.54 250 9.98 284 L, Cos. d. L. Cot. c. d. L. Tan. L. Sin. d. 1 P.P. 1 74' 436 16' / L, Sin, d, L, Tan, c, d. L. Cot, | L, Cos, d, p, p. o 9.44 034 4.4. 945 75 47 0.54 250 9.98 284 60 I 2 9.44078 9.44 122 44 9-45 797 945 84? .48 0.54 203 o-54 155 9.98 281 9.98 277 4 59 58 48 47 46 .3 9.44 1 66 44 945 892 .0 0.54 108 9.98 273 4 57 I 4.8 4.7 4.6 4 I 9.44 210 944 253 944 297 44 43 44 945 940 945 987 9.46 035 45 47 48 0.54 060 0.54013 0-53965 9.98 270 9.98 266 9.98 262 3 4 4 56 55 54 2 3 4 9.6 9.4 9.2 14.4 14.1 13.8 19.2 1 8.8 18.4 8 9 944 34i 944 38? 944 428 44 44 43 44 9.46 082 9.46 130 946 177 47 48 47 47 0.53918 0.53 870 o.53 823 9.98 259 9-98 255 9.98251 3 4 4 53 52 6 8 24.0 23.5 23.0 28.8 28.2 27.6 33-6 32-9 32-2 38.4 37.6 36.8 IO 944 472 4.4. 9.46 224 47 0.53 776 9.98 248 SO 9 43-2 42.3 41-4 ii 9.44516 9.46271 .,0 0-53 729 9.98 244 49 12 944 559 43 9.46319 4 0.53 68 1 9.98 240 4 48 45 44 43 13 9.44 602 43 9.46 366 47 0-53 634 9.98 237 3 47 15 16 17 9.44 646 9-44 689 944 733 944 776 44 43 44 43 9.46413 9.46 460 9.46 507 946 554 47 47 47 47 0.53587 0-53 540 0-53 493 0.53 446 9-98 233 9.98 229 9.98 226 9.98 222 4 4 3 4 46 45 44 43 2 3 4 s 4.5 4.4 4.3 9.0 8.8 8.6 13.5 13.2 12.9 18.0 17.6 17.2 22.5 22.0 21.5 18 19 9.44819 9.44 862 4.5 43 A_1 9.46 60 1 9.46 648 4/ 47 46 0-53 399 0.53352 9.98218 9.98215 4 3 42 6 7 27.0 26.4 25.8 31.5 30.8 30.1 20 944 905 4.5 9.46 694 47 0-53 306 9.98 211 4O 8 36.0 35.2 34.4 21 944 948 43 9.46 741 0-53 259 9.98 207 39 9 40-5 39-6 38-7 22 944 992 44 9.46 788 47 0.53212 9.98 2O4 3 38 23 945 35 43 946835 4/ 0-53 165 9.98 2OO 4 37 42 41 24 945 077 4 2 9.46 88 1 4 0-53 "9 9.98 196 4 36 25 945 I2 43 9.46 928 47 0.53072 9.98 192 4 35 i 84 8.2 26 945 163 43 AT. 946 975 47 16 0.53025 9.98 189 3 34 3 12.6 12.3 27 9 45 206 9.47021 0.52979 9.98 iS^ 33 4 16.8 16.4 28 945 249 43 9.47 068 47 Aft 0.52932 9.98 181 4 32 S 2I.O 20.5 29 945 292 43 947 "4 4 46 0.52886 9.98177 4 3 1 6 25.2 24.6 3O 945 334 9.47 1 60 47 0.52 840 9.98 174 6 30 7 29.4 28.7 3 1 32 945 377 945 4i9 42 947 207 947 253 4 6 Aft 0.52 793 0.52 747 9.98 170 9.98 1 66 4 29 28 5 9 33-6 32.8 37-8 36-9 33 945 462 43 947 299 4 0.52 701 9.98162 27 34 945 54 4 2 947 346 47 Aft 0.52 654 9.98159 j 3 26 4 3 35 36 945 547 945 589 43 42 947 392 947 438 4 46 A(\ 0.52608 0.52 562 9-98 155 ; 9.98151 25 24 i 2 0.4 0.3 0.8 0.6 37 9.45 632 43 9-47 484 46 Aft 0.52 516 9.98 147 4 2^ 3 1.2 0.9 38 945 6 74 4 2 947 530 4O Aft 0.52 470 9.98 144 3 22 4 1.6 1.2 39 945 7 l6 42 947 576 4 U 46 0.52424 9.98 140 4 21 5 2.O 1.5 40 945 758 4.1 9.47 622 46 0.52378 9.98 136 2O 6 2.4 1.8 ,, o _ 42 43 945 80 1 945 843 945 885 42 42 9.47 668 947 7H 947 76o 46 46 Aft 0.52332 0.52 286 0.52 240 9.98 132 9.98 129 9.98 125 3 4 19 18 17 8 9 3.2 2.4 3-6 2.7 44 4* 4 4 / 45 945 9 2 7 945 969 42 y.4/ aw 9 47 852 46 0.52 148 9.98117 4 IS 46 9.46011 4 2 947 897 45 A (\ 0.52 103 9.98113 4 14 4 444 47 48 49 9.46053 9.46 095 9.46 136 42 42 41 4.2 947 943 947 989 948035 46 46 4.C 0.52057 0.52011 0.51965 9.98 no 9.98 106 9.98 102 3 4 4 13 12 II 48 47 46 45 6.0 5.9 5.8 5.6 18.0 17.6 17.2 16.9 50 9.46178 4.2 9.48 080 46 0.51 920 9.98 098 IO 30.029.428.8 28.1 51 9.46 220 9.48 126 0.51 874 9.98 094 9 342.041.140.239.4 5 2 9.46 262 T 9.48171 45 Aft 0.51 829 9.98 090 4 8 53 946 33 4 1 9.48217 4 0.51 783 9.98087 3 7 3 333 54 946 345 9.46 386 41 9.48 262 9.48 307 45 11 0.51 738 0.51 693 9.98083 9.98 079 4 4 6 S 48 47 46 45 56 9.46 428 4 Z 948 353 40 0.51 647 9.98 075 4 4 8.0 7.8 7.7 7.5 57 58 9.46 469 9.46511 4 1 42 9.48 398 9.48 443 4o 45 0.51 602 o-S 1 557 9.98071 9.98 067 4 4 3 2 24.0 23.5 23.0 22.5 3 40.0 39.2 38.3 37.5 59 946 552 41 42 9.48 489 4.C 0.51 5" 9.98 063 4 I 60 9.46 594 948 534 0.51 466 9.98 060 O L, Cos. d. L. Cot, |c. d. L. Tan. L. Sin. d, t P, P, 73 C 17' 437 1 L, Sin, d. L. Tan, c. d, L, Cot, L, Cos, d, P, P, o 946 594 T 948 534 AC 0.51 466 9.98 060 4" 60 I 946 635 948 579 0.51 421 9.98 056 S9 2 3 946 676 9.46717 4 1 4i 948 624 948 669 45 45 0.51 376 0-5 1 33 1 9.98 052 9.98 048 4 4 58 57 45 44 43 4 6 8 9 946 758 9.46 800 946841 9.46 882 946 923 946 964 4 1 42 4i A I 9.48 714 948 759 9.48 804 9.48 849 9.48 894 9-48 939 4S 45 45 45 45 45 AC 0.51 286 0.51 241 0.51 196 0.51 151 0.51 106 0.51 061 9-98 044 9.98 040 9.98 036 9.98 032 9.98 029 9.98025 4 4 4 4 3 4 56 55 54 53 52 5 1 i 2 3 4 1 7 4-5 44 4-3 9.0 8.8 8.6 13.5 13.2 12.9 18.0 17.6 17.2 22.5 22.0 21.5 27.0 26.4 25.8 31.5 30.8 30.1 IO 947 005 ^ 948 984 AC 0.51 016 9.98021 SO 8 36.0 35.2 344 ii 947 45 949029 0.50971 9.98017 49 9 40.5 39-6 38-7 12 947086 J 949 073 44 0.50927 9.98013 48 13 947 I2 7 949 118 45 0.50 882 9.98009 47 14 947168 4 947 209 T 949 l6 3 949 207 45 44 0.50837 0.50 793 9-98005 9.98001 46 45 42 41 40 16 947 249 T, 949 252 45 0.50 748 9-97 997 44 i 4.2 4.1 4.0 1 8 19 20 9.47 290 947 330 947 37 i T" 1 40 41 40 41 949 296 949 34i 949 385 44 45 44 45 AA 0.50 704 0.50 659 0.50615 9-97 993 9-97 989 9-97 986 4 4 3 4 A 43 42 40 2 3 4 6 84 8.2 8.0 12.6 12.3 12.0 1 6.8 164 1 6.0 2I.O 2O-5 2O.O 25.2 24.6 24.0 9.47411 9-49 430 0.50570 9.97 982 21 947 45 2 4O 949 474 AC 0.50 526 9.97978 1 ~[ 39 7 29.4 28.7 28.0 22 947 492 41 949 5 1 9 AA 0.50481 9-97 974 38 8 33.6 32.8 32.0 23 947 533 4O 949 563 AA 0.50 437 9-97 97 37 9 37-8 36.9 36-0 24 947 573 9.49 607 0.50 393 9-97 966 36 25 947613 4 U 949652 0.50 348 9.97 962 35 26 947 654 949 696 0.50 304 9-9795 8 34 27 947 694 4 AO 949 740 44 0.50 260 9-97 954 33 39 5 4 3 28 2 9 947 734 947 774 40 4O 949 784 949 828 44 44 0.50 216 0.50 172 9-97 95 9.97 946 ' 32 i 2 3.9 0.5 04 0.3 7.8 i.o 0.8 0.6 3O 9.47814 4O 949 872 AA 0.50 128 9-97 942 30 3 11.7 1.5 1.2 0.9 31 947 854 949 9i6 0.50 084 9-97 938 29 4 15.6 2.O 1.6 1.2 32 9.47 894 4 949 960 44 0.50 040 9-97 934 28 5 19.5 2.5 2.0 1.5 33 947 934 4 9-5 4 44 0.49 996 9-97 930 27 b 23.4 3.0 24 1.8 34 P 947 974 948014 948 054 40 40 40 9.50 048 9.50092 9.50 136 44 44 44 049 952 049 908 0.49 864 9.97 926 9-97922 9.97918 * 26 2 5 24 9 27.3 3.5 2.8 2.1 31.2 4.0 3.2 24 35.1 4.5 3.6 2.7 37 948 094 40 9.50 180 44 049 820 9.97914 23 38 948 133 j9 9.50 223 4j> -49 777 9.97 910 22 39 9-4A 9-54 35 4* 0.45 650 9-97 497 4 44 i 3-7 3-6 3-5 17 18 19 9.51 883 9-5 I 9i9 9-5 1 955 3 36 36 9-54 390 9-54431 9-54 47 1 4 41 40 41 0.45 610 o-45 569 0-45 529 9-97 492 9.97488 9-97 484 5 4 4 t 43 42 2 3 4 7-4 7-2 7- 11. i 10.8 10.5 14.8 14.4 14.0 20 9.51 991 6 9-545*2 4O 0.45 488 9-97 479 40 5 6 22 2 21 6 21 O 21 22 9-52027 9.52063 36 16 9.54552 9-54 593 41 4O 0.45 448 0.45 407 9-97 475 9-97 47 5 A 39 38 8 25.9 25.2 24.5 29.6 28 8 28.0 23 9.52099 9-54 633 4O 0.45 367 9-97 466 C 37 Q 33-3 32-4 3*-5 24 9-52 135 ^ 9-54673 41 0-45 327 9-97 46i 36 25 9.52171 16 9-54 7 H 4 0.45 286 9-97457 4 35 26 9.52 207 9.54 754 0.45 246 9-97453 34 27 9.52 242 35 9-54 794 4 0.45 206 9-97 448 5 33 34 5 4 28 9-52 278 76 9.54835 4 1 A.O 0.45 165 9-97 444 4 32 I 3-4 0.5 0.4 29 9-52 3H o u ^6 9.54875 4O 0-45 * 25 9-97 439 3 1 2 6.8 1.0 0.8 30 9-5 2 35 7C 9.549I5 4O 0.45 085 9-97 435 30 3 10.2 1.5 1.2 3 1 32 33 34 9-52 385 9.52421 9-52456 9-52492 JJ 36 35 36 9-54955 9-54995 9-55035 9-55 75 4 o 40 40 40 0.45 045 0.45 005 0.44 965 0.44 925 9-97 430 9-97 426 9.97421 9.97417 4 5 4 c 29 28 27 26 4 6 8 13.6 2.0 1.6 17.0 2.5 2.0 20.4 3-0 2.4 23-8 3-5 2.8 27.2 4.0 3.2 3 9-52527 9-52 563 36 9-55 IJ 5 9-55 J 55 40 0.44 885 0.44 845 9.97412 9-97 408 4 25 24 9 30.6 4.5 3.6 37 9-52 598 35 76 9-55 195 4 4O 0.44805 9-97 403 5 23 38 9.52 634 0.44 765 9-97 399 22 39 9-5 2 669 35 16 9-55275 40 4 0-44 7 2 5 9-97 394 i> 21 4O 9-52 75 2C 9-553I5 1 0.44 685 9-97 390 c 2O 41 9.52 740 JJ 9-55 355 40 0.44 645 9.97 385 19 555 42 9-52 775 D 9-55 395 0.44 605 9.97 381 18 41 40 39 43 9.52811 36 9-55 434 0.44 566 9.97 376 17 o i 44 45 46 9.52 846 9.52 881 9.52916 35 35 9-55 474 9-55 5H 9-55 554 4 U 40 40 TO 0.44 526 0.44 486 0.44 446 9-97 372 9-97 367 9-97 363 4 5 4 16 15 i 2 3 4.1 4.0 3.9 12-3 12.0 II.7 20.5 20.0 19.5 28.7 28.O 27.3 47 48 9-52 95 1 9.52 986 35 7C 9-55 593 9-55 633 40 4 0.44 407 0.44 367 9-97 358 9-97 353 5 4 13 12 4 5 36.9 36.0 35.1 49 9.53021 9-55 673 2.Q 0-44 327 9-97 349 r II 50 9-53056 ^6 9-55 712 40 0.44 288 9-97344 IO 51 9-53092 9-55 752 70 0.44 248 9-97 340 : 9 444 52 53 9-53 126 9-53 161 35 9-55 79i 9.55831 40 0.44 209 0.44169 9-97 335 9-97 33 1 4 8 7 41 40 39 54 9-53 196 35 7C 9-55 870 39 40 0.44 130 9-97 326 5 6 o 5.1 5.0 4.9 55 9-5323I 9-55910 7Q 0.44 090 9-97 322 5 15.4 15.0 14.6 56 9-53 266 03 9-55 949 6? 0.44051 9.973I7 4 25.6 25.0 24.4 57 9-53301 35 9-55 989 4 O.44OII 9.97312 5 7 4 35-9 35-o 34-1 58 9-53 336 35 9.56028 39 0-43 972 9-97 308 4 2 59 9-53 37 7 = 9.56067 jy 4 o-43 933 9-97 33 4 I 60 9-53 405 9-5 6 107 0-43 893 9-97 299 L. Cos. d. L. Cot. c. d L. Tan. L. Sin. 1 d. ' P. P. 70' 440 20' / L, Sin. d, L, Tan, c, d, L, Cot, L, Cos, j d, P. P, 9-53 405 3C 9-56 107 3Q 0-43 893 9-97 299 e 6O I 2 3 4 I 8 9 9-53 440 9-53475 9-53 59 9-53544 9-53578 9-53613 9-53 647 9-53 682 9-53 7 l6 JJ 35 34 35 34 35 34 35 34 9.56 146 9.56 185 9.56 224 9.56 264 9-56 303 9.56 342 9.56 381 9.56 420 9-56459 39 39 40 39 39 39 39 39 -JQ 0.43 854 0.43815 0.43 776 o-43 736 0.43 697 0.43 658 0.43 619 0.43 580 0-43 54i 9-97 294 9-97 289 9.97 285 9.97 280 9-97 276 9.97271 9.97 266 9.97 262 9-97 2 57 5 4 5 4 5 5 4 5 59 58 57 56 55 54 53 5 2 5i i 2 3 4 6 7 40 39 38 4-0 3-9 3-8 8.0 7.8 7.6 I2.O 11.7 II.4 16.0 15.6 15.2 2O.O 19.5 19.0 24.0 23.4 22.8 28.0 27.3 26.6 10 9.53751 35 34 9-56498 jy -JQ 0-43 5 02 9-97 252 50 8 32.0 31.2 30.4 ii 12 13 14 15 16 J 7 18 19 9-53 785 9.53819 9-53 854 9-53 888 9-53922 9-53957 9.53991 9.54025 9-54059 J4 34 35 34 34 35 34 34 34 -JA 9.56537 9-56576 9-56615 9-56 654 9-56693 9.56 732 9.56771 9.56810 9.56 849 39 39 39 39 39 39 39 39 ^8 0-43 463 0.43 424 0.43 385 0-43 346 0-43 307 0.43 268 0.43 229 0.43 190 0.43 151 9-97 2 48 9-97 243 9.97 238 9-97 234 9-97 229 9-97 224 9.97 220 9-97 215 9.97 210 5 5 4 5 5 4 5 5 49 48 47 46 45 44 43 42 4i 9 2 3 4 36.0 35.1 34.2 37 35 34 3-7 3-5 3-4 7.4 7.0 6.8 I 1. 1 IO-5 IO.2 14.8 14.0 13.6 18.5 17.5 17.0 20 9.54093 j4 9-56 887 j 1Q 0-43 "3 9.97 206 5" 40 6 22.2 2I.O 2O.4 21 22 23 24 3 2 7 28 29 9.54127 9.54161 9.54 195 9.54 229 9.54 263 9.54 297 9-54331 9-54 365 9-54 399 o4 34 34 34 34 34 34 34 34 9.56926 9o6 965 9-57 4 9-57 042 9.57081 9.57 120 9-57 !5 8 9-57 197 9.57 235 jy 39 39 38 39 39 38 39 38 0.43 074 o-43 035 0.42 996 0.42 958 0.42 919 0.42 880 0.42 842 0.42 803 0.42 765 9.97 201 9-97 196 9-97 192 9.97 187 9.97 182 9-97 I7 8 9-97 1 73 9.97 168 9-97 l6 3 5 4 5 5 4 5 5 5 39 38 37 36 35 34 33 32 3i I 9 i 3 25-9 24.5 23.8 29.6 28.0 27.2 33-3 3i.5 3.6 33 5 4 3-3 0.5 0.4 6.6 i.o 0.8 9.9 1.5 1.2 132 20 i 6 30 9-54433 ,54 3 ? 9-57 274 jy 1& 0.42 726 9-97 X 59 C 30 s 16.5 2.5 2.O 3i 3 2 33 34 35 36 37 9-54 466 9-54 5 9-54 534 9-54 567 9.54 60 1 9.54 635 9.54 668 JJ 34 34 33 34 34 33 34 9.57312 9-57 35 1 9-57 389 9.57428 9-57 466 9-57 54 9-57 543 39 38 39 3 J 3 39 ^8 0.42 688 0.42 649 0.42 611 0.42 572 0.42 534 0.42 496 0.42 457 9-97 J 54 9.97 149 9-97 H5 9-97 HO 9-97 *35 9-97 J 3Q 9.97 126 5 4 5 5 5 4 5 29 28 2 7 26 2 5 24 23 6 8 9 19.8 3.0 2.4 23.1 3.5 2.8 26.4 4.0 3.2 29-7 4-5 3-6 38 39 9-54 7 02 9-54 735 33 1A. 9-57 5 Sl 9.57619 38 1Q 0.42 419 0.42 381 9-97 !2i 9.97 116 5 22 21 4O 9-54 769 o4 9-57 658 jy 78 0.42 342 9.97111 20 4i 42 43 44 45 46 47 48 49 9-54 802 9.54 836 9.54 869 9-54 93 9.54936 9-54 969 9-55003 9-55 036 9-55 069 JJ 34 33 34 33 33 34 33 33 11 9.57696 9-57 734 9-57 772 9.57810 9-57 849 9-57 887 9.5792? 9.57963 9.58001 38 38 38 39 38 38 38 38 ?8 0.42 304 0.42 266 0.42 228 0.42 190 0.42 151 0.42 113 0.42 075 0.42 037 0.41 999 9-97 I0 7 9 97 102 9.97097 9.97092 9.97 087 9.97 083 9.97078 9-97073 9.97 068 5 5 5 5 4 5 5 5 r 19 18 17 16 15 H 13 12 I I o i 2 3 4 5 555 40 39 38 4-0 3-9 3-8 12.0 11.7 11-4 2O.O 19.5 19.0 28.0 27.3 26.6 36.0 35.1 34.2 50 9.55 I02 jj -JA 9.58039 ?8 0.41 961 9.97 063 IO 544 5 1 52 53 54 55 56 3 59 9-55 U6 9.55 I6 9 9-55 202 9.55 23? 9-55 268 9-55 30i 9-55 334 9-55 367 9-55 400 J4 33 33 33 33 33 33 33 33 3^ 9.58077 9.5811? 9.58153 9.58191 9.58 229 9.58 267 9.58 304 9-58 342 9.58 380 38 38 38 38 38 37 38 38 ^8 0.41 923 0.41 885 0.41 847 0.41 809 0.41 771 0.41 733 0.41 696 0.41 658 0.41 620 9-97 59 9-97054 9.97 049 9-97 44 9-97 39 9-97 3? 9.97 030 9-97 02 I 9.97 020 5 5 5 5 4 5 5 5 C 9 8 7 6 5 4 3 2 I o 2 3 4 5 37 39 38 3.7 4.9 4.8 1 1. 1 14.6 14.2 18.5 24.4 23.8 25-9 34-i 33-2 33-3 60 9-55433 9.58418 0.41 582 9.97015 L, Cos, 1 d, L, Cot, |c.d. L, Tan, L, Sin. d, / P. P, 69' 441 r / L. Sin. d. L. Tan. c. d. L. Cot. L. Cos. d. P. P. 9-55 433 77 9.58418 77 0.41 582 9.97015 tr 60 x 9-55 466 9-58455 0.41 543 9.97010 59 2 3 9-55 499 9.55 532 33 33 9-58 493 9-58 53 1 38 0.41 507 0.41 469 9.97 005 9.97 ooi 4 58 57 38 37 36 4 9-55 564 32 9-58569 38 0.41 431 9.96 996 5 56 I 3-8 3-7 3-6 9-55 597 33 9.58 606 7 0.41 394 9.96991 5 55 2 7.6 7.4 7.2 6 9-55 630 33 9.58 644 8 0.41 356 9.96 986 5 54 3 11.4 ii. i 10.8 I 9 9-55 663 9-55 695 9-55 728 33 32 33 9.58681 9.58757 37 38 38 0.41 319 0.41 281 0.41 243 9.96981 9.96976 9.96971 5 5 53 52 4 I 7 15.2 14.8 14.4 19.0 18.5 18.0 22.8 22.2 21.6 26 6 2 29 30 30 29 30 29 30 29 30 29 30 29 29 30 29 29 30 29 29 29 2 9 30 29 29 29 29 29 29 29 29 29 29 29 29 29 28 29 29 29 28 29 29 29 28 29 28 9.62 785 35 35 35 36 35 35 35 35 35 34 35 35 35 35 35 35 34 35 35 35 35 34 35 35 34 35 34 35 35 34 35 34 35 34 35 34 35 34 34 35 34 34 35 34 34 35 34 34 34 34 35 34 34 34 34 34 34 34 34 34 0.37215 9.96 403 6 5 1 5 6 i 5 6 5 6 5 5 6 6 5 6 6 5 i 5 6 5 6 u 5 6 6 5 6 5 6 1 5 6 I 6 i 5 6 1 6 I 5 6 6 5 6 60 59 58 57 56 55 54 53 52 5i 50 49 48 47 46 45 44 43 42 4i 40 39 38 37 36 35 34 33 32 3i 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 U 13 12 II IO 9 8 7 6 5 4 3 2 O I 2 3 4 I 8 9 I 2 3 4 6 8 9 i i i 2 2 2 3 i i i 2 2 2 2 3 4 1 8 ' 36 35 34 3-6 3-5 3-4 7.2 7.0 6.8 0.8 10.5 10.2 4.4 14.0 13.6 8.0 17.5 17.0 1.6 21.0 20.4 5.2 24.5 23.8 8.8 28.0 27.2 2.4 31.5 30.6 30 29 28 3.0 2.9 2.8 6.0 5.8 5.6 9.0 8.7 8.4 2.O II. 6 II. 2 5.0 14.5 14.0 8.0 17.4 16.8 i.o 20.3 19.6 4.0 23.2 22.4 7.0 26.1 25.2 6 5 0.6 0.5 1.2 I.O 1.8 1.5 2.4 2.0 3.0 2. 5 3-6 3-o 4-2 3-5 4.8 4.0 5-4 4-5 9.59218 9-59 247 9o9277 9-59 37 9-59 336 9-59 366 9-59 396 9o9425 9-59455 9.62 820 9.62 855 9.62 890 9.62 926 9.62 961 9.62 996 9.63031 9.63 066 9.63 101 0.37 1 80 o-37 H5 0.37 no 0.37 074 -37 39 0.37 004 0.36 969 0-36 934 0.36 899 9.96 397 9.96 392 9.96 387 9-96 381 9.96 376 9.96 370 9.96 365 9.96 360 9-96 354 9-59 4*4 9-59 5 H 9-59 543 9-59 573 9-59 602 9.59 632 9.59 661 9-59 690 9-59 720 9-59 749 9-59 77* 9-63 135 0.36 865 9-96 349 9.63 170 9.63 205 9-63 240 9.63 275 9.63 310 9-63 345 9-63 379 9.63414 9.63 449 0.36 830 0.36 795 0.36 760 0.36 725 0.36 690 0.36 655 0.36 621 0.36586 0-3655 1 9-96 343 9-96 338 9.96 333 9.96 327 9.96 322 9.96316 9.96311 9.96 305 9.96 300 9.63 484 0.36 516 9.96 294 9.59 808 9-59 837 9-59 866 9-59 895 9-59 924 9-59954 9-59 983 9.60012 9.60041 9.63519 9-63 553 9.63 588 9.63 623 9.63 657 9.63 692 9.63 726 9.63 761 9.63 796 0.36481 0.36 447 0.36412 -3 6 377 0.36 343 0.36 308 0.36 274 0.36 239 0.36 204 9.96 289 9.96 284 9.96 278 9-96 273 9.96 267 9.96 262 9.96 256 9.96251 9.96 245 9.60 070 9.63 830 0.36 170 9.96 240 9.60099 9.60 128 9.60157 9.60 1 86 9.60215 9.60244 9.60 273 9.60 302 9-60331 9.63 865 9.63 899 9-63 934 9.63 968 9.64 003 9.64 037 9.64072 9.64 1 06 9.64 140 0-36 135 0.36 101 0.36 066 0.36 032 o-35 997 o-35 963 0.35 928 0.35 894 0.35 860 9.96 234 9.96 229 9.96 223 9.96 218 9.96 212 9.96 207 9.96 201 9.96 196 9.96 190 o 2 3 4 i c 2 3 4 5 666 36 35 34 3.0 2.9 2.8 9.0 8.8 8.5 15.0 14.6 14.2 2I.O 2O-4 i 27.0 26.2 25.5 33.0 32.1 31.2 5 5 35 34 3-5 3-4 IO.5 10.2 I 7 .5 I 7 .0 24-5 23.8 31.5 30.6 9.60 359 9-64I75 0.35 825 9.96 185 9.60388 . 9.60417 9.60 446 9.60 474 9.60 503 9.60532 . 9.60561 9.60589 9.60618 , 9.60 646 | 9.64 209 9.64 243 9.64 278 9.64312 9-64 346 9.64 381 9.64415 9.64 449 9.64 483 -35 79i -35 757 0.35 722 0.35 688 0-35 6 54 0.35 619 -35 585 o-3555i o-35 5*7 9.96 179 9.96 174 9.96 1 68 9.96 162 9.96 157 9.96151 9.96 146 9.96 140 9-96 135 29 29 28 29 28 29 28 29 28 28 9.64517 0-35 483 9.96 12 i 5i 52 53 54 3 GO 9.60675 I 9.60 704 9.60 732 9.60761 9.60 789 9.60818 9.60 846 9-6o 875 9.60 903 9-64 552 9.64 586 9.64 620 9.64 654 9.64 688 9.64 722 9.64 756 9.64 790 9.64 824 0.35 44* 0.354U 0.35 380 0.35 346 o.353i2 o-35 278 0.35 244 0.35 210 0-35 176 9.96 123 9.96 118 9.96 112 9.96 107 9.96 ioi 9.96095 9.96090 9.96 084 9-96079 9.96 073 9.60931 , 9.64858 0.35 142 L, Cos. d. L. Cot. c. d. L. Tan. L. Sin. d. ' P. P. 66' 444 24' / L. Sin. d. L, Tan, c. d. L, Cot, L, Cos, d, P.P. I 2 3 4 6 1 9 10 ii 12 13 H 15 16 17 18 19 20 21 22 23 24 25 26 2 29 3O 3i 3 2 33 34 35 36 3 39 4O 4i 42 43 44 45 46 47 48 49 50 5 1 52 53 54 55 56 57 58 59 6O 9.60931 29 28 28 29 28 28 28 29 28 28 28 28 28 28 28 28 29 27 28 28 28 28 28 28 28 28 2 7 28 28 28 27 28 28 27 28 28 27 28 27 28 27 28 27 28 27 28 27 27 28 27 27 27 28 27 27 27 27 28 27 27 9.64 858 34 34 34 34 34 34 34 34 34 33 34 34 34 34 33 34 34 33 34 34 33 34 34 33 34 33 34 33 34 33 34 33 34 33 34 33 "33 34 33 33 34 33 33 33 34 33 33 33 33 34 33 33 33 33 33 33 33 33 33 33 0.35 142 9.96 073 6 6 6 5 6 6 5 6 6 5 6 6 6 5 6 6 5 6 6 6 5 6 6 5 6 6 6 5 6 6 6 6 5 6 6 6 6 5 6 6 6 6 6 6 6 6 6 i 6 6 6 6 6 6 5 60 59 58 57 56 55 54 53 52 5 1 5O 49 48 47 46 45 44 43 42 4i 4O 11 37 36 35 34 33 3 2 3i 3O 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 H ".3 12 II 10 9 8 7 6 5 4 3 2 o 34 33 i 3-4 3-3 2 6.8 6.6 3 10.2 9.9 4 13-6 13-2 5 17.0 16.5 6 20.4 19.8 7 23.8 23.1 8 27.2 26.4 9 30.6 29.7 29 28 27 i 2.9 2.8 2.7 2 5.8 5.6 5.4 3 8.7 8.4 8.1 4 ii. 6 ii. 2 10.8 5 14.5 14.0 13.5 6 17.4 16.8 16.2 7 20.3 19.6 18.9 8 23.2 22.4 21.6 9 26.1 25.2 24.3 6 5 i 0.6 0.5 2 1.2 I.O 3 1.8 1.5 4 2.4 2.0 5 3- 2.5 6 3.6 3.0 7 4-2 3-5 8 4.8 4.0 9 5-4 4-5 9.60 960 9.60 988 9.61 016 9.61 045 9.61 073 9.61 101 9.61 129 9.61 158 9.61 1 86 9.64 892 9.64 926 9.64 960 9.64 994 9.65 028 9.65 062 9.65 096 9.65 130 9.65 164 0.35 108 0.35 074 0.35 040 0.35 006 0.34972 o-34 938 0.34 904 0.34 870 0.34 836 9.96 067 9.96 062 9.96056 9.96050 9.96045 9.96039 9.96 034 9.96 028 9.96 022 9.61 214 9.65 197 0.34 803 9.96017 9.61 242 9.61 270 9.61 298 9.61 326 9-6i 354 9.61 382 9.61411 9.61 438 9.61 466 9.65 231 9.65 265 9.65 299 9-65 333 9.65 366 9.65 400 9-65 434 9.65 467 9.65 501 0.34 769 0-34 735 0.34 701 0.34 667 o.34 634 0.34600 0.34 566 o-34 533 0.34 499 9.96011 9.96 005 9.96000 9-95 994 9.95 988 9-95 982 9-95 977 9-95 97 1 9-95 965 9.61 494 9-65 535 0-34 465 9.95 960 9.61 522 9.61 550 9.61 578 9.61 606 9.61 634 9.61 662 9.61 689 9.61 717 9.61 745 9.65 568 9.65 602 9.65 636 9.65 669 9-65 73 9.65 736 9.65 770 9.65 803 9-65 837 0-34 432 0-34 398 o-34 3 6 4 0-34331 0.34 297 0.34 264 0.34 230 0.34 197 0.34 163 9-95 954 9-95 948 9-95 942 9-95 937 9-95 93 1 9-95 925 9-95 920 9.95914 9.95 908 9.61 773 9.65 870 0.34 130 9-95 902 9.61 800 9.61 828 9.61 856 9.61 883 9.61 911 9.61 939 9.61 966 9.61 994 9.62 O2I 9.65 904 9-65 937 9.65971 9.66 004 9.66038 9.66071 9.66 104* 9.66 138 9.66 171 0.34 096 0.34 063 0.34029 0-33 996 0.33 962 0.33 929 0.33 896 0.33 862 0.33 829 9-95 897 9.95 891 9-95 885 9-95 8 79 9-95 873 9-95 868 9.95 862 9-95 856 9-95 850 9.62 049 9.66 204 0-33 796 9-95 844 9.62 076 9.62 IO4 9.62 131 9.62 159 9.62 1 86 9.62 214 9.62 241 9.62 268 9.62 296 9.66 238 9.66 271 9.66 304 9-66 337 9.66371 9.66 404 9.66 437 9.66 470 9.66 503 0.33 762 o-33 7 2 9 0.33 696 0.33 663 0.33 629 o-33 596 0-33 563 o-33 530 0-33 497 9-95 839 9^95 833 9-95 827 9.95821 9-95 815 9.95 810 9-95 804 9-95 798 9-95 792 665 34 33 34 ? 2.8 2.8 3.4 1 8.5 8.2 10.2 ; 14.2 13.8 17.0 1 19.8 19.2 23.8 4 25.5 24.8 30.6 g 31.2 30.2 9.62 323 9-66 537 o-33 463 9.95 786 9.62 350 9.62 377 9.62 405 9.62 432 9.62459 9.62 486 9.62513 9.62 541 9.62 568 9.66 570 9.66 603 9.66 636 9.66 669 9.66 702 9-66 735 9.66 768 9.66 80 1 9.66 834 0-33 430 0-33 397 0-33 364 0.33331 0.33 298 0-33 265 0.33 232 0-33 199 0.33 166 9-95 78o 9-95 775 9-95 7 6 9 9-95 7 6 3 9-95 757 9-95 75 1 9-95 745 9-95 739 9-95 733 9-62 595 9.66 867 0-33 133 9.95 728 L, Cos, d. L, Cot. c, d. L, Tan, L. Sin, d. r p, p, 65' 25 445 1 L. Bm. d, L, Tan, c. d. L, Cot. L, Cos, d, P. P. 9.62 505 27 9.66 867 27 0.33 133 9-95 728 6 6O I 2 3 4 8 9 9.62 622 9.62 649 9.62 676 9.62 703 9.62 730 9.62 757 9.62 784 9.62 8n 9.62838 27 27 27 2 7 27 9.66 900 9-66 933 9.66 966 9-66 999 9.67032 9.67 065 9.67 098 9.67 131 9-67 163 33 33 33 33 33 33 33 o 2 0.33 100 0.33067 0.33034 0.33001 0.32 968 0.32935 0.32 902 0.32 869 0.32 837 9-95 722 9.95 716 9.95 710 9-95 74 9-95 698 9-95 692 9-95 686 9.95 680 9-95 674 6 6 6 6 6 6 6 59 57 56 55 54 53 52 5i I 2 4 5 33 32 3-3 3-2 6.6 6.4 9-9 9-6 13.2 12.8 16.5 16.0 to 9.62 865 27 9.67 196 T? 0.32 804 9.95 668 5O 6 19.8 19.2 ii 12 13 "4 IS 16 18 19 9.62 892 9.62918 9.62 945 9.62972 9.62 999 9.63 026 9.63052 9.63079 9.63 106 27 2 7 27 27 26 27 27 9.67 229 9.67 262 9-67 293 9-67 327 9-67 360 9-67 393 9.67 426 9.67458 9.67491 33 33 32 33 33 32 1 1 0.32771 0-32 738 0.32 705 0.32 673 0.32 640 0.32 607 0.32 574 0.32 542 0.32 509 9-95 663 9-95 657 9-95651 9.95 6 45 9-95 639 9-95 633 9.95 627 9.95 621 9.95615 6 6 6 6 6 49 48 47 46 45 44 43 42 4i 8 9 2 23.1 22.4 26.4 25.6 29.7 28.8 27 26 2.7 2.6 c A c 2 20 9-63 133 */ 26 9.67 524 0.32476 9.95 609 6 40 3 8.1 7.8 21 22 2 3 24 25 26 27 28 29 9-63 159 9.63 1 86 9-63213 9.63 239 9.63 266 9-63 292 9-63 3*9 9-63 345 9-63 372 27 26 26 9-67 556 9.67 589 9.67 622 9-67 654 9.67 687 9.67 719 9.67 752 9-67 785 9.67817 33 3 2 33 32 33 77 0.32 444 0.32411 0.32 378 0.32 346 0.32313 0.32 281 0.32 248 0.32215 0.32 183 9.95 603 9-95 597 9-95 59i 9-95 585 9-95 579 9-95 573 9-95 567 9-95 56i 9-95 555 6 6 Q 6 6 6 5 39 38 37 36 35 34 33 32 4 8 9 10.8 10.4 J 3-5 !3.o 16.2 15.6 18.9 18.2 21.6 2O.8 24.3 23.4 3O 9-63 398 27 9.67 850 12 0.32 150 9-95 549 6 30 765 3 1 32 33 34 35 36 37 38 39 9-63 425 9.63451 9.63 478 9.63 504 9-63 53 1 9-63 583 9.63610 9.63 636 *l 26 2 7 2 7 26 26 26 26 9.67 882 9.67915 9.67 947 9.67 980 9.68012 9.68 044 9.68077 9.68 109 9.68 142 32 32 33 0.32 118 0.32 085 0.32053 0.32 020 0.31 988 0.31 956 0.31 923 0.31 891 0.31 858 9-95 543 9-95 537 9-95 53 1 9-95 525 9-955*9 9.955*3 9-95 57 9-95 5 9-95 494 6 6 6 6 6 6 6 5 29 28 27 26 25 24 23 22 21 i 2 3 4 I 9 0.7 0.6 0.5 1.4 1.2 1.0 2.1 1.8 1.5 2.8 2.4 2.O 3-5 3-o 2.5 4.2 3.6 3.0 4-9 4-2 3-5 5.6 4.8 4.0 6-3 5-4 4-5 4O 9.63 662 27 9.68 174 12 0.31 826 9-95 488 6 2O 42 A.1 9.63 689 9-63 7*5 06^ 7J.I 9.68 206 9.68 239 Q 68 271 33 32 0.31 794 0.31 761 0.11 720 9-95 482 9-95 476 Q. ^ 9-74 673 0.25 327 9.94112 50 7 21.0 20.3 16.1 ii 12 13 4 15 ID 19 9.68 807 9.68 829 9.68 852 9.68 875 9.68 897 9.68 920 9.68 942 9.68 965 9.68 987 22 23 22 2} 9-74 702 9-74 732 9-74 7 02 9.74 791 9.74 821 9-74851 9.74 880 9.74910 9-74 939 30 30 29 30 30 30 29 JO 0.25 268 0.25 238 0.25 209 0.25 179 0.25 149 0.25 1 20 0.25 090 0.25 061 9-94 105 9-94 098 9-94 090 9-94 083 9-94 076 9-94 069 9.94 062 9-94055 9-94 048 8 7 7 7 7 7 7 7 49 48 47 46 45 44 43 42 8 24.0 23.2 18.4 9 27.0 26.1 20.7 22 8 7 I 2.2 O.8 0.7 2 4.4 1.6 1.4 366 2/1 f T 20 9.69010 22 9-74 969 2Q 0.25 031 9.94041 4O 4 8.8 3.2 2.8 21 22 23 I 24 s 27 28 29 9.69 032 9.69055 9.69 077 9.69 loo 9.69 122 9.69 167 9.69 189 9.69 212 9.74 998 9.75 028 9.75 058 9-75 087 9-75 JI 7 9.75 146 9-75 J 7 6 9-75 205 9-75 235 30 3 29 30 30 29 0.25 002 0.24 972 0.24 942 0.24913 0.24 883 0.24 854 0.24 824 0.24 795 0.24 765 9-94 034 9.94027 9.94 020 9.94012 9-94 005 9-93 998 9-93 99i 9-93 984 9-93977 7 I 7 7 7 7 39 38 37 36 35 34 3i 5 1 1.0 4.0 3.5 6 13.2 4.8 4.2 7 15.4 5.6 4.9 8 17.6 6.4 5.6 9 19.8 7.2 6.3 30 9.69 234 22 9.75 264 30 0.24 736 9-9397 7 30 3i 32 33 34 35 36 37 38 39 9.69 256 9-69 279 9.69 301 9-69 345 9.69 368 9.69 390 9.69412 9-69 434 23 22 22 23 22 22 22 22 9-75 294 9.75 323 9-75 353 9-75 382 9.754H 9-75441 9-75 47 9-75 5 9-75 529 29 29 29 29 30 2Q 0.24 706 0.24 677 0.24 647 0.24618 0.24 589 0.24559 0.24 530 0.24 500 0.24471 9-93 963 9-93 955 9-93 948 9-93 94i 9-93 934 9-93 927 9-93 920 9.93912 9-93 905 8 7 7 7 7 8 7 7 29 28 27 26 25 24 22 21 8 8 30 29 ? i-9 i-8 2 5-6 5-4 ' 13.1 12.7 40 9.69 456 9-75 558 0.24 442 9-93 898 / 20 J 16.9 16.3 4i 42 43 44 2 47 48 49 9.69 479 9.69 501 9.69 523 9-69 545 9.69 567 9.69 589 9.69611 9-69 633 9-69 655 22 22 22 22 22 22 9-75 588 9.75617 9-75 647 9.75 676 9-75 75 9-75 735 9.75 764 9-75 793 9-75 822 29 30 29 29 29 JQ 0.24 412 0.24 383 0.24 353 0.24 324 0.24 295 0.24 265 0.24 236 0.24 207 0.24 178 9.93 891 9-93 884 9-93 876 9-93 869 9.93 862 9-93 855 9-93 847 9.93 840 9-93 833 1 7 7 7 8 7 7 19 18 17 16 15 13 12 II I 20.6 19.9 24.4 23.6 I 28.1 27.2 7 7 30 29 5O 9-69 677 22 9-75 852 2Q 0.24 148 9.93 826 IO o 52 53 54 55 56 $ 59 9.69 699 9.69721 9-69 743 9-69 7 6 5 9.69 787 9.69 809 9.69 831 9-69 853 9.69 875 22 22 22 22 22 22 22 22 9-75 881 9.75910 9-75 939 9-75 969 9-75 998 9.76027 9.76056 9.76086 9.76115 29 29 29 29 30 2Q 0.24 119 0.24 090 0.24061 0.24031 0.24002 0-23 973 0.23 944 0.23914 0.23 885 9.93819 9.93811 9.93 804 9-93 797 9-93 ~ 9-93 7 9-93 775 9-93 7^ 9 93 76 8 7 7 8 7 7 { 9 8 7 6 5 4 3 2 I 2 64 2 ' 10.7 10.4 1 15-0 H-5 7 19-3 1 8.6 5 23.6 22.8 7 27.9 26.9 6O 9.69 897 9-76 144 0.23 856 9-93 753 L. Cos. d. L. Cot. c, d. L. Tan. L. Sin. d, f P, P, R'M'D SCRV. 29 60' 450 30' / L, Sin, d. L, Tan. c, d, L. Cot. L. Cos. d, p, p, o 9.69 897 22 9.76 144 2Q 0.23 856 9-93 753 7 6O I 2 3 4 i 1 9 9.69919 9.69 941 9.69 963 9.69 984 9.70006 9.70028 9.70 050 9.70072 9.70093 22 22 21 22 22 22 22 21 22 9.76173 9.76 202 9.76231 9.76261 9.76 290 9.76319 9.76348 9-7 6 377 9.76 406 29 29 30 2 9 29 29 29 29 2Q 0.23 827 0.23 798 0.23 769 0-23 739 0.23 710 0.23 68 1 0.23 652 0.23 623 0.23 594 9-93 746 9-93 738 9-93 73i 9-93 724 9-93 7 1 7 9-93 79 9-93 72 9.93695 9.93 687 8 7 7 7 8 59 58 57 56 55 54 53 5 2 5i 30 29 28 I 3.0 2.9 2.8 2 6.0 5.8 5.6 3 9-0 8.7 8.4 4 I2.O II. 6 II. 2 5 15.0 14.5 14.0 IO 9.70115 22 9-76435 20 0.23 565 9.93 680 7 5O 6 18.0 17.4 i.6.8 ii 12 J 3 H 15 16 *7 18 19 9.70137 9.70159 9.70 180 9.70 202 9.70 224 9.70 245 9.70267 9.70 288 9.70 310 22 21 22 22 21 22 21 22 22 9.76 464 9-76493 9.76522 9-7 6 55 J 9-76 580 9.76 609 9.76 639 9.76 668 9.76 697 29 29 29 29 29 30 29 29 28 0.23 536 0.23 507 0.23 478 0.23 449 0.23 420 0.23391 0.23 361 0.23 332 0.23 303 9-93 673 9-93 665 9-93 658 9-93 650 9-93 643 9-93 636 9.93 628 9-93 621 9.93614 8 7 8 7 7 8 7 8 49 48 47 46 45 44 43 42 4i 8 24.0 23.2 22.4 9 27.0 26.1 25.2 22 21 I 2.2 2.1 2 4.4 4 .2 20 9-7 332 21 9.76 725 2Q 0.23 275 9.93 606 7 4O 3 6.6 6.3 21 22 23 24 2 5 26 2 7 28 29 9-7 353 9-7 375 9.70 396 9.70418 9-7 439 9.70461 9.70482 9.70 504 9-7 525 22 21 22 21 22 21 22 21 22 9-76 754 9.76 783 9.76 812 9.76841 9.76870 9.76 899 9.76928 9.76957 9.76 986 29 29 29 29 29 29 29 29 2Q 0.23 246 0.23217 0.23 1 88 0.23 159 0.23 130 0.23 101 0.23072 0.23 043 0.23014 9-93 599 9-93 59i 9-93 584 9-93577 9-93 569 9-93 562 9-93 554 9-93 547 9-93 539 8 7 7 8 7 8 39 38 37 36 35 34 33 3 2 3i 4 8.8 8.4 5 n.o 10.5 6 13.2 12.6 7 15.4 14.7 8 17.6 16.8 9 19.8 18.9 30 9-70 547 21 9.77015 20 O.22 985 9-93 532 3O 8 7 3i 32 33 34 35 36 37 38 39 9.70 568 9.70 590 9.70611 9-7 6 33 9.70 654 9.70 675 9.70 697 9.70718 9-7 739 22 21 22 21 21 22 21 21 22 9.77 044 9.77073 9.77 101 9-77 J 3 9-77 159 9.77 1 88 9.77217 9-77 246 9-77 274 29 28 29 29 29 29 29 28 2O O.22 956 O.22 927 0.22 899 O.22 870 0.22 841 O.22 8l2 0.22 783 0.22 754 O.22 726 9.93525 9-93 5 1 7 9-93 5 10 9-93 5 2 9-93 495 9-93 487 9-93 48o 9-93472 9-93 465 8 7 8 8 7 8 29 28 27 26 2 5 24 23 22 21 i 0.8 0.7 2 1.6 1.4 3 2.4 2.1 4 3.2 2.8 5 4-o 3-5 6 4.8 4.2 7 5-6 4-9 8 6.4 5.6 9 72 6.3 40 9.70 761 21 9-77 303 2Q O.22 697 9-93457 2O 41 42 9.70 782 9.70803 21 21 9-77 332 9.77361 29 29 0.22 668 O.22 639 9-93 45 9-93 442 8 7 19 18 43 44 45 46 % 49 9.7 824 9.70 846 9.70 867 9.70 888 9.70 909 9.70931 9.70952 22 21 21 21 22 21 21 9-77 39 9.77418 9-77 447 9.77476 9-77 55 9-77 533 9-77 562 28, 29 2 9 29 28 29 2Q O.22 582 0-22553 O.22 524 0.22495 0.22467 O.22 438 9-93 435 9-93427 9-93 420 9.93412 9-93 405 9-93 397 9-93 390 8 8 7 8 8 I 7 16 15 H 13 12 II 777 30 29 28 o 5O 9-70973 21 9-77 59i 28 O.22 409 9-93 382 7 10 2.1 2.1 2.O f\ A f\ o f\ r\ 5 1 52 53 54 H 57 58 59 9.70 994 9.71015 9.71 036 9.71058 9.71 079 9.71 loo 9.71 121 9.71 142 9.71 163 21 21 22 21 21 21 21 21 21 9.77619 9-77 648 9.77677 9-77 76 9-77 734 9-77 763 9-77 79i 9.77 820 9.77 849 29 29 29 28 29 28 29 29 28 0.22 381 O.22 352 0.22 323 O.22 294 O.22 266 0.22 237 O.22 209 O.22 l8o ,O.22 151 9-93 375 9-93 367 9-93 36o 9-93 352 9-93 344 9.93 337 9-93 329 9-93 322 9-93 3*4 8 7 8 8 7 8 8 7 9 8 7 6 5 4 3 2 I ' t 10.7 10.4 10.0 > 15.0 14.5 14.0 4 19.3 1 8.6 1 8.0 5 23.6 22.8 22.0 27.9 26.9 26.0 60 9.71 184 9.77877 O.22 123 9-93 37 O L, Cos, d. L, Cot, c, d. L. Tan, L. Sin, d, f P, P, 1 59' 31 451 f L. Sin. d. L. Tan, c. d. L. Cot, L. Cos. d. p. p. 9.71 184 o i 9.77877 20 O.22 123 9-93 37 8 60 I 2 3 4 i 8 9 9.71 205 9.71 226 9.71 247 0.71 289 9.71 310 9-7 : 33i 9-7.1 35- 9-7 1 373 21 21 21 21 21 21 21 21 9-77933 9-77963 9.77992 9.78020 9.78049 9.78077 9./8 135 29 28 28 29 28 29 28 0.22 094 O.22065 0.22037 0.22 008 0.21 980 0.21 951 0.21 923 O.2I 894 O.2I 865 9-93 299 9.93 291 9.93 284 9-93 276 9.93 269 9-93 261 9-93 253 9-93 246 9-93 238 8 7 8 I 8 8 g 59 58 57 56 55 54 53 52 5 1 29 28 i 2.9 2.8 2 5 .8 5 .6 3 8.7 8.4 4 n. 6 ii. 2 ^ 145 H-o IO 9.7i 393 21 9.78 163 2Q 0.21 837 9-93 230 5O 6 17.4 1 6.8 ii 12 13 H I S 16 *7 18 19 0.71 414 9-/i 435 9-7 1 45 6 9.71 477 9.71 498 9.71 519 9-7 1 539 9.71 560 9.71 581 21 21 21 21 21 20 21 21 21 9.78 192 9.78 220 9.78 249 9.78277 9.78 306 9-78334 9-78 363 9.78391 9.78419 28 29 28 2 9 28 2 9 28 28 Q 0.21 808 O.2I 780 0.21 75 I 0.21 723 O.2I 694 0.21 666 O.2I 637 O.2I 609 O.2I ^Sl 9-93 223 9-932I5 9-93 207 9.93 200 9-93 192 9-93 '84 9-93 i/7 9-93 l6 9 9-93 161 8 8 7 8 8 7 8 8 49 48 47 46 45 44 43 42 4i 7 20.3 19.6 8 23.2 22.4 9 26.1 25.2 21 20 I 1 2.1 2.0 2 4-2 4.0 20 9.71 602 2O 9.78448 28 0.21 552 9-93 ! 54 g 40 3 6 -3 6 -o 21 22 23 24 2 5 26 27 28 2 9 9.71 622 9-7 1 6 43 9.71 664 9.71 685 9-7 1 75 9.71 726 9-7 1 747 9.71 767 9.71 788 21 21 21 2O 21 21 2O 21 21 9.78476 9-/8 505 978533 9.78562 9.78 590 9.78618 9.78 647 9-78 675 9.78 704 29 28 2 9 28 28 2 9 28 29 28 O.2I 524 0.21 495 0.21 467 0.21 438 O.2I 410 O.2I 382 0.21 353 0.21 325 O.2I 296 9-93 M6 9-93 138 9-93I3 1 9-93 123 9-93II5 9-93 IQ 8 9-93 ioo 9-93 092 9-93 084 8 7 8 8 7 8 8 8 39 38 37 36 35 34 33 32 3i 4 8.4 8.0 5 10.5 10.0 6 12.6 12.0 7 14.7 14.0 8 1 6.8 1 6.0 9 18.9 18.0 30 9.71 809 2O 9-78/32 28 0.21 268 9-<>377 / 8 30 8 7 31 32 33 34 3 37 38 39 9.71 829 9.71 850 9.71 870 9.71 891 9.71911 9.71 932 9.71952 9-71 973 9.71 994 21 2O 21 2O 21 2O 21 21 2O 9.78 760 9-78 789 9.78817 9.78 845 9.78874 9.78 902 9.78 930 9-78 959 9.7898- 29 28 28 29 28 28 29 28 28 O.2I 240 0.21 211 O.2I 183 0.21 155 O.2I 126 O.2I 098 0.21 070 0.21 041 O.2I OI3 9-93 069 9.93061 9-93053 9.93 046 9-93 038 9-93 30 9.93022 9.93014 9.93007 8 8 7 8 8 8 8 I 29 28 27 26 25 24 23 22 21 i 0.8 0.7 2 1.6 1.4 3 2.4 2.1 4 3-2 2.8 5 4-o 3-5 6 4.8 4.2 7 5- 6 4-9 8 6.4 5.6 9 7.2 6.3 40 9.72014 2O 9.79015 28 0.20 985 9-92 999 8 2O 4i 42 9.72034 9.72055 21 9-79 043 9.79072 29 _Q 0.20957 O.20 928 9.92991 9-92 983 8 19 18 43 44 45 46 47 4 8 49 9.72075 9.72 096 9.72 116 9-72 137 9-/2 157 9.72177 9.72 198 21 2O 21 20 2O 21 2O 9.79 100 9-79 128 9.79 156 9-79 i*>5 9.79213 9-79 241 9.79 269 28 28 29 28 28 28 ?8 O.2O 9OO O.2O 872 0.20 844 0.2O 815 0.20 787 0.20 7=59 0.20731 9-92 97 6 9.92 968 9.92 960 9.92952 9.92 944 9.92936 9.92929 7 8 8 8 8 8 8 7 16 J 5 M 13 12 II 8 8 8 30 29 28 1.9 1.8 1.8 5O 9.72 218 2O 9-79 297 2Q O.2O 703 9.92921 8 IO 2 5- 6 5-4 5-2 o A or 8 S 5i 52 53 54 H 57 58 59 9.72 238 9.72259 9.72 279 9.72 299 9.72320 9.72 340 9.72 360 9.72 381 9.72401 21 20 2O 21 2O 2O 21 2O 2O 9-79 326 9-79354 9.79 382 9.79410 9-79438 9.79466 9-79 495 9-795 2 3 9-79 55 1 28 28 28 28 28 29 28 28 28 O.2O 674 O.2O 646 6.20 618 O.2O 590 O.20 562 0.20 534 0.20 505 0.20477 0.20 449 9.92913 9-92 95 9-92 897 9.92 889 9.92881 9.92 874 9.92 866 9.92 858 9 92 850 8 8 8 8 7 8 8 8 8 9 8 7 6 5 4 3 2 I 3 13.1 12.7 12.2 ? 16.9 16.3 15.8 5 20.6 19.9 19.2 24.4 23.6 22.8 7 28.1 27.2 26.2 6O "72421 9-79579 0.20421 9.92 842 o L. Cos. d. L. Cot. c. d. L. Tan. L. Sin. d. / p. p. 58 452 32' 1 L.Sln, d, L, Tan, c, d. L, Cot, L, Cos, d, | P, P, o 9.72421 20 9-79579 ?8 0.20421 9.92 842 8 6O I 9.72441 9-79 607 -78 0.20 393 9.92 834 8 S9 2 9.72461 9-79 635 28 0.20 365 9.92 826 8 58 3 9.72482 9-79 663 o o 0.20 337 9.92818 c 57 u 4 9.72 502 9-79 691 "?& O.2O 309 9.92 810 56 29 28 27 5 9.72522 20 9.79719 28 O.2O 28l 9.92 803 8 55 i 2.9 2.8 2.7 6 9.72 542 9-79 747 0.20 253 9-92 793 Q 54 2 5.8 5.6 5.4 8 9.72562 9.72 582 20 9-79 77 6 9.79 804 29 28 Q 0.20 224 O.2O 196 9.92 787 9.92 779 8 8 53 52 3 4 8.7 8.4 8.1 ii. 6 ii. 2 10.8 9 9.72 602 20 9-79 832 28 0.20 168 9.92 771 8 14.5 14.0 13.5 IO 9.72 622 21 9.79 860 28 O.2O 140 9.92 763 8 50 20 7 19 6 189 ii 12 13 9.72 643 9.72 663 9.72 683 2O 2O 9.79 888 9.79916 9-79 944 28 28 28 0.20 112 O.20O84 O.2OO56 9-92 753 9.92 747 9-92 739 8 8 8 49 48 47 8 9 23.2 22.4 21.6 26.1 25.2 24.3 14 9.72 703 9-79 972 ~0 O.2OO28 9.92 731 46 5 9-72 723 9.80000 ~Q o. 20 ooo 9.92 723 45 16 9-72 743 9.80028 _o 0.19972 9.92715 44 17 18 9-72 763 9.72783 2O 9.80056 9.80 084 25 28 08 0.19944 0.19 916 9.92 707 9.92 699 8 43 42 i 21 20 19 2.1 2.O 1.9 1 '9 9.72 803 2O 9.80 112 28 0.19888 9.92691 8 2 4.2 4.0 3.8 20 9.72 823 2O 9.80 140 28 0.19 860 9.92 683 8 4O 3 6.3 6.0 5.7 1 21 9-72 843 9.80 1 68 0.19832 9.92675 SQ 4 8-4 8.0 7.6 22 23 9.72863 9-72 883 20 9.80 195 9.80 223 2 V 28 0.19 805 0.19777 9.92 667 9.92659 8 38 37 6 10.5 10.0 9.5 12.6 I2.O II.4 24 25 26 9.72 902 9.72922 9.72 942 19 20 2O 9.80 251 9.80 279 9.80 307 2o 28 28 28 0.19 749 0.19 721 0.19693 9.92651 9.92 643 9-92 635 00 OO O 36 35 34 8 9 14.7 14.0 13.3 16.8 16.0 15.2 18.9 18.0 17.1 27 9.72962 9-8o 335 ?8 0.19665 9.92627 33 28 9.72982 9.80 363 _o 0.19637 9.92 619 ^2 29 9.73002 2O 9.80391 28 0.19 609 9.92 611 8 30 9.73022 9.80419 28 0.19 581 9-92 603 Q 30 987 3 1 3 2 9.73041 9.73061 20 9.80 447 9.80 474 2 7 0-19553 0.19526 9-9 2 593 9.92 587 8 29 28 i 2 0.9 0.8 0.7 1.8 1.6 1.4 33 9.73081 9.80 502 2 8 0.19498 9-92 579 8 27 s 2-7 2. 4 2.1 34 9.73 101 9.80 530 Q 0.19 470 9.92571 Q 26 4 3.6 3.2 2.8 35 9-73 121 9-8o 558 ?8 0.19442 9-92 563 o 25 5 4-5 4-0 3-5 36 9.73 140 1 9 9.80 586 _0 0.19 414 9-92 553 24 6 5.4 4.8 4.2 38 9-73 1 60 9.73 1 80 20 20 9.80 614 9.80 642 28 0.19 386 0.19358 9.92546 | o 9-92 538 1 * 23 22 8 6.3 5.6 4.9 7.2 6.4 5.6 39 9-73 200 9.80 669 28 0.19331 9-92 530 8 21 9 8.1 7.2 6.3 4O 9.73219 9.80 697 28 0.19303 9.92 522 8 20 41 9-73 239 9.80 725 08 0.19275 9.92514 IQ 42 9-8o 753 ?Q 0.19247 9.92 506 18 Q 71278 1 9 Q 8O 78l O IQ 2IQ 44 9-73 298 20 9.80 808 2 7 _0 0.19 192 9.92 490 8 1 7 16 9-73 3'8 20 9.80 836 _o O.I9 164 9.92 482 15 46 9-73 337 I 9 9.80 864 28 O.I9 136 9-92 473 9 14 47 9-73 357 9.80 892 0.19 108 9.92 465 n ft 8 7 48 49 9-73377 9-73 396 19 9.80919 9.80 947 28 28 0.19081 0.19053 9.92457 9.92 449 8 12 ii 29 28 28 SO 9.73416 IQ 9.80 975 28 0.19025 9.92441 8 10 T 1.8 1.8 2.0 51 9-73 435 9.81 003 0.18997 9.92433 9 2 5.4 5.2 6.0 52 53 54 55 9-73453 9-73474 9-73 494 9-73 5'3 19 20 19 2O 9.81 030 9.81 058 9.81 086 9.81 113 27 28 28 27 28 0.18970 0.18942 0.18914 0.18887 9-92423 9.92416 9.92 408 9.92 400 9 8 8 8 8 7 6 5 3 4 9.1 8.8 10.0 12.7 12.2 14.0 16.3 15.8 18.0 19.9 19.2 22.O 23.6 22.8 26.O & 9-73 533 9.81 141 28 0.18859 9.92 392 4 I 27.2 26.2 57 9-73552 1 9 9.81 169 0.18831 9.92 384 3 8 58 9-73572 9.81 196 27 0.18804 9.92 376 2 59 9-73591 1 9 9.81 224 28 0.18 776 9.92 367 1 i 60 9.73611 9.81 252 0.18748 9-92 359 L, Cos, d, L, Cot, |c, d. L. Tan, L, Sin. d, t P, P, 57 33' 453 / L, Sin, d, L, Tan, c, d. L, Cot. L, Cos, d. p.p. 9.73611 IQ 9.81 252 27 o.i 8 748 9-92 359 8 6O I 2 3 4 I 8 9 9-73 6 3 9-73 6 5 9-73 669 9-73 689 9-73 78 9-73 727 9-73 747 9-73 766 9-73 7 8 5 2O 19 2O 19 19 2O 19 19 2O 9.81 279 9.81 307 9-8i 335 9.81 362 9.81 390 9.81418 9.81 445 9-8 1 473 9.81 500 28 28 27 28 28 27 28 27 28 0.18 721 0.18693 o.i 8 665 0.18638 0.18 610 0.18582 o-i8555 0.18 527 0.18 500 9.92351 9-92 343 9-92 335 9-92 326 9.92318 9.92310 9.92 302 9.92 293 9.92 285 8 8 9 8 8 8 9 8 8 51 D 8 57 56 55 54 53 5 2 5 1 28 27 i 2.8 2.7 3 84 11 4 ii. 2 10.8 5 '4-o 13-5 6 16 8 16 2 IO 9-73 805 IQ 9.81 528 28 0.18 472 9.92 277 8 50 7 19.6 18.9 ii 12 13 J 4 15 16 J 7 18 19 9-73^4 9-73 843 9-73 863 9-73 882 9.73901 9-73921 9-73 940 9-73 959 973978 19 2O 19 19 20 19 19 19 IQ 9-8i 55 6 9.81 583 9.81 611 9.81 638 9.81 666 9.81 693 9.81 721 9.81 748 9.81 776 11 27 28 27 28 27 28 27 0.18444 0.18417 0.18389 0.18362 0.18334 0.18307 o.i 8 279 0.18 252 o.i 8 224 9.92 269 9.92 260 9.92 252 9.92 244 9-92 235 9.92 227 9.92219 9.92211 9.92 202 9 8 8 9 8 8 8 9 8 49 48 47 46 45 44 43 42 4i 8 22.4 21.6 9 25.2 24.3 20 19 18 i 2.0 1.9 1.8 2 4.0 3.8 3.6 2O 9-73997 2O 9.81 803 28 0.18 197 9.92 194 g 4O 3 6.0 5.7 5.4 21 22 23 24 2 5 26 2 7 28 29 9.74017 9.74036 9-74055 9.74 074 9-74 093 9.74H3 9-74 132 9-74I5I 9.74 170 19 19 19 19 2O 19 19 19 IQ 9.81 831 9.81 858 9.81 886 9.81913 9.81 941 9.81 968 9.81 996 9.82023 9.82 051 27 28 27 28 2 7 28 2 7 28 27 0.18 169 0.18 142 0.18 114 0.18087 o.i 8 059 o.i 8 032 0.18004 0.17977 0.17949 9.92 186 9.92 177 9.92 169 9.92 161 9-92 152 9.92 144 9.92 136 9.92 127 9.92119 9 8 8 9 8 8 9 8 8 39 38 37 36 35 34 33 3 2 3i 4 8.0 7.6 7.2 5 10.0 9.5 9.0 6 12.0 11.4 10.8 7 14.0 13.3 12.6 8 16.0 15.2 14.4 9 18.0 17.1 16.2 30 9.74 189 IQ 9.82078 */ 28 0.17922 9.92 in 30 9 8 3i 32 33 34 11 37 38 39 9.74208 9-74 227 9.74 246 9-74 265 9-74 284 9-74 33 9-74 322 9-74 34i 9-74 3 60 19 19 19 19 19 19 19 19 IQ 9.82 106 9.82 133 9.82 161 9.82 188 9.82215 9.82 243 9.82 270 9.82 298 9.82 325 27 28 27 27 28 27 28 27 27 0.17894 0.17867 0.17839 0.17812 0.17785 0.17757 0.17 730 0.17702 0.17673 9.92 IO2 9.92 094 9.92 086 9.92077 9.92 069 9.92 O6O 9.92052 9.92 044 9-92035 8 8 9 8 9 8 8 9 g 29 28 27 26 25 24 23 22 21 i 0.9 0.8 2 1.8 1.6 3 2.7 2.4 4 3-6 3-2 5 4-5 4-0 6 5.4 4-8 7 6.3 5.6 8 7.2 6.4 9 8.1 7.2 40 9-74 379 IQ 9.82 352 */ 28 o. 1 7 648 992027 20 41 42 43 9-74 398 9.74417 9.74 4^6 1 9 19 9.82 380 9.82 407 9.82 435 27 28 0.17620 0.17593 o. 17 z6z 9.92018 9.92 oio 9.92 OO2 8 8 19 18 17 44 45 46 47 48 49 9-74 455 9-74474 9-74 493 9-74 5 12 9-74531 9-74 549 19 19 19 19 19 18 IQ 9.82462 9.82 489 9.82517 9.82 544 9.82571 9-82 599 2 7 2 7 28 27 27 28 0.17538 0.17 5*11 0.17483 0.17456 0.17429 0.17 401 9-9i 993 9.91 985 9.91 976 9.91 968 9.91 959 9.91951 9 8 9 8 9 8 16 15 4 *3 12 II 998 28 27 27 1.6 1.5 1.7 50 9-74 568 9.82 626 ^7 0.17374 9.91 942 Q IO 2 4 i 4 ' 5 I' 1 5i 52 53 54 55 56 3 59 9-74 |87 9.74 OOD 9-74 62-5 9-74 644 9.74662 9.74681 9-74 7 9.74719 9-74 737 i y 19 19 19 18 19 19 19 18 IQ 9.82 653 9.82681 9.82 708 9-82 735 9.82 762 9.82 790 9.82817 9.82 844 9.82 871 27 28 27 27 27 28 27 27 3 0-17347 0.17319 0.17 292 0.17 263 0.17238 0.17 210 0.17 183 O.I7 156 O.I7 129 9-91 934 9.91 925 9.91 917 9.91 908 9.91 900 9.91 891 9.91 883 9.91 874 9.91 866 1 9 8 9 8 9 8 Q 9 8 7 6 5 4 3 2 7.8 7.5 8.4 J 10.9 10.5 1 1. 8 4 14.0 13.5 15.2 5 17.1 16.5 18.6 2O.2 19.5 21.9 7 23.3 22.5 25.3 9 26.4 25.5 60 9-74 75 6 9.82 899 0.17 101 9-91 857 O L, Cos. d. L, Cot. c, d. L. Tan. L, Sin. d. / P.P. 56' 454 34' 1 L. Sin. d, L, Tan. c. d. L. Cot. L, Cos. d. p. p. o 9-7475 6 IQ 9.82 899 27 0.17 101 9.91 857 8 60 I 2 3 4 i 8 9 9-74 775 9-74 794 9.74812 9.74831 9.74 850 9.74 868 9.74887 9.74 906 9-74 924 19 18 19 19 18 19 19 18 IQ 9.82 926 9-82 953 9.82 980 9.83 008 9.83035 9.83 062 9.83 089 9.83117 9.83 144 2 7 27 28 27 27 2 7 28 27 27 0.17074 0.17047 0.17 020 0.16 992 0.16 965 0.16938 0.16 911 0.16883 0.16856 9.91 849 9.91 840 9.91 832 9.91 823 9.91 815 9.91 806 9.91 798 9.91 789 9.91 781 9 8 9 8 9 8 9 8 59 58 57 56 55 54 53 S 2 5 1 28 27 26 i 2.8 2.7 2.6 2 5.6 5.4 5.2 3 8.4 8.1 7.8 4 1 1. 2 10.8 10.4 5 J 4-o 13-5 i3- IO 9-74 943 18 9-83 I7 1 27 o.i 6 829 9.91 772 50 6 16.8 16.2 15.6 ii 12 *3 H 15 16 ;i 19 9.74961 9-74 980 9-74 999 9.75017 9.75 036 9-75 54 9-75 73 9.75091 9.75 no 19 J 9 18 19 18 19 18 19 18 9.83 198 9-83 225 9.83 252 9.83 280 9-83 307 9-83 334 9.83 361 9.83 388 9.83415 27 27 28 2 7 27 27 2 7 27 27 0.16802 0.16775 o.i 6 748 o.i 6 720 o.i 6 693 0.16666 o.i 6 639 0.16 612 0.16585 9.91 763 9-91 755 9.91 746 9.91 738 9.91 729 9.91 720 9.91 712 9.91 703 9.91 695 8 9 8 9 9 8 9 8 49 48 47 46 45 44 43 42 41 7 19.6 18.9 18.2 8 22.4 21.6 20.8 9 25.2 24.3 23.4 19 18 i 1.9 1.8 2 3-8 3-6 20 9.75 128 IQ 9.83 442 28 0.16 558 9.91 686 4O 3 5-7 54 21 22 23 24 2 5 26 2 7 28 29 9-75 H7 9-75 165 9.75 184 9.75 202 9-75 221 9-75 239 9-75 258 9.75 276 9-75 294 18 19 18 19 18 19 18 18 IQ 9-83 47 9-83 497 9-83 524 9-8355 1 9.83 578 9.83 605 9.83 632 9-83 659 9.83 686 27 27 27 27 27 27 2 7 27 27 0.16530 o.i 6 503 0.16476 0.16449 0.16422 0.16395 0.16368 0.16 341 0.16 314 9.91 677 9.91 669 9.91 660 9.91 651 9.91 643 9.91 634 9.91 625 9.91 617 9.91 608 8 9 9 8 9 9 8 9 39 38 37 36 35 34 33 32 31 4 7.6 7.2 5 9-5 9- 6 11.4 10.8 7 13.3 12.6 8 15.2 14.4 9 17.1 16.2 3O 9.75313 18 9-83 7 J 3 27 0.16 287 9-9i 599 g 3O 9 8 3i 32 33 34 35 36 38 39 9-75 33i 9-75 35o 9-75 368 9-75 386 9-75 405 9-75 423 9-75 44i 9-75 459 9-75 478 19 18 18 19 18 18 18 19 18 9-83 740 9-83 768 9-83 795 9.83 822 9.83 849 9.83 876 9-83 903 9-83 930 9.83957 28 27 2 7 27 27 2 7 27 27 27 o.i 6 260 0.16 232 o.i 6 205 0.16 178 o.i 6 151 o.i 6 124 o.i 6 097 0.16070 0.16043 9.91 591 9.91 582 9-91 573 9-91 565 9-91556 9-91 547 9-91 538 9.91 530 9.91 521 9 9 8 9 9 9 8 9 29 28 27 26 25 24 23 22 21 i 0.9 0.8 2 1.8 1.6 3 2.7 2.4 4 3-6 3-2 5 4-5 4-0 6 5-4 4-8 7 6.3 5.6 8 7.2 6.4 9 8.1 7.2 4O 9-75 496 18 9.83 984 27 0.16016 9.91 512 8 20 41 42 9-75 5H 9-75 533 19 T S 9.84011 9.84 038 27 0.15989 0.15 962 9.91 504 9-9 1 495 9 19 18 43 44 45 46 47 48 49 9-75551 9-75 569 9-75 587 9-75 605 9.75 624 9-75 642 9.75 660 lo 18 18 18 19 18 18 18 9.84 065 9.84092 9.84119 9.84 146 9.84173 9.84 200 9.84 227 2 7 27 27 27 27 27 27 27 0.15935 0.15 908 0.15 881 0.15 854 0.15 827 0.15 800 o-'S 773 9.91 486 9.91 477 9.91 469 9.91 460 9-91 45 1 9.91 442 9.9i 433 9 9 8 9 9 9 1 17 16 15 H 13 12 II 988 28 28 27 1.6 1.8 1.7 50 9-75 678 18 9.84 254 26 0.15 746 9.91 425 10 2 4-7 5-2 5-i 5i 5 2 53 54 55 56 H 59 9-75 696 9-75 7 J 4 9.75 733 9-75 75 1 9-75 769 9-75 787 9-75 805 9-75 823 9-75 841 18 19 18 18 18 18 18 18 18 9.84 280 9.84 307 9-84 334 9.84361 9.84 388 9.84415 9.84 442 9.84469 9.84 496 2 7 27 2 7 27 2 7 27 27 27 27 0.15 720 0.15693 0.15 666 0.15 639 0.15 612 0.15585 O.I5558 o.i553i 0.15 504 9.91 416 9.9: 407 9.91 398 9.91 389 9.91 381 9.91 372 9-91 363 9.9i 354 9-91 345 9 9 9 8 9 9 9 9 1 7 6 5 4 3 2 I 7.8 8.8 8.4 3 IO.9 12.2 II. 8 4 14.0 15.8 15.2 I 17.1 19.2 18.6 20.2 22.8 21.9 7 23.3 26.2 25.3 9 *4 - 6O 9-75 859 9-84 523 - I 5477 9-91 336 L. Cos, d, L, Cot, |c, d L, Tan, L, Sin, d. t P, P, 55' 35' 455 / L. Sin. d. L. Tan. c, d. L. Cot. L. Cos. d. P. P. 9-75 859 18 9*4523 27 ^15 477 9.9i 336 8 60 I 2 3 4 6 I 9 9-75877 9-75 895 9-759I3 9-75931 9-75 949 9-75 967 9-75 985 9.76003 9.76021 18 18 18 18 18 18 18 18 18 9.84 550 9.84576 9-84 603 9.84 630 9.84 657 9.84 684 9.84711 9.84 738 9.84 764 26 27 2 7 2 7 27 27 27 26 27 0.15450 0.15424 0-15397 0.15370 0.15 343 0.15 316 0.15 289 0.15 262 0.15 236 9.91 328 9-91 3i9 9.91 310 9.91 301 9.91 292 9.91 283 9.91 274 9.91 266 9.91 257 9 9 9 9 9 9 8 9 59 58 57 56 55 54 53 52 5^ 2 3 4 8 27 26 2.7 2.6 5-4 5-2 8.1 7.8 10.8 10.4 13-5 i3-o 16.2 15.6 18.9 18.2 21.6 20.8 10 9.76039 18 9.84 791 / 27 0.15 209 9.91 248 5O 9 24.3 23.4 ii 12 13 14 II !7 18 19 9.76057 9.76075 9.76093 9.76 in 9.76 129 9.76 146 9.76 164 9.76 182 9.76 200 18 18 18 18 17 18 18 18 18 9.84818 9.84 845 9.84 872 9.84 899 9.84 925 9.84952 9.84979 9.85 006 9.85 033 *l 27 27 27 26 27 27 27 27 26 0.15 182 0.15 155 0.15 128 0.15 101 0.15075 0.15 048 0.15021 0.14994 0.14967 9.91 239 9.91 230 9.91 221 9.91 212 9.91 203 9.91 194 9.91 185 9.91 176 9.91 167 9 i i 9 I q 49 48 47 46 45 44 43 42 4i i 2 3 4 6 I 18 17 1.8 1.7 3-6 3-4 5-4 5-i 7.2 6.8 9.0 8.5 10.8 10.2 12.6 11.9 14.4 13.6 20 9.76218 18 9-85 059 0.14941 9.91 158 40 9 16.2 15.3 21 22 23 24 11 27 28 29 9.76 236 9.76253 9.76271 9.76 289 9.76 307 9-7 6 324 9.76 342 9.76360 9.76 378 !i 18 18 !7 18 18 18 I 7 9.85 086 9.85113 9.85 140 9.85 166 9-85 193 9.85 220 9.85 247 9-85 273 9.85 300 */ 2 7 2 7 20 2 7 27 27 26 27 07 0.14914 0.14887 0.14860 0.14834 0.14807 0.14 780 0.14753 0.14727 0.14 700 9.91 149 9.91 141 9.91 I 3 2 9.91 123 9.91 114 9.91 105 9.91 096 9.91 087 9.91 078 8 9 9 9 9 9 9 9 3| 3 37 36 35 34 33 32 3 1 2 3 4 7 10 9 8 i.o 0.9 0.8 2.0 1.8 1.6 3.0 2.7 2.4 4.0 3.6 3.2 5.0 4.5 4.0 6.0 5.4 4.8 7.0 6.3 5.6 30 9-7 6 395 18 9.85 327 0.14 673 9.91 069 30 8 8.0 7.2 6.4 3i 32 9-76413 9-7643I 18 1 7 9-85 354 9-85 38o 26 27 0.14 646 0.14 620 9.91 060 9.91051 9 9 29 28 9 9.0 8.1 7.2 33 34 35 36 37 38 39 9.76 448 9.76466 9.76 484 9.76 501 9.76519 9-76537 9-76 554 18 18 '7 18 18 !/ 18 9.85 407 9.85 434 9.85 460 9.85 487 9.85 5H 9.85 540 9-85 5 6 7 27 26 27 27 26 27 ?7 O.H593 0.14 566 0.14540 0.14513 0.14486 0.14 460 0.14433 9.91 042 9-91 033 9.91 023 9.91 014 9.91 005 9.90 996 9.90 987 9 10 9 9 9 9 2 / 26 2 5 24 23 22 21 i 2 10 10 27 26 1.4 1.3 4-0 3-9 68 6s 40 9.76572 18 9.85 594 -/ 26 0.14406 9.90 978 20 3 9-4 9- 1 4i 42 43 | 44 45 46 47 48 49 9.76 590 9.76 607 9.76625 9.76 642 9.76 660 9.76677 9.76 695 9.76712 9.76 730 !1 '7 18 17 18 \l I 7 9.85 620 9-85 647 9.85 674 9.85 700 9-85 7 2 7 9-85 754 9.85 780 9.85 807 9.85 834 27 27 20 27 2 7 26 27 27 2(> 0.14 380 o.i4353 0.14326 0.14 300 0.14273 0.14 246 0.14 220 0.14 193 0.14 1 66 9.90 969 9.90 960 9.90951 9.90 942 9.90 933 9.90 924 9.90913 9.90 906 9.90 896 9 9 9 9 9 9 9 10 19 18 1 7 16 *5 14 13 12 II 4 6 8 9 IO 12.2 11.7 14.8 14.3 17.6 16.9 20.2 19.5 23.0 22.1 25.6 24.7 _!L A 5O 9.76 747 1 / l8 9.85 860 27 0.14 140 9.90 887 Q IO 27 26 5i 52 53 54 55 5 57 ! 58 59 9.76 765 9.76782 9.76 800 9.76817 9-76835 9.76852 9.76870 9.76887 9.76 904 17 18 17 18 i? 18 '7 17 iS 9.85 887 9.85913 9.85 940 9.85 967 9-85 993 9.86 020 9.86 046 9.86073 9.86 100 26 2 7 27 26 27 26 2 7 27 26 0.14113 0.14087 0.14060 0.14033 0.14007 0.13 980 0.13954 0.13927 0.13 900 9.90 878 9.90 869 9.90 860 9.90851 9.90 842 9.90832 9.90 823 9.90814 9-9 805 9 1 9 9 9 10 o 9 9 q 9 8 7 6 5 4 3 2 I i 2 3 4 I 9 1.5 1.4 4-5 4-3 7-5 7-2 10.5 10. i 13-5 l 3- 16.5 15.9 19.5 1 8.8 I 22.5 21.7 25.5 24.6 6O 9.76922 9.86 126 0.13874 9.90 796 L. Cos. d. L. Cot. c. d. L, Tan. L. Sin. d. 1 ' P. P. 54' 456 36 C / L, Sin. d. L, Tan, c. d. L. Cot. L. Cos. d, P. P. o 9.76 922 17 9.86 126 27 0.13874 9.90 796 6O I 2 3 4 1 8 9 9-76 939 9-76957 9.76974 9.76991 9.77 009 9.77026 9-77 43 9.77061 9.77078 18 J 7 17 18 17 17 18 1 7 17 9.86 153 9.86179 9.86 206 9.86 232 9.86 259 9.86 285 9.86312 9-86 338 9.86 365 26 27 26 27 26 2 7 26 2 7 27 0.13847 0.13 821 0.13 794 0.13 768 0.13 741 o-i37i5 0.13688 0.13 662 0-1363? 9.90 787 9.90 777 9.90 768 9.90 759 9.90 750 9.90 741 9.90 731 9.90 722 9.90 713 IO 9 9 9 9 IO 9 9 59 58 57 56 55 54 53 5 2 5 1 i 2 3 4 27 26 2.7 2.6 5-4 S- 2 8.1 7.8 10.8 10.4 13-5 13-0 IO 9-77 95 1 7 9.86 392 26 o. 1 3 608 9.90 704 IO 5O 6 16.2 15.6 ii 12 13 14 15 16 II 19 9.77 112 9.77 130 9-77 M7 9-77 J 64 9-77 181 9.77 199 9.77216 9-77 233 9-77 250 18 '7 1 7 17 18 17 J 7 J 7 18 9.86418 9-86 445 9.86471 9.86 498 9.86 524 9-86551 9.86577 9.86 603 9.86 630 27 26 2 7 26 2 7 26 26 3 0.13582 0-13555 0.13529 0.13 502 0.13476 0.13449 0.13423 0-13397 0.13370 9.90 694 9.90 685 9.90 676 9.90 667 9.90657 9.90 648 9-90 639 9.90 630 9.90 620 9 9 9 IO 9 9 9 10 49 48 47 46 45 44 43 42 4i I 9 2 18.9 18.2 21.6 20.8 24.3 23.4 18 17 16 t.8 1.7 1.6 3-6 3-4 3-2 20 9.77 268 17 9.86 656 27 0.13 344 9.90 611 4O 3 5.4 5-i 4-8 21 22 23 2 4 25 26 2 7 28 29 9.77 285 9-77 302 9-773I9 9-77 336 9-77353 9-77 37 9-77 387 9-77 405 9.77422 n 1 7 1 7 1 7 1 7 J 7 18 J 7 I 7 9.86 683 9.86 709 9.86 736 9.86 762 9.86 789 9.86815 9.86 842 9.86 868 9.86 894 */ 26 27 26 27 26 27 26 26 27 O.I33I7 0.13 291 0.13 264 0.13 238 0.13211 0.13 185 0.13 158 0.13132 0.13 106 9.90 602 9.90 592 9-90 583 9.90574 9-90 565 9.90555 9.90 546 9-90 537 9.90527 10 9 9 9 10 9 9 IO 11 37 36 35 34 33 3 2 3 1 4 i ,; 7 i 8 i, 9 i< j.2 6.8 6.4 ?.o 8.5 8.0 D.8 IO.2 9.6 2.6 Il.g II. 2 1-4 13.6 12.8 3.2 15.3 14.4 3O 9-77 439 I 7 9.86 921 26 0.13079 9.90518 3O 10 9 3 1 32 33 34 35 36 37 38 39 9-77 456 9-77473 9-77 490 9-77 57 9-77 524 9-77 54i 9-77558 9-77575 9-77 592 17 J 7 17 '7 17 J 7 J 7 17 1 7 9-86 947 9.86974 9.87 ooo 9.87027 9-87053 9.87079 9.87 106 9.87 132 9.87 158 27 26 2 7 26 26 2 7 26 26 27 0.13053 0.13026 0.13000 0.12973 0.12947 O.I2 921 O.I 2 894 0.12868 O.I 2 842 9.90 509 9-90 499 9.90 490 9.90 480 9.90471 9.90 462 9.90452 9.90 443 9-90 434 10 9 10 9 9 IO 9 9 IO 29 28 27 26 25 24 23 22 21 i 2 3 4 I I 9 i.o 0.9 2.0 1.8 3.0 2.7 4.0 3.6 5-o 4-5 6.0 5.4 7-o 6.3 8.0 7.2 9.0 8.1 4O 9-77 609 1 / 17 9-87 185 *t 26 O.I28I5 9.90424 Q 20 4i 42 9.77 626 9-77 643 17 9.87 211 9.87 2 3 8 2 7 nf O.I 2 789 0.12 762 9.90415 9.90 405 10 19 18 43 44 4 46 47 48 49 9.77 660 9.77677 9-77 694 9.77711 9-77 728 9-77 744 9.77761 J 7 17 17 17 17 16 17 I 7 9.87 264 9.87 290 9-873I7 9-87 343 9.87 369 9.87 396 9.87422 26 % 26 27 26 26 O.I 2 736 O.I2 710 O.I 2 683 O.I2 657 O.I 2 631 O. I 2 604 O.I2 578 9.90 396 9.90 386 9-90377 9.90 368 9.90358 9.90 349 9-90 339 9 10 9 9 IO 9 IO *7 16 J 5 M 13 12 II i 9 9 27 26 1.5 1.4 50 9-77 778 1 / 17 9.87 448 27 0.12552 9.90 330 IO IO 2 4-5 4-3 5i 52 53 54 |P \H 59 9-77 795 9.77812 9-77 829 9-77 846 9.77 862 9.77879 9.77 896 9-779I3 9-77 930 '7 17 17 16 *7 17 "7 11 9-87 475 9.87 501 9.87527 9-87 554 9.87 580 9.87 606 9-87 633 9.87 659 9.87 685 26 26 27 26 26 27 26 26 26 0.12525 0.12499 0.12473 O.I 2 446 O.I 2 420 0.12394 O.I2 367 O.I2 341 O.I23I5 9-90 320 9.90311 9-90 301 9.90 292 9.90 282 9.90 273 9.90 263 9.90 254 9.90 244 9 10 9 10 9 10 9 IO Q 1 7 6 5 4 3 2 I 3 4 I I 9 7-5 7 z 10.5 10.1 13-5 13- 16.5 15.9 19.5 18.8 22.5 21.7 25.5 24.6 60 9.77 946 9.87711 O.I 2 289 9.90 235 O 1 L, Cos, d. L, Cot. c. d. L. Tan. L. Sin. d. i P. P. 53 37 457 / L, Sin, d. L. Tan, c, d. L, Cot, L, Cos, d. P, P. I 9-77 946 17 9.87711 27 ^O.I2 289 9-90 235 IO 6O I 2 3 4 I 8 9 9-77 963 9.77980 9-77997 9.78013 9.78 030 9.78 047 9.78063 9.78080 9.78097 17 i? 16 i/ 17 16 1 7 *7 16 9.87 738 9.87 764 9.87 790 9.87817 9.87 843 9.87 869 9.87 895 9.87 922 9.87 948 26 26 27 26 26 26 % 26 O.I 2 262 O.I 2 236 O.I2 21O 0.12 183 O.I2I57 0.12 131 0.12 105 0.12078 O.I2 052 9.90 225 9.90216 9.90 206 9.90 197 9.90 187 9.90 178 9.90 1 68 9.90159 9.90 149 9 10 9 10 9 10 9 10 IO H 57 56 55 54 53 5 2 5 1 I 2 3 4 27 26 2.7 2.6 5-4 5-2 8.1 7.8 10.8 10.4 13-5 i3-o T f\ -7 T C (\ 10 9-78113 I 7 9.87 974 26 O.I 2 O26 9.90 139 Q 50 7 18 9 18 2 ii 12 13 H !i *7 18 19 9.78 130 9-78 H7 9.78 163 9.78 180 9.78 197 9.78213 9.78 230 9.78 246 9.78 263 1 / 1 7 16 1 7 17 16 7 16 7 9.88000 9.88027 9.88053 9.88 079 9.88 105 9-88 131 9.88 158 9.88 184 9.88 210 27 26 26 26 26 27 26 26 26 O.I2OOO O.II973 0.11947 o.ii 921 o.i i 895 O.II 869 o.ii 842 o.ii 816 o.ii 790 9.90 130 9.90 1 20 9.90 in 9.90 101 9.90091 9.90082 9.90072 9.90063 9.90053 10 9 IO 10 9 10 9 10 IO 49 48 47 46 45 44 43 42 4i 8 9 i 2 21.6 20.8 24.3 23.4 17 16 1.7 1.6 34 3-2 20 9.78 280 1 / 16 9.88 236 ->6 o.ii 764 9.90 043 Q 40 3 5.1 4.8 21 22 23 24 3 27 28 29 9.78 296 9-783I3 9.78329 9.78 346 9.78 362 9-78 379 9-78 395 9.78412 9.78428 17 16 17 16 1 7 16 1 7 16 9.88 262 9.88 289 9.88315 9-88 341 9.88 367 9-88 393 9.88 420 9.88 446 9.88472 27 26 26 26 26 27 26 26 26 o.ii 738 o.ii 711 o.ii 685 o.ii 659 0.11633 o.ii 607 o.ii 580 o.ii 554 o.ii 528 9.90 034 9.90 024 9.90014 9.90 003 9-89 995 9-89 985 9.89 976 9.89 966 9.89 956 10 10 9 10 IO 9 10 IO 39 38 37 36 35 34 33 32 3i 4 I i 9 6.8 6.4 8.5 8.0 10.2 9.6 II.9 1 1. 2 13.6 12.8 15.3 14.4 30 9-78 445 I 7 16 9.88 498 26 o.ii 502 9.89 947 IO 3O 10 9 3i 32 33 34 35 36 3 39 9.78461 9.78478 9.78 494 9.78510 9./85 2 7 9-78 543 9.78 560 9.78576 9.78 592 J 7 16 16 17 16 17 16 16 9.88 524 9.88 550 9-88 577 9.88 603 9.88 629 9-88 653 9.88 68 1 9.88 707 9-SS 735 26 27 26 26 26 26 26 26 26 o.ii 476 o.ii 430 o.ii 423 o.ii 397 o.ii 371 0.11345 0.11319 o.ii 293 o.ii 267 9-89 937 9-89927 9.89918 9.89 908 9.89 898 9.89 888 9.89 879 9.89 869 9.89 859 IO 9 IO IO 10 9 10 IO 29 28 27 26 2 5 24 23 22 21 i 2 3 4 i 8 9 i.o 0.9 2.0 1.8 3.0 2.7 4.0 3.6 5-o 4-5 6.0 5.4 7.0 6.3 8.0 7.2 9.0 8.1 4O 9.78 609 X 7 16 9-88 759 o.ii 241 9.89 849 20 41 9.78625 17 9.88 786 9 88 812 z / 26 o.ii 214 on 1 88 9.89 840 Q 80 8lO 10 19 rC 42 43 44 tl 47 48 49 y./ U 4 z 9.78658 9-78 674 9.78691 9.78 707 9-78723 9-78 739 9.78 756 16 16 17 16 16 16 \l 9.88 838 9.88 864 9.88 890 9.88916 9.88 942 9.88 968 9.88 994 26 26 26 26 26 26 26 26 o.ii 162 o.ii 136 O.I I I IO o. 1 1 084 o.i i 058 o.ii 032 o.ii 006 9.89 820 9.89810 9.89 80 1 9.89 791 9.89 7 8l 9.89 771 9.89 761 IO 10 9 IO IO 10 IO 1 7 16 15 H 13 12 II o 10 10 27 26 1.4 1.3 4-o 3-9 5O 9.78772 ifi 9.89 020 26 0.10980 9.89 752 IO 7 6.8 6.5 5i 5 2 53 54 55 56 P 59 9.78 788 9.78 803 9.78821 9-78 837 9-78 853 9.78869 9.78 886 9.78902 9.78918 : 16 16 16 16 "7 16 16 16 9.89 046 9.89 073 9.89 099 9.89125 9.89 151 9.89177 9.89 203 9.89 229 9-89 255 27 26 26 26 26 26 26 26 26 0.10954 o.io 927 o.io 901 o.io 875 0.10849 0.10823 0.10797 o.io 771 0.10745 9.89 742 9.89 732 9.89 722 9.89712 9.89 702 9.89 693 9-89 683 9.89673 9.89 663 IO IO 10 IO 9 IO IO 10 9 8 7 6 5 4 3 2 I 4 I I 9 IO 9.4 9.1 12.2 11.7 14.8 14.3 17.6 16.9 2O.2 19.5 23.0 22.1 25.6 24.7 60 978934 9.89 281 o.io 719 9-89 653 O L. Cos. d. L, Cot. c, d. L. Tan, L, Sin. d, / P, P, 52' 458 38' / L, Sin. d. L. Tan. c. d. L. Cot. L. Cos. d. P.P. o 9-78934 16 9.89 28j 26 o.io 719 9.89 653 IO 60 I 2 3 4 6 I 9 9.78 950 9.78 967 9.78983 9.78 999 9.79015 9.79031 9-79 047 9.79063 9.79079 *7 16 16 16 16 16 16 16 1 6 9.89 307 9-89 333 9-89 359 9.89 385 9.89411 9-89437 9.89 463 9.89489 9-89 5 1 5 26 26 26 26 26 26 26 26 26 o.io 693 o.io 667 o.io 641 0.10615 o.io 589 0.10563 0.10537 o.io 511 0.10485 9.89 643 9-89 633 9.89 624 9.89 614 9.89 604 9.89 594 9-89 584 9-89 574 9.89 564 IO 9 IO 10 10 10 10 10 IO 59 58 57 56 55 54 53 5 2 5 1 i 2 3 4 1 26 25 2.6 2.5 5- 2 5- 7-8 7-5 10.4 10.0 13.0 12.5 15.6 15.0 IO 9-79 095 16 9.89541 26 0.10459 9-89 554 IO 50 7 18.2 17.5 ii 12 13 14 \l J 7 18 19 9.79111 9.79 128 9.79 144 9.79 1 60 9-79 176 9-79 192 9.79 208 9.79 224 9.79 240 17 16 16 16 16 16 16 16 16 9-89 5 6 7 9-89 593 9.89 619 9-89 645 9.89671 9-89 697 9.89 723 9.89 749 9.89 775 26 26 26 26 26 26 26 26 26 0.10433 0.10407 0.10381 0-10355 0.10329 o.io 303 0.10277 o.io 251 O.IO 22^ 9.89 544 9-89 534 9.89 524 9.89514 9.89 504 9.89 495 9.89485 9.89475 9.89465 10 IO IO IO 9 10 IO 10 IO 49 48 47 46 45 44 43 42 41 8 9 I 2 2O.8 2O.O 23-4 22.5 17 16 15 1.7 1.6 1.5 3-4 3-2 3-o 20 9.79 256 16 9.89 80 1 26 o.io 199 9-89 455 IO 40 3 .1 4.5 4.5 68 64 60 21 22 23 24 2 5 26 27 28 29 9-79 272 9.79 288 9-79 34 9.79319 9-79335 9-79 35 * 9-79 367 9-79 383 9-79 399 16 16 15 16 16 16 16 16 16 9.89 827 9.89 853 9-89 879 9.89 905 9.89931 9.89957 9.89 983 9.90 009 9-90 035 26 26 26 26 26 26 26 26 26 0.10173 o.io 147 O.IO 121 0.10095 0.10069 0.10043 0.10017 0.09 991 0.09 965 9-89 445 9-89 435 9.89425 9.89415 9.89 405 9-89 395 9-89 385 9-89 375 9.89 364 10 IO IO 10 IO 10 10 II IO 39 38 37 36 35 34 33 32 3 1 6 8 9 8.5 8.0 7.5 IO.2 9.6 9.O II.9 II. 2 10.5 13.6 12.8 12.0 15.3 14.4 13.5 11 10 9 3O 9-794I5 16 9.90061 2C 0.09 939 9-89 354 IO 3O 3i 32 33 34 35 36 i 39 9-79 43 1 9-79447 9-79 463 9.79478 9-79 494 9.79510 9-79 526 9-79 542 9-79 SS 8 16 16 15 16 16 16 16 16 I e 9.90 086 9.90 1 1 2 9.90 138 9.90 164 9.90 190 9.90 216 9.90 242 9.90 268 9.90 294 *;> 26 26 26 26 26 26 26 26 26 0.09 914 0.09 888 0.09 862 0.09 836 0.09 810 0.09 784 0.09 758 0.09 732 0.09 706 9-89 344 9-89 334 9.89 324 9.89314 9.89 304 9.89 294 9.89 284 9.89 274 9.89 264 IO 10 IO 10 IO 10 IO IO IO 29 28 27 26 25 24 23 22 21 i 2 3 4 6 8 9 i.i i.o 0.9 2.2 2.0 1.8 3-3 3-o 2.7 4.4 4.0 3.6 5-5 5- 4-5 6.6 6.0 5.4 7-7 7- 6.3 8.8 8.0 7.2 9.9 9.0 8.1 4O 9-79573 j 16 9.90 320 26 0.09 680 9.89 254 2O 4i 42 9-79 5 8 9 9-79 605 16 9.90 346 9.90371 25 0.09 654 0.09 629 9.89 244 9 89 233 II 19 18 43 44 45 46 47 48 49 9.79621 9-79 636 9.79 652 9.79 668 9-79 684 9-79 699 9-79 7'5 ID 15 16 16 16 II 16 9-90 397 9.90423 9.90 449 9-90 475 9.90 501 9.90527 9-90553 26 26 26 26 26 26 26 0.09 603 0.09 577 0.09551 0.09 525 0.09 499 0.09 473 0.09 447 9.89 223 9.89213 9.89 203 9.89 193 9-89 183 9.89 173 9.89 162 IO 10 IO 10 IO IO II IO *7 16 15 H J 3 12 I I o 10 10 9 26 25 26 1.3 1.2 1.4 50 9-79 73i 9.90578 *j 26 0.09422 9.89 152 IO 2 3-9 3-8 4-3 6 c 62 72 5i 52 53 54 1 58 59 9.79 746 9-79 762 9-79 778 9-79 793 9-79 809 9-79 825 9-79 840 9-79 856 9.79872 *i 16 16 15 16 16 15 16 16 I e 9.90 604 9.90 630 9.90 656 9.90 682 9.90 708 9-90 734 9-90 759 9.90 785 9.90811 26 26 26 26 26 25 26 26 26 0.09 396 0.09 370 0.09 344 0.09 3 1 8 0.09 292 0.09 266 0.09 241 0.09 213 0.09 189 9.89 142 9.89 132 9.89 122 9.89 112 9.89 101 9.89091 9.89081 9.89071 9.89 060 IO IO IO II IO IO 10 II 9 8 7 6 5 4 3 2 I 3 4 6 8 9 IO 9.1 8.8 10.1 11.7 11. 2 13.0 14.3 13.8 15.9 16.9 16.2 18.8 19.5 18.8 21.7 22.1 21.2 24.6 24-7 23-8 60 9-79 887 *3 9.90 837 0.09 163 9.89 050 O L, Cos. d. L. Cot. c. d. L. Tan. L. Sin. d. t P.P. 39' 459 f L, Sin. d. L. Tan. c. d. L. Cot. L. Cos. d, P.P. 9.79887 16 9.90 837 26 0.09 163 9.89 050 IO 6O 2 3 4 I I 9 9-79 903 9.79918 9-79 934 9-79 95 9-79 965 9.79 981 9.79 996 9.80012 9.80027 15 16 16 11 15 16 !I 9.90 863 9.90 889 9.90914 9.90 940 9.90 966 9.90 992 9.91 018 9.91 043 9.91 069 26 2 5 26 26 26 26 'A 26 0.09 137 0.09 i i i 0.09 086 0.09 060 0.09 034 0.09008 0.08 982 0.08 957 0.08 931 9.89 040 9.89 030 9.89 020 9.89 009 9.88 999 9.88989 9.88 978 9.88 968 9.88 958 IO IO II IO IO 1 1 10 10 IO 59 58 57 56 55 54 53 S 2 5i i 2 3 4 6 26 25 2.6 2.5 5-2 5- 7-8 7-5 10.4 10.0 13.0 12.5 I C 6 ISO IO 9.80 043 i c 9.91 095 26 0.08 905 9.88 948 1 1 SO 7 1 8.2 17.5 ii 12 13 14 11 17 18 19 9.80 058 9.80074 9.80 089 9.80 105 9.80 1 20 9.80 136 9.80151 9.80 166 9.80 182 1 j 16 15 16 II 15 15 16 T - 9.91 121 9.91 147 9.91 172 9.91 198 9.91 22 4 9.91 250 9.91 2/6 9.91 301 9.91 327 26 25 26 26 26 26 2 5 26 26 0.08 879 0.08 853 0.08 828 0.08 802 0.08 776 0.08 750 0.08 724 0.08 699 0.08 673 9.88937 9.88927 9.88917 9.88 906 9.88 896 9.88 886 9.88 875 9.88 865 9.8885? IO IO II 10 IO II IO 10 J I 49 48 47 46 45 44 43 42 4i 8 9 i 2 3 2O.8 2O.O 23.4 22.5 16 15 1.6 1.5 3-2 3-o 4-8 4-5 2O 9.80 197 1 J 16 9-9i 353 26 0.08 647 9.88 844 IO 40 4 6.4 6.0 21 22 23 24 2 5 26 27 28 29 9.80213 9.80 228 9.80 244 9.80 259 9.80 274 9.80 290 9.80 305 9.80 320 9.80 336 15 16 J 5 :i 15 15 16 I C 9-91 379 9.91 404 9.91 430 9.91 456 9.91 482 9.91 507 9-9i 533 9-91 559 9.91 585 25 26 26 26 25 26 26 26 2C 0.08 621 0.08 596 0.08 570 0.08 544 0.08518 0.08 493 0.08 467 0.08441 0.08415 9-88 834 9.88 824 9.88813 9.88 803 9.88 793 9.88 782 9.88 772 9.88 761 9.88751 IO II IO 10 II 10 II IO IO 39 38 37 36 35 34 33 ? 3 1 I I 9 8.0 7.5 9.6 9.0 II. 2 10.5 12.8 I2.O 14.4 13.5 11 10 30 9.80351 o 9.91 610 *J 26 0.08 390 9.88 741 30 3i 32 33 34 3 37 38 39 9.80 366 9.80 382 9.80 397 9.80412 9.80 428 9.80 443 9.80 458 9.80 473 9.80 489 I 5 16 15 '5 16 15 i5 11 I c 9.91 636 9.91 662 9.91 688 9-91 7 J 3 9-91 739 9.91 765 9.91 791 9.91 816 9.91 842 26 26 25 26 26 26 2 5 20 0.08 364 0.08 338 0.08 3 1 2 0.08 187 0.08 261 0.08 235 0.08 209 0.08 184 0.08 158 9.88 730 9.88 720 9.88 709 9.88 699 9.88 688 9.88 678 9.88 668 9.88 657 9.88 647 IO II 10 II IO 10 II 10 J I 29 28 2 7 26 25 24 23 22 21 3 4 6 8 9 3-3 3-o 4-4 4-0 5-5 5-o 6.6 6.0 7-7 7- 8.8 8.0 9-9 9-0 40 9.80 504 15 9.91 868 2C. 0.08 132 9.88 636 IO 20 4i 42 43 44 45 46 47 48 49 9.80519 9.80 534 9.80 550 9.80 565 9.80 580 9-8o 595 9.80610 9.80 625 9.80 641 !i 15 15 15 15 15 16 i - 9.91 893 9.91 919 9-9 i 945 9.91971 9.91 996 9.92 022 9.92 048 9.92 073 9.92 099 26 26 26 2 5 26 26 11 26 0.08 107 0.08081 0.08055 0.08 029 0.08 004 0.07 978 0.07 952 0.07 927 0.07 901 9.88 626 9.88615 9.88 605 9.88 594 9.88 584 9-88 573 9.88 563 9.88 552 9.88 542 II IO II IO II 10 1 1 10 I I 19 18 J 7 16 15 H 13 12 II i 2 11 11 26 25 1.2 I.I 3-5 3-4 5-9 5-7 50 9.80656 3 i r 9.92125 T - 9.88531 IO 10 3 8.3 8.0 5 52 53 54 55 56 p 59 9.80671 9.80 686 9.80 701 9.80716 9.80731 9.80 746 9.80 762 9.80 777 9.80 792 H 5 '5 15 15 16 15 15 1C 9.92 150 9.92 176 9.92 202 9.92 227 9.92 253 9.92 279 9.92 304 9-92 33 9.92 356 *J 20 26 - 5 26 26 -5 26 26 2C. 0.07 824 0.07 798 0.07 773 0.07 747 0.07 721 0.07 696 0.07 670 0.07 644 9.88521 9.88510 9.88 499 9.88 489 9.88478 9.88 468 9.88457 9.88 447 9.88430 II II 10 II 10 1 1 IO II 1 J 9 8 7 6 5 4 3 2 6 I 9 IO ii 10.6 10.2 13.0 12.5 iv4 14-8 17.7 17.0 20.1 19.3 22.5 21.6 24.8 23.9 60 9.80807 9.92 381 *3 0.07 619 9.88425 O L. Cos. d. . L. Cot. c. d. L. Tan. L. Sin. d. t p. p. 50' 460 40' / L. Sin. d. L. Tan. c. d. L. Cot. L. Cos. d. P. P. 9.80807 I e 9.92 381 ?6 0.07 619 9-88 425 10 60 I 2 3 4 I 9 9.80 822 9-80837 9.80 852 9.80 867 9.80 882 9.80897 9.80912 9.80 927 9.80 942 15 '5 15 15 15 15 1 S 15 T r 9.92 407 9-92 433 9.92 458 9.92 484 9.92510 9-92 535 9.92561 9.92 587 9.92 612 26 25 26 26 25 26 26 3 0.07 593 0.07 567 0.07 542 0.07 516 0.07 490 0.07 465 0.07 439 0.07413 0.07 388 9.88415 9.88 404 9-88 394 9-88 383 9-88 372 9.88 362 9.88351 9-88 340 9-88 330 ii 10 II II IO II II IO 1 1 59 58 57 56 55 54 53 52 5 1 2 3 4 6 26 25 2.6 2.5 5-2 5-o 7-8 7-5 10.4 10.0 13.0 12.5 15.6 15.0 10 9.80957 T C 9.92 638 21 0.07 362 9-88319 J J 50 7 g 15.2 17.5 ii 12 13 H 15 16 11 19 9.80 972 9.80987 9.8l 002 9.8l 017 9.8l 032 9.8l 047 9.81 061 9.81 076 9.81 091 L D 15 15 15 15 J 5 H 15 i5 T C 9.92 663 9.92 689 9.92715 9.92 740 9.92 766 9.92 792 9.92817 9.92 843 9.92 868 *3 26 26 25 26 26 25 26 25 26 0-07 337 0.07311 0.07 285 0.07 260 0.07 234 0.07 208 0.07 183 0.07 157 0.07 132 9.88 308 9.88 298 9.88 287 9.88 276 9.88 266 9-88 253 9.88 244 9.88 234 9.88 223 10 II II IO II II 10 II 1 1 49 48 47 46 45 44 43 42 4i 9 i 2 3 4 23-4 22.5 15 14 1.5 1.4 3.0 2.8 4-5 4-2 6.0 t;.6 20 9.81 106 1 J I c 9.92 894 26 0.07 1 06 9.88212 J J 4O 5 7-5 7- 21 22 23 24 3 2 29 9.81 121 9.81 136 9.81 151 9.81 1 66 9.81 1 80 9.81 195 9.8l 210 9 .8l 225 9.8l 240 *3 15 15 15 H J 5 i5 15 15 id. 9.92 920 9-92 945 9.92971 9.92 996 9-93 22 9-93 48 9-93 73 9.93 099 9.93 124 3 25 26 26 25 26 25 26 0.07 080 0.07 055 0.07 029 0.07 004 0.06 978 0.06952 0.06 927 0.06 901 0.06 876 9.88 201 9.88 191 9.88 180 9.88 169 9.88 158 9.88 148 9-88 137 9.88 126 9.88115 10 II II II 10 II II II IO 39 38 37 36 35 34 33 32 3 1 6 8 9 9.0 8.4 10.5 9.8 12.0 II. 2 13.5 12.6 11 10 I.I I.O 30 9.8l 254 T C 9-93 i?o 2C 0.06 850 9.88 105 J I 30 2 2.2 2.O 3i 32 33 34 3 37 38 39 9.8l 269 9.8l 284 9.8l 299 9.8l 314 9 .8l 328 9-8 1 343 9.81 358 9.81 372 9-8i 387 *3 15 15 15 H 15 15 H 15 I c 9-93 175 9.93 201 9.93 227 9-93 252 9.93 278 9-93 303 9-93 329 9-93 354 9-93 38o *3 26 26 2 5 26 25 26 2 5 26 26 0.06 825 0.06 799 0.06 773 0.06 748 0.06 722 0.06 697 0.06671 0.06 646 0.06 620 9.88 094 9.88083 9.88072 9.88061 9.88051 9.88 040 9.88 029 9.88018 9.88007 II II II 10 II II II II II 29 28 27 26 2 5 24 23 22 21 3 4 8 9 3-3 3-o 4.4 4.0 5-5 5- 6.6 6.0 7.7 7.0 8.8 8.0 9.9 9.0 40 9.81 402 A J 9.93 406 0.06 594 9.87 996 J I 2O 4i 42 43 44 45 46 47 48 49 9.81 417 9.81 431 9.81 446 9.81 461 9.81 475 9.81 490 9.81 505 9.81 519 9-8i 534 1 5 H *s 15 H 15 15 14 15 I e 9-93431 9-93457 9-93 482 9-93 5 8 9-93 533 9-93 559 9-93 584 9.93610 9-93 636 2 5 26 25 26 3 25 26 26 2C 0.06 569 0.06 543 0.06 518 0.06 492 0.06 467 0.06 441 0.06416 0.06 390 0.06 364 9.87 985 9-87975 9.87 964 9.87953 9.87 942 9.87931 9.87 920 9.87 909 9.87 898 IO II II II II II II II I J 19 18 1 7 16 5 H 13 12 II 2 11 10 10 26 26 25 1.2 1.3 1.2 3-5 3-9 3-8 5-9 6.5 6.2 5O 9.81 549 A D I A 9.93 66 1 ^5 26 0.06 339 9.87 887 IO IO 4 8.3 9.1 8.8 5i 52 53 54 55 5 6 9 59 9.81 563 9.81 578 9.81 592 9.81 607 9.81 622 9.81 636 9.81 651 9.81 665 9.81 680 '5 H '5 15 14 15 14 15 IA 9-93 687 9.93712 9-93 738 9-93 7 6 3 9-93 789 9.93814 9-93 840 9-93 865 9-93 891 2 5 26 25 26 25 26 2 5 26 2C 0.06 313 0.06 288 0.06 262 0.06 237 O.O6 211 0.06 1 86 0.06 1 60 0.06 135 0.06 109 9.87 877 9.87 866 9.87 85! 9.87 844 9.87 833 9.87822 9.87811 9.87 800 9.87 789 II II II II II II II II II 9 8 7 6 5 4 3 2 I 8 9 10 ii 13.0 14.3 13.8 15.4 16.9 16.2 17.7 19.5 18.8 2O. I 22.1 21.2 22.5 24.7 23.8 24.8 60 9.81 694 9.93916 0.06 084 9.87 778 L. Cos. d, L. Cot. c. d. L. Tan. L. Sin. d. f P.P. 49' 41 e 461 / L, Sin, d. L, Tan. c. d. L. Cot. L. Cos. d. P. P. j 9.81 694 j - 9.93916 26 0.06 084 9.87 778 1 1 6O I 2 3 4 1 8 9 9.81 709 9.81 723 9-8i 738 9.81 752 9.81 767 9.81 781 9.81 796 9.81 810 9.81 825 1 3 '4 15 H 15 14 15 H 15 9-93 942 9-93 967 9-93 993 9.94018 9.94 044 9.94 069 9-94095 9.94 120 9.94 146 3 2 5 26 25 26 % 2C 0.06 058 0.06 033 0.06 007 0.05 982 0.05 956 0.05 931 0.05 905 0.05 880 0.05 854 9.87 767 9.87 756 9-87 745 9-87 734 9-87 723 9.87712 9-87 701 9.87 690 9.87 679 u II II II II II II II J 1 59 58 57 56 55 54 53 52 5 1 2 3 4 6 26 25 2.6 2.5 5.2 5.0 7-8 7-5 10.4 10.0 13.0 12.5 15.6 15.0 IO 9.81 839 J 4 I - 9.94 171 ^j 26 0.05 829 9.87 668 1 1 5O 7 18.2 17.5 ii 12 13 14 !I 17 18 19 9.81 854 9.81 868 9.81 882 9.81 897 9.81 911 9.81 926 9.81 940 9-8i 955 9.81 969 *3 H H 15 H '5 H '5 M id. 9-94 197 9.94 222 9.94 248 9-94 273 9-94 299 9-94 324 9-94 35 9-94 375 9-94 40i 25 26 25 26 25 26 2 5 26 2r 0.05 803 0.05 778 0.05 752 0.05 727 0.05 701 0.05 676 0.05 650 0.05 625 0.05 599 9.87657 9.87 646 9-87 635 9.87 624 9.87613 9.87 601 9.87 590 9-87 579 9.87 568 II II II II 12 II II II j i 49 48 47 46 45 44 43 42 4i 9 i 2 3 2O.8 2O.O 23.4 22.5 15 14 1.5 1.4 3-o 2.8 4-5 4-2 2O 9.81 983 I r 9-94 426 *J ->6 0.05 574 9-87557 II 4O 4 6.0 5.6 21 22 23 24 11 2 7 28 29 9.81 998 9.82 OI2 9.82026 9.82 041 9.82 055 9.82 069' 9 82 084 9.82 098 9.82 112 14 H *5 H H 15 H H 9.94452 9-94477 9-94 53 9-94 528 9-94 554 9-94579 9.94 604 9-94 630 9-94 655 % 2 5 26 25 25 26 3 0.05 548 0.05 523 0.05 497 0.05 472 0.05 446 0.05 421 0.05 396 0.05 370 0.05 345 9.87 546 9-87 535 9-87 524 9-87 5 1 3 9.87 501 9.87 490 9-87 479 9.87 468 9.87457 II II II 12 II II II II 1 1 39 38 37 36 35 34 33 32 3i 6 8 9 7-5 7-0 9.0 8.4 10.5 9.8 12.0 I 1.2 13.5 12.6 12 11 3O 9.82 126 i - 9.94 68 1 2C 005319 9-87 446 30 i 1.2 I.I 3i 32 33 34 3 3 39 9.82 141 9-82 15^ 9.82 169 9.82 184 9.82 198 9.82 212 9.82 226 9.82 240 9.82 255 14 H 15 H H H M 15 9.94 706 9-94 73 2 9-94 757 9-94 783 9.94 808 9-94 834 9-94 859 9-94 884 9.94910 *3 26 25 26 3 25 2 5 26 2C 0.05 294 0.05 268 0.05 243 0.05 217 0.05 192 0.05 1 66 0.05 141 0.05 116 0.05 090 9-87 434 9.87423 9.87412 9.87 401 9.87 390 9.87 378 9.87 367 9-87 35 6 9-87 345 II II II II 12 II II II 1 1 29 28 27 26 25 24 23 22 21 2 3 4 5 6 8 9 2. 4 2.2 3-6 3-3 4-8 4-4 6.0 5.5 7.2 6.6 8.4 7.7 9.6 8.8 10.8 9.9 4O 9.82 269 H 9-94 935 *D 26 0.05 065 9-87 334 12 20 1 4i 42 43 44 45 46 47 48 49 9.82 283 9.82 297 9.82 311 9.82 326 9.82 340 9.82 354 9.82 368 9.82 382 9.82 396 H H 15 H H H M H 14 9.94961 9.94 986 9.95012 9-95 37 9-95 62 9-95 088 9-95 JI 3 9-95 *39 9-95 l6 4 3 25 2 5 26 2 5 26 2 5 26 0.05 039 0.05 014 0.04 988 0.04 963 0.04 938 0.04912 0.04 887 0.04 86 1 0.04 836 9.87 322 9-873" 9.87 300 9.87 288 9-87 277 9.87 266 9.87 255 9-87 243 9.87 232 II II 12 II II II 12 II 1 1 !7 16 15 M 13 12 II i 2 3 12 12 11 26 25 25 I.I 1.0 I.I 3-2 3- 1 3-4 5-4 S- 2 5-7 7-6 7.3 8.0 50 9.82 410 9-95 ! 9o 2C 0.04 810 9.87 221 1 2 IO 4 9.8 9.4 IO.2 5i 52 53 54 H 57 58 59 9.82 424 9.82439 9.82453 9.82467 9.82481 9.82 495 9.82 509 9.82 523 9-82537 15 H H H H H H H 9-95 215 9.95 240 9.95 266 9.95 291 9-953I7 9-95 342 9-95 3 6 8 9-95 393 9-95 4i8 2 5 26 25 26 25 26 25 M 0.04 785 0.04 760 0.04 734 0.04 709 0.04 683 0.04 658 0.04 632 0.04 607 0.04 582 9.87 209 9.87 I 9 8 9.87 I8 7 9.87175 9.87 164 9-87 153 9.87 141 9.87 130 9.87 119 II II 12 II II 12 II II 12 I 7 6 5 4 3 2 I i 1 1.9 II-5 12.5 4.1 13.5 14.8 6.2 15.6 17.0 8.4 17.7 19.3 0.6 19.8 21.6 2.8 21.9 23.9 4.9 24.0 - 6O 9-82551 9-95 444 0.04 556 9.87 I0 7 o L, Cos. d. L. Cot. c. d. L. Tan. L. Sin. d. t P. P. 48' 462 42 f L, Sin, d, L, Tan, c, d. L, Cot, L, Cos, d, p. P, o 9.82551 14. 9-95 444 2C 0.04 556 9.87 107 ii 6O I 2 3 4 6 9 9.82 565 9.82 579 9.82 593 9.82 607 9.82 621 9.82 635 9.82 649 9.82 663 9.82 677 H H *4 *4 H H H H 14. 9.95 469 9-95 495 9-95 520 9-95 545 9-95 57 1 9-95 596 9.95 622 9-95 647 9-95 672 26 25 25 26 25 26 25 25 26 0.04531 0.04 505 0.04 480 0-04 455 0.04 429 0.04 404 0.04 378 0.04 353 0.04 328 9.87 096 9.87085 9.87073 9.87 062 9.87050 9.87039 9.87 028 9.87 016 9.87 005 n 12 II 12 II II 12 II 12 59 58 57 56 55 54 53 5 2 5 1 I 2 3 4 I 26 25 2.6 2.5 5.2 5.0 7-8 7-5 10.4 10.0 13.0 12.5 15.6 15.0 IO 9.82 691 9.95 698 2C 0.04 302 9.86993 1 1 50 7 18.2 17.5 n 12 13 H 11 1 7 18 19 9.82 705 9.82719 9-82 733 9.82 747 9.82 761 9-82 775 9.82 788 9.82 802 9.82816 X 4 14 H 14 H H J 3 14 H 14. 9-95 723 9-95 748 9-95 774 9-95 799 9-95 825 9-95 850 9-95 875 9-95 90i 9.95 926 *J 3 25 26 25 25 26 3 0.04 277 0.04 252 0.04 226 0.04 201 0.04175 O.O4 150 O.O4 125 O.O4 099 O.O4 074 9.86 982 9.86 970 9.86 959 9.86947 9.86 936 9.86 924 9.86913 9.86 902 9.86 890 12 II 12 II 12 II II 12 II 49 48 47 46 45 44 43 42 4i 9 2 3 2O.8 2O.O 23.4 22.5 14 13 1.4 1.3 2.8 2.6 4-2 3-9 C ft C 20 9.82 830 9-95 95 2 O.O4 048 9.86879 12 4O 4 5- 5' 2 7 O 6 C 21 22 23 24 3 2 7 28 29 9.82 844 9.82 858 9.82872 9.82 885 9.82 899 9.82913 9.82927 -9.82941 9-82955 14 14 13 14 14 H H H 9-95977 9.96 002 9.96028 9-96053 9.96078 9.96 104 9.96 129 9-96 155 9.96 1 80 2 5 25 2 5 26 25 26 25 O.O4 O23 0.03 998 0.03 972 0.03 947 0.03 922 0.03 896 0.03 871 0.03 845 0.03 820 9.86 867 9.86855 9.86 844 9.86 832 9.86 821 9.86 809 9.86 798 9.86 786 9.86775 12 II II 12 II 12 II 12 39 38 37 36 35 34 33 32 3 1 6 I 9 8.4 7.8 9.8 9.1 1 1. 2 10.4 12.6 11.7 12 11 1.2 I.I 3O 9.82 968 1 6 I A 9.96 205 2 5 26 0.03 795 9-86 763 II 3O 2 2.4 2.2 3 1 32 33 34 35 36 37 38 39 9.82 982 9.82 996 9.83010 9.83023 9-83 037 9.83051 9.83 063 9.83 078 9.83 092 H H 13 H 14 H 13 H 14 9.96 231 9.96 256 9.96 281 9.96307 9-96 332 9.96357 9-96 383 9.96 408 9-96433 25 25 26 25 25 26 25 2 5 26 0.03 769 0.03 744 0.03 719 0.03 693 0.03 668 0.03 643 0.03 617 0.03 592 0.03 567 9-86 752 9.86 740 9.86 728 9.86717 9.86 705 9.86 694 9.86 682 9.86 670 9.86 659 I 2 12 II 12 II 12 12 II 12 29 28 27 26 25 24 23 22 21 3 4 6 8 9 3-6 3-3 4.8 4-4 6.0 5.5 7.2 6.6 8-4 7-7 9.6 8.8 10.8 9.9 4O 9.83 106 9-96 459 2C 0.03 541 9.86 647 I 2 20 4i 42 43 44 4 ! 46 47 48 49 9.83 120 9-83 133 9.83 147 9.83 161 9.83174 9.83 1 88 9.83 202 9-83215 9.83 229 13 H H !3 14 14 13 14 9.96 484 9.96510 9-96 535 9.96 560 9.96 586 9.96611 9.96 636 9.96 662 9.96 687 ^J 26 25 25 26 25 25 26 2 5 0.03 516 0.03 490 0.03 465 0.03 440 0.03414 0.03 389 0.03 364 0.03 338 0.03313 9-86 635 9.86 624 9.86612 9.86 600 9-86 589 9.86577 9-86 565 9-86554 9.86 542 II 12 12 II 12 12 II 12 19 18 17 16 15 H 13 12 II o i 2 3 4 12 11 11 26 26 25 I.I 1.2 I.I 3-2 3-5 34 5-4 5-9 5-7 7.6 8.3 8.0 50 9.83 242 M 9.96712 2 5 06 0.03 288 9-86 530 10 5 T I.O I^.O 12. C 51 5 2 53 54 55 56 11 59 9.83 256 9.83 270 9.83 283 9.83 297 9.83310 9-83 324 9-83 338 9-8335 1 9-83 36? 14 !3 14 13 14 H 13 H 9.96 738 9.96 763 9.96 788 9.96814 9.96 839 9.96 864 9.96 890 9.96915 9.96 940 25 25 26 25 25 26 25 % 0.03 262 0.03 237 O.O3 212 0.03 1 86 0.03 161 0.03 136 0.03 no 0.03 085 0.03 060 9.86518 9.86 507 9-86 495 9-86 483 9.86472 9.86 460 9.86 448 9.86436 9.86425 II 12 12 II 12 12 12 II 9 8 7 6 5 4 3 2 I i; 8 i % \f M 15.4 14.8 3.2 17.7 17.0 5.4 20.1 19.3 x6 22.5 21.6 2.8 24.8 23.9 1-9 60 9-83 378 *o 9.96 966 0.03 034 9.86413 L, Cos. d. L, Cot, c, d. L, Tan, L. Sin, d, t P, P, 47 43' 463 1 L. Sin. | d. L. Tan. |c. d.| L. Cot. L. Cos, d, p. p. o I 2 3 4 1 9 IO ii 12 13 H \l IS 19 20 21 22 23 24 2 5 26 3 29 30 3 1 32 33 34 35 36 37 38 39 4O 4i 42 43 44 45 46 47 48 49 50 5 1 52 53 54 55 56 P 59 6O 9-83 37 s H 13 H U 14 13 H 13 14 9.96 966 ; -5 3 2 5 3 25 25 2 5 26 25 3 2 5 25 26 2 5 25 26 2 5 25 26 25 25 2 5 26 25 25 26 25 25 26 2 5 25 2 5 26 25 3 25 25 26 25 25 3 25 2 5 26 25 25 3 25 3 25 25 25 26 0.03 034 9.86413 1 12 12 12 II 12 12 12 12 12 II 12 12 12 12 12 12 12 II 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 12 12 12 12 12 12 13 12 12 12 12 12 13 60 59 58 57 56 55 54 53 5 2 5 1 50 49 48 47 46 45 44 43 42 4i 40 39 38 37 36 35 34 33 3 2 3i 3O 29 28 27 26 25 24 23 22 21 2O 19 18 7 16 15 1.4 *3 12 II IO 9 8 7 6 5 4 3 2 O 2 3 4 i 8 9 i 2 3 4 I 9 2 3 4 6 8 9 28 25 2.6 2.5 5-2 5- 7-8 7-5 10.4 10.0 13.0 12.5 15.6 15.0 18.2 17.5 2O.8 2O.O 23.4 22.5 14 13 1.4 1.3 2.8 2.6 4-2 3-9 5-6 5-2 7.0 6.5 8.4 7.8 9.8 9.1 II. 2 IO.4 12.6 11.7 12 11 1.2 I.I 2. 4 2.2 3-6 3-3 4-8 4-4 6 - 5-5 7.2 6.6 8.4 7-7 9.6 8.8 10.8 9.9 9-83 392 9.83 405 9.83419 9-83 432 9.83 446 9-83 459 9- s 3 473 9.83 486 9-83 500 9-835^3 9.96991 9.97016 9.97042 9.97 067 9.97 092 9.97 118 9-97 H3 9.97 168 9.97 193 0.03 009 O.O2 984 0.02 958 0.02 933 O.O2 908 0.02 882 O.O2 857 O.O2 832 0.02 807 9.86401 ] 9-86 389 9.86377 9.86 366 9-86 354 9.86 342 9.86 330 9.86318 9.86 306 1 j 9.97 219 0.02 781 9.86 295 9-83 527 9.83 540 9-Sj 554 9-83 567 ; 9.83 581 9-83 594 9.83 608 9.83621 9-83 634 9.83 648 1 3 14 '3 H 1 3 '4 13 13 H 13 13 H 13 H !3 13 H 13 13 H I 3 1 3 U H 13 '3 13 H 13 13 13 U 13 13 13 13 14 *3 J3 13 U 13 U H 1 3 '3 13 13 13 9.97 244 9.97 269 9.97 295 9.97 320 9-97 345 9-97 37 1 9-97 396 9.97421 9-97 447 O.O2 756 0.02 731 0.02 705 0.02 680 0.02 655 O.O2 629 O.O2 604 0.02 579 0.02 553 9.86 283 9.86 271 9.86 259 9.86 247 9.86235 9.86 223 9.86211 9.86 200 9.86 1 88 9-97 472 0.02 528 9.86 176 9.83 66 1 9.83 674 9.83 688 9.83 701 9-83 7i3 9.83 728 9.83 741 9-83 755 9.83 768 9-97 497 9-97 523 9-97 548 9-97 573 9-97 598 9-97 62 4 9.97 649 9.97 674 9.97 700 O.O2 503 0.02 477 0.02 452 0.02 427 O.O2 402 0.02 376 O.O2 351 O.O2 326 0.02 300 9.86 164 9.86 152 9.86 140 9.86 128 9.86116 9.86 104 9.86092 9.86 080 9.86 068 9-83 781 9.97 725 O.O2 275 9.86 056 9-83 795 9.83 808 9.83821 9-83 834 9.83 848 9.83 861 9.83 874 9.83 887 9.83901 9-97 75 9-97 77 6 9.97 80 1 9.97 826 9-97851 9-97 877 9.97 902 9.97 927 9-97 953 O.O2 250 O.O2 224 0.02 199 0.02 1 74 O.O2 149 O.O2 123 O.O2 098 0.02 073 O.O2 047 9.86 044 9.86032 9.86 020 9.86 008 9.85 996 9.85 984 9.85 972 9.85 960 9.85 948 9.83914 9.97 978 O.O2 O2 2 9.85 936 i 2 3 4 I 8 9 IO ii 12 13 13 13 12 26 25 25 I.O I.O I.O 3-o 2.9 3.1 5.0 4.8 5.2 7.0 6.7 7.3 9.0 8.7 9.4 i i.o 10.6 11.5 13.0 12.5 13.5 15.0 14.4 15.6 17.0 16.3 17.7 19.0 18.3 19.8 2 I.O 2O.2 21.9 23.0 22.1 24.0 25.0 24.0 9.83 927 9.83 940 9-83 954 9.83 967 9.83 980 9-83 993 9.84006 9.84 020 984033 9.98 003 9.98029 9.98054 9.98079 9.98 104 9.98 130 9-98 155 9.98 1 80 9.98 206 o.oi 997 o.oi 971 o.oi 946 o.oi 921 o.oi 896 o.oi 870 o.oi 845 o.oi 820 o.oi 794 9.85 924 9.85912 9.85 900 9.85 888 9.85 876 9.85 864 9.85851 9.85 839 9.85 827 9.84 046 9.98 231 o.oi 769 9-85815 9.84059 9.84072 9.84 085 9.84098 9.84 112 9.84 125 9.84138 9.84 151 9.84 164 9.98 256 9.98 281 9.98 307 9-98 332 9-98 357 9.98 383 9.98 408 9-98433 9.98458 o.oi 744 o.oi 719 o.oi 693 o.oi 668 o.oi 643 o.oi 617 o.oi 592 o.oi 567 o.oi 542 9.85 803 9-85 79i 9.85 779 9-85 766 9-^5 754 9.85 742 9-85 730 9.85718 9.85 706 9.84177 9.98 484 o.oi 516 9.85 693 L. Cos. d, L. Cot. c. d. L. Tan. L. Sin. | d. ' P. P, 46 1 464 44' 1 L, Sin. d, L, Tan, c, d, L, Cot, L, Cos, d, P, P, 9.84177 T7 9.98484 2C o.oi 516 9.85 693 12 6O I 2 3 4 6 8 9 9.84 190 9.84 203 9.84 "2 1 6 9.84 229 9.84 242 9-84 255 9.84 269 9.84 282 9.84 295 13 1 3 !3 13 H 9.98 509 9.98 534 9.98 560 9.98 585 9.98 610 9.98 635 9.98 661 9.98 686 9.98711 25 26 25 2 5 2 5 26 25 25 26 o.oi 491 o.oi 466 o.oi 440 o.oi 415 o.oi 390 o.oi 365 o.oi 339 o.oi 314 o.oi 289 9.85 68 1 9.85 669 9-85 657 9.85 645 9.85 632 9.85 620 9.85 608 9-85 596 9-85 583 12 12 12 J 3 12 12 12 13 12 59 58 57 56 55 54 53 5i I 3 4 i 5 i 6 i 8,, 26 25 14 2.6 2.5 1.4 5.2 5.0 2.8 7.8 7.5 4.2 0.4 10.0 5.6 3.0 12.5 7.0 5.6 15.0 8.4 8.2 17.5 9.8 IO 9.84 308 13 9-98 737 2C o.oi 263 9.85 57i 12 50 92 3 A. 22 C 126 n 12 13 17 18 ' 19 9.84321 9-84 334 9-84 347 9.84 360 9-84 373 9.84385 9.84398 9.84411 9.84 424 13 13 13 12 13 9.98 762 9.98 787 9.98812 9.98 838 9.98 863 9.98 888 9.98913 9.98 939 9.98 964 25 25 26 25 25 26 2 5 2C o.oi 238 o.oi 213 o.oi 1 88 o.oi 162 o.oi 137 O.OI 112 o.oi 087 o.oi 061 o.oi 036 9-85 559 9.85 547 9-85 534 9.85 522 9.85510 9-85 497 9.85 48! 9-85 473 9.85 460 12 13 12 12 12 12 13 12 49 48 47 46 45 44 43 42 4i I 2 3 4 1 13 12 1.3 1.2 2.6 2.4 3-9 3-6 5-2 4-8 6.5 6.0 7.8 7.2 2O 9-84 437 I 3 9.98 989 26 o.oi on 9.85 448 12 40 7 9.1 8.4 21 22 23 24 9.84 450 9.84 463 9.84476 9.84489 13 13 13 13 9.99015 9-99 040 9-99 065 9.99 090 2 5 25 26 o.oo 985 o.oo 960 o.oo 935 0.00910 9-85 436 9.85 423 9.85411 9-85 399 n Rr -7 8 A 13 12 12 13 39 38 37 36 8 9 10.4 9.6 11.7 10.8 2 5 26 27 28 29 9.84515 9.84 528 9.84 540 9-84 553 13 J 3 12 13 I 3 9.99 116 9.99 141 9.99 1 66 9.99 191 9.99217 25 25 2 5 26 o.oo 859 o.oo 834 o.oo 809 o.oo 783 9-85 374 9.85 361 9-85 349 9-85 337 12 12 12 34 33 13 13 26 25 3O 9.84 566 I 3 9.99 242 2C o.oo 758 9-85 324 3O o I O I O 32 33 34 35 36 3 39 9.84 579 9.84 592 9.84 605 9.84618 9.84 630 9.84 643 9.84 656 9.84 669 9.84 682 13 13 13 12 13 13 13 12 9-99 267 9-99 293 9.99318 9-99 343 9.99 368 9-99 394 9.99419 9-99 444 9.99 469 *3 26 2 5 26 25 25 25 26 o.oo 733 o.oo 707 o.oo 682 0.00657 o.oo 632 o.oo 606 o.oo 581 o.oo 556 o.oo 531 9.85312 9-85 299 9.85 287 9.85 274 9.85 262 9.85 250 9.85 237 9.85 225 9.85 212 13 12 13 12 12 13 12 13 29 28 27 26 25 24 23 22 21 2 3 4 I I 9 IO 3.0 2.9 5.0 4.8 7.0 6.7 . 9.0 8.7 ii.o 10.6 13.0 12.5 15.0 14.4 17.0 16.3 19.0 18.3 40 9.84 694 9-99 495 2C o.oo 505 9.85 2OO 20 n 2I.O 2O.2 23 O 22 I 41 42 43 44 4 I 46 47 48 49 9.84 707 9.84 720 9-84 733 9-84 745 9.84 758 9.84 771 9.84 784 9.84 796 9.84809 13 12 13 12 13 13 9.99 520 9-99 545 9-99 57 9.99 596 9.99 621 9.99 646 9-99 672 9.99 697 9.99 722 25 25 26 25 25 26 2 5 25 o.oo 480 o.oo 455 o.oo 430 o.oo 404 o.oo 379 o.oo 354 o.oo 328 o.oo 303 o.oo 278 9.85187 9.85 175 9.85 162 9.85 15 9.85 137 9.85 125 9.85 112 9.85 100 9.85 08 7 12 12 13 12 J 3 12 13 19 18 16 J 5 H 13 12 II 12 13 2 25.0 24.0 12 12 26 25 I.I . I.O 3-2 3- 1 5-4 S- 2 5O 9.84 822 13 9-99 747 26 o.oo 253 9.85 074 IO 3 7- 6 7-3 5i 52 53 54 57 58 59 9-84 835 9.84 847 9.84 860 9.84873 9.84 885 9.84 898 9.84911 9.84 923 9.84 936 12 13 12 13 13 12 13 13 9-99 773 9-99 798 9.99 823 9-99 848 9.99 874 9.99 899 9.99 924 9-99 949 9-99 975 25 25 25 26 25 25 26 o.oo 227 0.00 202 o.oo 177 o.oo 152 o.oo 126 0.00 101 o.oo 076 o.oo 05 1 o.oo 025 9.85 062 9.85 049 9.85 037 9.85 024 9.85 OI2 9.84 999 9.84 986 9.84 974 9.84 961 13 12 12 13 13 12 13 12 9 8 7 6 5 4 3 2 4 8 9 IO n 12 9-8 9-4 11.9 11.5 14-1 13-5 16.2 15.6 18.4 17.7 20.6 19.8 22.8 21.9 24.9 24.0 60 9.84 949 o.ooooo o.ooooo 9.84 949 L, Cos, d, L, Cot, c, d. L, Tan, L. Sin, d, 1 P, P, 45' t TABLES XVII., XVIII. NATURAL TRIGONOMETRIC FUNCTIONS. R'M'D SI*RV. 30 465 466 TABLE XVII. NATURAL SINES AN COSINES. ^ Natural Sines. c \ b ^ Prop. Angle. 0' 10' 20' 30' 40' 50' 60' Angle, Parts for 1', .000000 .0029 09 .0058 18 .0087 27 .011635 .0145 44 .017452 89 2.9 I .017452 .0203 6 .0232 7 .0261 8 .0290 8 .03199 .0349 o 88 2.9 2 .0349 o 378i .0407 i .0436 2 0465 3 .0494 3 05234 87 2.9 3 0523 4 05524 .0581 4 .0610 5 0639 5 .0668 5 .0697 6 86 2.9 4 .0697 6 .0726 6 0755 6 .0784 6 .08136 .0842 6 .0871 6 85 2.9 5 .0871 6 .09005 .09295 0958 5 .0987 4 .10164 '1045 3 84 2-9 6 10453 .10742 .11031 .11320 .11609 .11898 .12187 83 2.9 7 .12187 .12476 .12764 13053 1334 1363 .1392 82 2.9 8 .1392 .142! .1449 .1478 1507 1536 .1564 81 2.9 9 .1564 !593 .1622 .1650 .1679 .1708 1736 80 2.9 10 .1736 !7 6 5 .1794 .1822 .1851 .1880 .1908 79 2.9 ii .1908 1937 .1965 .1994 .2022 .2051 .2079 78 2.9 12 .2079 .2108 .2136 .2164 .2193 .2221 .2250 77 2.8 13 .2250 .2278 .2306 2334 2363 .2391 .2419 76 2.8 H .2419 .2447 .2476 .2504 2532 .2560 .2588 75 2.8 15 .2588 .2616 .2644 .2672 .2700 .2728 .2756 74 2.8 16 .2756 .2784 .2812 .2840 .2868 .2896 .2924 73 2.8 17 .2924 .2952 .2979 .3007 3035 .3062 .3090 72 2.8 .18 .3090 .3118 3H5 3173 .3201 .3228 .3256 7i 2.8 19 3256 3283 33" 3338 3365 3393 .3420 70 2.7 20 .3420 3448 3475 3502 3529 3557 .3584 69 2.7 21 3584 .3611 3638 3665 .3692 37 ! 9 3746 68 2-7 22 3746 3773 .3800 .3827 3854 .3881 3907 67 2-7 23 3907 3934 .3961 .3987 .4014 .4041 .4067 66 2.7 24 .4067 .4094 .4120 .4147 4173 .4200 .4226 65 2.7 25 .4226 4253 .4279 4305 4331 4358 4384 64 2.6 26 .4384 .4410 4436 .4462 .4488 45 H 4540 63 2.6 27 4540 .4566 4592 .4617 4643 .4669 4695 62^ 2.6 28 4695 .4720 .4746 .4772 4797 4823 .4848 61 2.6 29 .4848 .4874 .4899 4924 495 4975 .5000 60 2-5 30 .5000 5025 5050 5075 .5100 5125 SJS 59 2-5 3i 5*50 5175 .5200 5225 5250 5275 5 2 99 58 2.5 32 .5299 5324 5348 5373 5398 .5422 5446 57 2.5 33 544^ 547 1 5495 55i9 5544 .5568 5592 56 2.4 34 5592 .5616 .5640 .5664 .5688 5712 5736 55 2.4 35 5736 .5760 5783 5807 5831 5854 5878 54 2.4 36 .5878 .5901 5925 .5948 5972 5995 .6018 53 2-3 37 .6018 .6041^; .6065 .6088 .6111 .6134 6i57 52 2.3 38 6157 .6180 .6202 .6225 .6248 .6271 .6293 5 1 2.3 '39 .6293 .6316 6338 6361 6383 .6406 .6428 50 2.3 40 .6428 .6450 .6472 .6494 6517 6539 .6561 49 2.2 4i .6561 .6583 .6604 .6626 .6648 .6670 .6691 48 2.2 42 .6691 6713 6734 .6756 .6777 .6799 .6820 47 2.2 43 .6820 .6841 .6862 .6884 .6905 .6926 .6947 46 2.1 44 .6947 .6967 .6988 .7009 .7030 .7050 .70^1 45 2.1 60' 50' 40' 30' 20' 10' 0' Angle. NATURAL SINES AND COSINES (continued). Natural Sines. 467 Prop. Angle 0' 10' 20' 30' 40' 50' 60' Angle Parts for 1'. 45 .7071 .7092 .7112 7133 .7153 7173 7 ! 93 44 2.0 46 7193 .7214 7234 7254 7274 .7294 .73H 43 2.0 47 73'4 7333 7353 7373 7392 7412 7431 42, 2.O 48 7431 745i .7470 .7490 759 1 7528 7547 4i 9 49 7547 .7566 7585 .7604 .7623 .7642 .7660 40 9 50 .7660 .7679 .7698 .7716 7735 7753 777U 39 9 5* .7771 .7790 .7808 .7826 .7844 .7862 .7880^ 38 .8 52 .7880 7898 .7916 7934 795 1 .7969 .7986 37 .8 53 .7986 .8004, .8021 8039 .8056 .8073 .8090 36 7 54 .8090 .8107. .8124 .8141 .8158 8i75 .8192 35 7 55 .8192 .8208 '.8225 .8241 .8258 .8274 .8290 34. .6 56 .8290 .8307 8323 8339 8355 8371 8387 33 .6 57 .8387 .8403 .8418 .8434 .8450 ^.8465 .8480 32 .6 58 .8480 .8496 .8511. 8526 8542 8557 8572 3i 5 59 .8572 .8587 .8601' .8616 .8631 .8646 .8660 3 5 6O .8660 .8675 .8689 .8704 .8718 .8732 .8746 29 1.4 61 .8746 .8760 .8774 .8788 .8802 .8816 .8829 28 1.4 62 .8829 .8843 .8857 .8870 .8884 8897 .8910 27 14 63 .8910 8923 .8936 8949 .8962 8975 .8988 26 3 64 .8988 .9001 .9013 .9026 .9038 .9051 .9063 25 3 65 .9063 9075 .9088 .9100 .9112 .9124 9135 24 .2 66 9 '35 .9147 -9159 .9171 .9182 .9194 9205 23 .2 67 .9205 .9216 .9228 9239 .9250 .9261 .9272 22 .1 68 .9272 .9283 9293 9304 9315 9325 9336 21 .1 69 .9336 9346 9356 9367 9377 9387 9397 20 I JO 70 9397 9407, V K .9417 .9426 9436 .9446 9455 19 I.O 7* "9455 9465* 9474 .9483 .9492 .9502 95 " 18 0.9 72 95" .9520 .9528 9537 9546 9555 9563 17 0.9 73 . -95 6 3 9572 .9580 .9588 9596 .9605 .9613 16 0.8 74 .9613 .9621 .9628 .9636 .9644 .9652 9659 15 0.8 75 .9659 .9667 .9674 .9681 .9689 ..9696 973 14 0.7 76 9703 .9710 .9717 9724 973 9737 9744 13 0.7 77 9744 975 9757 9763 .9769 9775 .9781 12 0.6 78 .9781 .9787 9793 9799 .9805 .9811 .9816 II 0.6 79 .9816 .9822 .9827 9833 .9838 9843 .9848 IO o-5 80 .9848 9853 .9858 9863 .9868 .9872 .9877 9 -5 81 .9877 .9881 .9886 .9890 9894 9899 9903 8 0.4 82 9903 .9907 .9911 .9914 .9918 ,.9922 9925 7 0.4 83 .9925 9929 9932 9936 9939 9942 9945 6 0.3 84 9945 .9948 995 ' 9954 9957 9959 .9962 5 o-3 85 .9962 .9964 9967 .9969 .9971 9974 .9976 4 O.2 86 .9976 .9978 .9980 .9981 9983 9985 .9986 3 0.2 87 .9986 .9988 9989 .9990 9992 9993 9994 2 O.I 88 9994 9995 .9996 9997 9997 .9998 .9998 I O.I 89 .9998 9999 9999 I.OOOO I.OOOO I.OOOO I.OOOO O.O 60' 50' 40' 30' 20' 10' 0' Angle. Natural Cosines. 468 TABLE XV11I. NATURAL TANGENTS AND COTANGENTS:* Natural Tangents. 1 Prop. Angle. 0' 10' 20' 30' 40' 50' 60' Angle. Parts for 1'. .00000 .0029 i .0058 2 .00873 .01164 0145 5 .01746 89 2.9 i .01746 .0203 6 .0232 8 .0261 9 .0291 o .0320 i .0349 2 88 2.9 2 .0349 2 037 8 3 .0407 5 f .0436 6 .0465 8 .0494 9 .0524 I .87 2.9 3 .0524 I 0553 3 0582 4 / ^06 1 1 6 .0640 8 .0670 o .0699 3 ^36 2-9 4 .0699 3 .0728 5 0757 8 .0787 o .08163 .084^6 .0874 9 85 2-9 5 .0874 9 .0904 2 0933 5 .09629 .0992 3 .1021 6 .1051 o 84 2.9 6 .1051 o .1080 5 .11099 "394 .11688 .11983 .12278 83 2.9 7 .12278 12574 .12869 -wts .1346 1376 .1405 82 3-o 8 .1405 1435 ^465 1495 .1524 '554 .1584 81 3-o 9 .1584 .1614 .1644 !673 1703 '733 !7 6 3 80 3-o 10 1763 1793 .1823 1853 .1883 .1914 .1944 79 3-o ii .1944 .1974 .2004 .2035 .2065 2095 .2126 78 3-o 12 .2126 .2156 .2186 .2217 .2247 .2278 .2309 77 3- 1 13 .2309 2339 .2370 .2401 2432 .2462 2493 76 3- 1 4 .2493 .2524 2555 .2586 .2617 .2648 .2679 75 3-i 15 .2679 .2711 .2742 2773 .2805 .2836 .2867 74 3-i 16 .2867 .2899 .2931 .2962 2994 .3026 .3057 73 3-2 17 3057 .3089 .3121 3153 3185 3217 3249 72 3-2 18 3249 .3281 33H 3346 3378 34" 3443 7 1 3-2 9 3443 347 6 .3508 3541 3574 .3607 .3640 70 3-3 20 .3640 3673 .3706 3739 3772 3805 3839 69 3-3 1 2I 3839 .3872 .3906 3939 3973 .4006 .4040 68 3-4 22 .4040 .4074 .4108 .4142 .4176 .4210 4245 67 3-4 23 4245 4279 43H 4348 .4383 .4417 445 2 66 3-5 24 445 2 .4487 .4522 4557 4592 .4628 .4663 65 3-5 25 .4663 .4699 4734 .4770 .4806 .4841 .4877 64 3-6 26 .4877 4913 495 .4986 .5022 5059 5095 63 3-6 27 595 5!32 .5169 .5206 5243" .5280 5317 62 3-7 28 5317 5354 5392 5430 5467 555 5543 61 3-8 29 5543 .5581 .5619 .5658 .5696 5735 5774 60 3-8 30 5774^ .5812 5851 .5890 ' 5930 5969 .6009 59 3-9 3 1 .6009 .6048 .6088 .6128 .6168 .6208 .6249 58 4.0 32" .6249 .6289 6330 637 i .6412 6453 .6494* 57. 4.1 33 .6494 .6536 6577 .6619 .6661 .6703 6 745 5* 4.2 34 6 745 .6787 .6830 .6873 .6916 6959 .7002 55 4-3 35 .7002 .7046 .7089 7*33 .7177 .7221 .7265 54 4-4 36 .7265 7310 7355 .7400 7445 .7490 7536 53 4-5 37 7536 758i .7627 7 6 73 .7720 .7766 7813 S 2 4.6 38 7813 .7860 .7907 7954 .8002 .8050 .8098 5 1 4-7 39 .8098 .8146 8i95 .8243 .8292 .8342 .8391 5 4-9 4O .8391 .8441 .8491 .8541 .8591 .8642 .8693 49 5-o 4i .8693 .8744 .8796 .8847 .8899 .8952 .9004 48 5-2 42 .9004 9057 .9110 .9163 .9217 .9271 9325 47 5-4 43 9325 .9380 9435 .9490 9545 .9601 9657 46 5-5 44 9657_ 97 * 3 .9770 .9827 .9884 .9942 1. 0000 45 5-7 60' 50' 40' 30' 20' 10' 0' Angle. d Natural Cotangents. NATURAL TANGKXTS AND COTANGENTS (continued). Natural Tangents. 469 Prop. Angle 0' 10' 20' 30' 40' 50' eo' Angle Parts for V. 45 I.OOOO 1.0058 1.0117 1.0176 1.0235 1.0295 1-0355 44 5-9 46 I -355 i .04 1 6 1.0477 1.0538 1.0599 i. 066 1 1.0724 43 6.1 47 1.0724 1.0786 1.0850 1.0913 1.0977 1.1041 1.1106 42 6.4 48 1.1106 1.1171 1.1237 1.1303 1.1369 1.1436 1.1504 4 1 6.6 49 1.1504 I - I 57 I 1.1640 1.1708 1.1778 1.1847 1.1918 40 6.9 50 1.1918 1.1988 1.2059 1.2131 1.2203 1.2276 1.2349 39 7- 2 5 1 1.2349 1.2423 ,1-2497 1.2572 1.2647 1.2723 1.2799 38 7-5 52 1.2799 1.2876 1.2954 1.3032 1.3111 1.3190 1-3270 37 7-9 53 1.3270 I-335I 1.3432 L3SI4 '3597 1.3680 J-3764 36 8.2 54 1.3764 1.3848 1-3934 1.4019 1.4106 I-4I93 1.4281 35 8.6 55 1.4281 1.4370 1.4460 1-4550 1.4641 M733 1.4826 34 9.1 56 1.4826 1.4919 1-5013 1.5108 1.5204 1.5301 1-5399 33 9.6 57 1-5399 1-5497 1-5597 1.5697 1.5798 1.5900 1.6003 32 10. 1 58 1.6003 1.6107 1.6212 1.6319 1.6426 1.6534 1.6643 31 10.7 59 1.6643 '6753 1.6864 1.6977 1.7090 1.7205 1.7321 30 "3 60 1.7321 1-7437 '7556 L7675 1.7796 1.7917 i .8040 29 12.0 61 1.8040 1.8165 1.8291 1.8418 1.8546 1.8676 1.8807 28 12.8 62 1.8807 1.8940 1.9074 1.9210 1-9347 1.9486 1.9626 27 13.6 63 1.9626 1.9768 1.9912 2.0057 2.0204 2-0353 2.0503 26 14.6 64 2.0503 2.0655 2.0809 2.0965 2.1123 2.1283 2.1445 25 15.7 65 2.1445 2.1609 2-1775 2.1943 2.2113 2.2286 2.2460 24 16.9 66 2.2460 2.2637 2.2817 2.2998 2.3183 2.3369 2-3559 23 I8. 3 67 2-3559 2.375 2.3945 2.4142 2.4342 2-4545 2-475 J 22 19-9 68 2-475 1 2.4960 2.5172 2.5386 2.5605 2.5826 2.6051 21 21.7 69 2.6051 2.6279 2.6511 2.6746 2.6985 2.7228 2-7475 2O 23.7 7O 2-7475 2.7725 2.7980 2.8239 2.8502 2.8770 2.9042 19 7 1 2.9042 2.9319 2.9600 2.9887 3.0178 3-0475 3-0777 18 72 3.0777 3.1084 3-1397 3.1716 3.2041 3-237 1 3.2709 17 73 3.2709 3-3052 3-3402 3-3759 3.4124 3-4495 34874 16 74 3-4874 3-5261 3-5656 3.6059 3.6470 3-6891 3-7321 '5 75 3-7321 3-776o 3.8208 3-8667 3-9I36 3-9617 4.0108 14 76 4.0108 4.0611 4.1126 4.1653 4-2193 4.2747 4-33I5 13 77 4.3315 i 4-3897 4-4494 4-5107 4.5736 4.6382 4.7046 12 78 4.7046 4-7729 4.8430 4-9152 4.9894 5.0658 5.1446 II 79 5.1446 5-2257 5-3093 5-3955 54845 5.5764 5.6713 IO 80 5-67I3 57694 5.8708 5-9758 6.0844 6.1970) 6.3138 9 81 6.3138 | 6.4348 6.5606 6.6912 6.8269 6.9682 7.1154 8 82 7.1154 7.2687 7.4287 7-5958 7.7704 7.9530 8.1443 7 83 8.1443 8.3450 8-5555 8.7769 9.0098 9-2553 9-5 J 44 6 84 9-5 I 44 9.7882 10.0780 10.3854 10.7119 11.0594 11.4301 5 85 11.4301 11.8262 12.2505 12.7062 13.1969 13.7267 14.3007 4 86 14.3007 114.9244 15.6048 16.3499 17.1693 18.0750 19.0811 3 87 19.0811 j 20.2056" 21.4704 22.90381-24.5418 26.4316 28.6363 2 88 28.6363 31.2416 34-3678 38.1885 42.9641 49.1039 57.2900 I 89 57.2900 68.7501 85.9398 114.5887 171.8854 343-7737 00 O 60' 50' 40' 30' 20' 10' 0' Angle. Natural Cotangents. . . 4 V ' 3 ^ - ^mO r^^^y^TT j ^T^n^r\ YC 13554 < 926464 THE UNIVERSITY OF CALIFORNIA LIBRARY ^-/l