LIBRARY OF THE UNIVERSITY OF CALIFORNIA. Gl FT OF Class f DEPARTMENT OF THE INTERIOR UNITED STATES GEOLOGICAL SURVEY GEORGE OTIS SMITH, DIRECTOR GEOGRAPHIC TABLES AND FORMULAS COMIM I.KI> BY SAMl'KL S. (JANNKTT WASHINGTON GOVERNMENT PRINTING OFFICE 1908 DEPARTMENT OF THE INTERIOR UNITED STATES GEOLOGICAL SURVEY GEORGE OTIS SMITH, DIRECTOR GEOGRAPHIC TABLES AND FORMULAS COMPILED BY SAMUEL S. GANNETT WASHINGTON GOVERNMENT PRINTING OFFICE 1908 r sin a B=HXcos a. 6 GEOGRAPHIC TABLES AND FORMULAS. REDUCTION TO CENTER. In fig. 2 let P= place of instrument; C= center of station; Q= measured angle at P between two objects, A and B; y angle at P between C and the left-hand object, B; r= distance CP; C' = unknown and required angle at C; D= distance AC; (r and D must be reduced to same unit, usually meters.) G=distance BC; A = angle at A between P and C; B= angle at B between P and C. FIG. 2. Reduction to center. Then, from the relation between the parts of the triangle, G : r :: sin y : sin B; hence sin B=^P- As the angles at A and B are very small, their sines may be regarded as equal to A sin 1" and B sin 1", respectively; hence . r sin y B=(m seconds) Gsinl ,, and sin (Q=by) r sin y D sin 1" G sin 1"' GEOGRAPHIC TABLES AND FORMULAS. In the use of this formula, proper attention should be paid to the signs of sin (Q+y) and sin y\ for the first term will be positive only when (Q+y) is less than 180 (the reverse with sin y) ; D being the distance of the right-hand object, the graduation of the instrument running from left to right. r being relatively small, the lengths of D and G are approximately computed with the angle Q. The following quantities must be known in addition to the measured angles in order to find the correction for reducing to center: 1. The angle measured at the instrument, P, between the center of the signal or station, C, and the first-observed station to the right of it, A. 2. The distance from the center of the instrument to the center of the station = r. 3. The approximate distances, D, G, etc.^ from the station occupied to the stations observed. The latter may be computed from the uncorrected angles. Example: Reduction to center from P to C. Constants: a. c. log sin 1" =5. 31443 log feet to log meters =9. 48402 log constant (for any station) 4. 79845 /=6.5 feet: log =0. 81291 log constant for this station 5. 61136 Angle Q-Y (CPA) 23 40' Angle (BPC) 3714 ; or 322 46' log sin angle 9. 6036 9. 7818 a. c. log distance 5. 3954 5. 3162 log T -f- constant 5.6114 5 6114 log correction . 0. 6104 0. 7094 correction to direction 4". 08 5". 12 correction to angle B P A=4".08 +5".12=9".20. GEOGRAPHIC TABLES AND FORMULAS. GRAPHIC REDUCTION TO CENTER. Approximate closure errors of triangles may be tested in the field before distances have been computed by scaling from the plot the distances between stations in miles and the perpendicular distance in feet from signal to line joining instrument and distant station. Then, since 1 foot at a distance of 40 miles subtends an angle of V (nearly), length of perpendicular in feet X 40 i = n = correction in seconds. number ot miles Example: Station P. Correction for swing on line B P, 30 miles in length from instrument to signal _3.8 feet X 40 _ -^- = 5 .1, correction for swing on line A P, 25 miles in length, 2.6 feet X 40 and correction to angle B P A = Q to reduce from instrument to sig- nal = 5.1" -f- 4.2" = 9.3", agreeing closely with the exact compu- tation. APPROXIMATE SPHERICAL EXCESS IN SECONDS. This may be obtained by dividing the area of the triangle in square miles by 75.5. SOLUTION OF TRIANGLES. Given two sides and included angle, to solve the triangle: FIG. 3. Solution of triangles; two sides and included angle given. Let x be an auxiliary angle; then tan wfr or log tan %=log a log J; tan i (A-B) = tan (a 45) tan (A+B); i (A+B)+* (A-B) = A; i(A+B)-i(A-B)=B; from which remaining parts can be computed. GEOGRAPHIC TABLES AND FORMULAS. 9 Example: Gwen log a=4. 3666779 Given C (spherical angle) 21 14' 54". 10 Given log 6=4. 2050498 Given | sph. exc. - . 10 (1) tan *=0. 1616281 =55 25' 25".41 -45 (5) Logtan(z-43)=1025' 25". 41=9. 2647291 (6) Log tan 79 22 33 .00=0.7268100 C (plane angle) = 21 14 54 .00 (2) 180 180 C=A-(-B=158 45 06 .00 (3) i (A+B) = 79 22' 33". 00 (4) 9. 9915391=tan i (A-B) 44 26 30 .90 sum=A=123 49' 03". 90 (8) difference=B= 34 56 02 .10 (9) (10) Check. A=123 B= 34 C= 21 49' 56 14 03". 02 . 54 . 90 a. c. 10 00 log a log sin log sin log sin =4. 3666779 A=0. 0804971 B=9. 7578749 C=9. 5592012 Sum = 180 00 00 .00 logc log b =4. =4. 0063762 2050499 THREE-POINT PROBLEM. If three points, forming a triangle of which the sides and angles are known or can be computed, be visible from a fourth point, P, it is required to determine the position of P. Set up the theodolite at P and measure the two angles subtended by any two of the given sides. This problem is of use in cases where, the regular triangulation hav- ing been completed, additional points are required for the topographic survey, or are needed for special service. The angles should be care- fully measured, and in the computations the logarithms should be car- ried to seven places of decimals. Three cases of its application are given, as in others, such as when P falls upon one or another of the sides of the known triangle, or on the prolongation of either, the case resolves itself into the solution of a simple triangle with one side and the angles given; or the problem is indeterminate, as when P is situated on the circumference of the circle passing through the three known points a contingency which rarely occurs. 10 GEOGRAPHIC TABLES AND FORMULAS. Example for each of the three cases. Given the side a=11204.5 Given the side 6= 7289.0 Given the side c= 6273.8 x Given the angle A =111 10' 54" Angle observed A P C=P' Angle observed A P B=P" To find A B P=x To find A C P =v FIG. 4. Three-point problem; computation. P'... 50 06' 12" P".. 43 50' 38" S.... 180 -i(A+P'+P") S.... 77 26' 08" c sin P' P' 49 47' 20" P".. . 44 09' 30" S. KA-P'-P") S 8 37' 02 tan Z= P'... 104 00' 00" P".. 100 20' 00" S ____ 180 (A+P'+P" S ____ 22 14' 33" tan =cot (Z+45 P ) tan S b sin P" y = S , but if tan be negative, then x = S , y = S-{-s logc 3.7975307 log sin P 7 9.8849100 colog b 6.1373320 colog sin P" 0. 1594574 log tan Z 9.9792301 Z... 43 37 X 49". 6 logcot(Z-f45) 8.3785397 log tan S 0.6519386 log tan . , 9. 0304783 6 07 X 21".7 S... . 77 26' 08".0 x.:.. 83 33' 29".7 y 71 18 X 46".3 Hence, P AB 52 35 X 52".3 P AC.. .58 35 X 01".7 Computation. logc 3.7975397 log sin P x 9. 8839061 colog b 6.1373320 colog sin P".... 0.1569894 log tan Z 9.9747583 Z... 43 20 7 09".2 logcot(Z+45) 8.4631818 log tan S 9.1805366 log tan 7.6437184 15 X 08". 1 8 37 X 02". x 8 52' 10". 1 y 8 21' 53".9 Hence, P A B 126 58' 19".9 P AC .. . 121 50' 46". 1 logc 3.7975307 log sin P' 9. 9869041 colog 6 6.1373320 colog sin P" 0. 0071016 log tan Z 9.9288684 Z... 40 19' 43".3 log cot (Z+45) 8. 9122794 log tan S 9.6116787 log tan 8. 5239581 ... 1 54' 50".04 S... 22 14' 33".00 x... 24 09' 23". 00 y... 20 19' 43".00 Hence, PAB.... 55 30' 37".00 PAC.. . 55 40' 17".00 GEOGRAPHIC TABLES AND FORMULAS. 11 As all the angles and a side in each triangle are now known, the other sides, or the distances from P to the three given points, can be readily computed. TO PB 7194.87 PA 8999.89 PC 8107.98 P A . . 8999. 89 PB 7194.94 PA 1388.54 PC 8107.91 PA., . 1388.54 P B 5256. 29 PA 2609.75 PC 6203.63 P A . . 2609. 75 The results are verified when both triangles give the same value for the line P A. GRAPHIC SOLUTION OF THE THREE-POINT PROBLEM. , 1. When new point is within the triangle formed by the three points, point sought is within the triangle of error. 2. When new point is on or near the circle passing through the other points, the location is uncertain. 3. When new point is within either of the three shaded segments of the circle (see diagram below), orient on middle point; then the line from middle point lies between true point and point of intersection of lines from other two points. 4. When new point is without the circle, orient on most distant point; then the point sought is always on the same side of the line from most distant point as the point of intersection of the other two lines. NOTE. Since a location can be made from any three points, whether correctly plotted or not, therefore always check such locations by means of a fourth point if possible. FIG. 5. Three-point problem; graphic solution. 12 GEOGRAPHIC TABLES AND FORMULAS. MICROMETER ALIDADES DETERMINATION OF CONSTANT AND VALUE OF DIVISION. R', R" = readings of micrometer screw. R =R' R" = difference of readings. d = value in seconds of arc of 1 division of micrometer head. A = angle subtended by targets in seconds of arc. C = micrometer constant or ratio. H = distance to targets, supposed at right angles to line of sight. B = length of base, or distance between targets. (D d = (2) C B HR sin. I" 1 HR B EXAMPLE. Readings taken on two targets 21.25 feet apart at right angles to the line of sight and at a measured horizontal distance of 2859.5 feet from the point of observation. R' R" R 550.0 -88.0 = 462.0 540.5 -76.5 = 464.0 etc. etc. etc. 462.075 mean of 20 readings. Computation of d by formula (1) : B =21.25 ft.. _ log. 1.32736 H =2859.5 ft..colog. 6.54371 sin 1" colog. 5.31443 R =462.075 ft. colog. 7.33528 d=-3".317 log. 0.52078 Computation of C by formula (2) : B = 21.25 ft.. colog. 8.67264 H = 2859.5 ft.. .log. 3.45629 R =462.075 ft. Jog. 2.66472 C =62180.. ..log. 4.79365 GEOGRAPHIC TABLES AND FORMULAS. 13 For computing distances use this formula: (3) H = ^ When the base is not at right angles to the line of sight as at b, or at the same elevation as the point of observation, the factors sin a and cos V must be introduced, a being the angle between the base and line of sight and V the vertical angle at A. The full formula for distances then becomes (A\ TT ^C sin a cos V R The plotted position of the base b should be prolonged on the field sheet in order to permit the measurement of the angle a with a large paper or other protractor, with greater accuracy. 14 GEOGRAPHIC TABLES AND FORMULAS. METHOD OF FIXING A MERIDIAN AT ANY TIME BY HOUR [Extracted from United States Land Survey Manual.] The annexed diagram (fig. 6) will show in their proper relation the various aspects of Polaris in its daily apparent motion around the north-polar point. This must be carefully studied, as the illustration of Table 1, for finding at any hour the hour angle and azimuth of Polaris, and the resulting meridian, at times when more direct methods are not available. Hour angle of Polaris. In fig. 6 the full vertical line represents a portion of the meridian passing through the zenith Z (the point directly overhead), and intersecting the northern horizon at the north point N, from which, for surveying purposes, the azimuths of Polaris FIG. 6. Aspects of Polaris. are reckoned east or west. The meridian is pointed out by the plumb line when it is in the same plane with the eye of the observer and Polaris on the meridian, and a visual representation is also seen in the vertical wire of the transit, when it covers the star on the meridian. When Polaris crosses the meridian it is said to culminate; above the GEOGRAPHIC TABLES AND FORMULAS. 15 pole (at S), the passage is called the upper culmination, in contradis- tinction to the lower culmination (at S'). In the diagram which the surveyor may better understand by hold- ing it up perpendicular to the line of sight when he looks toward the pole Polaris is supposed to be on the meridian, where it will be about noon on April 10 of each year. The star appears to revolve around the pole, in the direction of the arrows, once in every 23 h 56 m .l of mean solar time; it consequently comes to and crosses the meridian, or culminates, nearly four minutes earlier each successive day. The apparent motion of the star being uniform, one quarter of the circle will (omitting fractions) be described in 5 h 59 m , one half in ll h 58 m , and three quarters in 17 h 57 m . For the positions s n S 2 , S 3 , etc., the angles SPs 1? SPs 2 , SPs 3 , etc., are called hour angles of Polaris, for the instant the star is at s 19 S 2 , or S 3 , etc., and they are measured by the arcs Ss n Ss 2 , Ss 3 , etc., expressed (in these instructions) in mean solar (common clock) time, and are alwa} T s counted from the upper meridian (at S), to the west, around the circle from O h O m to 23 h 56 m .l, and may have any value between the limits named. The hoar angles, measured by the arcs Ss n Ss 2 , Ss 3 , Ss 4 , Ss 6 , and Ss tt , are approximately l h 8 m , 5 h 55 m , 9 h 4 m , 14 h 52 m , 18 h Ol m , and 22 h 48 m , respectively; their extent is also indicated graphically by broken fractional circles about the pole. Suppose the star observed at the point S 3 ; the time it was at S (the time of upper culmination), taken from the time of observation, will leave the arc Ss 3 , or the hour angle at the instant of observation; similar relations will obtain when the star is observed in any other position; therefore, in general: Subtract the time of upper culmination from the correct local mean time of observation; the remainder will be the hour angle of Polaris expressed in time, w the " argument for Table 3." The observation may be made at any instant when Polaris is visible, the exact time being carefully noted. 16 GEOGRAPHIC TABLES AND FORMULAS. TABLES. TABLE 1. Local mean (astronomical} time of the culminations and elongations of Polaris in the year 1902. [From Magnetic Declination Tables, U. S. Coast and Geodetic Survey. Computed for latitude 40 north and longitude 90 or 6 h west of Greenwich.]' Date. East elonga- tion. Upper culmi- nation. West elonga- tion. Lower culmi- nation. 1902 January 1 h m 45.8 h m 6 40.6 h m 12 35. 3 h m 18 38. 7 January 15 23 46. 6 5 45.3 11 40 17 43 4 February 1 22 39. 5 4 38.2 10 32 9 16 36 3 February 15 21 44. 2 3 42.9 9 37 7 15 41 March 1 20 49. 2 47.7 8 42.4 14 45 8 March 15 19 54. 1 52.7 7 47.3 13 50. 7 April 1 18 47. 45.6 6 40.3 12 43. 7 April 15 17 52 23 46 7 5 45 3 11 48 6 May 1 16 49 1 22 43 8 4 42 5 10 45 7 May 15 15 54. 2 21 48 9 3 47 6 9 50 8 June 1 14 47. 5 20 42. 3 2 40 9 8 44 2 June 15 13 52. 6 19 47. 4 1 46 7 49 3 July 1 12 50.0 18 44.8 43.4 6 46.7 July 15 11 55. 1 17 49. 9 23 44. 6 5 51.8 August 1 10 48. 6 16 43. 4 22 38. 4 45.3 August 15 9 53.7 15 48. 5 21 43. 1 3 50.4 September 1 8 47.1 14 41. 9 20 36. 5 2 43.8 September 15 . 7 52. 2 13 47. 19 41. 6 1 48.9 October 1 6 49.3 12 44. 1 18 38. 7 46.0 October 15 5 54.3 11 49. 1 17 43. 7 23 47. 2 November 1 4 47.5 10 42.3 16 36. 9 22 40. 4 November 15 . 3 52.3 9 47.1 15 41.8 21 45. 2 December 1 2 49.3 8 44. 1 14 38. 8 20 42. 2 December 15. 1 54.0 7 48.8 13 43. 6 19 46. 9 A. To refer the above tabular quantities to years subsequent to 1902: 1. 4 minutes. up to March 1 For year 1903 add (add 1904- 2.8 subtract 1. 1 1905 add 0.2 1906 " 1.5 1907 " 2.9 1908 " J4.2 [0.3 1909 " L7 1910 " 3.0 1911 " 4.4 on and after March 1 up to March 1 on and after March 1 GEOGRAPHIC TABLES AND FORMULAS. 17 B. To refer to any calendar day other than the first and fifteenth of each month: SUBTRACT the quantities below from the tabular quantity for the PRECEDING DATE. Day of month. Minutes. Number of days elapsed. 2 or 16 3.9 1 3 17 7.9 2 4 18 11.8 3 5 19 15.8 4 6 20 19.7 5 7 21 23.6 6 8 22 27.6 7 9 23 31.5 8 10 24 35.5 9 11 25 39.4 10 12 26 43.3 11 13 27 47.3 12 14 28 51.2 13 29 55.2 14 30 59.1 15 31 63.0 16 C. To refer the table to standard time and to the civil or common method of reckoning: ( a ) ADD to the tabular quantities four minutes for every degree of longitude the place is west of the standard meridian, and SUBTRACT when the place is east of the standard meridian. ( 6 ) The astronomical day begins twelve hours after the civil day, i. e. , begins at noon on the civil day of the same date, and is reckoned from to 24 hours. Consequently an astronomical time less than twelve hours refers to the same civil day, whereas an astronomical time greater than twelve hours refers to the morning of the next civil day. It will be noticed that for the tabular year two eastern elongations occur on January 12 and two western elongations on July 12. There are also two upper culminations on April 12 and two lower culmina- tions on October 12. The lower culmination either follows or pre- cedes the upper culmination by ll h 58 m .l. D. To refer to any other than the tabular latitude between the limits of 25 and 50 north: ADD to the time of west elongation O m .13 for every degree south of 40, and SUBTRACT from the time of west elonga- tion O m .18 for every degree north of 40. Reverse these operations for correcting times of east elongation. 4606108 2 18 GEOGRAPHIC TABLES AND FORMULAS. E. To refer to any other than the tabular longitude: ADD O m .16 for each 15 east of the ninetieth meridian, and SUBTRACT O m .16 for each 15 west of the ninetieth meridian. A few examples will illustrate the use of table 1. 1. Required the time of upper culmination of Polaris for a station in longitude 90 west, for March 3, 1904. h. m. Astron. time, U. C. of Polaris, 1904, March 1 2 46. 6 Reduction for two days, 7 m .9 (B) (subtract) 7.9 Local mean time U. C. of Polaris, 1904, March 3 2 38. 7 The required time may also be obtained by using the table in the opposite direction, i. e., by taking the time for March 15, and adding the reduction as follows: h. m. Astron. time U. C. of Polaris, 1904, March 15 1 51. 6 Reduction for twelve days, add 47. 3 Local mean time U. C. of Polaris, 1904, March 3 2 38. 9 In this case the two results are practically identical. If the compu- tation is made both ways, the results will check each other. B has been inserted to save the surveyor the -little trouble of making the multiplications; thus, for the above example, in the table under B, opposite the third or seventeenth day of the month in the left hand column, will be found the correction 7 m .9. Computing from a preceding date, for days between April 11 and 15 of any year, the reduction in B will be greater than the tabulated time of culmination, in which case 23 h 56 m .l will be added, to make the subtraction possible. 2. Required, for a station in longitude 90 west, the time of U. C. of Polaris for April 14, 1906: h. m. Astron. time, U. C. of Polaris, 1906, April 1 47. 1 Add.. 23 56.1 Sum 24 43.2 Reduction to April 14, subtract 51. 2 Local mean time U. C. of Polaris, April 14 23 52. Working from a following date, for days between 9th and 15th of April, the sum will exceed 23 h 56 m .l, and when this occurs subtract 23 h 56 m .l from the sum, and the remainder will be the required time. 3. Required, for a station in longitude 90 west, the time of U. C. of Polaris for April 10, 1904. h. m. Astron. time, U. C. of Polaris, 1904, April 15 23 45.6 Reduction for five days, add 19. 7 Sum 24 05. 3 Subtract.. ... 23 56.1 Local mean time, U. C. of Polaris, 1904, April 10 09. 2 For further application of table 1 see pp. 24 and 25. GEOGRAPHIC TABLES AND FORMULAS. 19 TABLE 2. Azimuth of Polaris when at elongation for any year between 1902 and 1910. Latitude. 1902.0 1903.0 1904.0 1905.0 1906.0 1907.0 1908.0 1909.0 1910.0 O ' o / o / o / o / o / / / O ' 25 1 20.5 1 20.1 1 19.8 1 19.4 1 19.1 1 18.7 1 18.4 1 18.1 1 17.7 26 21. L 20.8 20.5 20.1 19.8 19.4 19.1 18.7 18.4 27 21.9 21.5 21.2 20.8 20.5 20.1 19.8 19.4 19.1 28 22.6 22.2 21.9 21.6 21.3 20.9 20.5 20.1 19.8 29 23.4 26.0 22.7 22.4 22.1 21.7 21.3 20.9 20.5 30 24.2 23.9 23.5 23.1 22.8 22.4 22.1 21.7 21.3 31 26.1 24.7 24.4 24.0 23.6 23.2 22.9 22.5 22 2 32 26.0 25.6 25.3 24.9 24.5 24.1 23.8 23.4 23^1 33 27.0 26.6 26.2 25.9 25.5 25.1 24.7 24.3 24.0 34 28.0 27.6 27.2 26.9 26.5 26.1 25.7 25.3 25.0 35 29.0 28.7 28.3 27.9 27.5 27.1 26.8 26.4 26.0 36 30.1 29.8 29.4 29.0 28.6 28.2 27.9 27.5 27.1 37 31.3 30.9 30.5 30.1 29.7 29.3 29.0 28.6 28.2 38 32.6 32.2 31.8 31.4 31.0 30.6 30.2 29.8 29.4 39 33.9 33.5 33.1 32.7 32.3 31.8 31.4 31.0 30.6 40 35.2 34.8 34.4 34.0 33.6 38.2 32.8 32.4 32.0 41 36.7 36.2 35.8 35.4 35.0 34.6 34.2 33.8 33.4 42 38.2 37.7 37.3 36.9 36.5 36.0 35.6 35.2 34.8 43 39.8 39.3 38.9 38.5 38.1 37.6 37.2 36.8 36.3 44 41.4 41.0 40.5 40.1 39.7 39.2 38.8 38.4 37.9 45 43.2 42.7 42.3 41.8 41.4 40.9 40.5 40.1 39.6 46 45.0 44.6 44.2 43.7 43.2 42.7 42.3 41.9 41.4 47 46.9 46.5 46.0 45.6 45.1 44.6 44.2 43.7 43.3 48 49.0 48.6 48.1 47.7 47.2 46.7 46.3 45.8 45.3 49 51.2 50.7 50.2 49.8 49.3 48.8 48.4 47.9 47.4 50 1 53.5 1 53.0 1 52.5 1 52.0 1 51.5 1 51.0 1 50.6 1 50.1 1 49.6 The above table was computed with mean declination of Polaris for each year. A more accurate result will be had by applying to the tabular values the following correction, which depends on the difference of the mean and the apparent place of the star. The deduced azimuth will in general be correct within 0'.3. For middle of Correction. For middle of Correction. January * "/ 0.4 July . . / +0.3 February 0.3 August -1-0 1 March 2 September 1 April 0.0 October 3 May .. +0.2 November 6 June +0 3 December g 20 GEOGRAPHIC TABLES AND FORMULAS. TABLE 3. Azimuths of Polaris [From U. S. Land Survey Manual. The hour angles are expressed in mean solar time. The occurrence STAB AND AZIMUTH. W. of N. when hour angle is less than ll h 58 m . E. of N. when hour angle is greater than ll h 58 m . POLARIS above THE POLE. To determine the true meridian, the azi- muth will be laid off to the east when the hour angle is less than ll h 58 m , and to the west when greater than ll h 58 m . Time argument, the star's hour angle (or 23 h 56 m .l minus the star's hour angle), for the year Hours. | i g ! 1 j o s 1H rH OS Azimuths for latitude o 30 o 32 o 34 o 36 o 38 o 40 42 o 44 o 46 o 48 o 50 h. m. 5 9. 14. 19 24 28. 33. 38. 43 48 53 58 m. 5 9. 14. 19 24 29 33. 38. 43. 48 53 58 m. 5 9. 14. 19 24 29 34 38. 43. 48. 53. 58. m. 5 9. 14. 19. 24 29 34 39 44 48. 53. 58. m. 5 9. 14. 19. 24. 29 34 39 44 49 54 59 m. 5 10 14. 19. 24. 29. 34. 39 44 49 54 59 TO. 5 10 14. 19. 24. 29. 34. 39. 44. 49. 54. 59. m. 5 10 15 19. 24. 29. 34. 39. 44. 49. 54. IT 5 10 15 20. 26 31 36. 42 47. 53 58. 2 3. 5. 7 9 10. 12. 14 16 17. 19. 21. 23 25 27 28. 30. 32 33. 35. 37 39 40. 42. 44 46 47. 49. 51 53 54. 56. 58 2 3. 5. 7 9 11 12. 14. 16 18 20 21. 23. 25. 27 29 31 32. 34. 36 38 39. 41. 43 45 47 40. 50. 52 54 56 57. 59. 2 3. 5. 7. 9 11 13 14. 16. 18. 20. 22 24 26 27. 29. 31. 33 35 37 38. 40. 42. 44 46 48 49. 51. 53. 55. 57 59 eT 63 64. 66. 68. 70 72 74 76 77. 79. 81. 83 85 87 2 2 2 2 2 2 2. 2. 5 7 9. 12 14. 17 19 21. 24 26. 29 31. 34 36. 39 41. 43. 46 48. 50. 53 55 57. 62. 64. 67 69. 72 74. 76. 79 81. 84 86 88. 91 93. 95. 98 100. 103 105 107. 110 112 5. 7. 9. 11. 13 15 17. 19 21 22. 24. 26. 28. 30 32 34 36 38 39. 41. 43. 45. 47 49 51 53 55 56. 58. 62. 64. 66 68 70 72 74 75. 77. 79. 81. 83. 85 87 89 6 8 9. 11. 13. 15. 17. 19. 21. 23. 25 27 29 31 33 35 37 39 40. 42. 44. 46. 48. 50. 52. 54. 56. _58j "60 62 64 66 68 70 72 74 76 77. 79. 81. 83. 85. 87. 89. 91. 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 60 52 54 56 58 rio 62 64 66 68 70 72 74 76 78 80 82 84 86 &8 90 92 94 6 8. 10. 12. 14. 16. 18. 20. 22. 25 27 29 31 33 35 37 39. 41. 43. 45. 47. 49. 51. 53. 56 ^58_ 60 62 64 66 68 70 72 74. 76. 78. 80. 82. 84. 86. 88. 90. 93 95 97 6. 8. 10. 13 15 17 19. 21. 23. 26 28 30 32 34. 36. 38. 41 43 45 47 49 51. 53. 55. 57.| -60 62 64 66 68. 70. 72. 74. 77 79 81 83 85. 87. 89. 91. 94 96 98 100 6. 9 11 13. 15. 18 20 22. 24. 27 29 31. 33. 36 38 40 42. 44. 46. 49 51 53. 55. 57. "60" 62 64. 66. 68. 71 73. 75 77. 79. 82 84 86 88. 90. 92. 95 97 99. 101. 103. 7 9 11. 14 16 18. 21 23 25. 28 30 32. 35 37. 39. 42 44 46. 48. 51 53 55. 57. ~ 62 64. 66. 69 71. 73. 76 78 80. 82. 85 87 89. 91. 94 96 98. 101 103 105. 107. 7. 13 18 23 28 33. 38. 44 49 54. 8 13 18 23. 28. 33. 39 44. 50 55 8. 13. 18. 23. 29 34 39. 45 50. 55. 8. 14 19 24 29. 34. 40 45. 51 56. 9 14 19. 24. 29. 35 40. 46 51. 57 9. 14. 19. 25 30 35. 41 46. 52 57. 9. 15 20 25. 30. 36 41. 47 52. 58 2 6 11. 17 23 29 35 41. 48 54. 0. 6. 12 18 24 30 36 42. 49 55. 1. 7 12. 18. 24. 30. 37 43. 50 56. 2 7. 13. 19. 25. 31. 38 44. 51 57. 2. 8. 14 20 26 32. 38. 45 52 58. 3 9 15 21 27 33 39. 46 53 59. 4 9. 15. 21. 28 34 40. 47 54 4. 10. 16. 22. 28. 35 41. 48 55 1 2 9 17 25 33 42 51 PO- 3 1. 8. 16 23. 31. 39. 48. 2. 10 17 25 33 41 50 59. 3. 11 18. 26 34. 43 52 4. 12 19. 27. 35. 44. 53. 6 13 21 29 37 46 55 7 14. 22 30. 38. 47. 57 8 15. 23. 31. 40. 49. 59 60 61. 63. 65 67 69 70. 72. 74 76 77. 61. 63 65 66. 68. 70. 72 74 76 77. 79. 81. 83 85 1. 12. 24 37. 53. 3. 14. 26. 40. 57. 5. 16. 29 43. 7. 19 32 46. 9. 21 34. 50 II 23 37 53 4 8 19. 32 46. 10 22 34. 50 2 6. 42. 11 16 79. 5 5 40. 10 16 23. 32 81 83 1 GEOGRAPHIC TABLES AND FORMULAS. 21 for the use of surveyors. of a period after minutes of time or of an hour angle indicates that its value is O m .5 greater than printed.] STAR AND AZIMUTH. W. of N. when hour angle is less than 11>> 58 m . E. of N. when hour angle is greater than ll h 58. POLARIS below THE POLE, To determine the true meridian, the azi- muth will be laid off to the east when the hour angle is less than ll h 58 m , and to the west when greater than ll h 58. Time argument, the star's hour angle (or23 h 56 m .l minus the star's hour angle), for the year Hoars. I t t I 1 g ' S cs Azimuths for latitude o 30 o 32 34 o 36 o 38 o 40 o 42 o 44 o 46 o 48 o 50 h. 6 m. 9. 45 nt. 40. in. 34 56. in. 27 52. m. 18 48. m. 8 44 83 81. 79. 78 76 74. 72. 71 69 67. 65. 64 62 60. 85 83 81. 79. 77. 76 74 72. 70. 68. 67 65 63. 6J. 87 85 83 81. 79. 77. 76 74 72 70. 68. 66. 64. 63 61 "isr 57.' 55. 53. 52 50 48 46. 44. 42. 40. 39 37 35 33. 31. 29. 28 26 24 22 20. 18. 16. 15 13 11 9 7. 5. 3. 2 89 87 85 83. 81. 79. 77. 76 74 72 70 48 66. 64. 62. 60. -5T 57 55 53 51 49. 47. 45. 43. 41. 40 38 36 34 32 30. 28. 26. 24. 22. 21 19 17 15 13. 11. 9. 7. 5. 4 2 91. 89. 87. 85. 83. 81. 79. 77. 75. 74 72 70 68 66 64 62. 60. 58H 56. 54. 52. 50. 48. 46. 44. 43 41 39 37 35 33 31 29 27 25. 23 21. 19. 17. 15. 13. 11. 9. 8 4 2 94 92 90 88 86 84 82 80 78 76 74 72 70 68 66 64 62 |60 L ir 56 54 52 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 97 95 93 90. 88. 86. 84. 82. 80. 78. 76. 74. 72 70 68 66 64 62 60 100 98 96 91. 89. 87. 85. 83 81 79 77 74. 72. 70. 68 66 64 62 103. 101. 99. 97 95 92. 90. 88. 86 84 81. 79. 77. 75 73 70. 68. 66 64 62 59- 57. 55 53 50. 48. 46. 44 42 39. 37. 35. 33 31 28. 26. 24 22 20 17. 15. 13 11 9 6. 4. 2 107. 105. 103 100. 98. 96 94 91. 89 87 84. 82. 80 78 75. 73 71 68. 66. 64 |61. T5T 57 55 52. 50 48 45. 43. 41 39 36. 34 32 29. 27. 25 23 20. 18 16 13. 11. 9 7 4. 2. 112 109. 107 104. 102 100 97. 95 92. 90 88 85. 83 80. 78 76 73. 71 68. 66. 64 . L 5T 57 54. 52 49 47. 45 42. 40 38 35. 33 31 28. 26 23. 21. 19 16. 14 12 9. 7 4. 2. m. 39 m. 34 57 13 27 39. 50. 4 18. 31. 42. 53 0. 16 29 40. 51. 13 26. 38. 49. 59. 10 24 36. 47. 57. 7 21. 34. 45. 56 4 19 32 43. 54 0. 16 29. 41. 52. 8 2. 11. 20 28 36 43. 50. 57. 1 10 18. 27 35 42. 49. 56. 8. 17. 25. 33. 41. 48. 55. 7 16 24. 32. 40 47. 54. 5. 14. 23 31 39 46. 53. 4 13 21. 30 38 45. 52. 2. 11. 20. 28. 36. 44. 51. 59 1 10 19 27. 35. 43 50. 58 58. 57 55 53. 51. 49. 48 46 44. 42. 41 39 37. 35. 34 32 30 28. 26. 25 23 21. 19. 18 16 14 12. 10. 9 7 5. 3. 2 59. 58 56 54. 52. 50. 49 47 45. 43. 41. 40 38 36 34. 32. 31 29 27 25. 23. 22 20 18 16. 14. 12. 11 9 7 5. 3. 2 4. 11 17. 24 30 36 42 48 54 59. 3. 10. 17 23 29. 35. 41. 47. 53 59 2. 9. 16 22. 28. 35 41 47 52. 58. 1. 8. 15 21. 28 34 40 46 52 57. 1 7. 14. 20. 27 33. 39. 45. 51. 57 c 6. 13. 20 26. 32. 38. 45 51 56. 5. 12 19 25. 32 38 44 50 56 5 n - 18 24. 31 37. 43. 49. 55. 58 55. 53. 51. 49. 47. 45. 43. 41 39 37 35 33 31 29 27 25 22. 20. 18. 16. 14. 12. 10. 8 6 4 2 59. 57. 55. 53. 51 49 47 45 42. 40. 38. 36 34 32 30 27. 25. 23. 21. 19 17 15 12. 10. 8. 6. 4 2 To 5 10. 16 21. 27 32 37. 42. 48 53 58 1. 10 15. 21 26. 32 37 42. 47. 52. 58 4 9. 15 20. 26 31. 36. 42 47. 52. 57. 3. 9 14. 20 25. 31 36. 41. 47 52 57. 3 8. 14 19. 25 30. 36- 41. 46. 52 57 2. 8 13. 19. 25 30 35. 41 46. 51. 57 2 7. 13 19 24. 30 35 40. 46 51 56. 1. 7 12. 18. 24 29. 35 40 45. 51 56 11 3 8. 13. 18. 23. 28. 33. 38. 43. 48 53 58 3 8 13 18 23 28. 33 38 43 48 53 58 2. 8 13 18 23 28 33 38 43 48 53 58 2. 7. 12. 18 23 28 33 38 43 48 53 58 2 7 12. 17. 22. 28 33 38 43 48 53 58 2 7 12. 17. 22. 27. 33 38 43 48 53 58 1. 7 12 17. 22. 27. 32. 38 43 48 53 58 1. 6. 12 17 22 27. 32. 37. 43 48 53 58 22 GEOGRAPHIC TABLES AND FORMULAS. Table 3 gives for various hour angles, expressed in mean solar time and for even degrees of latitude from 30 to 50 degrees, the azimuths of Polaris for eight years, computed for average values of the north polar distance of the star, the arguments being the hour angle (or 23 h 56 m .l minus the hour angle when the latter exceeds ll h 58 m ), which is termed the time argument, a and the latitude of the place of obser- vation. The table is so extended that azimuths may be taken out by inspection and all interpolation avoided, except such as can be per- formed mentally. The hours of the "time arguments " are placed in the columns headed " hours," on the left of each page. The minutes of the time argu- ments will be found in the columns marked u m," under the years for which they are computed, and they are included between the same heavy zigzag lines which inclose the hours to which they belong. The time arguments are given to the nearest half minute; the occur- rence of a period after the minutes of any one of them indicates that its value is O m .5 greater than printed, the table being so arranged to economize space. The table will be used as follows: Find the hours of the time argu- ment in the left-hand column of either page; then, between the heavy lines which inclose the hours, find the minutes in the column marked at the top with the current year. On the same horizontal line with the minutes the azimuth will be found under the given latitude, which is marked at the -top of the right-hand half of each page. Thus, for 1904, time argument O h 43 m , latitude 36, find O h on left-hand page, and under 1904 find 43 m on tenth line from the top, and on same line with the minutes, under latitude 36, is the azimuth 17'. For 1908, time argument 9 h 33i m , latitude 48, the azimuth is 1 Ij-', found on the twenty-first line from the top of right-hand page. If the exact time argument is not found in the table, the azimuth should be proportioned to the difference between the given and tabu- lar values of said argument. The table has been arranged to give the azimuths by simple inspec- tion. No written arithmetical work is required, all being performed mentally. It will always be sufficient to take the nearest whole degree of latitude and use it as above directed, except for a few values near the top of either page where the difference of azimuths for 2 differ- ence of latitude amounts to four or five minutes of arc. a The vertical diameter SS', fig. 6, divides the apparent path of Polaris into two equal parts, and for the star at any point Se on the east side is a corresponding point s t on the west side of the meridian, for which azimuth Nw is equal to the azimuth Ne. The arc, Ss! 8%, taken from the entire circle (or 23P 56*.!), leaves the arc Sse, and its equal Ss lt expressed in time, may be used to find, from table 3, the azimuth Nw, which is equal to Ne. The hour angles entered in table 3 include only those of the west half of the circle ending at S, and when an hour angle greater than ll h 58 m results from observation it will be subtracted from 23 h 66 m .l, and the remainder will be used as the "time argument" for the table. The surveyor should not confound these two quantities. The hour angle itself always decides the direction of the azimuth and defines the place of the star with reference to the pole and meridian, as noted at top of table 3. See examples. GEOGRAPHIC TABLES AND FORMULAS. 23 The attention of the observer is directed to the fact that he should always use one day of twenty-four hours as the unit when he subtracts the time of culmination from the time of observation. In any case when the time of upper culmination, taken from table 1, for the given date would be numerically greater than the astronomical time of observation, the former time will be taken out for a date one day earlier than the date of observation. The surveyor will decide when such condition exists by comparing the time given in the table with his astronomical time of observation. (See Example 4 and explana- tions in footnotes, page 24.) The watch time to be used when making observations on Polaris at all times except elongation should be as accurate as can be obtained. Looking at table 3 near top of page 20, the surveyor will observe that for a difference of four minutes in the time argument there is a change of about two minutes in azimuth; consequently, to obtain the azimuth to the nearest whole minute of arc, the local mean time, upon which all depends, should be known within two minutes. When the observer uses standard railroad time he will correct the same for the difference of longitude between his station and the standard meridian for which the time is given at the rate of four minutes of time for each degree of the difference in arc. Thus, if the difference in longi- tude is 6 45', the equivalent in time will be twenty-seven minutes. The difference of longitude may be taken from a good map. The cor- rection will be subtracted from the standard railroad time of observa- tion when the surveyor's station is west, or added when east of the standard meridian, as the case m&y require, to obtain local time. It is immaterial where the surveyor obtains the standard time provided he gets it right, a result which will be gained most easily by a direct personal comparison at a telegraph office. If the direction of the meridian is known with an error not greater than one-fourth of a degree, the local time can be obtained to the nearest minute by observing the sun's transit by the following method, suggested by Mr. H. L. Baldwin, jr. The transit being in meridian and carefully leveled, place the tele- scope so that it will point toward the sun at the time the latter comes to the meridian and allow the magnified image of the sun to fall upon a notebook or sheet of white paper about 1 foot distant from eyepiece. The telescope should be slightly out of focus (lengthened) to get best results, the best focal position to be determined by trial. When the vertical cross wire bisects the sun's image, note the time by watch. This will be the time of apparent noon. To get time of mean noon, correct the noted time by adding or subtracting the equation of time, taken from the Nautical Almanac u to reduce apparent noon to mean noon," or get this from any almanac giving "sun fast" or "sun slow" time. 24 GEOGRAPHIC TABLES AND FORMULAS. Example. June 20, 1903. h. m. s. Watch time of sun's transit 11 50 25 Equation of time +1 04 Local mean noon 11 51 29 Or watch slow 8 31 The error of observation should not exceed two or three seconds and the error resulting from incorrect meridian will be approximately four seconds for each 1' error in meridian. APPLICATIONS OF TABLES 1 AND 3. 1. Required the hour angle and azimuth of Polaris, for a station in latitude 46 N., longitude 90 W., at 8 h 24 m p. m., November 7, 1910. h. m. Astronomical time of observation, 1910, November 7 8 24. Equivalent to time of November 6 32 24. h. m. Astron. time, TJ. C. Polaris, November 1 (table 1) . . 10 45. 3 Reduction to November 6 ( B ) , subtract & 19. 7 Astron. time, U. C. Polaris, November 6 10 25. 6, subtract . '10 25. 6 Hour angle of Polaris, at observation 21 58. 4 Subtract from.. ... ^23 56.1 Time argument for table 3 1 57. 7 Azimuth of Polaris, at observation 51' E. 2. Required the hour angle and azimuth of Polaris, for a station in latitude 4i 12' N., longitude 94 W., at 6 h 16 m a. m., November 19, 1904. h. m. Astronominal time of observation, 1904, November 18 18 16. h. m. Astron. time, U. C. Polaris, November 15 (table 1) . . 9 47. 1 Reduction to November 18, subtract 11. 8 Astron. time, U. C. Polaris, November 18 9 35. 3, subtract . 9 35. 3 Hour angle of Polaris, at observation, and time argument for table 3 ^8 40. 7 Azimuth of Polaris, at observation (table 3) , 72' or fl 12' W. The following four examples illustrate any difficulties in the use of tables 1 and 3: a By reference to the above table, the surveyor will observe that the times, between November 1 and 15, are greater than 8>> 24">; consequently, the culmination for one day earlier, November 6, will be used. bFrom table 1, opposite sixth day of month. c To subtract, take one day from November 7, and add its equivalent, 24 h , to8 h 24 m , making, Novem- ber 6, 32 h 24 m (which is the time expressed by November 7, 8 h 24 m ); then subtract in the usual manner. dSee last clause of footnote, page 22. In case the hour angle comes out greater than ll h 58 m , subtract it from 23 h 56 m .l; see example 4, above. /The hour angle being less than 11>> 58>, the azimuth is west; see precepts? top of table 3. GEOGRAPHIC TABLES AND FORMULAS. 25 EVENING OBSERVATIONS. 1. February 20, 1904, at 7 h 42 m .5 p. m., local mean time, Polaris is observed at a station in southern California, latitude 36, longitude 117. h. m. Time of observation 7 42. 5 h. m. From table 1, U. C. Polaris, February 15 3 45. 7 Reduction to February 20 19. 7 3 26. Time elapsed since preceding culmination 4 16. 5 From table 3 corresponding azimuth is 80 / .5=1 20'.5. 2. May 9, 1904, at 8 h 56 m .4 p. m., local mean time, Polaris is observed at a station in northeastern Minnesota, latitude 48, longitude 90. The nearest culmination is that of May 8. h. m. Time of observation May 9, 1904, 8 h 56 m .4, or May 8 32 56. 4 h. m. From table 1, U. C., May 1, 1904 22 42. 7 Reduction to May 8 27. 6 22 15. 1 Time elapsed since preceding culmination 10 41. 3 From table 3, eorresponding azimuth is 34'. MORNING OBSERVATIONS. 3. May 10, 1904, at 5 h 13 m a. m., local mean time, or May 9, 17 h 13 m , astronomical time, Polaris is observed at a station in northeastern Minnesota, latitude ^8, longitude 90. h. m. Time of observation, May 9, 1904 17 13. h. m. From table 1, U. C., May 1 22 42.7 Reduction to May 9 31. 5 22 11.2 Time to elapse to next following culmination 4 58. 2 From table 3 corresponding azimuth is 104'.3=1 44'. 3 4. February 21, 1904, at 5 h 10 m a. m., local mean time, Polaris is observed at a station in southern California, latitude 36, longitude 117. The nearest culmination is on February 21. h. m. Time of observation, February 20 17 10. h. m. From table 1, U. C., February 15 3 45.7 Reduction to February 20 19. 7 h. m. 3 26.0+23 56.1=27 22.1 Time to elapse to next following culmination 10 12. 1 From table 3, corresponding azimuth is 39'. 3. 26 GEOGRAPHIC TABLES AND FORMULAS. TABLE 4. AZIMUTH AND APPARENT ALTITUDE OP POLARIS AT DIFFERENT HOUR ANGLES. [From U. S. Coast and Geodetic Survey Report for 1895.] The accompanying tables are intended for field use, to facilitate placing an instrument in the meridian. They are also suitable for determining the approximate latitude or meridian. They contain the azimuth of Polaris at intervals of fifteen minutes in hour angle for each degree of north latitude from 30 to 60, and the apparent alti- tude at the same intervals and for each fifth degree of latitude. The tables are computed for the declination of Polaris 88 46', but the rate of change in both azimuth and altitude is given with the argument V increase in declination. 6 The tables are intended to be used in con- nection with the American Ephemeris, where are given the apparent right ascension and declination of Polaris for each day in the year. The approximate local time will in general be known with sufficient accuracy from standard time and the approximate longitude of the place. The following example explains the use of the tables and the derivation of the hour angle of Polaris: Position, latitude 36 20' N., longitude 5 h 20 m 30 s W. of Greenwich. h. m. s. Time of observation, July 10, 1895, standard (75th mer. ) mean time 8 52 40 p. m. Reduction to local time 20 30 Local mean time 8 32 10 Reduction to sidereal time (Table III, Amer. Ephem. ) -f 1 24 Sidereal time mean noon, Greenwich, July 10, 1895 7 12 38 Correction for longitude, 5 h 20 m 30 s (Table III, Amer. Ephem.) + 53 Local sidereal time 15 47 05 Apparent right ascension of Polaris, July 10, 1895 1 20 18 Hour angle before upper culmination 9 33 13 a The tables were computed with the following formulas: sinj ten a = cos.9~taiTfi - siiF^TcosY sin h = sin

= latitude, 8 = declination, h = true altitude, a e = azimuth at elongation, t e hour angle at elongation. b As the corrections are given with proper sign for increase in declination over 88 46', they are to be applied with reversed sign while the declination is less than 88 46', as it will be until near the close of the century. GEOGRAPHIC TABLED FORMULAS. 27 Declination of table Apparent declination, July 10, 1895 Increase in declination o / // 88 46 88 44 47 - 1 13= Values from tables (interpolated) azimuth 54 12, apparent altitude 35 21.8 Correction for 1'.2 increase in declination +52 1.0 55 04 East of north 35 20.8 It is to be remembered that Polaris is east of the meridian for twelve hours before upper culmination, and west of the meridian for twelve hours after. By setting the instrument at the apparent altitude and sweeping- near the meridian Polaris can ordinarily be found and the instrument placed in the meridian some time before dark. With transit instruments not provided with horizontal arc, the value of the azimuth adjusting screw may be readily determined and used. Without the American Ephemeris these tables may be conveniently used for obtaining the approximate meridian or latitude, in connection with Bulletin 14, United States Coast and Geodetic Survey, a where are given the approximate mean times of culminations of Polaris, and the mean declinations for various epochs. a Approximate Times of Culminations and Elongations and of the Azimuths at Elongation of Polaris for the Years between 1889 and 1910. The mean places of Polaris are given as follows: a 1895 . . . h. m. 8. 1 20 30.08 / // 88 44 6268 1900 1 22 33 76 88 46 26 66 1905 1 24 42 48 88 48 00 31 1910 1 26 56.58 88 49 33 61 28 GEOGRAPHIC TABLES AND FORMULAS. TABLE 4. Azimuth and apparent altitude Hour angle before or after upper culmination. Azimuth of Polaris computed for declination 88 46'. Latitude 30. Latitude 31. Latitude 32. Latitude 33. Latitude 34. Latitude 35. h. m. 15 05 40 05 43 05 47 05 51 05 55 06 00 30 11 18 11 25 11 33 11 41 11 49 11 58 45 16 53 17 04 17 15 17 27 17 40 17 53 1 00 22 23 22 38 22 53 23 09 23 26 23 44 1 15 27 48 28 06 28 25 28 45 29 06 29 28 1 30 33 05 33 26 33 49 34 13 34 38 35 04 1 45 38 13 38 38 39 04 39 32 40 00 40 30 2 00 43 12 43 40 44 09 44 40 45 12 ! 45 46 2 15 47 58 48 29 49 02 49 36 50 12 50 50 2 30 52 32 53 06 53 42 54 19 54 59 55 40 2 45 56 52 57 29 58 07 58 48 59 30 1 00 15 3 00 1 00 58 1 01 37 1 02 18 1 03 01 1 03 46 1 04 34 3 15 1 04 47 1 05 28 1 06 12 1 06 58 1 07 46 1 08 36 3 30 08 19 1 09 02 1 09 48 1 10 36 1 11 27 1 12 20 3 45 11 33 1 12 18 1 13 06 1 13 56 1 14 49 1 15 45 4 00 14 28 1 15 15 1 16 05 1 16 57 1 17 52 1 18 50 4 15 17 04 1 17 52 1 18 44 1 19 37 1 20 34 1 21 34 4 30 19 19 1 20 09 1 21 02 1 21 57 1 22 55 1 23 57 4 45 21 14 1 22 05 1 22 59 1 23 55 1 24 55 1 25 57 5 00 22 48 1 23 40 1 24 35 1 25 32 1 26 32 1 27 36 5 15 24 08 1 24 53 1 25 48 1 26 46 1 27 47 1 28 51 5 30 24 51 1 25 44 1 26 40 1 27 38 1 28 39 1 29 44 5 45 25 20 1 26 13 1 27 09 1 28 07 1 29 09 1 30 14 6 00 25 27 1 26 19 1 27 15 1 28 14 1 29 15 1 30 20 6 15 25 12 1 26 04 1 26 59 1 27 57 1 28 59 1 30 03 6 30 24 34 1 25 27 1 26 21 1 27 19 1 28 19 1 29 23 6 45 23 36 1 24 27 1 25 21 1 26 18 1 27 17 1 28 20 7 00 22 16 1 23 06 1 23 59 1 24 55 1 25 53 1 26 55 7 15 20 35 1 21 25 1 22 16 1 23 10 1 24 08 1 25 08 7 30 18 34 1 19 22 1 20 12 1 21 05 1 22 00 1 22 59 7 45 16 13 1 16 59 1 17 48 1 18 39 1 19 33 1 20 29 8 00 13 33 1 14 17 1 15 04 1 15 53 1 16 45 1 17 39 8 15 10 34 1 11 16 1 12 01 1 12 48 1 13 37 1 14 29 8 30 1 07 17 1 07 57 1 08 40 1 09 25 1 10 12 1 11 01 8 45 1 03 43 1 04 22 1 05 02 1 05 44 1 06 29 1 07 15 9 00 59 54 1 00 30 1 01 07 1 01 47 1 02 29 1 03 12 9 15 55 49 56 23 56 58 57 34 58 13 58 54 9 30 51 31 52 01 52 34 53 08 53 43 54 21 9 45 46 59 47 27 47 57 48 28 49 00 49 34 10 00 42 16 42 42 43 08 43 36 44 05 44 35 10 15 37 23 37 45 38 08 38 33 38 59 39 26 10 30 32 20 32 39 32 59 33 20 33 43 34 06 10 45 27 09 27 25 27 42 28 00 28 18 28 38 11 00 21 51 22 04 22 18 22 32 22 47 23 03 11 15 16 28 16 38 16 .48 16 59 17 10 17 22 11 30 11 01 11 08 11 14 11 22 11 29 11 37 11 45 05 31 05 34 05 38 05 42 05 45 05 49 Elongation : Azimuth . . . 1 25 27 1 26 20 1 27 16 1 28 14 1 29 16 1 30 20 h. m. s. h. m. 8. //. m. s. h. m. s. h. m. s. h. m. s. Hour angle. 5 57 09 5 57 02 5 56 55 5 56 48 5 56 40 5 56 33 GEOGRAPHIC TABLES AND FOEMULA8. of Polaris at different hour angles. 29 Azimuth of Polaris computed for declination 88 46'. Correction for 1' in- crease in declina- tion of Polaris. Hour angle before or after upper culmi- nation. Latitude 36. Latitude 37. Latitude 38. Latitude 39. Latitude 40. Latitude 30. Latitude 40. 06 05 06 10 06 15 06 20 06 26 - 5 // - 5 h. TO. 15 12 08 12 18 12 28 12 39 12 50 g -10 30 18 07 a is 22 18 38 18 54 19 11 14 -16 45 24 02 24 22 24 43 25 04 25 27 -18 21 1 00 29 51 30 15 30, 41 31 08 31 36 -23 26 1 15 35 31 36 00 36 31 37 02 37 36 27 -31 1 30 41 02 41 35 42 11 42 47 43 26 31 -36 1 45 46 22 47 00 47 39 48 21 49 04 35 -40 2 00 51 29 52 11 52 55 53 41 54 29 -39 45 2 15 56 23 57 09 57 57 58 47 59 40 -43 -49 2 30 1 01 02 1 01 51 1 02 43 1 03 37 1 04 34 -46 -53 2 45 1 05 24 1 06 17 1 07 12 1 08 10 1 09 12 50 -57 3 00 1 09 29 1 10 25 1 11 24 1 12 25 1 13 30 -53 -60 3 15 1 13 16 1 14 14 1 15 16 1 16 21 1 17 29 -56 -63 3 30 1 16 43 1 17 44 1 18 49 1 19 57 1 21 08 -58 -66 3 45 1 19 50 1 20 54 1 22 01 1 23 11 1 24 25 -61 -69 4 00 1 22 36 1 23 42 1 24 51 1 26 03 1 27 20 63 72 4 15 1 25 01 1 26 08 1 27 19 1 28 33 1 29 52 64 74 4 30 1 27 03 1 28 12 1 29 24 1 30 40 1 32 00 66 75 4 45 1 28 42 1 29 52 1 31 06 1 32 23 1 33 44 -68 -76 5 00 1 29 59 1 31 09 1 32 24 1 33 42 1 35 04 -69 -77 5 15 1 30 52 1 32 03 1 33 18 1 34 37 1 35 59 -69 -78 5 30 1 31 21 1 32 33 ] 33 48 | 1 35 07 1 36 30 70 78 5 45 1 31 27 1 32 39 1 33 54 1 35 13 1 36 35 -70 78 6 00 1 31 10 1 32 21 1 33 36 1 34 54 1 36 16 -69 -78 6 15 1 30 30 1 31 40 1 32 54 1 34 11 1 35 32 -68 -77 6 30 1 29 26 1 30 35 1 31 48 1 33 04 1 34 24 67 76 6 45 1 27 59 1 29 07 1 30 18 1 31 33 1 32 52 -66 75 7 00 1 26 11 1 27 17 1 28 26 1 29 39 1 30 56 -65 -73 7 15 1 24 00 1 25 04 1 26 12 1 27 23 1 28 38 -64 -72 7 30 1 21 28 1 22 30 1 23 36 1 24 45 25 57 62 -69 7 45 1 18 36 1 19 36 1 20 39 1 21 45 22 54 60 -66 8 00 1 15 24 1 16 21 1 17 22 1 18 25 19 31 -57 -64 8 15 1 11 53 1 12 48 1 13 45 1 14 45 15 48 -54 -61 8 30 1 08 04 1 08 56 1 09 50 1 10 47 11 47 51 -58 8 45 1 03 58 1 04 47 1 05 38 1 06 31 07 27 -48 54 9 00 59 37 1 00 22 1 01 09 1 01 59 02 51 -45 -50 9 15 55 00 55 42 56 25 57 11 57 59 -42 -46 9 30 50 10 50 48 51 27 52 09 52 53 -38 -42 9 45 45 08 45 42 46 17 46 54 47 34 34 -38 10 00 39 54 40 24 40 55 41 28 42 03 -30 -34 10 15 34 30 34 57 35 24 35 52 36 22 -26 -29 10 30 28 59 29 20 29 43 30 07 30 32 -22 -24 10 45 23 19 23 37 23 55 24 14 24 35 18 -20 11 00 17 35 17 48 18 02 18 16 18 31 13 15 1JL 15 11 46 11 54 12 04 12 13 12 23 - 9 -10 11 30 05 53 05 58 06 02 06 07 06 12 - 4 - 5 11 45 1 31 28 1 32 40 1 33 55 1 35 14 1 36 36 -69 -78 h. m. s. h. m. s. h. TO. 8. h. TO. 8. h. TO. 8. 8. 8. 5 56 25 5 56 17 5 56 09 5 56 00 5 55 52 + 2 + 3 30 GEOGRAPHIC TABLES AND FORMULAS. TABLE 4. Azimuth and apparent altitude Azimuth of Polaris computed for declination 88 46'. Hour angle before or after upper elimination. Latitude Latitude Latitude Latitude Latitude Latitude 40. 41. 42. 43. 44. 45. h. m. 15 06 26 06 32 06 39 06 45 06 52 07 00 30 12 50 13 03 13 15 13 29 13 43 13 58 45 19 11 19 30 19 48 20 08 20 29 20 52 1 00 25 27 25 51 26 16 26 43 27 10 27 40 1 15 31 36 32 05 32 36 33 09 33 44 34 21 1 30 37 36 38 11 38 48 39 27 40 09 40 52 1 45 43 26 44 07 44 50 45 35 46 22 47 12 2 00 49 04 49 50 50 39 51 29 52 23 53 19 2 15 54 29 55 20 56 14 57 10 58 10 59 12 2 30 59 40 1 00 35 1 01 34 1 02 36 1 03 41 1 04 49 2 45 1 04 34 1 05 34 1 06 38 1 07 44 1 08 54 1 10 08 3 00 1 09 12 1 10 16 1 11 24 1 12 35 1 13 50 1 15 09 3 15 1 13 30 1 14 38 1 15 50 1 17 06 1 18 25 1 19 49 3 30 1 17 29 1 18 41 1 19 57 1 21 16 1 22 39 1 24 08 3 45 1 21 08 1 22 23 1 23 42 1 25 04 1 26 32 1 28 04 4 00 1 24 25 1 25 43 1 27 05 1 28 31 1 30 01 1 31 37 4 15 1 27 20 1 28 40 1 30 04 1 31 33 1 33 07 1 34 45 4 30 1 29 52 1 31 14 1 32 41 1 34 12 1 35 48 1 37 29 1 4 45 1 32 00 1 33 24 1 34 53 1 36 25 1 38 04 1 39 47 5 00 1 33 44 1 35 10 1 36 40 1 38 14 1 39 54 1 41 38 5 15 1 35 04 1 36 30 1 38 02 1 39 37 1 41 18 1 43 04 5 30 1 35 59 1 37 26 1 38 58 1 40 34 1 42 16 1 44 02 5 45 1 36 30 1 37 57 1 39 29 1 41 05 1 42 47 1 44 34 6 00 1 36 35 1 38 02 1 39 34 1 41 10 1 42 51 1 44 38 6 15 1 36 16 1 37 43 1 39 14 1 40 49 1 42 30 1 44 16 6 30 1 35 32 1 36 58 1 38 28 1 40 03 1 41 42 1 43 27 6 45 1 34 24 1 35 48 1 37 17 1 38 50 1 40 28 1 42 12 7 00 1 32 52 1 34 15 1 35 42 1 37 13 1 38 49 1 40 31 7 15 1 30 56 1 32 17 1 33 42 1 35 11 1 36 45 1 38 24 7 30 1 28 38 1 29 56 1 31 19 1 32 46 1 34 17 1 35 53 7 45 1 25 57 1 27 13 1 28 33 1 29 56 1 31 25 1 32 58 8 00 1 22 54 1 24 07 1 25 24 1 26 45 1 28 10 1 29 40 8 15 1 19 31 1 20 41 1 21 55 1 23 12 1 24 33 1 25 59 8 30 1 15 48 1 16 55 1 18 05 1 19 18 1 20 35 1 21 57 8 45 1 11 47 1 12 49 1 13 55 1 15 05 1 16 18 1 17 35 9 00 1 07 27 1 08 26 1 09 28 1 10 33 1 11 41 1 12 54 9 15 1 02 51 1 03 45 1 04 43 1 05 43 1 06 47 1 07 54 9 30 57 59 58 49 59 42 1 00 38 1 01 37 1 02 38 9 45 52 53 53 39 54 27 55 18 56 11 57 07 10 00 47 34 48 15 48 58 49 44 50 32 51 22 10 15 42 03 42 39 43 18 43 58 44 40 45 25 10 30 36 22 36 53 37 26 38 01 38 38 39 16 10 45 30 32 30 58 31 26 31 55 32 26 32 58 11 00 24 35 24 56 25 18 25 42 26 06 26 32 . 11 15 18 31 18 47 19 04 19 22 19 40 20 00 11 30 12 23 12 34 12 45 12 57 13 09 13 23 11 45 06 12 06 18 06 23 06 29 06 36 06 42 Elongation: Azimuth . . . 1 36 36 1 38 03 1 39 35 1 41 11 1 42 53 1 44 40 h. m. s. h. m. s. h. m. s. h. m. s. h. m. s. h. m. s. Hour angle . 5 55 52 5 55 43 5 55 34 5 55 24 5 55 14 5 55 04 GEOGEAPHIC TABLES AND FORMULAS. of Polaris at different hour angles Continued. 31 Correction for 1' in- TTrtiiT Azimuth of Polaris computed for declination 88 46'. crease in declina- Hour angle tion of Polaris. before or after Latitude Latitude Latitude Latitude Latitude Latitude Latitude upper culmi- 46. 47. 48. 49. 50. 40. 50. nation. 07 08 07 16 07 25 07 34 07 44 - 5 6 h. m. 15 14 13 14 30 14 48 15 06 15 25 -10 -13 30 21 15 21 40 22 06 22 33 23 02 16 -19 45 28 11 28 44 29 18 29 55 30 33 21 -25 1 00 34 59 35 40 36 23 37 08 37 56 -26 32 1 15 41 38 42 26 43 17 44 11 45 08 -31 -38 1 30 48 05 49 01 49 59 51 02 52 07 -36 -43 1 45 54 19 55 22 56 28 57 38 58 52 40 -49 2 00 1 00 18 1 01 28 1 02 41 1 03 59 1 05 21 45 -54 2 15 1 06 01 1 07 17 1 08 38 1 10 03 1 11 32 -49 59 2 30 1 11 26 1 12 48 1 14 15 1 15 47 1 17 24 -53 -64 2 45 1 16 32 1 18 00 1 19 33 1 21 11 1 22 54 -57 -68 3 00 1 21 17 1 22 50 1 24 29 1 26 13 1 28 02 -60 -72 3 15 1 25 40 1 27 18 1 29 02 1 30 51 1 32 46 -63 -76 3 30 1 29 41 1 31 23 1 33 11 1 35 05 1 37 06 -66 80 3 45 33 17 1 35 03 36 55 1 38 54 1 40 59 -69 -83 4 00 36 29 1 38 18 40 14 1 42 16 1 44 25 -72 -86 4 15 39 15 1 41 08 43 06 1 45 11 1 47 24 -74 -88 4 30 41 35 1 43 30 45 31 1 47 39 1 49 54 -75 -90 4 45 43 29 1 45 25 47 28 1 49 38 1 51 55 -76 -91 5 00 44 55 1 46 53 48 57 1 51 08 1 53 27 ' 77 -92 5 15 45 54 1 47 53 49 58 1 52 10 1 54 30 -78 -93 5 30 46 26 1 48 25 50 30 1 52 43 1 55 03 -78 -94 5 45 46 31 1 48 29 50 34 1 52 46 1 55 06 -78 -93 6 00 1 46 08 1 48 05 1 50 10 1 52 21 1 54 40 78 -93 6 15 1 45 18 1 47 14 1 49 17 1 51 27 1 53 44 -77 -92 6 30 1 44 01 1 45 56 1 47 56 1 50 04 1 52 20 -76 -91 6 45 1 42 18 1 44 10 1 46 09 1 48 14 1 50 27 75 -89 7 00 1 40 09 1 41 59 1 43 54 1 45 57 1 48 06 73 87 7 15 1 37 35 1 39 21 1 41 14 1 43 13 1 45 19 -72 -85 7 30 1 34 36 1 36 19 1 38 08 1 40 03 1 42 05 -69 -82 7 45 1 31 14 1 32 53 1 34 38 1 36 29 1 38 26 -66 -79 8 00 1 27 29 1 29 04 1 30 44 1 32 30 1 34 22 -64 -76 8 15 1 23 23 1 24 53 1 26 28 1 28 09 1 29 55 -61 -72 8 30 1 18 56 1 20 21 1 21 51 1 23 26 1 25 07 -58 -68 8 45 1 14 10 1 15 30 1 16 54 1 18 23 1 19 57 -54 -64 9 00 1 09 05 1 10 19 1 11 38 1 13 01 1 14 28 -50 -59 9 15 1 03 44 1 04 52 1 06 04 1 07 21 1 08 41 -46 -55 9 30 58 07 59 09 1 00 15 1 01 24 1 02 38 -42 -50 9 45 52 16 53 12 54 11 55 13 56 19 -38 -45 10 00 46 12 47 01 47 53 48 49 49 47 34 -40 10 15 39 57 40 40 41 25 42 12 43 02 -29 -34 10 30 33 32 34 08 34 46 35 26 36 08 -24 -29 10 45 27 00 : 27 28 27 59 28 31 29 05 -20 -23 11 00 20 20 20 42 21 05 21 29 21 55 -15 -18 11 15 13 36 13 51 14 06 14 22 14 39 -10 -12 11 30 06 49 06 56 07 04 07 12 07 21 - 5 6 11 45 1 46 32 1 48 31 1 50 36 1 52 48 1 55 08 78 93 h. m. s. h. m. 8. h. m. s. h. m. a. h. m. s. 8. 8. 5 54 53 5 54 42 5 54 31 5 54 20 5 54 07 + 3 + 5 32 GEOGEAPHIC TABLES AND FORMULAS. TABLE 4. Azimuth and apparent altitude Hour angle before or after upper culmination. Azimuth of Polaris computed for declination 88 46'. Latitude 60. Latitude 51. Latitude 52. Latitude 53. Latitude 64. Latitude 55. h. m. 15 07 44 07 54 08 05 08 17 08 29 08 42 30 15 25 15 46 16 08 16 31 16 56 17 22 45 23 02 23 33 24 06 24 41 25 18 25 57 1 00 30 33 31 14 31 58 32 44 6 33 33 34 25 1 15 37 56 38 47 39 40 40 38 41 38 42 43 1 30 45 08 46 08 47 12 48 20 49 32 50 49 1 45 52 07 53 17 54 31 55 49 57 12 58 41 2 00 58 52 1 00 11 1 01 34 1 03 03 1 04 37 1 06 16 2 15 1 05 21 1 06 48 1 08 21 1 09 59 1 11 43 1 13 33 2 30 1 11 32 1 13 08 1 14 48 1 16 35 1 18 29 1 20 30 2 45 1 17 24 1 19 07 1 20 55 1 22 51 1 24 54 1 27 04 3 00 1 22 54 1 24 44 1 26 41 1 28 44 1 30 55 1 33 15 3 15 1 28 02 1 29 59 1 32 02 1 34 13 1 36 32 1 39 00 3 30 1 32 46 1 34 49 1 36 58 1 39 16 1 41 42 1 44 18 3 45 1 37 06 1 39 14 1 41 29 1 43 52 1 46 25 1 49 07 4 00 1 40 59 1 43 12 1 45 32 1 48 01 1 50 39 1 53 27 4 15 ] 44 25 1 46 42 1 49 07 1 51 40 1 54 23 1 57 16 4 30 1 47 24 1 49 44 1 52 13 1 54 50 1 57 37 2 00 35 4 45 1 49 54 1 52 17 1 54 49 1 57 29 2 00 20 2 03 21 5 00 1 51 55 1 54 21 1 56 54 1 59 37 2 02 31 2 05 35 5 15 1 53 27 1 55 54 1 58 29 2 01 15 2 04 10 2 07 16 5 30 1 54 30 1 56 58 1 59 34 2 02 20 2 05 16 2 08 23 5 45 1 55 03 1 57 31 2 00 08 2 02 53 2 05 50 2 08 58 6 00 1 55 06 1 57 34 2 00 10 2 02 56 2 05 52 2 08 58 6 15 1 54 40 1 57 06 1 59 41 2 02 26 2 05 21 2 08 26 6 30 1 53 44 1 56 09 1 58 43 2 01 25 2 04 18 2 07 22 6 45 1 52 20 1 54 42 57 14 1 59 54 2 02 44 2 05 45 7 00 1 50 27 1 52 47 55 15 1 57 52 2 00 39 2 03 36 7 15 1 48 06 1 50 23 52 48 1 55 21 1 58 04 2 00 57 7 30 1 45 19 1 47 32 49 52 1 52 21 1 54 59 1 57 47 7 45 1 42 05 44 13 46 29 1 48 53 1 51 26 1 54 08 8 00 38 26 40 29 42 40 1 44 58 1 47 25 1 50 01 8 15 34 22 36 20 1 38 25 1 40 38 1 42 58 1 45 27 8 30 29 55 31 48 1 33 47 1 35 52 1 38 06 1 40 28 8 45 25 07 26 53 1 28 45 1 30 44 1 32 50 1 35 04 9 00 19 5r 1 21 37 1 23 22 1 25 13 1 27 11 1 29 17 9 15 14 28 1 16 01 1 17 38 1 19 22 1 21 12 1 23 08 9 30 08 41 1 10 06 1 11 36 1 13 12 1 14 53 1 16 40 9 45 1 02 38 1 03 55 1 05 17 1 06 44 1 08 16 1 09 53 10 00 56 19 57 28 58 42 1 00 00 1 01 23 1 02 50 10 15 49 47 50 48 51 53 53 02 54 15 55 32 10 30 43 02 43 56 44 52 45 51 46 54 48 01 10 45 36 08 36 52 37 39 38 29 39 22 40 18 11 00 29 05 29 41 30 18 30 58 31 41 32 26 11 15 21 55 22 22 22 50 23 20 23 52 24 26 11 30 14 39 14 57 15 16 15 37 15 58 16 21 11 45 07 21 07 30 07 39 07 49 08 00 08 11 Elongation: Azimuth 1 55 08 1 57 36 2 00 13 2 Q2 59 2 05 55 2 09 02 h. m. s. h. m. s. h. m. s. h. m. e. h. m. 8. h. m. s. Hour angle. 5 54 07 5 53 54 5 53 41 5 53 27 5 53 12 5 52 57 ^S GEOGRAPHIC TABLES AND FORMULAS. of Polaris at different hour angles Continued. 33 Azimuth of Polaris computed for declination 88 46'. Correction for 1' in- crease in declina- tion of Polaris. Hour angle before or after upper culmi- nation. Latitude 56. Latitude 57. Latitude 58. Latitude 59 Latitude 60. Latitude 50. Latitude 60. o / /> o / // / II O ' // Of" // h. TO. 08 56 09 12 09 28 09 45 10 03 -6 - 8 15 17 50 18 20 18 53 19 27 20 04 -13 - 17 30 26 39 27 24 28 12 29 03 29 58 19 25 45 35 21 36 20 37 23 38 31 39 44 25 - 33 1 00 43 52 45 06 46 24 47 48 49 19 -32 - 41 1 15 52 11 53 39 55 12 56 52 58 40 -38 - 49 1 30 1 00 16 1 01 56 1 03 44 1 05 40 1 07 44 -43 - 57 1 45 1 08 03 1 09 57 1 11 58 1 14 08 1 16 28 49 - 64 2 00 1 15 31 1 17 37 1 19 52 1 22 16 24 51 54 - 71 2 15 1 22 39 1 24 56 1 27 24 1 30 01 32 50 -59 - 78 2 30 1 29 23 1 31 52 1 34 31 1 37 21 40 23 -64 - 84 2 45 1 35 43 1 38 22 1 41 12 ] 44 13 47 28 68 - 89 3 00 1 41 37 1 44 25 1 47 25 1 50 37 54 03 72 - 94 3 15 1 47 03 1 50 00 1 53 08 1 56 30 2 00 07 -76 - 99 3 30 1 52 00 1 55 04 1 58 21 2 01 51 2 05 37 -80 -104 3 45 1 56 26 1 59 37 2 03 01 2 06 40 2 10 34 -83 108 4 00 2 00 21 2 03 38 2 07 09 2 10 54 2 14 55 86 111 4 15 2 03 44 2 07 06 2 10 42 2 14 32 2 18 39 88 114 4 30 2 06 34 2 10 00 2 13 40 2 17 35 2 21 47 90 -116 4 45 2 08 51 2 12 20 2 16 03 2 20 02 2 24 17 -91 -118 5 00 2 10 34 2 14 05 2 17 50 2 21 51 2 26 09 -92 119 5 15 2 11 42 2 15 14 2 19 01 2 23 04 2 27 23 -93 -120 5 30 2 12 17 2 15 50 2 19 36 2 23 39 2 27 58 94 -120 5 45 2 12 17 2 15 49 2 19 35 2 23 37 2 27 56 93 -120 6 00 2 11 44 2 15 14 2 18 59 2 22 59 2 27 15 -93 -119 6 15 2 10 37 2 14 05 2 17 47 2 21 44 2 25 57 -92 118 6 30 2 08 57 2 12 21 2 16 00 2 19 53 2 24 03 91 116 6 45 2 06 44 2 10 05 2 13 39 2 17 27 2 21 32' 89 114 7 00 2 04 00 2 07 16 2 10 45 2 14 27 2 18 26 -87 111 7 15 2 00 45 2 03 55 2 07 18 2 10 54 2 14 46 -85 108 7 30 1 57 00 2 00 04 2 03 20 2 06 49 2 10 32 -82 104 7 45 1 52 47 1 55 43 1 58 52 2 02 12 2 05 47 79 -100 8 00 1 48 06 50 54 1 53 54 1 57 06 2 00 32 76 - 96 8 15 1 42 58 45 39 1 48 30 1 51 32 1 54 47 -72 - 91 8 30 1 37 26 39 57 1 42 39 1 45 31 1 48 35 -68 - 86 8 45 1 31 30 33 51 1 36 23 1 39 05 1 41 57 64 - 80 9 00 1 25 12 27 24 1 29 44 1 32 14 1 34 55 59 - 75 9 15 1 18 34 1 20 36 1 22 45 1 25 03 1 27 30 -55 - 69 9 30 1 11 37 1 13 28 1 15 25 1 17 31 1 19 45 -50 63 9 45 1 04 23 1 06 03 1 07 48 1 09 41 1 11 41 45 - 56 10 00 56 54 58 22 59 55 1 01 34 1 03 20 -40 - 50 10 15 49 12 50 27 51 48 53 14 54 45 -34 - 43 10 30 41 18 42 21 43 28 44 40 45 57 29 36 10 45 33 14 34 05 34 59 35 57 36 59 23 - 29 11 00 25 02 25 41 26 21 27 05 27 51 18 - 22 11 15 16 45 17 10 17 38 18 07 18 38 -12 14 11 30 08 23 08 36 08 50 09 04 09 20 - 6 7 11 45 2 12 21 2 15 54 2 19 40 2 23 43 2 28 02 -93 120 h. TO. 8. h. TO. 8. h. TO. 8. h. m. s. h. TO. 8. 8. 8. 5 52 41 5 52 24 5 52 06 5 51 47 5 51 27 + 5 + 7 4606108- 34 GEOGRAPHIC TABLES AND FORMULAS. TABLE 4. Azimuth and apparent altitude of Polaris at different hour angles Continued. Apparent altitude of Polaris, computed for declination 88 46' and Correc- Hour mean refraction. tion Hour angle forl' angle oefore in- before or after crease or after upper culmi- nation. Latitude 30. Latitude 35. Latitude 40. Latitude 45. Latitude 50. Latitude 55. Latitude 60. in dec- i nation of Po- upper culmi- nation. laris. h. m. / h. m. 000 31 15.6 36 15.3 41 15.1 46 14.9 51 14.8 56 14.6 61 14.5 1.0 000 015 31 15.4 36 15.2 41 14.9 46 14.8 51 14.6 56 14.4 61 14.3 -1.0 015 030 31 14.9 36 14.7 41 14.5 46 14.3 51 14.2 56 14.0 61 "13.8 1.0 030 045| 31 14.2 36 13.9 41 13.7 46 13.5 51 13.3 56 13.2 61 13.0 -1.0 045 100 31 13.0 35 12.8 41 12.5 46 12.3 51 12.2 56 12.0 61 11.9 -1.0 100 115 31 11.6 36 11.3 41 11.1 46 10.9 51 10.8 56 10.6 61 10.4 0.9 1 15 130 31 09.9 36 09.6 41 09.4 46 09.2 51 09.0 56 08.8 61 08.6 0.9 130 145 31 07.9 36 07.6 41 07.3 46 07.2 51 07.0 56 06.8 61 06.6 0.9 145 200 31 05.6 36 05.3 41 05.0 46 04.8 51 04.6 56 04.4 61 04.2 0.8 200 215 31 03.0 36 02.7 41 02.4 46 02.2 51 02.0 56 01.8 61 01.6 -0.8 215 230 31 00.1 35 59.8 40 59.5 45 59.3 50 59.1 55 58.9 60 58.7 -0.8 230 245 30 57.0 35 56.7 40 56.5 45 56.2 50 56.0 55 55.8 60 55.5 -0.7 245 300 30 53.7 35 53.4 40 53.1 45 52.9 50 52.6 55 52.3 60 52.1 -0.7 300 315 30 50.1 35 49.8 40 49.5 45 49.2 50 49.0 55 48.8 60 48.5 0.6 315 330 30 46.4 35 46.0 40 45.7 45 45.5 50 45.2 55 45.0 60 44.7 0.6 330 345 30 42.4 35 42.1 40 41.8 45 41.5 50 41.3 55 41.0 60 40.7 0.5 345 400 30 38.3 35 38.0 40 37.6 45 37.4 50 37.1 55 36.8 60 36.5 0.5 400 415 30 34.0 35 33.6 40 33.3 45 33.0 50 32.8 55 32.5 60 32.1 -0.4 415 430 30 29.6 35 29.2 40 28.9 45 28.5 50 28.3 55 28.0 60 27.6 -0.4 430 445 30 25.0 35 24.6 40 24.3 45 24.0 50 23.7 55 23.4 60 23.0 -0.3 445 500 30 20.4 35 20.0 40 19.7 45 19.4 50 19.1 55 18.8 60 18.4 -0.2 500 515 30 15.6 35 15.3 40 14.9 45 14.6 50 14.3 55 14.0 60 13.6 -0.2 515 530 30 10.8 35 10.4 40 10.1 45 09.9 50 09.6 55 09.2 60 08.8 0.1 530 545 30 06.0 35 05.6 40 05.3 45 05.0 50 04.7 55 04.4 60 04.0 0.0 545 600 30 01.2 35 00.8 40 00.5 45 00.2 49 59.9 54 59.5 59 59.1 0.0 600 615 29 56.4 34 56.0 39 55.6 44 55.3 49 55.0 54 54.7 59 54.3 +0.1 615 630 29 51.6 34 51.2 39 50.8 44 50.5 49 50.2 54 49.9 59 49.6 +0.1 630 645 29 46.8 34 46.4 39 46.0 44 45.7 49 45.5 54 45.1 59 44.8 +0.2 645 700 39 42.1 34 41.7 39 41.4 44 41.1 49 40.8 54 40.4 59 40.1 +0.3 700 715 29 37.5 34 37.1 39 36.8 44 36.4 49 36.2 54 35.8 59 35.4 + 0.4 715 730 29 33.0 34 32.6 39 32.3 44 32.0 49 31.7 54 31.4 59 31.0 +0.4 730 745 29 28.6 34 28.2 39 27.9 44 27.6 49 27.3 54 27.0 59 26.7 +0.5 745 800 29 24.4 34 24.0 39 23.7 44 23.4 49 23.1 54 22.8 59 22.5 +0.5 800 815 29 20.3 34 19.9 39 19.6 44 19.3 49 19.0 54 18.8 59 18.4 +0.6 815 830 29 16.4 34 16.0 39 15.7 44 15.4 49 15.2 54 14.9 59 14.6 +0.6 830 845 29 12.7 34 12.3 39 12.0 44 11.7 49 11.5 54 11.2 59 11.0 +0.7 845 900 29 09.2 34 08.8 39 08.5 44 08.3 49 08.1 54' 07.9 59 07.6 +0.7 900 915 29 05.9 34 05.5 39 05.3 44 05.0 49 04.8 54 04.5 59 04.3 +0.8 915 930 29 02.8 34 02.5 39 02.2 44 02.0 49 01.8 54 01.5 59 01.3 +0.8 930 945 29 00.0 33 59.7 38 59.4 43 59.2 48 59.0 53 58.8 58 58.6 +0.8 945 1000 28 57.5 33 57.2 38 56.9 43 56.7 48 56.6 53 56.4 58 56.1 +0.9 1000 1015 28 55.3 33 55.0 38 54.7 43 54.5 48 54.3 53 54.1 58 53.9 +0.9 1015 1030 28 53.3 33 53.0 38 52.8 43 52.5 48 52.4 53 52.1 58 52.0 +0.9 1030 1045 28 51.6 33 51.3 38 51.1 43 50.8 48 50.7 53 50.5 58 50.3 +0.9 1045 1100 28 50.2 33 49.9 38 49.7 43 49.5 48 49.4 53 49.1 58 49.0 +1.0 1100 1115 28 49.2 33 48.9 38 48.6 43 48.4 48 48.2 53 48.0 58 47.9 +1.0 11 15 1130 28 48.4 33 48.1 38 47.8 43 47.6 48 47.5 53 47.2 58 47.1 +1.0 1130 1145 28 47.9 33 47.6 38 47.4 43 47.1 48 47.0 53 46.8 58 46.7 +1.0 1145 1200 28 47.7 33 47.4 38 47.2 43 47.0 48 46.8 53 46.7 58 46.6 +1.0 1200 GEOGRAPHIC TABLES AND FORMULAS. 35 \g 2.908 8.723 4O 15 00 5 N e Z .006" 10' 2.9H 8.73+ \ f> -cb r IE 5 f y .006" ' 05' TV B.9J5 6.745 m, \ IS 4OQO' h \ Z.9I9 J 8.755 I D 15 f 10 ' 07 Vs' OS' 9000' FIG. 7. Construction of polyconic projection. 15' of latitude and longitude; scale 1:48000. Construc- tion lines (to be drawn in pencil) dotted; final projection lines full. EXAMPLE OF USE OF PROJECTION TABLES. Let it be required to construct a projection for the area between parallels of 40 OCK and 40 15' and meridians 90 (XX and 90 15 X on a scale of 1:48000 (4,000 feet=l inch). For this scale it is customary to show meridians or parallels at intervals of 5 minutes, though any other desired interval may be adopted. Through the center of the paper (see diagram, fig. 7) draw two fine pencil lines a-b and c-d exactly perpendicular to each other. The vertical line will be the meri- dian of 90 07 X 30" and the intersection of the horizontal line with the vertical line will be a point on the parallel of 40 07 X 30". From the column headed "Meridional distance" Table 9, page 82, opposite 40 in column " Latitude of parallel," take OF THE 36 GEOGEAPHIC TABLES AND FORMULAS. the value of a latitude interval of 5 X , which is 7.588 inches; lay off half of this interval or 3.794 inches, on the central meridian above and below the horizontal line; these distances will give points e and/, on the parallels of 40 10 X and 40 05 X , respectively. The distance, 7.588 inches, laid off above and below the latter points will give points g and Ti for latitudes 40 15' and 40 OO 7 . Through each of these points draw a line parallel to the horizontal line and perpendicular to the vertical line first drawn. In a similar manner lay off points on the east and west lines through latitude points 40 (h), and 40 15 X (g), by measuring from the meridian east and west dis- tances obtained from the columns headed "Abscissas of developed parallel" in Table 9, page 82, for the -appropriate latitude and for the longitude intervals of 2Y and 7Y- Thus, for 40, the tabular value for 2J X is 2.919 inches, for 5' it is 5.837 inches, and for 1\' it is 8.755 inches. The points so found (i, j, k, I) will be on the meridians of 90 00', 90 05', 90 1(K, and 90 15'. Find similar points for latitude 40 15 7 , and join corresponding points with light pencil lines. In order to find points on these meridians where each parallel of latitude crosses, take from the columns headed "Ordinates of developed parallel" in Table 9, on the same page, opposite the given latitude 40, the distance for the "Longitude interval" 2y and 7J' (the value of 2y for the 1:48000 scale is inappreciable, being less than 0.001 inch); lay these distances off northward along the meridian from the horizontal lines, giving points x, y, z, etc., on the desired parallels, and through these points draw curved lines concave toward the north. After testing the accuracy of the plotting by com- paring the length of the diagonals /-i=/-Z, h-m=h-n, etc., the projection may be inked in. In a similar manner projections may be constructed for other scales or areas, Table 7, for the scale of 1:63360 (1 mile to 1 inch), may be used for any even fraction or multiple of a mile. The distance between parallels being found from column "Meridional distance;" distances not given may be found by simple proporticn except for "ordinates of developed parallel," which increase as the square of the distance from the central meridian. For scales of any number of thousands of feet to 1 inch, use suitable fractions of the distance given for scale 1:12000 (1,000 feet to 1 inch) in Table 10. For maps of large areas Table 5 gives the actual or full scale distances in meters. These may be divided by the proper scale ratio and the distances so found platted with a metric scale or reduced to feet by the table on page 268; the X values are the dis- tances from the central horizontal line measured to the north or south, and the corresponding Y values give the offsets northward to points on the curved parallels. The distances measured east and west from the central meridian are those in the part of Table 5 entitled "Arcs of the parallel" (p. 39), each to be taken for the proper latitude. For projections of large extent the meridians differ sensibly from straight lines and they as well as the parallels must be drawn as curves. GEOGRAPHIC TABLES AMD FORMULAS. 37 TABLE 5. For projection of maps of large areas. [The ratio of the yard to the meter as stated by Clarke, namely, 1 meter = 1.093623 yards = 39.370432 inches, is that used in the table.] LENGTHS OF DEGREES OF THE MERIDIAN. Latitude. Meters. Statute miles. Latitude. Meters. Statute miles. o 110, 567. 2 68. 704 45 111, 130. 9 69. 054 1 110, 567. 6 68.704 46 111, 150. 6 69. 066 2 110, 568. 6 68. 705 47 111,170.4 69. 079 3 110,570.3 68. 706 48 111,190.1 69. 091 4 110, 572. 7 68. 708 49 111, 209. 7 69. 103 5 110, 575. 8 68. 710 50 111, 229. 3 69. 115 6 110,579.5 68. 712 51 111,248.7 69. 127 7 110, 583. 9 68. 715 52 111,268.0 69. 139 8 110, 589. 68. 718 53 111, 287. 1 69. 151 9 110, 594. 7 68. 721 54 111,306.0 69. 163 10 110, 601. 1 68. 725 55 111, 324. 8 69. 175 11 110,608.1 68. 730 56 111, 343. 3 69. 186 12 110,615.8 68. 734 57 111,361.5 69. 197 13 110, 624. 1 68. 739 58 111,379.5 69. 209 14 110, 633. 68. 744 59 111,397.2 69. 220 15 110, 642. 5 68. 751 60 111, 414. 5 69. 230 16 110, 652. 6 68. 757 61 111,431.5 69. 241 17 110, 663. 3 68.764 62 111,448.2 69. 251 18 110,674.5 68. 771 63 111,464.4 69. 261 19 110,686.3 68. 778 64 111,480.3 69. 271 20 110,698.7 68. 786 65 111, 495. 7 69. 281 21 110,711.6 68. 794 66 111,510.7 69. 290 22 110,725.0 68. 802 67 111,525.3 69. 299 23 110, 738. 8 68. 811 68 111,539.3 69. 308 24 110, 753. 2 68. 820 69 111, 552. 9 69. 316 25 110, 768. 68.829 70 111, 565. 9 69. 324 26 110, 783. 3 68. 839 71 111,578.4 69. 332 27 110, 799. 68. 848 72 111, 590. 4 69. 340 28 110, 815. 1 68. 858 73 111, 601. 8 69. 347 29 110, 831. 6 68. 869 74 111,612.7 69. 354 30 110/848. 5 68. 879 75 111,622.9 69. 360 31 110, 865. 7 68. 890 76 111, 632. 6 69. 366 32 110, 883. 2 68. 901 77 111, 641. 6 69. 372 33 110, 901. 1 68. 912 78 111, 650. 69. 377 34 110, 919. 2 68. 923 79 111, 657. 8 69. 382 35 110, 937. 6 68. 935 80 111, 664. 9 69. 386 36 110,956.2 68. 946 81 111,671.4 69. 390 37 110, 975. 1 68. 958 82 111, 677. 2 69. 394 38 110, 994. 1 68. 969 83 111, 682. 4 69. 397 39 111,013.3 68. 981 84 111, 686. 9 69.400 40 111, 032. 7 68. 993 85 111, 690. 7 69. 402 41 111, 052. 2 69. 006 86 111, 693. 8 69.404 42 111,071.7 69. 018 87 111, 696. 2 69. 405 43 111,091.4 69. 030 88 111, 697. 9 69. 407 44 111,111.1 69. 042 89 111, 699. 69. 407 45 111, 130. 9 69. 054 90 111, 699. 3 69. 407 a These quantities express the number of meters and statute miles contained within an arc of which the degree of latitude named is the middle; thus, the quantity 111,032.7, opposite latitude 40, is the 38 GEOGRAPHIC TABLES AND FORMULAS. TABLE 5. For projection of maps of large areas Continued. [Extracted from Appendix No. 6, U. S. Coast and Geodetic Survey Report for 1884.] LENGTHS OF DEGREES OF THE PARALLEL. Latitude. Meters. Statute miles. Latitude. Meters. Statute miles. o o 111,321 69. 172 45 78, 849 48. 995 1 111, 304 69. 162 46 77,466 48. 136 2 111,253 69. 130 47 76, 058 47. 261 3 111, 169 69. 078 48 74, 628 46. 372 4 111,051 69. 005 49 73, 174 45. 469 5 110,900 68. 911 50 71, 698 44. 552 6 110, 715 68. 795 51 70, 200 43. 621 7 110,497 68. 660 52 68, 680 42. 676 8 110,245 68. 504 53 67, 140 41.719 9 109, 959 68. 326 54 65, 578 40. 749 10 109,641 68.129 55 63, 996 39. 766 11 109, 289 67. 910 56 62, 395 38. 771 12 108, 904 67. 670 57 60, 774 37. 764 13 108, 486 67. 410 58 59, 135 36. 745 14 108, 036 67. 131 59 57, 478 35. 716 15 107, 553 66. 830 60 55, 802 34. 674 16 107, 036 66. 510 61 54,110 33. 623 17 106, 487 66. 169 62 52,400 32. 560 18 105, 906 65. 808 63 50, 675 31.488 19 105, 294 65. 427 64 48,934 30. 406 20 104,649 65. 026 65 47, 177 29. 315 21 103, 972 64.606 66 45, 407 28. 215 22 103, 264 64. 166 67 43, 622 27. 106 23 102, 524 63. 706 68 41, 823 25. 988 24 101,754 63. 228 69 40, 012 24. 862 25 100, 952 62. 729 70 38, 188 23. 729 26 100, 119 62. 212 71 36, 353 22. 589 27 99, 257 61. 676 72 34, 506 21. 441 28 98, 364 61. 122 73 32,648 20. 287 29 97,441 60. 548 74 30, 781 19. 127 30 96, 488 59. 956 75 28, 903 17. 960 31 95, 506 59. 345 76 27, 017 16. 788 32 94, 495 58. 716 77 25,123 15. 611 33 93, 455 58. 071 78 23, 220 14. 428 34 92, 387 57. 407 79 21, 311 13. 242 35 91, 290 56. 725 80 19, 394 12. 051 36 90, 166 56. 027 81 17, 472 10. 857 37 89, 014 55. 311 82 15, 545 9.659 38 87, 835 54. 579 83 13, 612 8.458 39 86, 629 53. 829 84 11,675 7.255 40 85, 396 53.063 85 9,735 6.049 41 84, 137 52. 281 86 7,792 4.842 42 82, 853 51. 483 87 5,846 3.632 43 81,543 50. 669 88 3,898 2.422 44 80, 208 49. 840 89 1,949 1.211 45 78, 849 48. 995 90 0.000 GEOGRAPHIC TABLES AND FOKMULAS. 39 TABLE 5. For projection of maps of large areas Continued. [Extracted from Appendix No. 6, U. S. Coast and Geodetic Survey Report for 1884.] ARCS OF THE PARALLEL IN METERS. Latitude. Value of 1'. Latitude. Value of 1'. Latitude. Value of 1'. / o / O f 24 00 1695. 9 33 00 1557. 6 42 00 1380. 9 10 1693. 7 10 1554. 7 10 1377. 3 20 1691.5 20 1551. 7 20 1373. 7 30 1689. 3 30 1548. 7 30 1370. 40 1687. 40 1545. 8 40 1366. 4 50 1684. 8 50 1542. 8 50 1362. 7 25 00 1682. 5 34 00 1539. 8 43 00 1359. 1 10 1680. 3 10 1536. 8 10 1355. 4 20 1678. 20 1533. 7 20 1351. 7 30 1675. 7 30 1530. 7 30 1348. 40 1673. 3 40 1527. 6 40 1344. 3 50 1671.0 50 1524. 6 50 1340. 5 26 00 1668. 7 35 00 1521. 5 44 00 1336. 8 10 1666. 3 10 1518. 4 10 1333. 1 20 1663. 9 20 1515. 3 20 1329. 3 30 1661. 5 30 1512. 2 30 1325. 5 40 1659. 1 40 1509. 1 40 1321. 7 50 1656. 7 50 1505. 9 50 1318.0 27 00 1654.3 36 00 1502. 8 45 00 1314. 2 10 1651. 8 10 1499. 6 10 1310. 3 20 1649. 4 20 1496.4 20 1306. 5 30 1646. 9 30 1493. 2 30 1302. 7 40 1644.4 40 1490.0 40 1298. 8 50 1641.9 50 1486. 8 50 1295.0 28 00 1639. 4 37 00 1483. 6 46 00 1291.0 10 1636.9 10 1480. 3 10 1287. 2 20 1634. 3 20 1477. 1 20 1283. 3 30 1631.8 30 1473. 8 30 1279. 4 40 1629. 2 40 1470. 5 40 1275. 5 50 1626. 6 50 1467. 2 50 1271.6 29 00 1624. 38 00 1463. 9 47 00 1267. 6 10 1621.4 10 1460. 6 10 1263. 7 20 1618. 8 20 1457. 3 20 1259. 7 30 1616. 1 30 1453. 9 30 1255. 8 40 1613.5 40 1450. 6 40 1251. 8 50 1610.8 50 1447. 2 . 50 1247. 8 30 00 1608. 1 39 00 1443. 8 48 00 1243. 8 10 1605. 4 10 1440. 4 10 1239. 8 20 1602. 7 20 1437. 20 1235. 8 30 1600. 30 1433. 6 30 1231. 7 40 1597. 3 40 1430. 2 40 1227. 7 50 1594. 5 50 1426. 7 50 1223. 6 31 00 1591. 8 40 00 1423. 3 49 00 1219. 6 10 1589. 10 1419.8 10 1215.5 20 1586. 2 20 1416. 3 20 1211.4 30 1583. 4 30 1412. 8 30 1207. 3 40 1580. 6 40 1409. 3 40 1203. 2 50 1577. 8 50 1405. 8 50 1199. 1 32 00 1574. 9 41 00 1402. 3 50 00 1195. 10 1572. 1 10 1398. 8 10 1190. 8 20 1569. 2 20 1395. 2 20 1186. 7 30 1566. 3 30 1391. 6 30 1182. 5 40 1563.4 40 1388. 1 40 1178. 4 50 1560.5 50 1384. 5 50 1174. 2 40 GEOGRAPHIC TABLES AND FORMULAS. TABLE 5. For projections of maps of large areas Continued. COORDINATES OF CURVATURE. Natural scale. Values of X and Y in meters. Latitude 24. Latitude 25. Latitude 26. Longi- tude. X Y Longi- tude. X Y Longi- tude. X Y o / / 1 1 00 101,753 361 1 00 100, 951 372 1 00 100,118 383 2 00 203,500 1,445 2 00 201,896 1,489 2 00 200, 231 1,532 3 00 305, 237 3,250 3 00 302,831 3,351 3 00 300, 332 3,447 4 00 406, 959 5,778 4 00 403, 749 5,957 4 00 400,416 6,128 6 00 508,660 9,028 5 00 504,645 9,307 5 00 500.476 9,574 6 00 610, 336 13,001 6 00 605, 514 13, 401 6 00 600,506 13, 786 7 00 711, 981 17, 695 7 00 706, 349 18, 239 7 00 700,501 18, 763 8 00 813,590 23,109 8 00 807, 146 23,821 8 00 800,456 24, 505 9 00 915, 159 29,245 9 00 907, 899 30,146 9 00 900,364 31,011 10 00 1. 016, 681 36, 102 10 00 1,008,603 37, 215 10 00 , 000, 218 38, 282 11 00 1,118,152 43,679 11 00 1,109,252 45,026 11 00 ,100,015 46, 316 12 00 1,219,566 51, 977 12 00 1,209,841 53, 578 12 00 , 199, 747 55,114 13 00 1,320,919 60,994 13 oe 1,310,364 62,873 13 00 ,299,409 64,675 14 00 1, 422, 205 70, 731 14 00 1,410,815 72,909 14 00 , 398, 994 74,998 15 00 1,523,420 81,186 15 00 1,511,190 83, 685 15 00 ,498,498 86, 082 16 00 1,624,558 92,360 16 00 1,611,483 95,202 16 00 , 597, 914 97,928 17 00 1,725,614 104, 251 17 00 1,711,688 107, 458 17 00 , 697, 237 110,534 18 00 1, 826, 583 116, 859 18 00 1,811,800 120, 453 18 00 , 796, 460 123, 899 19 00 1, 927, 460 130,184 19 00 1,911,813 134, 186 19 00 , 895, 578 138,023 20 00 2,028,240 144, 225 20 00 2,011,722 148, 656 20 00 1,994,585 152,905 21 00 2, 128, 918 158, 981 21 00 2, 111, 522 163, 862 21 00 2, 093, 475 168, 544 22 00 2,229,488 174, 451 22 00 2,211,207 179,805 22 00 2,192,243 184, 939 23 00 2,329,946 190, 634 23 00 2, 310, 771 196, 482 23 00 2, 290, 882 202, 089 24 00 2,430,287 207,530 24 00 2,410,210 213, 894 24 00 2, 389, 387 219, 993 25 00 2, 530, 505 225, 1S8 25 00 2,509,518 232, 038 25 00 2,487,753 238,650 26 00 2, 630, 596 243,458 26 00 2, 608, 689 250, 914 26 00 2, 585, 973 258, 061 27 00 2,730,554 262,487 27 00 2, 707, 718 270, 521 27 00 2,684,042 278, 222 28 00 2, 830, 374 282, 225 28 00 2, 806, 600 290,859 28 00 2,781,953 299, 132 29 00 2, 930, 052 302, 671 29 00 2,905,329 311,925 29 00 2,879,702 320,788 30 00 3,029,582 323,825 30 00 3,003,900 333,718 30 00 2, 977, 281 343, 197 GEOGRAPHIC TABLES AND FORMULAS. 41 TABLE 5. For projections of maps of large areas Continued. COORDINATES OF CURVATURE. Natural scale. Values of X and Y in meters. Latitude 27. Latitude 28. Latitude 29. Longi- tude. X Y Longi- tude. X Y Longi- tude. X Y o / o / o / 1 00 99,256 393 1 00 98, 363 403 1 00 97,439 412 2 00 198,505 1,573 2 00 196, 719 1,612 2 00 194,872 1,649 3 00 297, 742 3,539 3 00 295,062 3,627 3 00 292, 291 3,710 4 00 396,960 6,291 4 00 393,385 6,447 4 00 389,689 6,595 5 00 4%, 154 9,829 5 00 491 , 682 10,073 5 00 487, 059 10, 305 6 00 595, 316 14,154 6 00 589, 945 14,505 6 00 584,394 14, 838 7 00 694, 440 19,264 7 00 688,168 19, 741 7 00 681,687 20, 194 8 00 79S, 522 25,159 8 00 786, 347 25, 782 8 00 778,931 26,374 9 00 892,554 31,839 9 00 884,472 32, 627 9 00 876, 120 33,376 10 00 991,529 39,303 10 00 982, 537 40,276 10 00 973, 246 41, 199 11 00 1,090,442 47,551 11 00 1,080,537 48, 728 11 00 1,070,302 49,845 12 00 1,189,287 56,583 12 00 ,178,464 57,983 12 00 1,167,282 59, 313 13 00 1,288,057 66,398 13 00 1, 276, 312 68,040 13 00 1,264,178 69, 601 14 00 1, 386, 746 76,995 14 00 ,374,075 78,899 14 00 1,360,983 80,706 15 00 1,485,348 88,374 15 00 , 471, 745 90,558 15 00 1,457,691 92, 631 16 00 1,583,857 100,534 16 00 ,569,315 103, 017 16 00 1,554,295 105, 375 17 00 1,682,267 113, 474 17 00 , 666, 781 116,2/5 17 00 1,650,787 118, 935 18 00 1,780,570 127, 193 18 00 , 764, 135 130,331 18 00 1,747,161 133,311 19 00 1,878,762 141,690 19 00 1,861,371 145, 185 19 00 1,843,410 148,602 20 00 1,976,836 156,966 20 00 1,958,481 160,835 20 00 1,939,527 164,506 21 00 2, 074, 786 173, 018 21 00 2,055,460 177.280 21 00 2,035,505 181,324 22 00 2, 172, 606 189, 845 22 00 2, 152, 302 194,518 22 00 2, 131, 338 198, 953 23 00 2, 270, 289 207,447 23 00 2,248,998 212,550 23 00 2, 227, 020 217, 392 24 00 2, 367, 830 225,823 24 00 2,345,544 231, 374 24 00 2,322,539 236,640 25 00 2,465,222 244, 970 25 00 2,441,932 250, 988 25 00 2,417,893 256, 695 26 00 2, 562, 459 264,889 26 00 2,538,156 271, 391 26 00 2, 513, 074 277,558 27 00 2, 659, 535 285,577 27 00 2,634,210 292, &82 27 00 2,608,075 299, 224 28 00 2,756,445 307,035 28 00 2, 730, 087 314, 559 28 00 2,702,890 321, 694 29 00 2,853,181 329, 259 29 00 2, 825, 779 337,321 29 00 2,797,511 344, 964 80 00 2, 949, 739 352,249 30 00 2,921,284 360,866 30 00 2,891,931 369, 036 GEOGRAPHIC TABLES AND FORMULAS. TABLE 5. For projections of maps of large areas Continued. COORDINATES OF CURVATURE. Natural scale. Values of X and Y in meters. Latitude 30. Latitude 31. Latitude 32. Longi- tude. X Y Longi- tude. X Y Longi- tude. X Y o / 1 00 96, 487 421 / 1 00 95,505 429 o / 1 00 94, 494 437 2 00 192, 967 1,684 2 00 191, 002 1,717 2 00 188,980 1,748 3 00 289, 432 3,789 3 00 286,484 3,863 3 00 283, 449 3,933 4 00 385, 875 6,735 4 00 381,943 6,867 4 00 377, 894 6,991 5 00 482, 288 10, 523 5 00 477,371 10, 729 5 00 472, 307 10,922 6 00 578,665 15, 153 6 00 572, 760 15, 450 6 00 566, 680 15, 727 7 00 674, 998 20, 623 7 00 668, 103 21, 027 7 00 661, 004 21, 404 8 00 771,279 26,934 8 00 763, 392 27, 461 8 00 755, 272 27, 954 9 00 867, 502 34,084 9 00 858,619 34,751 9 00 849, 475 35, 375 10 00 963,658 42, 074 10 00 953, 777 42, 897 10 00 943, 605 43, 667 11 00 1,059,741 50,903 11 00 1,048,858 51,898 11 00 1, 037, 655 52, 829 12 00 1,155,744 60, 570 12 00 1, 143, 854 61, 753 12 00 1,131,616 62, 861 13 00 1, 251, 658 71,074 13 00 1,238,758 72,462 13 00 1, 225, 480 73, 761 14 00 1,347,477 82, 415 14 00 1, 333, 561 84,024 14 00 1,319,239 85, 529 15 00 1, 443, 193 94, 591 15 00 1, 428, 257 96, 437 15 00 1,412,885 98, 164 16 00 1, 538, 800 107, 603 16.00 1,522,837 109, 701 16 00 1,506,411 111,664 17 00 1, 634, 290 121,449 17 00 1, 617, 294 123, 815 17 00 1,599,808 126, 029 18 00 1, 729, 654 136, 127 18 00 1,711,621 138,777 18 00 1, 693, 067 141, 256 19 00 1, 824, 887 151,637 19 00 1, 805, 810 154,586 19 00 1, 786, 182 157,346 20 00 1, 919, 982 167, 977 20 00 1,899,852 171, 241 20 00 1, 879, 144 174, 296 21 00 2,014,930 185, 147 21 00 1, 993, 740 188, 741 21 00 1,971,946 192, 105 22 00 2, 109, 725 203, 143 22 00 2, 087, 468 207, 085 22 00 2,064,579 210, 772 23 00 2,204,359 221,966 23 00 2, 181, 027 226, 270 23 00 2, 157, 035 230, 295 24 00 2, 298, 825 241, 616 24 00 2,274,411 246,295 24 00 2, 249, 305 250, 672 25 00 2, 393, 116 262, 089 25 00 2, 367, 610 267, 159 25 00 2, 341, 385 271, 901 26 00 2, 487, 224 283,383 26 00 2,460,618 288,860 26 00 2, 433, 264 293, 981 27 00 2, 581, 144 305, 498 27 00 2, 553, 427 311,396 27 00 2,524,935 316, 910 28 00 2, 674, 867 328, 432 28 00 2, 646, 029 334, 765 28 00 2, 616, 390 340, 686 29 00 2,768,385 352, 183 29 00 2, 738, 418 358,966 29 00 2, 707, 621 365, 307 30 00 2,861,694 376, 749 30 00 2,830,585 383, 997 30 00 2, 798, 621 390, 770 GEOGRAPHIC TABLES AND FORMULAS. 43 TABLE 5. For projections of maps of large areas Continued. COORDINATES OF CURVATURE. Natural scale. Values of X and Y in meters. Latitude 33. Latitude 34. Latitude 35. Longi- tude. X Y Longi- tude. X Y Longi- tude. X Y o / o / o / 1 00 93,454 444 1 00 92,385 451 1 00 91,289 457 2 00 186; 899 1,777 2 00 184, 762 1,803 2 00 182, 568 1,828 3 00 280,328 3,997 3 00 277, 121 4,057 3 00 273, 830 4,112 4 00 373,731 7,106 4 00 369,454 7,212 4 00 365,064 7,310 5 00 467,100 11,102 5 00 461,751 11,268 5 00 456, 261 11-, 421 6 00 560,428 15,986 6 00 554,004 16, 225 6 00 547, 412 16, 445 7 00 653,704 21, 757 7 00 646,205 22, 082 7 00 638,509 22, 381 8 00 746,922 28, 414 8 00 738,344 28,839 8 00 729, 542 29, 229 9 00 840, 072 35, 957 9 00 830, 413 36, 494 9 00 820,501 36, 987 10 00 933, 146 44,385 10 00 922,403 45, 048 10 00 911,379 45, 656 11 00 1,026,136 53, 697 11 00 1, 014, 305 54,499 11 00 1,002,165 55,234 12 00 1.1W.033 63,893 12 00 1,106,110 64,846 12 00 1,092,850 65,721 13 00 1,211,829 74, 971 13 00 1, 197, 809 76,089 13 00 1, 183, 426 77,115 14 00 1,304,515 86,931 14 00 1,289,395 88,227 14 00 1,273,884 89, 415 15 00 1,397,083 99, 771 15 00 1,380,858 101,258 15 00 1,364,214 102, 619 16 00 1,489,526 113,491 16 00 1,472,190 115,180 16 00 1,454,407 116, 728 17 00 1,581,834 128, 089 17 00 1,563,381 129, 993 17 00 1,544,454 131,738 18 00 1,673,998 143,564 18 00 1,654,423 145, 696 18 00 1,634,347 147, 650 19 00 1, 766, Oil 159, 914 19 00 1, 745, 308 162, 287 19 00 1,724,076 164, 460 20 00 1,857,866 177, 138 20 00 1,836,026 179,763 20 00 1,813,632 182, 168 21 00 1,949,553 195,234 21 00 1,926,569 198, 124 21 00 1,903,006 200, 772 22 00 2,041,062 214,201 22 00 2,016,929 217, 368 22 00 1,992,190 220, 268 23 00 2, 132, 387 234, 037 23 00 2, 107, 097 237, 493 23 00 2,081,174 240. 657 24 00 2,223,521 254, 740 24 00 2, 197, 065 258, 497 24 00 2, 169, 949 261,936 25 00 2,314,453 276,309 25 00 2,286,823 230,378 25 00 2, 258, 507 284, 102 26 00 2,405,175 298, 741 26 00 2,376,363 303, 134 26 00 2, 346, 838 307, 154 27 00 2, 495, 680 322,034 27 00 2,465,677 326, 763 27 00 2,434,934 331,089 28 00 2,585,961 346, 187 28 00 2,554,756 351, 262 28 00 2, 522, 787 355, 905 29 00 2,676,007 371, 197 29 00 2, 643, 591 376, 629 29 OC 2, 610, 386 381,598 30 00 2, 765, 812 397, 061 30 00 2, 732, 175 402, 863 30 00 2,697,724 408, 168 44 GEOGRAPHIC TABLES AND FORMULAS. TABLE 5. For projections of maps of large areas Continued. COORDINATES OF CURVATURE. Natural scale. Values of X and Y meters. Latitude 36. Latitude 37. Latitude 38. Longi- tude. X Y Longi- tude. X Y Longi- tude. X Y o / / o / 1 00 90,164 462 1 00 89, 012 467 1 00 87, 833 472 2 00 180, 319 1,850 2 00 178, 015 1,870 2 00 175, 656 1.888 3 00 270,455 4,162 3 00 266, 997 4,207 3 00 263,458 4,247 4 00 360, 562 7,399 4 00 355, 951 7,479 4 00 351, 230 7,549 5 00 450, 631 11, 560 5 00 444,865 11, 685 5 00 438,962 11, 795 6 00 540,653 16, 645 6 00 533, 730 16, 824 6 00 526, 643 16, 983 7 00 630, 618 22,652 7 00 622, 536 22, 896 7 00 614, 263 23,112 8 00 720, 517 29, 583 8 00 711,273 29,901 8 00 701,812 30, 183 9 00 810, 340 37,435 9 00 799, 932 37,838 9 00 789, 280 38,195 10 00 900,078 46, 209 10 00 888,503 46,706 10 00 876, 657 47, 145 11 00 989, 720 55,903 11 00 976,975 56,503 11 00 963, 933 57, 034 12 00 1, 079, 259 66,515 12 00 1,065,340 67, 229 12 00 1,051,098 67,860 13 00 1,168,684 78,046 13 00 1,153,587 78,882 13 00 1,138,141 79,622 14 00 1,257,987 90,494 14 00 1,241,707 91,462 14 00 1,225,053 92, 319 15 00 1,347,156 103, 856 15 00 1, 329, 690 104, 967 15 00 1,311,823 105, 949 16 00 1, 436, 184 118, 133 16 00 1, 417, 526 119, 395 16 00 1,398,441 120,511 17 00 1,525,061 133, 323 17 00 1,505,206 134, 745 17 00 1,484,899 136, 002 - 18 00 1, 613, 777 149, 423 18 00 1, 592, 721 151, 015 18 00 1,571,185 152,421 19 00 1,702,324 166,433 19 00 1,680,059 168,203 19 00 1,657,289 169, 767 20 00 1, 790, 691 184,350 20 00 1,767,211 186, 307 20 00 1,743,202 188,037 21 00 1, 878, 870 203, 173 21 00 1, 854, 169 205, 326 21 00 1,828,914 207,229 22 00 1,966,851 222,899 22 00 1,940,922 225,258 22 00 1,914,415 227, 341 23 00 2, 054, 625 243, 527 23 00 2, 027, 462 246,099 23 00 1,999,694 248, 370 24 00 2, 142, 183 265,055 24 00 2,113,777 267, 849 24 00 2,084,743 270, 315 25 00 2,229,516 287,479 25 00 2, 199, 860 290,503 25 00 2,169,551 293, 172 26 00 2,316,613 310, 798 26 00 2, 285, 699 314, 061 26 00 2, 254, 109 316, 939 27 00 2,403,467 335,009 27 00 2,371,287 338,519 27 00 2,338,406 341, 613 28 00 2, 490, 068 360, 111 28 00 2, 456, 612 363, 874 28 00 2, 422, 433 367, 192 29 00 2, 576, 407 386,099 29 00 2,541,667 390, 125 29 00 2, 506, 181 393, 672 30 00 2,662,475 412, 971 30 00 2,626,441 417, 267 30 00 2, 589, 639 421, 050 GEOGRAPHIC TABLES AND FORMULAS. 45 TABLE 5. For projections of maps of large areas Continued. COORDINATES OF CURVATURE. Natural scale. Values of X and Y in meters. Latitude 39. Latitude 40. Latitude 41. Longi- tude. X Y Longi- tude. X Y Longi- tude. X Y O 1 O i / 1 00 86,627 476 1 00 85,394 479 1 00 84, 136 482 2 00 173, 243 1,903 2 00 170, 778 1,916 2 00 168, 260 1,927 3 00 259, 8o9 4,281 3 00 256, 140 4,311 3 00 252, 363 4,335 4 00 346,403 7,611 4 00 341,470 7,663 4 00 336,432 7,706 5 00 432, 925 11,891 5 00 426, 757 11,972 5 00 420, 457 12,039 6 00 519, 396 17,121 6 00 511,990 17,238 6 00 504,428 17,335 7 00 605,803 23,300 7 00 597, 158 23,460 7 00 588,332 23, 591 8 00 692, 138 30,428 8 00 682, 252 30, 637 8 00 672,159 30,807 9 00 778, 388 38,504 9 00 767,260 38,768 9 00 755, 897 38,983 10 00 864,545 47, 527 10 00 852, 171 47,852 10 00 839, 537 48,118 11 00 950, 598 57,496 11 00 936,975 57,888 11 00 923, 067 58, 209 12 00 1,036,536 68,409 12 00 1,021,661 68,875 12 00 1, 006, 475 69,256 13 00 1,122,349 80,266 13 00 1,106,218 80,811 13 00 1,089,752 81,258 14 00 1,208,027 93,064 14 00 1, 190, 636 93,695 14 00 1, 172, 886 94, 212 15 00 1,293,559 106,802 15 00 1,274,904 107, 525 15 00 1,255,866 108, 117 16 00 1,378,934 121,479 16 00 1,359,012 122, 300 16 00 1, 338, 681 122, 971 17 00 1,464,144 137,093 17 00 1,442,949 138,017 17 00 1,421,321 138, 773 18 00 1,549,177 153, 642 18 00 1,526,704 154,675 18 00 1, 503, 775 155, 520 19 00 1,634,023 171,124 19 00 1,610,267 172, 272 19 00 ,586,031 173,210 20 00 1, 718, 671 189, 537 20 00 1,693,628 190,805 20 00 , 668, 079 191,841 21 00 1,803,113 208,878 21 00 1,776,775 210, 272 21 00 , 749, 909 211,409 22 00 1,887,337 229,146 22 00 1,859,698 230, 671 22 00 ,831,509 231,914 23 00 1,971,333 250, 337 23 00 1,942,387 251,998 23 00 1,912,869 253, 352 24 00 2, 055, 091 272,450 24 00 2, 024, 833 274, 252 24 00 1,993,978 275, 719 25 00 2, 138, 602 295, 481 25 00 2,107,023 297, 430 25 00 2,074,826 299, 014 26 00 2,221,854 319,429 26 00 2, 188, 948 321,528 26 00 2, 155, 402 323, 233 27 00 2,304,838 344, 289 27 00 2,270,597 346,543 27 00 2,235,695 348, 374 28 00 2, 387, 545 370, 059 28 00 2,351,961 372,473 28 00 2, 315, 695 374,432 29 00 2,469,963 396,736 29 00 2, 433, 029 399,314 29 00 2, 395, 392 401,404 30 00 2,552,084 424, 317 30 00 2, 513, 790 427,063 30 00 2, 474, 774 429, 287 46 GEOGRAPHIC TABLES AND FORMULAS. TABLE 5. For projections of maps of large areas Continued. COORDINATES OF CURVATURE. Natural scale. Values of X and Y in meters. - Latitude 42. Latitude 43. Latitude 44. Longi- tude. X Y Longi- tude. X Y Longi- tude. X Y o / o / O 1 1 00 82,851 484 1 00 81,541 485 1 00 80, 206 486 2 00 165, 691 1,935 2 00 163,071 1,941 2 00 160, 401 1,945 3 00 248,508 4,354 3 00 244, 578 4,367 3 00 240, 572 4,375 4 00 331,292 7,739 4 00 326, 050 7,763 4 00 320,708 7,778 5 00 414,030 12,092 5 00 407, 476 12, 129 5 00 400, 797 12, 152 6 00 496, 712 17, 410 6 00 488, 844 17, 464 6 00 480, 827 17,496 7 00 579,325 23, 693 7 00 570, 143 23,766 7 00 560, 786 23,811 8 00 661, 861 30, 941 8 00 651,361 31,036 8 00 640, 662 31, 094 9 00 744,305 39, 152 9 00 732, 486 39,272 9 00 720, 445 39, 345 10 00 826,648 48, 325 10 00 813,508 48,474 10 00 800,122 48,563 11 00 908, 879 58, 459 11 00 894, 415 58, 639 11 00 879,681 58, 746 12 00 ' 990,985 69, 553 12 00 975, 195 69, 766 12 00 959, 110 69,893 13 00 1,072,956 81,605 13 00 1,055,837 81,854 13 00 1,038,399 82,002 14 00 1, 154, 781 94, 614 14 00 1, 136, 329 94,901 14 00 1, 117, 535 95,072 15 00 1,236,449 108, 577 15 00 1,216,661 108, 905 . 15 00 , 196, 507 109, 100 16 00 1,317,948 123, 493 16 00 1,296,820 123,864 16 00 ,275,303 124,084 17 00 1,399,267 139, 360 17 00 1,376,795 139, 777 17 00 , 353, 911 140,023 18 00 1, 480, 395 156, 175 18 00 1, 456, 575 156, 640 18 00 , 432, 320 156,913 19 00 1,561,321 173, 937 19 00 1, 536, 148 174,451 19 00 ,510,519 174,753 20 00 1,642,035 192, 642 20 00 1, 615, 505 193, 209 20 00 1, 588, 496 193, 540 21 00 1, 722, 524 212, 289 21 00 1, 694, 632 212,909 21 00 1,666,240 213, 270 22 00 1,802,779 232, 874 22 00 1, 773, 519 233, 551 22 00 1,743,738 233, 942 23 00 1, 882, 788 254, 396 23 00 1,852,155 255, 129 23 00 1,820,930 255, 552 24 00 1,962,540 276,850 24 00 1, 930, 528 277, 642 24 00 1,897,955 278,096 25 00 2, 042, 024 300, 234 25 00 2, 008, 628 301,087 25 00 1,974,650 301,572 26 00 2,121,230 324, 544 26 00 2,086,443 325, 459 26 00 2,051,055 325, 977 27 00 2, 200, 146 349, 778 27 00 2, 163, 963 350,750 27 00 2, 127, 159 351, 306 28 00 2, 278, 762 375,932 28 00 2,241,176 376, 974 28 00 2, 202, 950 377, 555 29 00 2, 357, 067 403,002 29 00 2,318,071 404,109 29 00 2,278,417 404,722 30 00 2,435,052 430, 985 30 00 2, 394, 639 432, 157 30 00 2, 353, 550 432, 801 GEOGEAPHIC TABLES AND FORMULAS. 47 TABLE 5. For projections of maps of large areas Continued. COORDINATES OF CURVATURE. Natural scale. Values of X and Y in meters. Latitude 45. Latitude 46. Latitude 47. Longi- tude. X y Longi- tude. X Y Longi- tude, X Y / 1 00 78,847 486 / 1 00 77,464 486 o / 1 00 76, 056 485 2 00 157, 682 1,946 2 00 154, 915 1,945 2 00 152, 100 1,942 3 00 236, 493 4,378 3 00 232, 342 4,376 . 3 00 228,119 4,368 4 00 315, 269 7,783 4 00 309,732 7,779 4 00 304, 101 7,765 5 00 393,9% 12, 160 5 00 387, 074 12, 153 5 00 380, 034 12, 131 6 00 472,663 17,508 6 00 464,354 17, 498 6 00 455,904 17,467 7 00 501,258 23,826 7 00 541,562 23, 813 7 00 531,700 23, 770 8 00 629, 769 31,114 8 00 1 00 73, 172 482 o / 1 00 71,696 479 2 00 149, 239 1,936 2 00 146, 331 1,928 2 00 143,379 1,917 3 00 223,827 4,355 3 00 219,465 4,337 3 00 215,037 4,313 4 00 298, 377 7, 742 4 00 . 292, 561 7,709 4 00 286, 656 7,667 5 00 372,877 12,095 5 00 365,606 12, 044 5 00 358, 224 11, 978 6 00 447, 314 17, 414 6 00 438, 588 17, 340 6 00 429, 727 17,246 7 00 521, 677 23,698 7 00 511,493 23, 598 7 00 501,154 23, 469 8 00 595, 951 30, 946 00 584, 310 30, 815 8 00 572,492 30,646 9 00 670, 125 39, 157 9 00 657,026 38,991 9 00 643, 727 38, 777 10 00 744, 186 48,329 10 00 729, 627 48, 123 10 00 714, 847 47, 859 11 00 818, 123 58, 461 11 00 802, 102 58,212 11 00 785, 839 57, 891 12 00 891,921 69, 552 12 00 874, 438 69,254 12 00 856,691 68, 872 13 00 965, 570 81,598 13 00 946,622 81,248 13 00 927, 389 80, 798 14 00 1,039,056 94, 598 14 00 1,018,642 94, 191 14 00 997, 922 93, 669 15 00 1,112,367 108, 551 15 00 1,090,485 108, 082 15 00 1,068,277 107, 482 16 00 1,185,491 123,453 16 00 1,162,138 122, 918 16 00 1,138,440 122,234 17 00 1,258,416 139, 302 17 00 1, 233, 591 138, 697 17 00 1,208,400 137, 923 18 00 1,331,129 156,096 18 00 1,304,829 155,416 18 00 1, 278, 144 154,546 19 00 1, 403,"618 173,832 19 00 1,375,840 173, 071 19 00 1,347,660 172, 099 20 00 , 475, 871 192,506 20 00 1,446,613 191,660 20 00 1,416,934 190,581 21 00 ,547,876 212, 116 21 00 1,517,135 211, 180 21 00 1,485,956 209, 987 22 00 ,619,620 232, 658 22 00 1,587,394 231,627 22 00 1,554,711 230, 314 23 00 ,691,091 254, 128 23 00 1,657,378 252, 998 23 00 1, 623, 189 251,559 24 00 , 762, 279 276, 524 24 00 1,727,073 275,288 24 00 1,691,377 273, 717 25 00 1,833,170 299,842 25 00 1, 796, 470 298, 495 25 00 1,759,262 296, 785 26 00 1,903,752 324, 077 26 00 1,865,554 322,614 26 00 1,826,833 320, 758 27 00 1,974,015 349,225 27 00 1,934,315 347, 640 27 00 1,894,077 345, 633 28 00 2, 043, 945 375,283 28 00 2, 002, 740 373, 570 28 00 1,960,983 371,404 29 00 2, 113, 531 402,245 29 00 2, 070, 817 400, 399 29 00 2, 027, 538 398,068 30 00 2, 182, 762 430, 107 30 00 2, 138, 536 428, 123 30 00 2, 093, 731 425, 619 GEOGRAPHIC TABLES AND FORMULAS. 49 TABLE 6. Coordinates for projection of maps (scale [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. o / 00 10 20 30 40 50 1 00 10 20 30 40 50 2 00 10 20 30 40 50 3 00 10 20 30 40 50 4 00 10 20 30 40 50 5 00 10 20 30 40 50 6 00 10 20 30 40 50 7 00 10 20 30 40 50 8 00 Inches. Inches. 2.922 2.922 2.922 2.922 2.922 2.921 2.921 2.921 2.921 2.921 2.920 2.920 2.920 2.920 2.919 2.919 2.918 2.918 2.918 2.917 2.917 2.916 2.916 2.915 2.915 2.914 2.913 2.913 2.912 2.911 2.911 2.910 2.909 2.908 2.908 2.907 2.906 2.905 2.904 2.903 2.902 2.901 2.900 2.899 2.898 2.897 2.896 2. S'.)f> 2.894 Inches. 5.844 5.843 5.843 5.843 5.843 5.843 5.843 5.842 5.842 5.841 5.841 5.840 5.840 5.839 5.839 5.838 5.837 5.836 5.836 5.835 5.834 5.832 5.831 5.830 5.829 5.828 5.827 5.825 5.824 5.823 5.822 5.820 5.818 5.817 5.815 5.813 5.812 5.810 5.808 5.806 5.804 5.802 5.800 5.798 5.7% 5.794 5.791 5.789 5.787 Inches. 8.765 8.765 8.765 8.765 8.764 8.764 8.764 8.763 8.763 8.762 8.761 8.761 8.760 8.759 8.758 8.757 8.756 8.755 8.753 8.752 8.750 8.749 8.747 8.746 8.744 8. 742 8.740 8.738 8.736 8.734 8.732 8.730 8.727 8.725 8.722 8.720 8.718 8.715 8. 712 8.709 8.706 8.703 8.701 8.697 8.604 8.6% 8.687 8.684 8.680 Inches. 11.687 11.687 11.686 11.686 11.686 11.686 11.685 11.684 11.684 11.683 11.682 11.681 11.680 11.678 11.677 11.676 11. 674 11. 673 11.671 11.669 11. 667 11.665 11.663 11.661 11.659 11.656 11.654 11.651 11.648 11.646 11.643 11.640 11.636 11.633 11.630 11. 627 11. 624 11.620 11.616 11.612 11.608 11.604 11.601 11.596 11.592 11.587 11. 583 11. 578 11.574 Inches. 14.609 14. 608 14.608 14.608 14.608 14.607 14.606 14.606 14.604 14.604 14.602 14.601 14.600 14. 598 14.5% 14.594 14. 592 14. 591 14.589 14.586 14.584 14.581 14. 578 14. 576 14. 574 14. 570 14.567 14.564 14.560 14.557 14.554 14.550 14.546 14. 542 14.538 14.534 14. 530 14. 524 14. 520 14. 515 14.510 14.506 14.501 14. 496 14.490 14. 484 14. 478 14. 473 14. 468 Inches. 17. 531 17.530 17. 530 17.530 17. 529 17.528 17. 528 17. 527 17. 525 17.524 17. 522 17. 521 17. 520 17.518 17.516 17. 513 17. 511 17.509 17.507 17.504 17.501 17. 497 17. 494 17. 491 17.488 17. 484 17.480 17. 476 17.473 17.468 17.465 17. 459 17.455 17.450 17. 445 17.440 17.435 17. 429 17. 424 17.418 17.413 17.407 17.401 17. 395 17.387 17 381 17.374 17.3b8 17. 361 Longi- tude inter- val. 1 5.804 11.608 17. 412 23.216 29.020 5 10 15 20 25 30 Inches. 0.000 .000 .000 .000 .000 .000 Inches. 0.000 .000 .000 .001 .001 .001 5.840 11.608 17.412 23.216 29.020 2 3 5.804 11.608 17.412 23.216 29.020 "~5." 804" 11.608 17.413 23.217 29.021 5 10 15 ,20 25 30 0.000 .000 .001 .001 .002 .003 0.000 .000 .001 .002 .003 .004 4 5 5.804 11.609 17. 413 23.217 29.022 5 10 15 20 25 30 0.000 .001 .001 .002 .004 .005 0.000 .001 .002 .003 .005 .007 5.804 11.609 17.414 23.218 29.022 6 7 o 5 10 15 20 25 30 0.000 .001 .002 .004 .006 .008 0.000 .001 .002 .004 .006 .009 5.805 11.609 17.414 23.219 29.024 8 5.805 11.610 17. 415 23.220 29.025 5 10 15 20 25 30 0.000 .001 .003 .005 .007 .'010 4606108- 50 GEOGRAPHIC TABLES AND FORMULAS. TABLE 6. Coordinates for projection of maps (scale T 2sVoo) Continued. [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. O ' 8 00 10 20 30 40 50 9 00 10 20 30 40 50 10 00 10 20 30 40 50 11 00 10 20 30 40 50 12 00 10 20 30 40 50 13 00 10 20 30 40 50 14 00 10 20 30 40 50 15 00 10 20 30 40 50 16 00 Inches. Inches. 2.894 2.892 2.891 2.890 2.888 2.887 2.886 2.885 2.883 2.882 2.881 2.879 2.878 2.876 2.875 2.873 2.872 2.870 2.869 2. 867 2.865 2.864 2.862 2.860 2.858 2.857 2.855 2.853 2.851 2.849 2.847 2.846 2.844 2.842 2.840 2.838 2.836 2.834 2.831 2.829 2.827 2.825 2.823 2.821 2.818 2.816 2.814 2.812 2.809 Inches. 5.787 5.784 5.782 5.779 5.777 5.775 5.772 5.769 5.767 5.764 5.761 5.758 5.755 5.752 5.749 5. 746 5.743 5.740 5. 737 5.734 5.730 5.727 5.724 5.720 5.717 5.713 5.709 5.706 5. 702 5.698 5.695 5.691 6.687 5.683 5.679 5.675 5.671 5.667 5.663 5.658 5.654 5.650 5.646 5.641 5.637 5.632 5.628 5.623 5. 619 Inches. 8.680 8.677 8.673 8.669 8.666 8.662 8.658 8.654 8.650 8.646 8.642 8.637 8.633 8.628 8.624 8.619 8.614 8.610 8.606 8.601 8.596 8.590 8.585 8.580 8.575 8.570 8.564 8.559 8. 553 8. 548 8.542 8.536 8.530 8. 524 8.519 8. 513 8.507 8.500 8.494 8.488 8.481 8.475 8.469 8.462 8.455 8.448 8.441 8.435 8.428 Inches. 11. 574 11.569 11.564 11. 559 11.554 11.549 11.544 11.539 11.533 11. 528 11.522 11. 516 11.511 11.504 11. 498 11.492 11.486 11. 480 11. 474 11.468 11.461 11.454 11.447 11.440 11.434 11. 426 11.419 11.412 11.404 11.397 11.390 11. 382 11. 374 11. 366 11.358 11.350 11.342 11.334 11. 326 11.317 11.308 11.300 11.292 11. 282 11.274 11.264 11.255 11. 246 11. 237 Inches. 14. 468 14. 461 14. 455 14. 448 14. 442 14. 436 14. 430 14.424 14. 416 14.410 14. 402 14. 396 14.388 14.380 14. 373 14. 366 14. 358 14.350 14. 342 14. 334 14. 326 14. 318 14.309 14.300 14. 292 14. 282 14. 274 14. 264 14. 256 14. 246 14. 237 14. 228 14. 218 14. 208 14. 198 14. 188 14.178 14. 168 14.157 14. 146 14. 136 14. 125 14.114 14. 103 14. 092 14,080 14. 069 14. 058 14.046 Inches. 17. 361 17. 353 17. 346 17. 338 17. 331 17. 324 17.317 17. 308 17.300 17.291 17.283 17. 275 17. 266 17.257 17. 248 17. 239 17. 229 17. 220 17.211 17.201 17. 191 17.181 17. 171 17. 161 17. 150 17. 139 17. 128 17. 117 17. 107 17. 095 17. 084 17. 073 17. 061 17. 049 17.038 17. 026 17. 014 17. 001 16. 988 16. 975 16. 963 16.950 16. 937 16. 924 16.910 16. 897 16.883 16. 870 16. 856 Longi- tude inter- val. 8 9 5. 805 11.610 17. 416 23.221 29. 026 ""5." 806" 11.611 17.417 23.222 29. 028 5 10 15 20 25 30 Inches. 0.000 .001 .003 .005 .007 .010 Inches. 0.000 .001 .003 .005 .008 .012 10 11 0.000 .002 .004 .006 .010 .014 5.806 11. 612 17.417 23.223 29. 029 5 10 15 20 25 30 0.000 .001 .003 .006 .009 .013 5.806 11.612 17. 419 23. 225 29. 031 12 13 5 10 15 20 25 30 0.000 .002 .004 .007 .011 .016 0.000 .002 .004 .007 .012 .017 5.807 11.613 17. 420 23.226 29. 033 5.807 11.614 17.421 23. 228 29.035 14 15 5 10 25 20 25 30 0.000 .002 .004 .008 .012 .018 0.001 .002 .005 .009 .013 .019 5.808 11.615 17. 422 23. 230 29. 038 16 5.808 11.616 17. 424 23. 232 29. 040 5 10 15 20 25 30 0.001 .002 .005 .009 .014 .020 GEOGRAPHIC TABLES AND FORMULAS. TABLE 6. Coordinates for projection of maps (scale j^V^o") Continued. [From Smithsonian Geographical Tables.] 51 Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. o / 16 00 10 20 30 40 50 17 00 10 20 30 40 50 18 00 10 20 30 40 50 19 00 10 20 30 40 50 20 00 10 20 30 40 50 21 00 10 20 30 40 50 22 00 10 20 30 40 50 23 00 10 20 30 40 50 24 00 Inches. Inches. 2.809 2.807 2.804 2.802 2.800 2.797 2.795 2.792 2.790 2.787 2.785 2.782 2.780 2.777 2. 774 2.772 2.769 2.766 2.764 2.761 2.758 2.755 2.752 2.750 2.747 2.743 2.741 2.738 2.735 2. 732 2. 729 2. 72C 2. 723 2.720 2.717 2.714 2.710 2.707 2. 704 2.701 2.697 2.694 2.691 2.688 2.684 2.681 2.677 2.674 2.671 Inches. 5.619 5.614 5.609 5.604 5.599 5.595 5.590 5.585 5.580 5.575 5.570 5.564 5.559 5.554 5.549 5.M3 5.538 5.533 5.527 5.522 5.516 5.510 5.505 5.499 5.493 5.487 5.482 5.476 5.470 5.464 5.458 5.452 5.445 5.439 5.433 5.427 5.421 5.414 5.408 5.401 5.395 5.388 5.382 5.375 5.368 5.362 5.355 5.348 5.341 Inches. 8.428 8.421 8.414 8.406 8.399 8.392 8.385 8.377 8.369 8.362 8.354 8.347 8.339 8.331 8.323 8.315 8.307 8.299 8.291 8.282 8.274 8.266 8.257 8. 249 8.240 8.231 8. 222 8.213 8.204 8.1% 8.187 8.177 8.168 8.159 8.150 8.141 8.131 8.122 8.112 8.102 8.092 8.083 8. 073 8.063 8.053 8.042 8.032 8.022 8.012 Inches. 11.237 11.228 11.218 11.208 11.199 11. 189 11. 180 11. 170 11.159 11.149 11. 139 11. 129 11. 119 11.108 11.097 11.087 11. 076 11.065 11.054 11. 043 11.032 11.021 11.009 10. 998 10. 987 10. 975 10. 963 10. 951 10. 939 10.928 10. 916 10.903 10.891 10. 878 10. 866 10. 854 10. 842 10.829 10. 816 10. 802 10.790 .10.777 10.764 10.750 10. 737 10. 723 10.710 10. 696 10. 683 Inches. 14. 046 14. 034 14. 022 14. 010 13. 998 13. 986 13. 974 13. 962 13. 949 13. 936 13.924 13.911 13. 898 13. 885 13. 872 13.859 13.845 13.832 13.818 13.804 13.790 13. 776 13. 762 13. 748 13. 734 13.719 13. 704 13. 689 13. 674 13. 660 13. 645 13. 629 13. 614 13. 598 13. 583 13. 568 13. 552 13. 536 13. 520 13.503 13.487 13. 471 13. 455 13. 438 13. 421 13. 404 13.387 13. 371 13.354 Inches. 16.856 16. 841 16. 827 16.813 16. 798 16. 784 16. 769 16. 754 16. 739 16. 724 16.709 16. 693 16. 678 16. 662 16.646 16. 630 16.614 16. 598 16.582 16.565 16.548 16. 531 16. 514 16. 497 16. 480 16. 462 16.445 16. 427 16. 409 16. 391 16. 373 16. 355 16. 336 16. 318 16.300 16. 281 16. 262 16. 243 16. 223 16. 204 16.184 16. 165 16. 145 16. 125 16. 105 16. 085 16. 064 16. 045 16. 024 Longi- tude inter- val. 16 17 5.809 11.617 17. 426 23.234 29.043 5 10 15 20 25 30 Inches. 0.001 .002 .005 .009 .014 .020 Inches. 0.001 , .002 .005 .010 .015 .021 5.809 11.618 17. 427 23.236 29.046 18 19 5.810 11.619 17. 429 23. 239 29.049 5 10 15 20 25 30 0.001 .002 .006 .010 .016 .022 0.001 .003 .006 .010 .016 .024 5.810 11.621 17. 431 23.242 29. 052 20 21 5 10 15 20 25 30 o. 061 .003 .006 .011 .017 .025 0.001 .003 .006 .011 .018 026 5.811 11.622 17.433 23. 244 29.055' 5. 812 11.623 17. 435 23.247 29. 058 22 23 5 10 15 20 25 30 0.001 .003 .007 . 012 .018 .027 0.001 .003 .007 .012 .019 .028 5. 812 11.625 17.437 23. 250 29. 062 "~5.'813' 11.626 17.439 23. 252 29.066 24 5 10 15 20 25 30 0.001 .003 .007 .013 .020 .028 52 GEOGRAPHIC TABLES AND FORMULAS. TABLE 6. Coordinates for projection of maps (scale TITTTOTT) Continued [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. / 24 00 10 20 30 40 50 25 00 10 20 30 40 50 26 00 10 20 30 40 50 27 00 10 20 30 40 50 28 00 10 20 30 40 50 29 00 10 20 30 40 50 30 00 10 20 30 40 50 31 00 10 20 30 40 50 32 00 Inches. "'5~8i4' 11. 628 17.442 23.256 29.069 Inches. 2.671 2.667 2.664 2.660 2.657 2.653 2.650 2.646 2.642 2. 639 2.635 2.631 2.628 2.624 2.620 2.616 2.613 2.609 2.605 2. 601 2.597 2.593 2.589 2.586 2.582 2.578 2.574 2.570 2.566 2.562 2.558 2.553 2.549 2.545 2.541 2.537 2.533 2.528 2.524 2.520 2.515 2.511 2.507 2.502 2.498 2.493 2.489 2.485 2.480 Inches. 5.341 5.334 5.327 5.320 5.313 5.306 5.299 5.292 5.285 5.278 5.270 5.263 5.256 5.248 5.240 5.233 5.225 5 218 5.210 5.203 5.195 5.187 5.179 5.171 5.163 5.155 5.147 5.139 5.131 5.123 5.115 5.107 5.098 5.090 5.082 5.073 5.065 5.056 5.048 5. 039 5. 031 5.022 5.014 5.005 4.996 4.987 4.978 4.969 4.960 Inches. 8. 012 8.002 7.991 7.981 7.970 7.960 7.949 7.938 7.927 7.916 7.905 7.894 7.883 7.872 7.861 7.849 7.838 7.827 7.816 7. 804 7.792 7.780 7.768 7.757 7.745 7.733 7.721 7.709 7.697 7.685 7. 673 ' 7.660 7.648 7.635 7.622 7.610 7.598 7.585 7.572 7. 559 7.546 7.533 7.520 7.507 7.494 7.480 7.46T 7.454 7.441 Inches. 10.683 10. 669 10.655 10.641 10. 627 10.613 10.599 10.584 10. 570 10.555 10. 540 10. 526 10. 511 10. 496 10. 481 10. 466 10. 451 10. 436 10. 421 10. 405 10.390 10.374 10.358 10. 342 10. 327 10. 311 10.294 10. 278 10. 262 10. 246 10. 230 10. 213 10. 197 10.180 10. 163 10. 146 10. 130 10. 113 10. 096 10. 078 10.061 10. 044 10. 027 10.009 9.992 9.974 9.956 9.938 9.921 Inches. 13. 354 13. 336 13. 319 13. 301 13.284 13. 266 13. 249 13. 231 13.212 13. 194 13. 176 13. 157 13. 139 13. 120 13. 101 13. 082 13.063 13. 045 13.026 13.006 12. 987 12. 967 12. 947 12.928 12.909 12.889 12.868 12. 848 12.828 12.808 12. 788 12. 767 12..746 12. 725 12.704 12.683 12. 662 12.641 12. 620 12. 598 12.577 12.555 12. 534 12. 512 12.490 12. 467 12.445 12. 423 12.401 Inches. 16.024 16.003 15. 982 15. 961 15. 940 15. 919 15. 898 15. 877 15.854 15. 833 15.811 15.788 15. 767 15. 744 15. 721 15. 698 15. 676 15.654 15. 631 15. 608 15.584 15.560 15. 537 15.514 15.490 15.466 15.442 15.418 15.394 15.369 15.345 15. 320 15.295 15. 270 15. 245 15. 220 15. 195 15. 169 15. 143 15. 118 15.092 15.066 15.040 15. 014 14.987 14. 960 14. 934 14.908 14.881 Longi- tude inter- val. 24 25 5 10 15 20 25 30 Inches. 0.001 .003 .007 .013 .020 .028 Inches. 0.001 .003 .007 .013 .020 .029 5.815 11.629 17. 444 23.259 29. 074 26 27 5. 816 11. 631 17.446 23.262" 29. 077 5 10 15 20 25 30 0.001 .003 .008 .013 .021 .030 0.001 .003 .008 .014 .022 .031 5.816 11.633 17. 449 23.265 29.082 28 29 5 10 15 20 25' 30 0.001 .004 .008 .014 .022 .032 0.001 .004 .008 .014 .023 .032 5.817 11. 634 17. 451 23.268 29. 086 5.818 Ik 636 17.454 23.272 29.090 30 31 5 10 15 20 25 30 0.001 .004 .008 .015 .023 .033 0.001 .004 .008 .015 .023 .034 5.819 11. 638 17.457 23.276 29.094 32 5.820 11.640 17.460 23. 280 29. 100 5 10 15 20 25 30 0.001 .004 .009 .015 .024 .034 GEOGRAPHIC TABLES AND FORMULAS. TABLE 6. Coordinates for projection of maps (scale T ^nnr) Continued. [From Smithsonian Geographical Tables.] 53 Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. W longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. o / 32 00 10 20 30 40 50 33 00 10 20 30 40 50 34 00 10 20 30 40 50 35 00 10 20 30 40 50 36 00 10 20 30 40 50 37 00 10 20 30 40 50 38 00 10 20 30 40 50 39 00 10 20 30 40 50 40 00 Inches. Inches. 2.480 2.476 2.471 2.467 2.462 2.458 2.453 2.448 2.444 2.439 2.434 2.429 2.425 2.420 2.415 2.410 2.406 2.401 2.396 2.391 2.386 2.381 2.377 2.372 2.367 2.362 2.357 2.351 2.346 2.341 2.336 2.331 2.326 2.321 2.316 2.311 2.305 2.300 2.295 2.290 2. 284 2.279 2.274 2.268 2.263 2.258 2.252 2.247 2.241 Inches. 4.960 4.951 4.942 4.933 4.924 4.915 4.906 4.896 4.887 4.878 4.868 4.859 4.850 4.840 4.830 4.821 4.811 4.802 4.792 4. 782 4.773 4.763 4.753 4.743 4.733 4.723 4.713 4.703 4.693 4.683 4.673 4.662 4.652 4.642 4.631 4.621 4.611 4.600 4.590 4.579 4.568 4.558 4.548 4.537 4.526 4.515 4.504 4.493 4.483 Inches. 7.441 7.427 7.413 7.400 7.386 7.373 7.359 7.345 7.331 7.316 7.302 7.288 7.274 7.260 7.246 7.231 7.217 7.203 7.188 7.174 7.159 7.144 7.130 7.115 7.099 7.085 7.070 7.055 7.039 7.024 7.009 6.994 6.978 6.963 6.947 6.932 6.916 6.900 6.884 6.869 6.853 6.837 6.821 6.805 6.789 6.773 6.756 6.740 6.724 Inches. 9.921 9.903 9.884 9.866 9.848 9.830 9.812 9.793 9.774 9. 755 9.736 9.718 9.699 9.680 9.661 9.642 9.622 9.604 9.584 9.565 9.545 9.526 9.506 9.486 9.466 9.446 9.426 9.406 9.386 9.366 9.345 9.325 9.304 9.284 9.263 9.242 9.222 9.200 9.179 9.158 9.137 9.116 9.095 9.073 9.052 9.030 9.008 8.987 8.965 Inches. 12. 401 12.379 12.355 12. 333 12. 310 12.288 12.265 12.241 12. 218 12.194 12. 171 12. 147 12. 124 12.100 12. 076 12.052 12.028 12.004 11.980 11.956 11. 932 11.907 11.883 11.858 11.833 11.808 11. 783 11. 757 11. 732 11.707 11.682 11.656 11.630 11.605 11.579 11.553 11.527 11.501 11. 474 11.448 11.421 11.395 11. 369 11. 342 11.315 11.288 11. 261 11.234 11.207 Inches. 14.881 14.854 14. 827 14.800 14. 772 14. 745 14. 717 14.689 14.661 14. 633 14. 605 14. 576 14.549 14. 520 14.491 14. 462 14.434 14.405 14. 376 14. 347 14. 318 14.288 14. 259 14. 230 14.200 14. 170 14. 139 14.109 14. 078 14. 048 14. 018 13. 987 13.956 13. 925 13.894 13.864 13.832 13.801 13. 769 13. 737 13. 705 13. 673 13.642 13. 610 13. 577 13.545 13. 513 13.480 13.448 Longi- tude inter- val. 32 33 5.821 11.642 17.462 23.283 29.104 5 10 15 20 25 30 Inches. 0.001 .004 .009 .015 .024 .034 Inches. 0.001 .004 .009 .016 .024 .035 5.822 11.643 17.465 23.287 29.109 34 35 5.823 11.645 17.468 23.291 29.113 5 10 15 20 25 30 0.001 .004 .009 .016 .025 .036 0.001 .004 .009 .016 .025 .036 5.824 11.647 17.471 23.294 29.118 36 37 5 10 15 20 25 30 0.001 .004 .009 .013 .025 .036 0.001 .004 .009 .016 .026 . .037 5.824 11.649 17. 473 23.297 29.122 5.826 11.651 17. 477 23.302 29.128 38 39 5 10 15 20 25 30 0.001 .004 .009 .017 .026 .037 0.001 .004 .009 .017 .026 .037 5.827 11.653 17.480 23.306 29.133 40 5.828 11.655 17.483 23.310 29.138 5 10 15 20' 25 30 0.001 .004 .009 .017 .026 .038 54 GEOGRAPHIC TABLES AND FORMULAS. TABLE 6. Coordinates for projection of maps (scale T ^\nnj) Continued. [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15'longi tude. 20'longi tude. 25' longi- tude. 30'longi tude. o / 40 00 10 20 30 40 50 41 00 10 20 30 40 50 42 00 10 20 30 40 50 43 00 10 20 30 40 50 44 00 10 20 30 40 50 45 00 10 20 30 40 50 46 00 10 20 30 40 50 47 00 10 20 30 40 50 48 00 Inches. Inches. 2.241 2.236 2.230 2.225 2.219 2.214 2.208 2.203 2.197 2.192 2.186 2.180 2.175 2.169 2.163 2. 157 2. 152 2.146 2.140 2.135 2.129 2.123 2.117 2.111 2.105 2.099 2. 093 2.087 2.081 2.076 2.070 2.064 2.057 2.051 2.045 2.039 2.033 2.027 2.021 2.015 2.009 2.003 1.996 .990 .984 .978 .971 .965 1.959 Inches. 4.483 4.472 4.461 4.450 4.439 4.428 4.417 4.406 4.394 4.383 4.372 4.360 4.349 4.338 4.326 4.315 4.303 4.292 4.281 4.269 4.257 4.246 4.234 4.222 4.210 4.199 4.187 4. 175 4.163 4.151 4.139 4.127 4.115 4.103 4.091 4.079 4.067 4.054 4.042 4.030 4.017 4.005 3.992 3.980 3.968 3.955 3.943 3.930 3.917 Inches. 6.724 6.707 6.691 6.674 6.658 6.641 6.625 6.608 6.591 6.575 6.558 6.541 6.524 6.507 6.490 6.472 6.455 6.438 6.421 6.403 6.386 6.368 6.351 6.333 6.316 3. 298 6.280 6.262 6.244 6.227 6.209 6.191 6.172 6.154 6.136 6.118 6.100 6.081 6.063 6.044 6.026 6.008 5.989 5.970 5.951 5.933 5. 914 5.895 5.876 Inches. 8. 965 8.943 8.921 8.899 8.877 8.855 8.834 8.811 8.788 8.766 8.744 8.721 8.698 8.676 8.653 8.630 8.607 8.584 8.561 8.538 8.514 8.491 8.468 8.444 8.421 8.397 8.373 8.350 8.326 8.302 8.278 8.254 8.230 8.206 8.181 8.157 8.133 8.108 8.084 8.059 8.034 8.010 7.985 7.960 7.935 7.910 7.885 7.860 7.835 Inches. 11. 207 11. 179 11. 152 11. 124 11.097 11.069 11.042 11. 014 . 10.985 10. 958 10. 929 10.901 10. 873 10.844 10. 816 10. 787 10. 759 10.730 10.702 10. 672 10. 643 10. 614 10.585 10. 556 10. 526 10. 496 10. 467 10. 437 10.407 10. 378 10. 348 10. 317 10. 288 10. 257 10. 226 10. 197 10. 166 10. 136 10. 104 10. 074 10. 043 10. 013 9.981 9.951 9.919 9.888 9.857 9.826 9.794 Inches. 13.448 13.415 13. 382 13. 349 13.316 13.283 13.250 13.217 13.183 13. 149 13. 115 13. 081 13. 048 13. 013 12. 979 12. 945 12. 910 12. 876 12.842 12.807 12. 772 12. 737 12. 701 12. 667 12. 631 12. 596 12. 560 12. 524 12. 489 12. 453 12. 417 12..381 12. 345 12.308 12. 272 12.236 12. 199 12.163 12. 125 12. 089 12. 052 12. 015 11. 978 11.941 11.903 11. 866 11. 828 11. 791 11. 752 Longi- tude inter- val. 40 41 5.829 11.657 17. 486 23. 314 29. 143 5 10 15 20 25 30 Inches. 0.001 .004 .009 .017 .026 .038 Inches. 0.001 .004 .009 .017 .026 .038 5.830 11. 659 17. 489 23.319 29. 149 42 43 5.831 11.661 17. 492 23. 323 29.154 5 10 15 20 25 30 0.001 .004 .010 .017 .026 .038 0.001 .004 .010 .017 .027 .038 5. 832 11. 663 17. 495 23.327 29. 159 44 45 5 10 15 20 25 30 0.001 .004 .010 .017 .027 .038 0.001 .004 .010 .017 .027 .038 5.833 11.666 17. 498 23. 331 29. 164 5.834 11. 668 17.501 23.335 29. 169 46 47 5 10 15 20 25 30 0.001 .004 .010 .017 .027 .038 0.001 .004 .010 .017 .027 .038 5.835 11. 670 17.504 23. 339 29. 174 ""5." 836* 11. 672 17.508 23. 344 29. 180 48 5 10 15 20 25 30 0.001 .004 .010 .017 .026 .038 GEOGRAPHIC TABLES AND FORMULAS. TABLE 6. Coordinates for projection of maps (scale i^-sWo) Continued. 55 [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. / 48 00 10 20 30 40 50 49 00 10 20 30 40 50 50 00 10 20 30 40 50 51 00 10 20 30 40 50 52 00 10 20 30 40 50 53 00 10 20 30 40 50 54 00 10 20 30 40 50 55 00 10 20 30 40 50 56 00 Inches. Inches. 1.959 1.952 1.946 1.940 1.933 1.927 1.921 1.914 1.908 1.901 1.895 1.888 1.882 1.875 1.869 1.862 1.856 1.849 1.842 1.836 1.829 1.823 1.816 1.809 1.803 1.796 1.789 1.782 1.776 1.769 1.762 1.755 1.748 1.742 1.735 1.728 1.721 1.714 1.707 1.700 1. 694 1.687 1.680 1.673 1.666 1.659 1.652 1.645 1.638 Inches. 3.917 3.905 3.892 3.879 3.867 3.854 3.841 3.828 3.815 3.803 3.790 3.777 3.764 3.750 3.737 3.724 3.711 3.698 3.685 3.672 3.658 3.645 3.632 3.618 3.605 3.592 3.578 3.565 3.551 3.538 3.524 3.511 3.497 3.483 3.470 3.456 3.442 3.429 3.415 3.401 3.387 3.373 3.359 3.345 3.331 3.317 3.303 3.289 3.275 Inches. 5.876 5.857 5.838 5.819 5.800 5.781 5.762 5.743 5.723 5.704 5.684 5.665 5.646 5.626 5.606 5.587 5.567 5.547 5.528 5.507 5.488 5.468 5.448 5.428 5.408 5.388 5.367 5.347 5.327 5.307 5.287 5.266 5. 246 5.225 5.205 5.184 5.164 5.143 5.122 5.101 5.080 5.060 5.039 5.018 4.997 4.976 4.955 4.934 4.913 Inches. 7.835 7.810 7.784 7.759 7.733 7.708 7.682 7.657 7.631 7.605 7.579 7.553 7.527 7.501 7.475 7.449 7.422 7.396 7.370 7.343 7.317 7.290 7.264 7.237 7.210 7.184 7.156 7.130 7,103 7.076 7.049 7.022 6.994 6.967 6.940 6. 912 6.885 6.857 6.830 6.802 6.774 6.746 6.713 6.691 6.663 6.635 6.607 6.579 6.551 Inches. 9.794 9.762 9.730 9.699 9.667 9.635 9.603 9.571 9.539 9.507 9.474 9.442 9.409 9.376 9.344 9.311 9.278 9.245 9.212 9.179 9.146 9.113 9.080 9.046 ,9.013 8.980 8.946 8. 912 8.878 8.844 8.811 8.777 8.742 8.708 8.674 8.640 8.606 8.572 8.537 8.502 8.468 8.433 8.398 8.364 8.328 8.294 8.258 8.224 8.188 Inches. 11. 752 11. 714 11.677 11.638 11.600 11.562 11.523 11.485 11. 446 11. 408 11.369 11.330 11. 291 11.251 11.212 11. 173 11.134 11.094 11.055 11.015 10. 975 10.936 10. 895 10.855 10. 816 10.775 10. 734 10. 694 10.654 10. 613 10. 573 10. 532 10.491 10.450 10. 409 10.368 10. 327 10.286 10. 244 10. 202 10. 161 10. 120 10. 078 10. 036 9.994 9.952 9.910 9.868 9.826 Longi- tude inter- val. 48 49 5.837 11. 674 17.511 23.348 29.185 5 10 16 20 25 30 Inches. 0.001 .004 .010 .017 .026 .038 Inches. 0.001 .004 .010 .017 .026 .038 5.838 11. 676 17. 514 23.352 29. 190 50 51 5.839 11. 678 17. 517 2:',. :tv, 29. 194 5 10 15 20 25 30 0.001 .004 .009 .017 .026 .038 0.001 .004 .009 .017 .026 .037 5.840 11. 680 17.520 23.360 29.200 52 53 5 10 15 20 25 30 0.001 .004 .009 .017 .026 .037 0.001 .004 .009 .016 -.026 .037 5.841 11.682 17.523 23.364 29.204 5.842 11.684 17. 526 23.368 29.210 54 55 5 10 15 20 25 30 0.001 .004 .009 .016 .025 .036 0.001 .004 .009 .016 .025 .036 5.843 11.686 17.529 23.372 29.214 56 5.844 11.688 17.532 23.376 29.220 5 10 15 20 25 30 0.001 .004 .009 .016 .025 .036 GEOGRAPHIC TABLES AND FORMULAS. TABLE 6. Coordinates for projection of maps (scale y^V^o ) Continued. [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. o / 56 00 10 20 30 40 50 67 00 10 20 30 40 50 58 00 10 20 30 40 50 59 CO 10 20 30 40 50 60 00 10 20 30 40 50 61 00 10 20 30 40 50 62 00 10 20 30 40 50 63 00 10 20 30 40 50 64 00 Inches. Indies. 1.638 1.631 1.624 1.616 1.609 1.602 1.595 1.588 1.581 1.574 1.566 1.559 1.552 1.545 1.538 1.530 " 1.523 1.516 1.509 1.501 1.494 1.487 1.479 1.472 1.465 1.457 1.450 1.442 1.435 1. 428 1.320 1.313 1.405 1.398 1.390 1.383 1. 375 1.368 1.360 1.353 1.345 1.338 1.330 1.322 1.315 1.307 1.300 1.292 1.284 Inches. 3.275 3.261 3. 247 3.233 3.219 3.204 3.190 3.176 3.162 3.147 3.133 3.119 3.104 3.090 3. 075 . 3.061 3,046 3.032 3.017 3.003 2.988 2. 973 2.959 2.944 2. 929 2. 914 2.900 2:885 2.870 2.855 2.840 2. 825 2.810 2.795 2.781 2.766 2.751 2.736 2. 720 2.705 2.690 2.675 2.660 2.645 2.630 2.614 2.599 2.584 2.569 Inches. 4.913 4.892 4.870 4.849 4.828 4.807 4.785 4.764 4.742 4.721 4.699 4.678 4.656 4.634 4.613 4.591 4.569 4.547 4.526 4.504 4.482 4.460 4.438 4.416 4.394 4. 372 4.349 4. 327 4.305 4.283 4.261 4.238 4.216 4.193 4.171 4.148 4.126 4.103 4.081 4.058 4.035 4.013 3.990 3.967 3.944 3.921 3.899 3.876 3.853 Inches. 6.551 6.522 6.494 6.466 6.437 6.409 6.380 6.352 6.323 6.294 6.266 6.237 6.208 6.179 6.150 6.122 6.092 6.063 6.034 6.005 5.976 5.946 5.917 5.888 5.858 5. 829 5.799 5.770 5.740 5.710 5.681 5.651 5.621 5.591 5.561 5.531 5.501 5.471 5.441 5.410 5.380 5.350 5.320 5.290 5.259 5.228 5.198 5.168 5.137 Inches. 8.188 8.153 8.118 8.082 8.046 8.011 7.976 7.940 7.904 7.868 7.832 7.796 7.760 7.724 7.688 7. -52 7. 616 7.579 7.543 7.506 7.470 7.433 7.396 7.360 7.323 7.286 7.249 7.212 7. 175 7.138 7.101 7.064 7.026 6.988 6.952 6.914 6.877 6.839 6.801 6.763 6.726 6.688 6.650 6.612 6.574 6.536 6.498 6.460 6.422 Inches. 9.826 9.784 9.741 9.698 9.656 9.613 9.571 9. 527 9.485 9.442 9.398 9.356 9.313 9. 269 9.226 9.182 9.139 9.095 9. 052 9.008 8.963 8.920 8.876 8.831 8.788 8.743 8.699 8.654 8.610 8.566 8. 521 8.476 8.431 8.386 8. 342 8.297 8.252 8.207 8.161 8.116 8.071 8.026 7.980 7.934 7.889 7.843 7.797 7.751 7.706 Longi- tude inter- val. 56 57 5.845 11.690 17.535 23.380 29. 224 5 10 15 20 25 30 Inches. 0.001 .004 .009 .016 .025 .036 Indies. 0.001 .001 .009 .016 .024 .035 5.846 11.692 17. 537 23. 383 29.229 58 59 5.847 11. 694 17. 540 23.387 29. 234 5 10 15 20 25 30 0.001 .004 .009 .015 .024 .034 0.001 .004 .008 .015 .024 .034 5.848 11. 695 17.543 23. 391 29. 238 ""5." 849" 11. 697 17.546 23. 394 29. 243 60 61 5 10 15 20 25 30 0.001 .004 .008 .015 .023 .033 0.001 .004 .008 .014 .023 .033 5.850 11.699 17.549 23. 398 29. 248 5 10 15 20 25 30 62 63 0.001 .004 .008 .014 .022 .032 0.001 .003 .008 .014 .022 .031 5.850 11. 701 17. 551 23. 402 29. 252 64 5.851 11.702 17.554 23. 405 29.256 5 10 15 20 25 30 O.OC1 .OC. .008 .013 .021 ' .030 GEOGRAPHIC TABLES AND FORMULAS. TABLE 6. Coordinates for projection of maps (scale yWinnr) Continued. [From Smithsonian Geographical Tables.] 57 Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. O 1 64 00 10 20 30 40 50 65 00 10 20 30 40 50 66 00 10 20 30 40 50 67 00 10 20 30 40 50 68 00 10 . 20 30 40 50 69 00 10 20 30 40 50 70 00 10 20 30 40 50 71 00 10 20 30 40 50 72 00 Inches. Inches. .284 .277 .269 .261 .254 .246 .238 .231 .223 .215 .207 .200 1.192 1.184 1.176 1.168 1.161 1.153 1.145 1.137 1.129 1.121 1.113 1.106 1.098 1.090 1.082 1.074 1.066 1.058 1.050 1.042 1.034 1.026 1.018 1.010 1.002 .994 .986 .978 .970 .962 .954 .946 .938 .930 .922 .914 .906 Inches. 2.569 2.553 2.538 2.523 2.507 2.492 2.477 2.461 2.446 2.430 2.415 2.399 2.384 2.368 2.352 2.337 2.321 2.305 2.290 2.274 2.258 2.243 2.227 2.211 2.195 2.180 2.164 2.148 2.132 2.116 2.100 2.084 2.068 2.052 2.037 2.021 2.005 1.989 .972 .956 .940 .924 .908 .892 .876 .860 .844 1.828 1.811 Inches. 3.853 3.830 3.807 3.784 3.761 3.738 3.715 3.692 3.668 3.645 3. 622 3.599 3.575 3.552 3.529 3.505 3.482 3.458 3.435 3.411 3.388 3.364 3.340 3.317 3.293 3.269 3.246 3.222 3.198 3.174 3.151 3.127 3.103 3.079 3.055 3.031 3.007 2.983 2.959 2.935 2.911 2.886 2.862 2.838 2. 814 2.790 2.765 2.741 2.717 Inches. 5.137 5.106 5.076 5.045 5.014 4.984 4.953 4.922 4.891 4.860 4.829 4.798 4.767 4.736 4.705 4.673 4.642 4.611 4.580 4.548 4.517 4.485 4.454 4.422 4.391 4.359 4.328 4.296 4.264 4.232 4.201 4.169 4.137 4.105 4.073 4.041 4.009 3.977 3.945 3.913 3.881 3.848 3.816 3.784 3.752 3.720 3.687 3.655 3.623 Inches. 6.422 6.383 6.345 6.307 6.268 6.230 .6.192 6.153 6.114 6.075 6.037 5.998 5.959 5.920 5.881 5.842 5.803 5.764 5.725 5.685 5.646 5.607 5.567 5.528 5.489 5.449 5.410 5.370 5.330 5.291 5.251 5.211 5.171 5.131 5.092 5.052 5.012 4. 972 4.931 4.891 4.851 4.811 4.771 4.730 4.690 4.650 4.609 4.569 4.529 Inches. 7.706 7.660 7.614 7.568 .7. 522 7.476 7.430 7.384 7.337 7.290 7.244 7.198 7.151 7.104 7.057 7.010 6.963 6.916 6.869 6. 822 6.775 6.728 6.680 6.634 6.586 6.539 6.491 6.443 6.396 6.349 6.301 6.253 6.205 6.157 6.110 6.062 6.014 5. 966 5.917 5. 869 5. 821 5.773 5.725 5.676 5.628 5.579 5.531 5.483 5.434 Longi- tude inter- val. 64 65 5.852 11.704 17.556 23.408 29.260 "~5." 853" 11.706 17.558 23.411 29.264 5 10 15 20 25 30 Inches. 0.001 .003 .008 .013 .021 .030 Inches. 0.001 .003 .007 .013 .020 .029 66 67 5.854 11.707 17.561 23.414 29.268 5 10 15 20 25 v30 0.001 .003 .007 .013 .020 .029 0.001 .003 .007 .012 .019 .028 5.854 11.709 17.563 23.418 29.272 68 69 5 10 15 20 25 30 0.001 .003 .007 .012 .019 .027 0.001 .003 .006 .011 .018 .026 5.855 11.710 17.565 23.420 29.276 5.856 11.712 17.567 23.423 29.279 70 71 5 10 15 20 25 30 0.001 .003 .006 .011 .017 .024 0.001 .003 .006 .010 .016 .024 5.856 11. 713 17. 570 23.426 29.282 "~5.~ 857" 11. 714 17.572 23.429 29.286 72 5 10 15 20 25 30 0.001 .003 .006 .010 .016 .023 58 GEOGRAPHIC TABLES AND FORMULAS. TABLE 6. Coordinates for projection of maps (scale T ^V^o) Continued. [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. ~1 Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. o / 72 00 10 20 30 40 50 73 00 10 20 30 40 50 74 00 10 20 30 40 50 75 00 10 20 30 40 50 76 00 10 20 30 40 50 77 00 10 20 30 40 50 78 00 10 20 30 40 50 79 00 10 20 30 40 50 80 00 Inches. Inches. .906 .898 .889 .881 .873 .865 .857 .849 .841 .832 .824 .816 .808 .800 .791 .783 .775 .767 .759 .750 .742 .734 .726 .717 .709 .701 .692 .684 .676 .668 .659 .651 .643 .634 .626 .618 .609 .601 .593 .584 .576 .568 .559 .551 .542 .534 .526 .517 .509 Inches. 1.811 1.795 1.779 1.763 1.746 1.730 1.714 1.697 1.681 1.665 1.648 1.632 1.616 1.599 1.583 1.566 1.550 1.534 "517 1.501 1.484 1.468 1.451 1.435 1.418 1.402 1.385 1.368 1.352 1.335 1.319 1.302 1.285 1.269 1. 252 1.235 1.219 1.202 1.185 1.169 1.152 1. 135 1.119 1.102 1.085 1.068 1.052 1.035 1.018 Inches. 2. 717 2.G93 2.668 2.644 2.620 2.595 2.571 2.546 2. 522 2. 497 2. 473 2. 448 2.424 2. 399 2.374 2.350 2.325 2.300 2.276 2.251 2.226 2.201 2.177 2.152 2.127 2. 102 2.078 2.053 2. 028 2.003 1.978 1.953 1.928 1.903 1.878 1.853 1.828 1.803 1.778 1.753 1.728 1.703 1.678 1.653 1.628 1.602 1.577 1.552 1.527 Inches. 3.623 3.590 3. 558 3.525 3.493 3.460 3.428 3.395 3. 362 3.330 3. 297 3.264 3.232 3.199 3.160 3.133 3.100 3.067 3.034 3.002 2. 968 2.935 2.902 2.870 2.836 2.803 2.770 2. 737 2.704 2.671 2.638 2. 604 2. 571 2. 538 2.504 2.471 2.438 2.404 2.371 2.338 2.304 2.270 2.237 2. 204 2.170 2. 136 2. 103 2.070 2.036 Inches. 4. 529 4.488 4.447 4.407 4.366 4.325 4.285 4. 244 4.203 4.162 4.121 4.081 4.040 3.999 3.957 3.916 3.875 3.834 3.793 3.752 3.711 3.669 3.628 3.587 3.546 3.504 3.463 3. 421 3.380 3.339 3.297 3.256 3.214 3.172 3.131 3.089 3.047 3.005 2.964 2.922 2.880 2.838 2.797 2.755 2.713 2.671 2.629 2.587 2. 45 Inches. 5.434 5.386 5.336 5. 288 5.239 5.190 5.141 5. 092 5.044 4.994 4. 94.) 4.897 4.847 4.798 4.748 4. 699 4.650 4.601 4.552 4.502 4.453 4.403 4.354 4.304 4.255 4. 205 4.155 4.105 4.056 4.006 3.956 3.907 3.856 3.806 3.757 3.706 3.656 3.606 3.556 3.506 3.456 3.406 3.356 3.305 3.255 3. 205 3.155 3.104 3.054 Longi- tude inter- val. 72 73 5.858 11. 716 17. 573 23. 431 29.289 5 10 15 20 25 30 Inches. 0.001 .003 .006 .010 .016 .023 Inches. 0.001 .002 .005 .010 .015 .021 5.858 11. 717 17. 575 23.434 29. 292 5.859 11.718 17. 577 23. 436 29. 295 74 75 5 10 15 20 25 30 0.001 .002 .005 .009 .014 .020 0.001 .002 .005 .009 .013 .019 5.860 11.719 17. 578 23. 438 29. 298 5.860 11. 720 17. 580 23.440 29.300 76 77 5 10 15 20 25 30 0.001 .002 .005 .008 .013 .018 0.000 .002 .004 .007 .012 .017 5.860 11.721 17. 582 23. 442 29. 302 ""s.'sei" 11. 722 17.583 23. 444 29.304 ""s.'sei" 11. 723 17.584 23. 445 29.306 78 79 5 10 15 20 25 30 0.000 .002 .004 .007 .011 .016 0.000 .002 .004 .006 .010 .014 GEOGRAPHIC TABLES AND FORMULAS. 59 TABLE 7. Coordinates for projection of maps (scale [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10'longi- tude. 15' longi- tude. 20' longi- tude. - 25' longi- tude. 30' longi- tude. o / 00 10 20 30 40 50 1 00 10 20 30 40 50 2 00 10 20 30 40 50 3 00 10 20 30 40 50 4 00 10 20 30 40 50 5 00 10 20 30 40 50 6 00 10 20 30 40 50 7 00 Inches. Inches. 5.704 5.764 5.764 5.764' 5.764 5.764 5.764 5.763 5.763 5.762 5.762 5.761 5.761 5.760 5.759 5.759 5.758 5.757 5.756 5.756 5.754 5. 753 5.752 5.751 5.750 5.749 5.748 5.746 5.745 5.744 5.743 5.741 5.739 4 5.738 5.736 5.735 5.733 5. 731 5.729 5.727 5.726 5.724 5. 722 Inches. 11. 529 11. 528 11. 528 11. 528 11.528 11. 527 11. 527* 11. 526 11.525 11.524 11. 524 11.523 11. 522 11. 520 11. 519 11.517 11.516 11. 514 11.513 11.511 11.509 11.507 11.505 11.503 11.501 11. 498 11,4% 11.493 11.490 11.488 11.485 11.482 11.479 11.476 11.472 11. 469 11.466 11.462 11.458 11.455 11.451 11. 447 11.443 Inches. 17. 293 17. 293 17. 292 17. 292 17. 291 17. 291 17.291 17. 289 17. 288 17.287 17. 285 17. 284 17.283 17. 281 17. 278 17.276 17. 274 17. 272 17. 270 17. 267 17.264 17. 260 17. 257 17.254 17. 251 17. 247 17. 243 17. 240 17. 236 17. 232 17. 228 17. 223 17.218 17. 213 17.209 17. 204 17. 199 17. 193 17. 188 17. 182 17. 177 17. 171 17.165 Inches. 23.058 23. 057 23.056 23. 056 23. 055 23.054 23.054 23. 052 23.050 23.049 23.047 23. 045 23.044 23.041 23.038 23.035 23. 032 23. 029 23.026 23. 022 23. 018 23.014 23. 010 23.006 23.002 22. 996 22. 991 22.986 22. 981 22. 976 22. 970 22.964 22. 958 22. 951 22.945 22. 938 22.932 22.924 22.917 22.910 22. 902 22. 894 22. 887 Inches. 28. 822 28. 821 28. 821 28. 820 28. 819 28.818 28.818 28.816 28. 813 28.811 28. 809 28.807 28. 805 28. 801 28.797 28. 794 28. 790 28. 786 28. 783 28. 778 28. 773 28. 767 28. 762 28. 757 28. 752 28. 746 28.739 28. 733 28. 726 28. 720 28. 7l3 28. 705 28. 697 28. 689 28. 681 28. 673 28. 665 28. 656 28. 646 28. 637 28.628 28. 618 28. 609 Inches. 34.586 34.585 34. 585 34. 583 34.583 34. 582 34.581 34. 579 34.576 34.573 34.571 34.568 34.565 34.561 34. 556 34.552 34. 548 34.543 34.539 34.533 34.527 34.520 34. 514 34. 508 34.502 34. 495 34. 487 34. 479 34. 471 34. 463 34. 456 34. 446 34. 436 34. 427 34. 417 34. 408 34.398 34.387 34. 375 34.364 34. 353 34.342 34.330 Longi- tude inter- val. 1 11. 451 22. 901 34.352 45.803 57.254 68.704 11. 451 22. 901 34.352 45.803 57.254 08. 704 11.451 22.902 34.353 45.804 57.254 68.705 5 10 15 20 25 30 Inch. 0.000 .000 .000 .000 .000 .000 Inch. 0.000 .000 .001 .001 .002 .003 2 3 5 10 15 20 25 30 0.000 .001 .001 .002 .004 .005 0.000 .001 .002 .003 .005 ,098 11. 451 22.902 34.353 45.804 57. 255 68.706 4 5 11. 451 22.903 34.354 45.805 57.256 68.708 5 10 15 20 25 30 0.000 .001 .OJ3 .005 .007 .011 0.000 .001 .003 .006 .009 .013 11.452 22.903 34.855 45.806 57.258 68. 710 6 7 5 10 15 20 25 30 0.000 .002 .004 .007 .011 .016 0.000 .002 .005 .008 .013 .018 11. 452 22.904 34.356 45.808 57.260 68.712 GEOGRAPHIC TABLES AND FORMULAS. TABLE?. Coordinates for projection of maps (scale ^3^7) Continued. [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. O ' 1 00 10 20 30 40 50 8 00 10 20 30 40 50 9 00 10 20 30 40 50 10 00 10 20 30 40 50 11 00 10 20 30 40 50 12 00 10 20 30 40 50 13 00 10 20 30 40 50 14 00 Inches. 68. 712 Inches. 5.722 5.720 5.717 5.715 5.713 5.711 5.709 5.706 5.704 5.701 5.699 5.696 5.694 5.691 5.688 5.686 5. 683 5.680 5.677 5.674 5.671 5.668 5.665 5.662 5.659 5.656 5.652 5. 649 5.646 5.642 5.639 5.636 5.632 5.628 5.625 5. 621 5.618 5.614 5.610 5.606 5.602 5.598 5.594 Inches. 11.443 11.439 11.435 11.430 11.426 11. 422 11.417 11.412 11.407 11.403 11. 398 11. 393 11.388 11.382 11. 377 11.371 11. 366 11.360 11.355 11.349 11.343 11.337 11.331 11.324 11.318 11.312 11.305 11.298 11.292 11.285 11. 278 11.271 11. 264 11.257 11.250 11. 242 11.235 11. 227 11.220 11.212 11.204 11. 196 11.188 Inches. 17. 165 17. 159 17. 152 17. 146 17.139 17. 132 17. 126 17. 119 17.111 17.104 17.096 17.089 17.082 17. 073 17.065 17.057 17.049 17.040 17. 032 17. 023 17. 014 17.005 16.996 16.987 16.978 16.968 16.958 16. 948 16.938 16.928 16.918 16. 907 16. 896 16.885 16.874 16.864 16.853 16. 841 16. 829 16. 818 16.806 16. 794 16.783 Inches. 22.887 22. 878 22. 869 22. 861 22. 852 22. 843 22.834 22.825 22. 815 22.805 22.795 22.786 22.776 22.764 22.754 22. 742 22.732 22. 720 22. 710 22.698 22. 685 22.673 22. 661 22.649 22. 637 22. 624 22.610 22. 597 22.584 22.570 22. 557 22.5*42 22. 528 22. 514 22. 499 .22.485 22. 470 22.455 22. 439 22. 424 22. 408 22.392 22.377 Inches. 28.609 28. 598 28.587 28. 576 28.565 28.554 28.543 28.531 28. 519 28. 507 28.494 28. 482 28. 470 28.456 28. 442 28.428 28.415 28. 401 28.387 28.372 28. 357 28.342 28.327 28. 311 28. 296 28.280 28. 263 28. 246 28.230 28. 213 28. 196 28. 178 28. 160 28. 142 28. 124 28.106 28.088 28.069 28. 049 28.030 28. 010 27. 991 27. 971 Incites. 34. 330 34. 317 34. 304 34. 291 34. 278 34.265 34.252 34.237 34. 222 34.208 34.193 34. 178 34.163 34.147 34.130 34. 114 34. 097 34. 081 34.064 34.046 34. 028 34. 010 33. 992 33.973 33.955 "33.935 33.915 33.895 33.875 33.855 33.835 33.814 33. 792 33.770 33. 749 33. 727 33. 706 33.682 33. 659 33.635 ' 33.612 33.589 33.565 Longi- tude inter- val. 7 8 11.452 22.905 34.358 45. 810 57. 262 68.715 5 10 15 20 25 30 Inch. 0.000 .002 005 .008 .013 .018 Inch. 0.001 .002 .005 .009 .014 .021 11. 453 22.906 34.359 45. 812 57.265 68.718 9 10 11.454 22.907 33.361 45. 814 57.268 68.722 5 10 15 20 25 30 0.001 .003 .006 .010 .016 .023 0.001 .003 .006 .011 .018 .026 11. 454 22.909 34.263 45.817 57. 272 68.726 11 12 11.455 22. 910 34.365 45.820 57.275 68.730 5 10 15 20 25 30 0.001 .003 .007 .013 .020 .028 0.001 .003 .008 .014 .021 .031 11.456 22. 912 34. 367 45.823 57.279 68.735 13 14 5 10 15 20 25 30 0.001 .004 .008 .015 .023 .033 0.001 .004 .009 .016 .025 .035 11.457 22.913 34.370 45. 827 57.284 68.740 GEOGRAPHIC TABLES AND FORMULAS. 61 TABLE 7. Coordinates for projection of maps (scale [From Smithsonian Geographical Tables.] Continued. Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. O ' 14 00 10 20 30 40 50 15 00 10 20 30 40 50 16 00 10 20 30 w 50 17 00 10 20 30 40 50 18 00 10 20 30 40 50 19 00 10 20 30 40 50 20 00 10 20 30 40 50 21 00 9 Inches. 68.740 Inches. 5.594 6.590 5.586 5.582 5.578 5.573 5.569 5.565 5.560 5.556 5.551 5.547 5.542 5.538 5.533 5.528 5.524 5.519 5.514 5.509 5.504 5-499 o7494 5.489 5.484 5.479 5.473 5.468 5.463 5.458 5.452 5.447 5.441 5.436 5.430 5.424 5.419 5.413 5.407 5.401 5.396 5.390 5.384 Inches. 11.188 11.180 11. 172 11. 163 11.155 11.147 11.138 11.130 11. 121 11. 112 11.103 11.094 11.085 11.076 11.066 11.057 11.047 11.038 11.028 11.018 11.008 10.998 10.988 10. 978 10.968 10. 957 10.947 10.936 10. 926 10. 915 10.905 10.893 10.882 10. 871 10.860 10.849 10.838 10. 826 10. 814 10.803 10. 791 10. 779 10.768 Inches. 16. 783 16. 770 16.758 16. 745 16.733 16. 720 16.708 16.694 16.681 16.667 16.654 16. 641 16.628 16. 613 16.599 16.585 16. 571 16.556 16.542 16. 527 16. 512 16.497 16. 482 16. 467 16.452 16.436 16. 420 16. 404 16.389 16. 373 16.357 16. 340 16. 324 16. 307 16. 290 16.274 16.257 16. 239 16.222 16. 204 16. 187 16.169 16. 151 Inches. 22.377 22.360 22.344 22.327 22. 310 22.294 22.277 22.259 22.241 22.223 22.206 22.188 22.170 22.151 22. 132 22. 113 22.094 22.075 22.056 22.036 22.016 21.996 21. 976 21.956 21.936 21. 915 21.894 21. 872 21.852 21.830 21.809 21.787 21. 765 21. 742 21. 720 21. 698 21. 676 21.652 21. 629 21.605 21. 582 21.558 21.535 Inches. 27. 971 27.950 27.930 27.909 27.888 27.867 27.846 27. 824 27.802 27. 779 27. 757 27.735 27.713 27.689 27.665 27.642 27. 618 27.594 27. 571 27.546 27.521 27. 495 27. 470 27.445 27.420 27.394 27.367 27.341 27. 315 27.288 27. 262 27.234 27. 206 27.178 27. 150 27. 123 27.095 27.065 27.036 27.007 26.978 26. 948 26. 919 Inches. 33.565 33.540 33.515 33.490 33.465 33.440 33.415 33.389 33. 362 33.335 33. 308 33. 282 33.255 33.227 33.198 33.170 33.142 33.113 33.085 33.055 33.025 32.994 32.964 32. 934 32.904 32.872 32.840 32.809 32. 777 32. 746 32. 714 32.680 32. 647 32. 614 32. 580 32. 547 32.513 32. 478 32.443 32.408 32. 373 32.338 32.303 Longi- tude inter- val. 14 15 11.458 22.915 34.373 45.830 57.288 68.746 5 10 15 " 20 25 30 Inches. 0.001 .004 .009 .018 .025 .035 Inches. 0.001 .004 .009 .017 .026 .038 11.459 22.917 34.376 45.834 57.293 68.752 16 17 11.460 22.919 34.379 45.838 57.298 68.758 ' 5 10 15 20 25 30 0.001 .004 .010 .018 .028 .040 0.001 .005 .011 .019 .029 .042 11.461 22.921 34.382 45.843 57.304 68.764 18 19 11.462 22.924 34.386 45.848 57. 310 68:771 5 10 15 20 25 30 0.001 .005 .T)ll .020 .031 .044 0,001 .005 .012 .021 .032 .046 11.463 22.926 34.390 45.853 57. 316 68.779 20 21 5 10 15 20 25 30 0.001 .005 .012 .022 .034 .049 0.001 .006 .013 .022 .035 .051 11.464 22.929 34.394 45.858 57.322 68.787 02 aEOGKAPHIC TABLES AND FOKMULA8. TABLE 7. Coordinates for projection of maps (scale -$3^-3} Continued. [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. o / 21 00 10 20 30 40 50 22 00 10 30 30 40 50 23 00 10 20 30 40 50 24 00 10 20 30 40 50 25 00 10 20 30 40 50 26 00 10 20 30 40 50 27 00 10 20 30 40 50 28 00 Inches. 68. 787 Inches. 5.384 5.378 5.372 5.366 5.359 5.353 . 5..347 5.341 5.334 5.328 5.322 5.315 5.309 5.302 5.296 5.289 5. 282 5.276 5.269 5. 263 5.256 ' 5.249 5. 242 5.235 5.227 5.220 5.213 5.206 5.199 5.191 5.184 ' 5. 177 5.169 5.162 5.154 5.147 5.140 5.132 5.124 5.116 5.109 5.101 5.093 Inches. 10. 768 10. 755 10. 743 10. 731 10. 719 10. 707 10. 694 10.682 10. 669 10. 656 10. 643 10. 631 10.618 10.604 10. 591 10. 578 10.565 10.551 10. 538 10. 526 10. 512 10. 498 10. 483 10. 469 10. 455 10. 441 10. 426 10. 412 10. 397 10.383 10.369 10.354 10. 339 10. 324 10.309 10.294 10.279 10.264 10. 248 10.233 10. 218 10.202 10. 187 Inches. 16. 151 16. 133 16.115 16.097 16. 078 16. 060 16.042 16. 022 16.003 15.984 15. 965 15. 946 15.927 15.907 15. 887 15. 867 15. 847 15. 827 15.807 15. 789 15. 767 15. 74fi 15. 725 15. 704 15. 682 15.661 15.639 15. 618 15. 596 15. 575 15.553 15.531 15.508 15. 486 15. 463 15. 441 15. 419 15. 396 15. 373 15. 349 15. 326 15. 303 15. 280 Inches. 21. 535 21.511 21.486 21.462 21.438 21.413 21. 389 21. 363 21.338 21. 312 21.287 21. 261 21. 236 21. 209 21. 182 21.156 21. 129 21. 102 21. 076 21. 052 21.023 20. 995 20. 967 20. 938 20. 910 20.881 20.852 20. 824 20. 795 20. 766 20. 737 20. 708 20. 678 20. 648 20. 618 20. 588 20. 558 20. 528 20. 497 20. 466 20. 435 20. 404 20. 374 Inches. 26. 919 26.889 26.858 26. 828 26. 797 26. 767 26.736 26. 704 26. 672 26.641 26. 609 26!577 26.545 26. 511 26. 478 26. 445 26. 412 26. 378 26.345 26. 315 26.279 26. 244 26.209 26. 173 26. 137 26. 101 26. 065 26. 029 25. 993 25. 958 25. 922 25.884 25.847 25. 810 25. 772 25. 735 25. 698 25. 659 25. 621 25.582 25.544 25. 505 25. 467 Inches. 32. 303 32. 566 32.230 32. 193 32. 156 32. 120 32. 083 32. 045 82. 006 31. 969 31.930 31.892 31.853 31.813 31. 774 31.733 31. 694 31. 654 31. 614 31. 577 31. 535 31. 493 31.450 31.408 31. 365 31.322 31. 279 31.235 31. 192 31. 149 31.106 31.061 31.017 30. 972 30. 927 30. 882 30.838 30. 791 30. 745 30. 699 30. 653 30. 607 30. 560 c Longi- tude inter- val. 21 22 11.466 22. 932 34. 397 45. 863 57.329 68. 795 5 10 15 20 25 30 Inches. 0.001 .006 .013 .022 .035 .051 Inches. 0.001 .006 .013 .023 .036 .052 11. 467 22. 934 34. 401 45. 868 57. 336 68.803 23 24 11.469 22.937 34.406 45. 874 57. 343 68. 812 5 10 15 20 25 30 0.001 .006 .014 .024 .038 .054 0.002 .006 .014 .025 .039 .056 11.470 22.940 34. 410 45.880 57.350 68.'821 25 26 5 10 15 20 25 30 0.002 .006 .014 .026 .040 .058 0.002 .007 .015 .026 .041 .059 11. 472 22. 943 34. 415 45.886 57. 358 68.830 11. 473 22.946 34.419 If). S'.fJ 57. 365 68.838 27 28 5 10 15 20 25 30 0.002 .007 .015 .027 .042 .061 0.002 .007 .016 .028 .043 .063 11. 475 22.950 34. 424 45.899 57. 374 68.849 GEOGRAPHIC TABLES AND FORMULAS. 63 TABLE 7. Coordinates for projection of maps (scale ^3^) Continued. [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. o / 28 00 10 20 30 40 50 29 00 10 20 30 40 50 30 00 10 20 30 40 50 31 00 10 20 30 40 50 32 00 10 20 30 40 50 33 00 10 20 30 40 50 3-1 00 10 20 30 40 50 35 00 Inches. 68.849 Inches. 5.093 5.085 5.077 5.069 5.061 5.054 5.046 5.037 5.029 5.021 5.013 5.004 4.996 4.988 4.979 4.971 4.962 4.954 4.945 4.937 4.928 4.919 4.910 4.902 4. 893 4.884 4.875 4.866 4.857 4.848 4.839 4.830 4.821 4.812 4.802 4.793 4.784 4.774 4.765 4.755 4.746 4.737 4.727 Inches. 10. 187 10. 171 10. 155 10. 139 10. 123 10. 107 10.091 10. 075 10.058 10.042 10. 025 10.009 9.993 9.976 9.959 9.942 9.925 9.908 9.891 9.873 9.856 9.838 9.821 9.804 9.786 9.768 9.750 0.732 9.714 9.696 9.679 9.660 9.642 9. 623 9.605 9.586 9.568 9.549 9.530 9. 511 9.492 9.473 9.454 Inches. 15.280 15. 256 15.232 15. 208 15. 185 15. 161 15. 137 15. 112 15.087 15.063 15.038 15. 013 14. 989 14.963 14. 938 14.912 14.887 14.862 14.836 14.810 14.784 14.758 14. 731 14. 705 14. 679 14.652 14. 625 14. 598 14.572 14.545 14.518 14.490 14. 462 14. 435 14. 407 14. 379 14. 352 14. 323 14. 295 14. 267 14.238 14.210 14. 181 Inches. 20. 374 20.342 20. 310 20. 278 20. 246 20. 214 20. 182 20. 1-50 20.117 20.084 20. 051 20. 018 19.985 19. 951 19. 917 19. 883 19. 849 19. 815 19. 782 19. 747 19. 712 19.677 19.642 19.607 19. 572 19.536 19.500 19. 465 19.429 19. 393 19. 357 19.320 19. 283 19. 246 19. 210 19.173 19. 136 19. 098 19.060 19.022 18. 984 18.946 18.908 Inches. 25.467 25. 427 25.387 25. 347 25. 308 25. 268 25.228 25. 187 25.146 25. 105 25.064 25.022 24. 981 24. 939 24. 896 24. 854 24. 812 24. 769 24. 727 24. 683 24. 640 24. 596 24. 552 24.509 24.465 24. 420 24. 376 24. 331 24.286 24. 241 24. 196 24.150 24. 104 24. 058 24.012 23.966 23.920 23. 872 23. 825 23. 778 23. 730 23. 683 23. 636 Inches. 30.560 30. 513 30.465 30. 417 30. 369 30.321 30. 274 30.224 30. 175 30. 126 30.076 30.027 29. 978 29. 927 29. 876 29.825 29. 774 29. 723 29. 672 29. 620 29.568 29.515 29. 463 29.411 29.358 29. 305 29. 251 29. 197 29. 143 29. 089 29. 036 28. 980 28. 925 28.870 28.814 28. 759 28. 704 28. 647 28.590 28. 533 28. 476 28.420 28. 363 Longi- tude inter- val. 28 29 11. 476 22.953 34.430 45.906 57.383 68.859 5 10 15 20 25 30 Inches. 0.002 .007 .016 .028 .043 .063 Indies. 0.002 .007 .016 .028 .044 .064 11.478 22. 957 34.435 45. 913 57. 391 68.870 30 31 " 11.480 22.960 34. 440 45.920 57.400 68.880 11.482 22.964 34.446 45.927 57.409 68.891 5 10 15 20 25 30 0.002 .007 .016 .029 .045 .065 0.002 .007 .017 .030 .046 .067 32 33 11.484 22.967 34.451 45. 934 57.418 68.902 11. 4a5 22. 971 34.456 45. 942 57. 427 68.913 5 10 15 20 25 30 0.002 .007 .017 .030 .047 .068 0.002 .008 .017 .031 .048 .069 34 35 5 10 15 20 25 30 0.002 .008 .017 .031 .049 .070 0.002 .008 .018 .031 .049 .071 11.487 22. 975 34.462 45.949 57.437 68.924 64 GEOGRAPHIC TABLES AND FORMULAS. TABLE 7. Coordinates for projection of maps (scale -$-3^-5) Continued. [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. o / 35 00 10 20 30 40 50 36 00 10 20 30 40 50 37 00 10 20 30 40 50 38 00 10 20 30 40 50 39 00 10 20 30 40 50 40 00 10 20 30 40 50 41 00 10 20 30 40 50 42 00 Inches. 68. 924 Inches. 4.727 4.717 4.708 4.698 4.688 4. 679 4.669 4.659 4.649 4.639 4.629 4.619 4.609 4.599 4.589 4.579 4.568 4.558 4.548 4.538 4. 527 4.517 4.506 4.496 4.486 4.475 4.464 4.454 4.443 4.433 - 4.' 422 4.411 4.400 4.389 4.378 4.368 4.357 4.346 4.335 4.324 4.312 4.301 4.290 Inches. 9.454 9.435 9.415 9.396 9.377 9.357 9.338 9.318 9.298 9.278 9. 258 9.238 9.219 9.198 9.178 9.157 9.137 9.117 9.096 9.076 9.055 9.034 9.013 8.992 8.971 8.950 8.929 8.908 8.886 8.865 8.844 8.822 8.800 8.779 8.757 8.735 8.713 8.691 8.669 8.647 8.625 8.603 8.581 Inches. 14. 181 14. 152 14. 123 14.094 14.065 14. 036 14.007 13. 977 13. 947 13.917 13.887 13.858 13.828 13. 797 13. 767 13. 736 13. 706 13. 675 13.645 13. 613 13.582 13. 551 13.520 13.488 13.457 13.425 13. 393 13.361 13. 330 13.298 13.266 13. 233 13.201 13.168 13. 135 13. 103 13. 070 13. 037 13.004 12. 971 12. 937 12.904 12. 871 Inches. 18.908 18. 870 18. 831 18.792 18. 753 18. 714 18. 676 18. 636 18.596 18.556 18.517 18. 477 18. 437 18. 396 18.356 18. 315 18.274 18.234 18. 193 18. 151 18. 109 18. 068 18. 026 17. 984 17.943 17.900 17.858 17.815 17.773 17. 730 17.688 17. 644 17. 601 17. 557 17.514 17.470 17.427 17. 383 17. 338 17.294 17.250 17. 205 17. 161 Indies. 23. 636 23. 587 23. 539 23.490 23.442 23. 393 23.345 23. 295 23.245 23. 195 23.146 23.0% 23.046 22.995 22. 944 22.894 22.843 22. 792 22. 741 22.689 22. 637 22.585 22. 533 22. 481 22.429 22.375 22. 322 22. 269 22. 216 22. 163 22.110 22.055 22. 001 21. 947 21. 892 21.838 21. 784 21. 728 21. 673 21.618 21.562 21.507 21.451 Inches. 28.363 28. 305 28. 246 28.188 28.130 28.072 28. 014 27.954 27. 894 27.835 27. 775 27. 715 27.656 27.594 27. 533 27.472 27.411 27.350 27.289 27.227 27.164 27. 102 27. 039 26. 977 26. 914 26.851 26. 787 26. 723 26. 659 26. 595 26.532 26. 466 26.401 26.336 26. 271 26. 206 26. 140 26. 074 26.007 25.941 25. 875 25. 808 25. 742 Longi- tude inter- val. 35 36 11. 489 22. 978 34. 468 45. 957 57. 446 68.935 5 10 15 20 25 30 Inches. 0.002 .008 .018 .031 .049 .071 Inches. 0.002 .008 .018 .032 .050 .072 11.491 22.983 34.474 45. 965 57.457 68.948 37 38 11. 493 22. 986 34.480 45.973 57.466 68. 959 5 10 15 20 25 30 0.002 .008 .018 .032 .050 .073 0.002 .008 .018 .033 .051 .073 11. 495 22.990 34.485 45. 980 57. 475 68.970 39 40 11.497 22.994 34. 491 45.988 57.485 68. 982 5 10 15 20 25 30 0.002 .008 .018 .033 .051 .074 0.002 .008 .019 .033 .052 .074 11.499 22.998 34.497 45.996 57. 495 68.994 41 42 5 10 15 20 25 30 0.002 .008 .019 .033 .052 .075 0.002 .008 .019 .033 .052 .075 11.501 23.002 34.503 46.004 57.506 69.007 GEOGEAPHIC TABLES AND FOEMULA8. 65 TABLE 7. Coordinates for projection of maps (scale ro^nr) Continued. [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10 7 longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. o / 42 00 10 20 30 40 50 43 00 10 20 30 40 50 44 00 10 20 30 40 50 45 00 10 20 30 40 50 46 00 10 20 30 40 50 47 00 10 20 30 40 50 48 OQ 10 20 30 40 50 49 00 Inches. 69.007 Inches. 4.290 4.279 4.268 4.256 4.245 4.234 4.222 4.211 4.199 4.188 4.176 4.165 4.153 4.142 4.130 4.118 4.106 4.095 4.083 4.071 4.059 4.047 4.035 4.023 4.011 3.999 3.987 3.975 3.963 3.951 3.938 3.926 3.914 3.901 3.889 3.877 3.864 3.852 3.839 3.827 3.814 3.802 3.789 Inches. 8.581 8.558 8.535 8.513 8.490 8.467 8.445 8.422 8.399 8.376 8.353 8.330 8.307 8.283 8.260 8.236 8.213 8.189 8.166 8.142 8.118 8.094 8.070 8.046 8.023 7.998 7.974 7.950 7.925 7.901 7.877 7.852 7.827 7.803 7.778 7.753 7.729 7.704 7.679 7.653 7.628 7.603 7.678 Inches. 12. 871 12.837 12.803 12.769 12.735 12. 701 12.667 12.633 12. 598 12.564 12.529 12. 494 12.460 12.425 12.390 12.354 12.319 12.284 12. 249 12. 213 12. 177 12. 141 12. 105 12. 070 12.034 11.997 11.961 11.925 11.888 11.852 11. 815 11. 778 11. 741 11.704 11.667 11.630 11.593 11.555 11. 518 11.480 11.442 11. 405 11.367 Inches. 17. 161 17. 116 17. 071 17. 025 16.980 16.935 16.890 16.844 16. 798 16. 751 16. 705 16. 659 16. 613 16.566 16. 519 16. 473 16.426 16. 379 16.332 16.284 16.236 16.188 16. 141 16.093 16.045 15.997 15.948 15.899 15. 851 15.802 15.754 15.704 15.655 15.606 15.556 15.507 15.457 15. 407 15.357 15.307 15.257 15.206 15.156 Inches. 21. 451 21.395 21.338 21. 282 21.225 21. 169 21. 112 21.054 20.997 20.939 20.882 20.824 20.767 20.708 20.649 20. 591 20.532 20.473 20. 415 20.355 20.295 20.236 20. 176 20. 116 20.056 19.996 19. 935 19. 874 19. 813 19. 753 19.692 19.630 19.569 19.507 19.445 19. 383 19. 322 19.259 19.196 19. 134 19. 071 19.008 18.945 Inches. 25. 742 25.674 25.606 25.538 25. 470 25.402 25.334 25.265 25.1% 25.127 25.058 24. 989 24.920 24.849 24. 779 24. 709 24.638 24. 568 24. 498 24. 426 24.354 24.283 24. 211 24. 139 24.068 23. 995 23.922 23.849 23. 776 23. 703 23. 630 23.556 23. 482 23.408 23.334 23. 260 23. 186 23.111 23.035 22.960 22.885 22.810 22.734 Longi- tude inter- val. 42 43 11.503 23.006 34.510 46. 013 57. 516 69. 019 5 10 15 20 25 30 Inches. 0.002 .008 .019 .033 .052 .075 Inches. 0.002 .008 .019 .033 .052 .075 11.505 23.010 34.515 46.020 57.525 69.030 44 45 11.507 23.014 34.522 46.029 57.536 69.043 5 10 15 20 25 30 0.002 .008 .019 .034 .052 .075 0.002 .008 .019 .034 .053 .076 11.509 23. 018 34.528 46.037 57.546 69.055 46 47 11.511 23.023 34.534 46.045 57.557 69.068 5 10 15 20 25 30 0.002 .008 .019 .034 .063 .076 0.002 .008 .019 .034 .052 .075 11. 513 23.027 34.540 46.053 57.567 69.080 48 49 5 10 15 20 25 30 0.002 .008 .019 .033 .052 .075 0.002 .008 .019 .033 .052 .075 11. 516 23.031 34.546 46.062 57. 577 69.093 4606108 5 66 GEOGEAPHIC TABLES AND FORMULAS. TABLE 7. Coordinates for projection of maps (scale -5^-5-5) Continued. [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. o / 49 00 10 20 30 40 50 50 00 10 20 30 40 5C 51 00 10 20 30 40 50 52 00 10 20 30 40 50 53 00 10 20 30 40 50 54 00 10 20 30 40 50 55 00 10 20 30 40 50 56 00 Inches. 69. 093 Inches. 3.789 3.776 3.764 3.751 3.738 3.725 3.713 3.700 3.687 3.674 3.661 3.648 3.635 3.622 3.609 3.596 3.583 3.570 3.556 3.543 3.530 3.516 3.503 3.490 3.477 3.463 3.450 3.436 3.423 3. 409 3.396 3.382 3.368 3.355 3.341 3.327 3.314 3.300 3.286 3.272 3.258 3.245 3.231 Inches. 7.578 7.553 7.527 7.502 7.476 7.451 7.425 7.399 7.374 7.348 7.322 7.296 7.270 7.244 7.218 7. 191 7.165 7.139 7.113 7.086 7.060 7.033 7.006 6.980 6.953 6.926 6.899 6.872 6.845 6.818 6.791 6.764 6.737 6.709 6.682 6.655 6.628 6.600 6.572 6.545 6.517 6.489 6.462 Inches. 11. 367 11. 329 11. 291 11. 253 11. 214 11.176 11.138 11.099 11. 060 11.021 10. 983 10.944 10.905 10. 866 10.827 10. 787 10. 748 10. 709 10. 669 10.629 10. 589 10.550 10. 510 10. 470 10.430 10.389 10. 349 10.309 10.268 10. 228 10.187 10. 146 10. 105 10.064 10.023 9.982 9.941 9.900 9.859 9.817 9.776 9.734 9.693 Inches. 15. 156 15. 105 15. 054 15.003 14. 952 14.901 14.850 14. 799 14. 747 14. 695 14. 644 14. 592 14.540 14. 488 14.436 14. 383 14. 330 14. 278 14.226 14. 172 14.119 14.066 14.013 13.960 13.906 13.852 13. 798 13. 745 13. 691 13. 637 13.583 13.528 13. 474 13.419 13.364 13. 310 13.255 ' 13.200 13. 145 13. 089 13. 034 12. 979 12. 924 Inches. 18.945 18. 882 18. 818 18. 754 18.690 18. 627 18.563 18.499 18. 434 18. 369 18. 305 18. 240 18. 176 18. 110 18.045 17. 979 17. 913 17. 848 17. 782 17. 716 17.649 17. 583 17. 516 17.450 17.383 17. 316 17. 248 17. 181 17. 114 17.046 16.979 16. 910 16. 842 16. 774 16.706 16. 637 16.569 16.500 16. 431 16. 362 16. 293 16. 224 16. 155 Inches. 22. 734 22. 658 22. 581 22.505 22.429 22. 352 22.276 22. 198 22.121 22.043 21.965 21.888 21. 811 21. 732 21. 653 21. 574 21.496 21. 417 21. 338 21. 259 21. 179 21.099 21.019 20. 939 20. 860 2(7. 779 20. 698 20.617 20. 536 20. 455 20.374 20.292 20. 210 20. 128 20.047 19.964 19.883 19.800 19. 717 19. 634 19. 551 19. 468 19.385 Longi- tude inter- val. 49 50 11. 517 23. 035 34. 552 46. 070 57. 587 69. 105 5 10 15 20 25 30 Inches. 0.002 .008 .019 .033 .052 .075 Inches. 0.002 .008 .019 .033 .052 .075 11.520 23. 039 34.558 46. 078 57. 598 69. 117 51 52 11.521 23.043 34.564 46. 086 57. 607 69. 128 5 10 15 20 25 30 0.002 .008 .019 .033 .051 .074 0.002 .008 .018 .033 .051 .073 11. 523 23. 047 34. 570 46.094 57. 617 69.140 53 54 11.525 23.051 34.576 46. 102 57. 627 69. 152 5 10 15 20 25 30 0.002 .008 .018 .032 .050 .073 0.002 .008 .018 .032 .050 .072 11.527 23.055 34. 582 46.109 57. 636 69.164 55 56 5 10 15 20 25 30 0.002 .008 .018 .032 .049 .071 0.002 .008 .018 .031 .049 .070 11. 529 23.059 34.588 46. 117 57.646 69. 176 GEOGRAPHIC TABLES AND FOEMTTLAS. 67 TABLE 7. Coordinate* for projection of maps (scale ^STS) Continued. [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. o / 56 00 10 20 30 40 50 57 00 10 20 30 40 50 58 00 10 20 30 40 50 59 00 10 20 30 40 50 60 00 10 20 30 40 50 61 00 10 20 30 40 50 62 00 10 20 30 40 50 63 00 Inches. 69. 176 Inches. 3.231 3.217 3.203 3.189 3.175 3.161 3.147 3.133 3.119 3.104 3.090 3.076 3.062 3.048 3.034 3.019 3.005 2.991 2.976 2.962 2.947 2.933 2.918 2.904 2.890 2.875 2.860 2.846 2.831 2.816 2.802 2.787 2.772 2.758 2.743 2.728 2.713 2.699 2.684 2.669 2.654 2.639 2.624 Inches. 6.462 6.434 6.406 6.378 6.350 6.322 6.294 6.266 6.237 6.209 6.181 6.152 6.124 6.096 6.067 6.038 6.010 5.981 5.953 5.924 5.895 5.866 5.837 5.808 5.779 5.750 5.721 5.691 5.662 5.633 6.604 5.574 5.545 5.115 5.486 5.456 5.427 5.397 5.367 5.337 5.308 5.278 5.248 Inches. 9.693 9.651 9.609 9.567 9.525 9.483 9.441 9.398 9.356 9.314 9.271 9.229 9.186 9.143 9.101 9.058 9.015 8.972 8.929 8.885 8.842 8.799 8.755 8.712 8.669 8.625 8.581 8.537 8.493 8.450 8.406 8.361 8.317 8.273 8.229 8.184 8.140 8.0% 8.051 8.006 7.961 7.917 7.872 Inches. 12.924 12.868 12. 812 12.756 12.700 12.644 12.588 12.531 12. 475 12. 418 12.362 12.305 12.248 12. 191 12.134 12. 077 12.020 11.962 11.905 11.847 11.790 11. 732 11.674 11. 616 11.558 11.500 11.441 11.383 11. 324 11.266 11.208 11.148 11.090 11.030 10.972 10. 912 10.854 10.794 10.734 10. 675 10. 615 10.556 10.4% Inches. 16.155 16.085 16. 015 15.945 15. 875 15.805 15.735 15.664 15.594 15.523 15.452 15.381 15. 311 15.239 15.168 15.0% 15.025 14.953 14.882 14.809 14. 737 14.665 14.592 14. 520 14.448 14. 375 14.302 14.229 14.156 14. 083 14. 010 13. 936 13.862 13.788 13. 715 13. 641 13.567 13. 493 13. 418 13.344 13. 269 13. 195 13.120 Inches. 19.385 19.301 19.217 19. 134 19.050 18.966 18.882 18. 797 18. 712 18.627 18.542 18.457 18. 373 18.287 18. 201 18. 115 18.029 17.944 17.858 17. 771 17.684 17.597 17.510 17. 424 17. 337 17. 249 17.162 17. 074 16.987 16. 899 16.811 16. 723 16.634 16.546 16.457 16.369 16.280 16. 191 16. 102 16. 012 15.923 15. 833 15.744 Longi- tude inter- val. 56 57 11.531 23.063 34.594 46.125 57.656 69.188 5 10 15 20 25 30 Inches. 0.002 .008 .018 .031 .049 .070 Inches, 0.002 .008 .017 .031 .048 .069 11.533 23.066 34.599 46.132 57.666 69.199 58 59 11.535 23.070 34.605 46.140 57. 675 69. 210 5 10 15 20 25 30 0.002 .008 .017 .030 .047 .068 0.002 .007 .017 .030 .046 .067 11.537 23.074 34.610 46. 147 57.684 69.221 60 61 11.539 23.077 34.616 46.154 57.693 69.232 5 10 15 20 25 30 0.002 .007 .016 .029 .045 .065 0.002 .007 .016 .029 .045 .064 11.540 23.081 34.621 46. 162 57.702 69.242 62 63 5 10 15 20 25 30 0.002 .007 .016 .028 .044 .063 0.002 .007 .015 .027 .043 .061 11.542 23.084 34.626 46.168 57. 710 69.253 68 GEOGEAPHIC TABLES AND FORMULAS. TABLE 7. Coordinates for projection of maps (scale TOOT) Continued. [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. o / 63 00 Iv. 20 30 40 50 64 00 10 20 30 40 50 65 00 10 20 30 40 50 66 00 10 20 30 40 50 67 00 10 20 30 40 50 68 00 10 20 30 40 50 69 00 10 20 30 40 50 70 00 Inches. 69. 253 . Inches. 2.624 2.609 2.594 2.579 2.564 2.549 2.534 2.519 2.504 2.488 2.473 2.458 2.443 2.428 2.412 2.397 2.382 2.366 2.351 2.336 2.320 2.305 2.290 2.274 2.259 2.243 2.228 2.212 2.197 2.181 2.166 2.150 2.134 2.119 2.103 2.088 2.072 2.056 2.040 2.025 2.009 1.993 1.977 Inches. 5.248 5.218 5.188 5.158 5.128 5.098 5.068 5.037 5.007 4.977 4.947 4.916 4.886 4.855 4.825 4.794 4.764 4.733 4.702 4.672 4.641 4.610 4.579 4.548 4.518 4.487 4.455 4.424 4.393 4.362 4.331 4.300 4.269 4.237 4.206 4.175 4.144 4. 112' 4.081 4.049 4.018 3.986 3.955 Inches. 7.872 7.827 7.782 7.737 7.692 7.647 7.602 7.556 7.511 7.465 7.420 '7. 374 7.329 7.283 7.237 7.191 7.145 7.100 7.054 7.007 6.961 6.915 6.869 6.823 6.776 6.730 6.683 6.637 6.590 6.543 6.497 6.450 6.403 6.356 6.309 6.263 6.216 6.169 6.121 6.074 6.027 5.980 5.932 Inches. 10.496 10. 436 10. 376 10. 316 10.256 10. 196 10. 136 10.075 10. 014 9.954 9.893 9.832 9.772 9.711 9.650 9.588 9.527 9.466 9.405 9.343 9.282 9.220 9.158 9.097 9.035 8.973 8.911 8.849 8.787 8.724 8.662 8.600 8.538 8.475 8.412 8.350 8.288 8.225 8.162 8.099 8.036 7.973 7.910 Inches. 13.120 13.045 12. 970 12.895 12.820 12. 745 12.670 12. 594 12. 518 12. 442 12.367 12. 291 12. 215 12.139 12.062 11. 986 11.909 11. 833 11.756 11. 679 11. 602 11.525 11.448 11. 371 11.294 11.217 11. 139 11.061 10.984 10.906 10. 828 10. 750 10. 672 10. 594 10. 516 10.438 10.360 10.281 10.202 10. 124 10. 045 9.966 9.888 Inches. 15. 744 15. 654 15.564 15.473 15. 383 15.293 15. 203 15. 112 15.022 14.930 14.840 14. 749 14.658 14.566 14.474 14.383 14.291 14.199 14. 107 14. 015 13. 922 13.830 13. 738 13.645 13.553 13.460 13.366 13.273 13. 180 13. 087 12. 994 12.900 12. 806 12. 712 12. 619 12. 525 12. 431 12. 337 12. 242 12. 148 12.054 11. 959 11.865 Longi- tude inter- val. 63 64 11.544 23. 087 34. 631 46.175 57.718 69.262 5 10 15 20 25 30 Inches. 0.002 .007 .015 .027 .043 .061 Inches. 0.002 .007 .015 .026 .041 .060 11.545 23.091 34.636 46. 182 57. 727 69. 272 65 66 11.547 23. 094 34.641 46. 188 57.735 69.282 5 10 15 20 25 30 0.002 .006 .014 .026 .040 .058 0.002 .006 .014 .025 .039 .056 11.548 23.097 34.646 46. 194 57. 742 69.291 67 68 11.550 23.100 34.650 46.200 57.750 69.300 5 10 15 20 25 30 0.001 .006 .014 .024 .038 .054 0.001 .006 .013 .023 .036 .053 11.552 23.103 34.654 46.206 57. 758 69.309 69 70 5 10 15 20 25 30 0.001 .006 .013 .022 .035 .051 0.001 .005 .012 .022 .034 .049 11.553 23.106 34.659 46.212 57.764 69. 317 GEOGRAPHIC TABLES AND FORMULAS. 69 TABLE 7. Coordinates for projection of maps (scale ^0-5-7) Continued. [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15 7 longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. o / 70 00 10 20 30 40 50 71 00 10 20 30 40 50 72 00 10 20 30 40 50 73 00 10 20 30 40 50 74 00 10 20 30 40 50 75 00 10 20 30 40 50 76 00 10 20 30 40 50 77 00 Inches. 69. 317 Inches. 1.977 1.962 1.946 1.930 1.914 1.898 1.882 1.866 1.850 1.835 1.819 1.803 1.787 1.771 1.755 1.739 1.723 1.707 1.691 1.674 1.658 1.642 1.626 1.610 1.594 1.578 1.562 1.545 1.529 1.513 1.497 . 1.480 1.464 1.448 1.432 1.415 1.399 1.383 1.366 1.350 1.334 1.317 1.301 Inches. 3.955 3.923 3.892 3.860 3.828 3.796 3.765 3.733 3.701 3.669 3.637 3.605 3.574 3.542 3.509 3.477 3.445 3.413 3.381 3.349 3.317 3.284 3.252 3.220 3.188 3.155 3.123 3.091 3.058 3.026 2.993 2.961 2.928 2.896 2.863 2.831 2.798 2.765 2.733 2.700 2.667 2.634 2.602 Inches. 5.932 5.885 5.837 5.790 5.742 5.695 5.647 5.600 5.552 5.504 5.456 5.408 5.360 5.312 5.264 5.216 5.168 5.120 5.072 5.024 4.975 4.927 4.878 4.830 4.782 4.733 4.685 4.636 4.587 4.539 4.490 4.441 4.392 .4.344 4.295 4.246 4.197 4.148 4.099 4.050 4.001 3.952 3.903 Inches. 7.910 7.846 7.783 7.720 7.656 7.593 7.530 7.466 7.402 7.338 7.275 7.211 7.147 7.083 7.019 6.955 6.891 6.826 6.762 6.698 6.634 6.569 6.504 6.440 6.376 6.311 6.246 6.181 6.116 6.052 5.987 5.922 5.856 5.792 5.726 5. 661 5.5% 5.530 5.465 5.400 5.334 5.269 5.204 Inches. 9.888 9.808 9.729 9.650 9.571 9.491 9,412 9.333 9.253 9.173 9.094 9.014 8.934 8.854 8.774 8.694 8.614 8.533 8.453 8.373 8.292 8.211 8.131 8.050 7.970 7.889 7.808 7.727 7.645 7.565 7.484 7.402 7.321 7.240 7.158 7.077 6.995 6.913 6.832 6.750 6.668 6.586 6.505 Inches. 11.865 11. 770 11. 675 11. 579 11.485 11. 389 11.294 11. 199 11. 103 11.008 10. 912 10. 816 10. 721 10. 625 10.528 10. 432 10.336 10. 240 10. 144 10.047 9.950 9.853 9.757 9.660 9.563 9.466 9.369 9.272 9.175 9.077 8.980 8.882 8.785 8.687 8.590 8.492 8.394 8.296 8.198 8.099 8.002 7.903 7.805 Longi tude inter- val. 70 71 11.554 23.109 34.663 46.217 57. 772 69.326* / 5 10 15 20 25 30 Inches. 0.001 .005 .012 .022 .034 .049 Inches. 0.001 .005 .012 .021 .032 .047 11.556 23.111 34.667 46.222 57. 778 69.334 72 73 11.557 23.114 34.670 46.227 57.784 69.341 5 10 15 20 25 30 0.001 .005 .011 .020 .031 .044 0.001 .005 .011 .019 .029 .042 11.558 23.116 34.674 46.232 57.790 69.348 74 75 11.559 23.118 34.677 46.236 57.796 69.355 5 10 15 20 25 30 0.001 .004 .010 .018 .028 .040 0.001 .004 .009 .017 .026 .038 11.560 23.120 34.681 46.241 57.801 69.361 76 77 5 10 15 20 25 30 0.001 .004 .009 .016 .025 .036 0.001 .004 .008 .015 .023 .033 11.561 23.122 34.683 46.244 57.806 69. 367 70 GEOGRAPHIC TABLES AND FORMULAS. TABLE 7. Coordinates for projection of maps (scale -$-3^-5-0) Continued. [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longi- tude. 10' longi- tude. 15' longi- tude. 20' longi- tude. 25' longi- tude. 30' longi- tude. o / 77 00 10 20 30 40 50 78 00 10 20 30 40 50 79 00 10 20 30 40 50 80 00 Inches. 69. 367 Inches. 1.301 1.284 1.268 1.252 1.235 1.219 1.202 1.186 1.169 1.153 1.136 1.120 1/104 1.087 1.070 1.054 1.037 1.021 1.004 Inches. 2.602 2.569 2.536 2.503 2.470 2.438 2.405 2.372 2.339 2.306 2.273 2.240 2.207 2.174 2. 141 2.108 2.075 2.042 2.009 Inches. 3.903 3.854 3.804 3.765 3.706 3.656 3.607 3.558 3.508 3.459 3.410 3.360 3.311 3.261 3.211 3.162 3.112 3.062 3.013 Inches. 5.204 5.138 5.072 5.006 4.941 4.875 4.810 4.744 4.678 4.612 4.546 4.480 4.414 4.348 4.282 4.216 4.150 4.083 4.017 Inches. 6.505 6.423 6.341 6.258 6.176 6.094 6.012 5.930 5.847 6.765 5.683 5.600 5.518 5.435 5.352 5.270 5.187 5.104 5.022 Inches. 7.805 7.707 7.609 7.510 7.411 7.313 7.214 7.115 7.016 6.918 6.819 6.720 6.621 6.522 6.422 6.323 6. 224 6.125 6.026 Longi- tude inter- val. 77 78 11.562 23. 124 34.686 46. 248 57. 810 69. 373 5 10 15" 20 25 30 Inches. 0.001 .004 .008 .015 .023 .033 Inches. 0.001 .003 .008 .014 .021 .031 11.563 23. 126 34.689 46.252 57.814 69. 377 79 80 11.564 23.127 34.691 46.255 57. 818 69.382 5 10 15 20 25 30 0.001 .003 .007 .013 .020 .028 0.001 .003 .006 .011 .018 .026 GEOGRAPHIC TABLES AND FORMULAS. TABLE 8. Coordinates for projection of maps (scale 71 Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 2i' longi- tude. 5' longi- tude. 7i' longi- tude. 10' longi- tude. 12|' lon- gitude. 15' longi- tude. o / 25 00 05 10 15 20 25 30 35 40 45 50 55 26 00 05 10 15 20 25 30 35 40 45 50 55 27 00 05 10 15 20 25 30 35 40 45 60 55 28 00 05 10 15 20 26 30 35 40 45 50 56 29 00 Inches. Inches. 2.650 2.648 2.646 2.644 2.642 2.641 2.639 2.637 2.635 2.633 2. 631 2.630 2.628 2.626 2.624 2.622 2.620 2.618 2.617 2.615 2.613 2.611 2.609 2.607 2.605 2.603 2.601 2.599 2. 597 2.595 2.593 2.591 2.590 2.588 2.586 2.584 2.582 2.580 2.578 2.576 2.574 2.572 2.570 2.568 2.566 2.564 2.562 2.560 2.558 Inches. 5.299 5.296 5.292 5.288 5.285 5.281 5.277 5.274 5.270 5.266 5.263 5.259 5.256 5.252 5. 248 5.244 5.241 5.237 5.233 5.229 5.225 5.222 5.218 5.214 5.210 6.207 5.203 5.199 5.195 5.191 5.187 5.183 5.179 5.175 5.171 5.167 5.163 5.159 5.155 5.151 5.147 5.143 6.139 5.135 5.131 5.127 5.123 5.119 5.115 Inches. 7.949 7.944 7.938 7.933 7.927 7.922 7.916 7.911 7.905 7.900 7.894 7.889 7.883 7.878 7.872 7.866 7.861 7.855 7.849 7.844 7.838 7.833 7.827 7.821 7.816 7.810 7.804 7.798 7.792 7.786 7.780 7.774 7.769 7.763 7.757 7.751 7.745 7.739 7.733 7.727 7.721 7.715 7.709 7.703 7.697 7.691 7.685 7.679 7.673 Inches. 10. 599 10. 591 10.584 10. 577 10.569 10.562 10.555 10.548 10.540 . 10. 533 10. 526 10. 518 10. 511 10.504 10.496 10. 489 10.481 10. 473 10.466 10.458 10.451 10. 443 10. 436 10. 428 10. 421 10. 413 10. 405 10.397 10.389 10.382 10. 374 10. 366 10.358 10.350 10. 342 10.335 10. 327 10. 319 10. 311 10.303 10.294 10.286 10. 278 10. 270 10.262 10.254 10. 246 10.238 10.230 Inches. 13. 248 13. 239 13. 230 13.221 13. 212 13.203 13. 194 13. 184 13. 175 13. 166 13. 157 13. 148 13. 139 13. 129 13. 120 13. Ill 13. 101 13.092 13. 082 13. 073 13.064 13.054 13.045 13.035 13.026 13. 016 13.006 12.997 12. 987 12. 977 12.967 12. 957 12. 948 12.938 12.928 12.918 12.908 12. 898 12.888 12. 878 12. 868 12.858 12.848 12.838 12.828 12. 818 12.808 12. 798 12.788 Inches. 15.898 15.887 15. 876 15.865 15.854 15.843 15.832 15. 821 15.810 15.799 15. 788 15. 777 15. 766 15. 755 15. 744 15. 733 15. 721 15. 710 15.699 15.688 15. 676 15.665 15.654 15.642 15. 631 15. 620 15.608 15.596 15.584 15. 572 15. 561 15.549 15.537 15. 525 15. 514 15.502 15.490 15. 478 15.466 15.454 15. 442 15.430 15. 418 15. 405 15. 393 15. 381 15.369 15. 357 15.345 Longi- tude inter- val. 25 26 5.815 11.629 17. 444 23.259 29.074 34.888 / 2i 5 7* 10 12i 15 Inches. 0.000 .002 .004 .007 .010 .015 Inches. 0.000 .002 .004 .007 .010 .015 5.816 11.631 17.447 23.262 29. 078 34.893 27 2i 5 i? m 15 Inches. 0.000 .002 .004 .007 .011 .015 6.816 11.633 17.449 23.265 29.082 34.898 27 28 2 5 7 10 12^ 15 Inches. 0.000 .002 .004 .007 .011 .015 Inches. 0.000 .002 .004 .007 .011 .016 5.817 11.634 17.451 23.268 29.085 34.903 29 '? $ JP Inches. 0.000 .002 .004 .007 .011 .016 72 GEOGRAPHIC TABLES AND FORMULAS. TABLE 8. Coordinates for projection of maps (scale ralrnr) Continued. Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 21'longi tude. 5' longi- tude. 74' longi- tude. 10'longi tude. 121' lon- gitude. 15'longi tude. o t 29 00 05 10 15 20 25 30 35 40 45 50 55 30 00 05 10 15 20 25 30 35 40 45 50 55 31 00 05 10 15 20 25 30 35 40 45 50 55 32 00 05 10 15 20 25 30 35 40 45 50 55 33 00 Inches, Inches. 2.558 2.555 2.553 2.551 2.549 2.547 2.545 2.543 2.541 2.539 2.537 2.535 2.533 2.530 2.528 2.526 2.524 2.522 2.520 2. 518 2.515 2. 513 2.511 2.509 2.507 2.505 2.502 2.500 2.498 2.496 2.494 2.491 2.489 2.487 2.485 2.482 2. 480 2.478 2.476 2.473 2.471 2.469 2.467 2.464 2.462 2.460 2.458 2.455 2.453 Inches. 5.115 5.111 5.107 5.103 5.098 5.094 5.090 5.086 5.082 5.078 5.073 5.069 5.065 5.061 5.057 5.052 5.048 5.044 5.039 5.035 5.031 5.026 5.022 5.018 5.014 5.009 5.005 5.000 4.996 4.991 4.987 4.983 4.978 4.974 4.969 4.965 4.960 4.956 4.951 4.947 4.942 4.938 4.933 4.929 4.924 4.920 4.915 4.910 4.906 Inches. 7.673 7.666 7.660 7.654 7.648 7.641 7.635 7.629 7.623 7.616 7.610 7.604 7.598 7.591 7.585 7.578 7.572 7.565 7.559 7.552 7.546 7.540 7.533 7.527 7.520 7.514 7.507 7.500 7.494 7.487 7.480 7.474 7.467 7.460 7.454 7.447 7.441 7.434 7.427 7.420 7.413 7. 407 7.400 7. 393 7.386 7.379 7.372 7.366 7.359 Inches. 10. 230 10. 222 10. 213 10. 205 10. 197 10. 188 10. 180 10. 172 10.164 10.155 10. 147 10. 138 10.130 10.122 10. 113 10.104 10.0% 10.087 10. 079 10. 070 10.061 10. 053 10.044 10.036 10.027 10. 018 10.009 10.000 9.992 9.983 9.974 9.965 9.956 9.947 9.938 9.930 9.921 9.912 9.903 9.894 9.884 9.875 9.866 9.857 9.848 9.839 9.831 9.821 9. 812 Inches. 12.788 12. 777 12. 767 12. 756 12. 746 12. 735 12. 725 12. 715 12. 704 12.694 12. 684 12. 673 12.663 12. 652 12.641 12.630 12. 620 12.609 12. 598 12.587 12. 577 12.566 12. -555 12.544 12.534 12. 523 12. 512 12.500 12.489 12. 478 12. 467 12.456 12.445 12. 434 12.423 12. 412 12. 401 12. 390 12.378 12. 367 12.356 12.344 12.333 12. 322 12. 310 12. 299 12.287 12. 276 12. 265 Inches. 15. 345 15. 333 15. 320 15. 308 15.295 15. 283 15.270 15. 258 15. 245 15. 233 15.220 15. 208 15. 195 15. 182 15. 169 15. 157 15.144 15. 131 15. 118 15. 105 15. 092 15. 079 15.066 15.053 15.040 15.027 15. 014 15.000 14. 987 14. 974 14.961 14.948 14. 934 14.921 14.908 14. 894 14.881 14. 868 14.854 14.840 14. 827 14. 813 14.800 14. 786 14. 772 14. 759 14. 745 14. 731 14. 718 Longi- tude inter- val. 29 30 5.818 11. 636 17.454 23.272 29.090 34.908 2| 5 71 10 124 15 Inches. 0.000 .002 .004 .007 .011 .016 Inches. 0.000 .002 .004 .007 .012 .017 5.819 11.638 17.457 23.276 29. 095 34.913 31 24 5 71 10 11* 0.000 .002 .004 .008 .012 .017 5.820 11.640 17.460 23.280 29.100 34.919 Longi- tude inter- val. 31 32 21 5 71 10 121 15 Inches. 0.000 .002 .004 .008 .012 .017 Inches. 0.000 .002 .004 .008 .012 .017 5.821 11.642 17. 462 23.283 29.104 34.925 33 21 5 71 10 121 15 0.000 .002 .004 .008 .012 .017 GEOGRAPHIC TABLES AND FORMULAS. 73 TABLE 8. Coordinates for projection of maps (scale srl^) Continued. [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 2i' longi- tude. 5' longi- tude. 7i' longi- tude. 10' longi- tude. 12' lon- gitude. 15' longi- tude. o / 33 00 05 10 15 20 25 30 35 40 45 50 55 34 00 05 10 15 20 25 30 35 40 45 50 55 35 00 05 10 15 20 25 30 35 40 45 50 55 36 00 05 10 15 20 25 30 35 40 45 50 55 37 00 Inches. Inches. 2.453 2.451 2.448 2.446 2.444 2.441 2.439 2.437 2.434 2.432 2.430 2.427 2.425 2.423 2.420 2.418 2.415 2.413 2.411 2.408 2.406 2.403 Inches. 4.906 4.901 4.897 4.892 4.887 4.882 4.878 4.873 4.868 4.864 4.859 4.854 4.850 4.845 4.840 4.835 4.831 4.826 4.821 4.816 4.811 4.807 4.802 4.797 4.792 4.787 4.782 4.777 4.773 4.768 4.763 4.758 4.753 4.748 4.743 4.738 4.733 4.728 4.723 4.718 4.713 4.708 4.703 4.698 4.693 4.688 4.683 4.678 4.673 Inches. 7.359 7.352 7.345 7.338 7.331 7.324 7.317 7.310 7.303 7.2% 7.289 7.2S2 7.275 7.267 7.260 7.253 7.246 7.239 7.231 7.224 7.217 7.210 7.203 7.195 7.188 7.181 7.174 7.166 7.159 7.151 7.144 7.137 7.129 7.122 7.115 7.107 7.100 7.092 * 7.085 7.077 7.070 7.062 7.055 7.047 7.039 7.032 7.024 7.017 7.009 Inches. 9.312 9.802 9.793 9.784 9.774 9.765 9.756 9.746 9.737 9.728 9.718 9.709 9.700 9.690 9.680 9.671 9.661 9.652 9.642 .632 9.623 9.613 9.604 9.594 9.584 9.574 9.565 9.555 9.545 9.535 9.525 9.516 9.506 9.496 9.486 9.476 9.466 9.456 9.446 9.436 9.426 9.416 9.406 9.396 9.386 9.376 9.366 9.356 9.345 Inches. 12. 265 12.253 12. 241 12. 230 12. 218 12.206 12. 195 12.183 12. 171 12. 160 12.148 12. 136 12. 124 12. 112 12.100 12.088 12.076 12.064 12. 052 12. 040 12.028 12. 016 12.004 11.992 11.980 11.968 11. 956 11.944 11. 931 11. 919 11.907 11. 895 11.882 11. 870 11.858 11.845 11.833 11. 820 11. 808 11. 795 11. 783 11. 770 11.758 11. 745 11. 732 11. 720 11. 707 11.694 11.682 Inches. 14. 718 14.704 14.690 14. 676 14. 662 14.648 14. 633 14. 619 14. 605 14. 591 14. 577 14.563 14.549 14.535 14. 520 14.506 14.492 14. 477 14. 463 14.448 14. 434 14.420 14. 405 14. 391 14. 376 14. 362 14. 347 14.332 14. 318 14. 303 14.288 14. 273 14.259 14.244 14.229 14. 214 14.200 14. 185 14. 169 14. 154 14. 139 14. 124 14.109 14.094 14. 079 14.064 14.048 14. 033 14.018 Longi- tude inter- val. 33 34 5.822 11.643 17.465 23.287 29.109 34.930 V 7 10 12* 15 Inches. 0.000 .002 .004 .008 .012 .017 Inches. 0.000 .002 .004 .008 .012 .018 35 5.823 11.645 17.468 23.291 29.113 34.936 > 7 10 m 15 Inches. 0.000 .002 .004 .008 .012 .018 2.401 2.399 2.3% 2.394 2.391 2.389 2.386 2.384 2.381 2.379 2.376 2.374 2.372 2.369 2.367 2.364 2.362 2.359 2.357 2.354 2.352 2.349 2.346 2.344 2.341 2.339 2.336 5.824 11. 647 17. 471 23.294 29.118 34.942 Longi- tude inter- val. 35 36 '? 3? }? Inches. 0.000 .002 .004 .008 .012 .018 Inches 0.001 .002 .005 .008 .013 .018 5.824 11.649 17.473 23.297 29.122 34.946 37 i 2i 5 7* 10 12* 15 Inches. 0.001 .002 .005 .008 .013 .018 74 GEOGRAPHIC TABLES AND FORMULAS. TABLE 8. Coordinates for projection of maps (scale ^^0) Continued. [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 2' longi- tude. 5' longi- tude. 7i' longi- tude. 10' longi- tude. 12i' lon- gitude. 15' longi- tude. / 37 00 05 10 16 20 25 30 35 40 45 50 55 38 00 05 10 15 20 25 30 35 40 45 50 55 39 00 05 10 15 20 26 30 35 40 45 50 55 40 00 05 10 15 20 25 30 35 40 45 50 55 41 00 Inches. Inches. 2.336 2. 334 2.331 2.329 2.326 2.323 2.321 2.318 2.316 2.313 2.311 2.308 2.305 2.303 2.300 2.298 2.295 2.292 2.290 2.287 2.284 2.382 2.279 2.276 2.274 2.271 2.268 2.266 2.263 2.260 2.258 2.255 2. 252 2.250 2.247 2.244 2.241 2.239 2.236 2.233 2.230 2.228 2.225 2.222 2.219 2.217 2.214 2.211 2.208 Inches. 4.673 4.667 4.662 4.657 4.652 4.647 4.642 4.637 4.631 4.626 4.621 4.616 4.611 4.606 4.600 4.595 4.590 4.584 4.579 4.574 4.569 4.563 4.558 4.553 4.547 4.542 4.537 4.531 4. 526 4.521 4.515 4.510 4.504 4.499 4.494 4.488 4.483 4.477 4.472 4.466 4.461 4.455 4.450 4.444 4.439 4.433 4.428 4.422 4.417 Inches. 7.009 7.001 6.994 6.986 6.978 6.970 6.963 6.955 6.947 6.939 6.932 6.924 6.916 6.908 6.900 6.892 6.885 6.877 6.869 6.861 6.853 6.845 6.837 6.829 6.821 6.813 6.805 6.797 6.789 6.781 6.773 6.765 6.757 6.748 6.740 6.732 6.724 6.716 6.708 6.699 6.691 6.683 6.675 6.666 6.658 6.650 6.642 6.633 6.625 Inches. 9.345 9.335 9. 325 9.314 9.304 9.294 9.283 9.273 9.263 9.253 9. 242 9.232 9.222 9.211 9.201 9.190 9.179 9.169 9.158 9.148 ^.137 9.127 9.116 9.106 9.095 9.084 9.073 9.063 9.052 9.041 9.030 9.020 9.009 8.998 8.987 8.976 8.966 8.955 8.944 8.933 8.922 8.911 8.899 8.888 8.877 8.866 8.855 8.844 8. 833 Inches. 11. 682 11. 669 11.656 11. 643 11. 630 11. 617 11. 604 11. 591 11. 578 11.566 11. 553 11.540 11. 527 11. 514 11.501 11.488 11. 474 11.461 11.448 11.435 11. 422 11.408 11. 395 11. 382 11. 369 11. 355 11. 342 11. 328 11. 315 11.301 11.288 11.274 11.261 11. 247 11.234 11. 221 11.207 11. 193 11.180 11. 166 11. 152 11. 138 11. 124 11. Ill 11.097 11.083 11.069 11.056 11.042 Inches. 14. 018 14.003 13. 987 13. 972 13. 956 13. 941 13. 925 13. 910 13. 894 13. 879 13. 863 13. 848 13. 832 13. 817 13.801 13. 785 13. 769 13. 753 13. 737 13. 722 13. 706 13.690 13. 674 13.658 13. 642 13. 626 13. 610 13. 594 13. 578 13. 562 13. 545 13. 529 13. 513 13. 497 13.481 13.465 13.448 13. 432 13. 415 13. 399 13.382 13. 366 13.349 13. 333 13. 316 13.300 13.283 13. 267 13.250 Longi- tude inter- val. 37 38 5.826 11.651 17. 477 23.302 29. 128 34.954 f 7 10 12^ 15 Inches. 0.001 .002 .005 .008 .013 .018 Inches. 0.001 .002 .005 .008 .013 .019 ""5." 827" 11. 653 17.480 23.306 29.133 34.960 39 21 5 7i 10 12* 15 Inches. 0.001 .002 .005 .008 .013 .019 5.828 11.655 17. 483 23.310 29.138 34.966 Longi- tude inter- val. 39 40 f U 10 12i 15 Inches. 0.001 .002 .005 .008 .013 .019 Indies. 0.001 .002 .005 .008 .013 .019 5.829 11. 657 17.486 23. 314 29. 143 34.972 41 2 5 7i 10 12* 15 Inches. 0.001 .002 .005 .008 .013 .019 GEOGRAPHIC TABLES AND FORMULAS. 75 TABLE S. Coordinates for projection of maps (scale ssi^y) Continued. [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. Zi'longi- tude. 5' longi- tude. IV longi- tude. 10' longi- tude. 12A' lon- gitude. 15' longi- tude. O 1 41 00 05 10 15 20 25 30 35 40 45 50 55 42 00 05 10 15 20 26 30 35 40 45 50 55 43 00 05 10 15 20 25 30 35 40 45 50 55 44 00 05 10 15 20 25 30 35 40 45 50 55 45 00 Inches. Inches. 2.208 2.206 2.203 2.200 2.197 2.194 2.192 2.189 2.186 2.183 2.180 2.178 2.175 2.172 2.169 2.166 2.163 2.160 2.158 2.155 2.152 2.149 2.146 2. 143. 2.140 2.137 2.134 2.132 2.129 2.126 2.123 2.120 2.117 2.114 2.111 2.108 2.105 2.102 2.099 2.096 2.093 2.090 2.087 2.084 2.081 2.078 2.076 2.073 2.070 Inches. 4.417 4.411 4.406 4.400 4.394 4.389 4.383 4.377 4.372 4.366 4.361 4.355 4.349 4.344 4.338 4.332 4.326 4.321 4.315 4.309 4.304 4.298 4.292 4.286 4.281 4.275 4.269 4.263 4.257 4.251 4.246 4.240 4.234 4.228 4.222 4.216 4.210 4.205 4.199 4.193 4.187 4.181 4.175 4.169 4.163 4.157 4.151 4.145 4.139 Inqhes. 6. 625 6.617 6.608 6.600 6.591 6.583 6.575 6.566 6.558 6.549 6.541 6.533 6.524 6.515 6.507 6.498 6.490 6.481 6. 472 6.464 6.455 6.447 6.438 6.429 6.421 6.412 6.403 6.395 6.386 6.377 6.368 6.359 6.351 6.342 6.333 6.324 6.316 6.307 6.298 6.289 6.280 6.271 6,262 6.253 6.244 6.235 6.227 6.218 6.209 Inches. 8.833 8.822 8.811 8.800 8.789 8.777 8.766 8.755 8.744 8.732 8.721 8.710 8.699 8.687 8.676 8.664 8.653 8.641 8.630 8.618 8.607 8.596 8.584 8.573 8.561 8.550 8.538 8.526 8.514 8.503 8.491 8.479 8.468 8.456 8.444 8.432 8.421 8.409 8.397 8.385 8.373 8.361 8.350 8.338 8.326 8.314 8.302 8.290 8.278 Inches. 11.042 11.028 11.014 11.000 10. 986 10. 972 10. 958 10.944 10.930 10. 916 10.902 10.888 10. 873 10.859 10.845 10.830 10. 816 10.802 10. 787 10. 773 10. 759 10.744 10. 730 10. 716 10. 701 10.687 10.672 10.658 10.643 10.628 10. 614 10.599 10.585 10. 670 10.555 10.541 10. 526 10. 511 10.496 10. 482 10. 467 10. 452 10. 437 10. 422 10.407 10.392 10. 377 10.363 10.348 Inches. 13.250 13. 233 13.216 13.200 13.183 13.166 13. 149 13. 132 13. 115 13. 099 13.082 13. 065 13.048 13. 031 13. 014 12.996 12. 979 12. 962 12.945 12.928 12. 910 12.893 12. 876 12.859 12.842 12. 824 12.807 12. 789 12. 772 12.754 12. 736 12. 719 12. 701 12.684 12.666 12.649 12.631 12.613 12.596 12.578 12.560 12.542 12.524 12.506 12.489 12.471 12.453 12.435 12.417 Longi- tude inter- val. 41 42 5.830 11.659 17.489 23.319 29.149 34.978 '9. ,5 4 J? Inches. 0.001 .002 .005 .008 .013 .019 Inches. 0.001 .002 .005 .008 .013 .019 5.831 11.661 17.492 23.323 29.154 34.984 43 'l 4 7* 10 12* 15 Inches. 0.001 .002 .005 .008 .013 .019 Longi- tude inter- val. 43 44 5.832 11.663 17.495 23.327 29.159 34.990 2* 5 $ m 15 Inches. 0.001 .002 .005 .008 .013 .019 Inches. 0.001 .002 .005 .009 .013 .019 5.833 11.666 17.498 23.331 29.164 34.997 45 2i 5 7i 10 124 15 Inches. 0.001 .002 .005 .009 .013 .019 76 GEOGRAPHIC TABLES AND FORMULAS. TABLE 8. Coordinates for projection of maps (scale TI ^) Continued. [From Smithsonian Geographical Tables.] Lati- tude of parallel. Meridio- nal dis- tances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 2i'longi tude. 5' longi- tude. 7' longi- tude. 10'longi tude. 12F lon- gitude. 15'longi tude. / 45 00 05 10 15 20 25 30 35 40 45 50 55 46 00 05 10 15 20 25 30 35 40 45 50 55 47 00 05 10 15 20 25 30 35 40 45 ' 50 55 48 00 05 10 15 20 25 30 35 40 45 50 55 49 00 05 10 15 20 25 30 35 40 45 50 55 50 00 Inches. Inches. 2.070 2.067 2.064 2.061 2.058 2.054 2.051 2.048 2.045 2.042 2.039 2.036 2.033 2.030 2.027 2.024 2.021 2.018 2.015 2.012 2.009 2.006 2.003 1.999 1.996 1.993 1.990 1.987 1.984 1.981 1.977 1.974 1.971 1.968 1.965 1.962 1.959 1.956 1.952 1.949 1.946 1.943 1.940 1.937 1.933 1.930 1.927 1.924 1.921 1.917 1.914 1.911 1.908 1.905 1.901 1.898 1.895 1.892 1.888 1.885 1.882 Inches. 4.139 4.133 4.127 4.121 4.115 4.109 4.103 4.097 4.091 4.085 4.079 4.073 4.067 4.060 4.054 4.048 4.042 .036 .030 4.023 .017 .011 4.005 3.999 3.993 3.986 3.980 3.974 3.968 3.961 3.955 3.949 3.943 3.936 3. 930 3.924 3.917 3.911 3.905 3.898 3.892 3.886 3.879 3.873 3.867 3.860 3.854 3.848 3.841 3.835 3.828 3.822 3.815 3.809 3.802 3.796 3.790 3.783 3.777 3.770 3.764' Inches. 6.209 6.200 6.191 6.181 6.172 6.163 6.154 6.145 6.136 6.127 6.118 6.109 6.100 6.091 6.081 6.072 6.063 6.054 6.044 6.035 6.026 6.017 6.008 5.998 5.989 5.980 5.970 5.961 5.951 5. 942 5.933 5.923 5.914 5.904 5.895 5.886 5.876 5.867 5.857 5.848 5.838 5.829 5.819 5.810 5.800 5.790 5.781 5.771 5.762 5.752 5.742 5.733 5.723 5.713 5.704 5.694 5.684 5.675 5.665 5.655 5.646 Inches. 8.278 8.266 8.254 8.242 8.230 8.218 8.206 8.194 8.181 8.169 8.157 8.145 8.133 8.121 8.108 8.096 8.084 8.072 8.059 8.047 8.035 8.022 8.010 7.998 7.985 7.973 7.960 7.948 7.935 7.923 7.910 7.898' 7.885 7.872 7.860 7.848 7.835 7.822 7.810 7.797 7.784 7.771 7.759 7.746 7.733 7.721 7.708 7.695 7.682 7.670 7.657 7.644 7.631 7.618 7.605 7.592 7.579 7/566 7.553 7.540 7.528 Inches. 10. 348 10. 333 10. 318 10. 302 10. 287 10. 272 10. 257 10. 242 10. 227 10. 212 10. 197 10. 182 10. 166 10. 151 10. 136 10. 120 10. 105 10. 090 10. 074 10. 059 10. 043 10. 028 10.013 9.997 9.982 9.966 9.950 9.935 9.919 9.903 9.888 9.872 9.856 9.841 9.825 9.809 9.794 9.778 9.763 9.746 9.730 9.714 9.698 9.683 9.667 9.651 9.635 9.619 9.603 9.587 9.571 9.555 9.538 9.522 9.506 9.490 9.474 9.458 9.442 9.426 9.409 Inches. 12. 417 12. 399 12. 381 12. 363 12. 345 12. 327 12. 308 12.290 12. 272 12. 254 12. 236 12. 218 12. 200 12. 181 12. 163 12. 144 12. 126 12. 107 12. 089 12. 070 12.052 12. 033 12.015 11.996 11.978 11. 959 11.940 11.922 11.903 11.884 11.865 11.846 11. 828 11. 809 11.790 11. 771 11. 752 11.733 1J.714 11.695 11.676 11.657 11. 638 11 619 11.600 11.581 11.562 11.543 11.524 11.504 11. 485 11.466 11.446 11.427 11.407 11.388 11. 369 11.349 11.330 31.311 11.291 Longi- tude inter- val. 45 46 5.834 11. 668 17. 501 23.335 29. 169 35.003 24 5 ,5* * Inches. 0.001 .002 .005 .009 .013 .019 Inches. 0.001 .002 .005 .009 .013 .019 5.835 11. 670 17.504 23. 339 29. 174 35.009 47 ' f i? 12J 15 Inches. 0.001 .002 .005 .008 .013 .019 5.836 11. 672 17.508 23.344 29.180 35.015 Longi- tude inter- val. 47 48 '? 74 10 12i 15 Inches. 0.001 .002 .005 .008 .013 .019 Inches. 0.001 .002 .005 .008 .013 .019 5.837 11. 674 17. 511 23. 318 29. 185 35.021 49 24 5 7* 10 12| 15 Inches. 0.001 .002 .005 .008 .013 .019 5.838 11.676 17. 514 23.352 29.190 35.027 - 49 50 '? 74 10 12* 15 Inches. 0.001 .002 .005 .008 .013 .019 Inches. 0.001 .002 .005 .008 .013 .019 GEOGRAPHIC TABLES AND FOEMULAS. 77 TABLE 9. Coordinates for projection of maps (scale [Prepared by S. S. Gannett.] Latitude of parallel. Abscissas of developed parallel. Ordinates of devel- oped parallel. Longitude interval. 2*' 5' 7*' 1(X 15' Longitude interval. Inch. / 25 00 05 07* 10 15 20 22* 25 30 35 % 45 50 52* 55 60 26 00 05 07* 10 15 20 22* 25 30 35 2 45 50 52* 55 60 27 00 05 07* 10 15 20 22* 25 30 35 S 45 50 52* 55 60 Inches. 3.450. .448 .446 .445 .443 3.441 .440 .438 .436 3.434 .433 .431 .429 3.426 .425 .424 .422 3.422 .419 .418 .417 .414 3.412 .410 .409 .407 3.405 .403 .402 .'400 3.397 .396 .394 .392 3.392 .390 .388 .387 .385 3.382 .380 .379 .377 3.374 .373 .371 .369 3.367 .365 .364 .361 Inches. 6.900 .895 .893 .890 .886 6.881 .879 .876 .872 6.867 .865 .862 .858 6.852 .850 .848 .843 6.843 .838 .836 .833 .828 6.824 .821 .819 .814 6.809 .806 .804 .799 6.794 .792 .789 .784 6.784 .779 .777 '.774 .769 6.764 .761 .759 .754 6.749 .746 .743 .738 6.733 .730 .728 .723 Inches. 10.350 .343 .339 .336 .329 10.322 .318 .314 .307 10.300 .297 .293 .286 10. 279 .276 .272 .264 10.264 .257 .253 .250 .243 10.236 .232 .238 .221 10. 214 .210 .206 .198 10. 191 .188 .184 .176 10. 177 .169 .165 .161 .153 10. 146 .142 .138 .131 10. 124 .120 .116 .108 10.100 .095 .092 .084 Inches. 13.800 .790 .786 .781 .772 13.772 .758 .753 .744 13. 734 .730 .725 .715 13.705 .700 .696 .686 13.686 .677 .672 .666 .657 13.647 .642 .638 .628 13. 618 .612 .608 .598 13.588 .583 .578 .569 13.569 .559 .554 .548 .538 13. 528 .523 .518 .508 13. 498 .492 .487 .477 13. 467 .461 .456 .446 Inches. 20.700 .685 .678 .671 .657 20.643 .636 .629 .615 20.601 .594 .587 .573 20. 558 .551 .544 .529 20.529 .514 .506 .499 .485 20. 471 .464 .457 .442 20.427 .419 .412 .397 20.382 .375 .367 .353 20.353 .338 .330 .322 .307 20.292 .284 .277 .262 20. 247 .239 .231 .215 20.200 .191 .184 .169 / 5 71 10 15 0.002 .005 .008 .019 Latitude interval. Meridional distance. 1 2 3 4 5 6 7 8 9 10 Inches. 1.514 3.028 4.542 6.057 7.571 9.085 10.599 12. 114 13. 628 15.142 Longitude interval. Inch. 5 .? 15 0.002 .005 .009 .020 Latitude interval. Meridional distance. 1 2 3 4 5 6 7 8 9 10 Inches. 1.515 3.029 4.544 6.058 7.573 9. 087 10.602 12. 115 13. 631 15. 145 Longitude interval. Inch. 5 ,? 15 0.002 .005 .009 .020 Latitude interval. Meridional distance. 1 2 3 4 5 6 7 8 9 10 Inches. 1.515 3.029 4. 544 6.058 7.574 9.087 10.603 12. 117 13. 632 15. 147 This table can be used for even multiples or divisions of the y^A scale, as indicated in the two fol- lowing cases. Scale M taj,: For a given latitude the meridional distance for a certain latitude inter- val and the abscissas and ordinates for a certain longitude interval are double the values given in the table. Scale 5B ijj : For a given latitude the meridional distance for a certain latitude interval and the abscissas and ordinates for a certain longitude interval are half the values given in the table. 78 GEOGRAPHIC TABLES AND FORMULAS. TABLE 9. Coordinates for projection of maps (scale 53-^) Continued. Latitude of parallel. Abscissas of developed parallel. Ordinates of devel- oped parallel. Longitude interval. 2*' 5' 71' 10' 15' Longitude interval. Inch. / 28 00 05 07J 10 15 20 22| 25 30 35 % 45 50 52J 55 60 29 00 05i 07 10 15 20 22J 25. 30 35 I" 45 50 52* 55 60 30 00 05 07i 10 15 20 22| 25 30 35 45 50 S J 60 Inches. 3.361 .359 .357 .356 .354 3.352 .350 .349 .346 3.343 .342 .340 .338 3.336 .334 .333 .330 3.330 .328 .326 .325 .322 3.319 .318 .317 .314 3.311 .310 .309 .305 3.303 .302 .300 .298 3.298 .295 .294 .292 .289 3.286 .285 .284 .281 3.278 .277 .275 .273 . 3.270 .268 .267 .264 Inches. 6.723 .718 .715 .713 .708 6.703 .700 .698 .692 6.687 .684 .681 .676 6.671 .668 .666 .660 6.660 .655 .652 .649 .644 6.638 .636 .633 .628 6.622 .620 .617 .611 6.605 .603 .600 .595 6.595 .590 .587 .584 .578 6.572 .570 .567 .562 6.556 .553 .550 .545 6.540 .537 .534 .528 Inches. 10.084 .077 .072 .069 .061 10.054 .050 .046 .038 10. 030 .026 .022 .014 10.006 .002 9.998 .990 9.990 .982 .978 .974 .966 9.958 .954 .950 .942 9.934 .930 .925 .916 9.908 .904 .900 .892 9.892 .884 .880 .876 .867 9.858 .855 .850 .842 9.824 .830 .826 .818 9.810 .805 .801 .792 Inches. 13. 446 .436 .430 .425 .415 13.405 .400 .395 .384 13. 373 .368 .363 .352 13.342 .336 .331 .320 13. 320 .310 .304 .299 .288 13.277 .271 .266 .255 13. 245 .239 .234 .222 13. 211 .206 .200 .190 13.190 .179 .173 .168 .156 13. 145 .140 .134 .123 13. 112 .106 .101 .090 13.080 .074 .068 .056 Inches. 20. 169 .154 .145 .138 .123 20. 108 .100 .092 .076 20.060 .052 .044 .028 20.013 .005 19. 997 .981 19. 980 .964 .956 .948 .932 19. 915 .907 .899 .883 19.867 .859 .850 .833 19 816 .808 .800 .785 19. 785 .768 .760 .751 .734 19. 717 .710 .701 .685 19.668 .659 .651 .635 19. 619 .611 .602 .584 5 - i? 15 0.002 .005 .009 .021 Latitude interval. Meridional distance. 1 2 3 4 5 6 7 8 9 10 Inches. 1.515 3.030 4.545 6.060 7.575 9.090 10.605 12. 120 13.635 15.150 Longitude interval. Inch. f 5 i? 15 0.002 .005 .009 .021 Latitude interval. Meridional distance. 1 2 3 4 5 6 *7 8 9 10 Inches. 1.515 3.030 4.545 6.060 7.575 9.090 10.605 12.122 13.637 15. 152 Longitude interval. Inch. 5 7| 10 15 0.002 .005 .009 .021 Latitude interval. Meridional distance. 1 2 3 4 5 6 7 8 9 10 Inches. 1.515 3.030 4.545 6.061 7.576 9.092 10.608 12. 123 13.638 15.154 GEOGRAPHIC TABLES AND FORMULAS. L-. TABLE 9. Coordinates for projection of maps (scale ?J%-Q-Q) Continued. 79 Latitude of parallel. Abscissas of developed parallel. Ordinates of devel- oped parallel. Longitude interval. W 5' 7|' 10' 15' Longitude interval. Inch. / 31 00 05 07* 10 15 20 8* 30 35 3 ^ 45 - 50 52i 55 60 32 00 05 07* 10 15 20 22J 25 30 35 3 30 35 % 45 50 S 1 60 38 00 05 07* 10 15 20 % 30 35 37* 40 45 50 s? 60 39 00 05 07i 10 15 20 9 30 35 % 45 50 52J 55 60 Inches. 3.042 .038 .037 .035 .032 3.028 .027 .024 .022 3.019 .017 .015 .012 3.009 .006 .005 .001 3.001 2.998 .997 .995 .991 2.988 .987 .984 .981 2.978 .976 .974 .971 2.968 .966 .964 .960 2.960 .957 .955 .954 .950 2.946 .945 .943 .940 2.936 .934 .933 .929 2.926 .924 .922 .919 Inches. 6.084 .077 .074 .070 .064 6.057 .053 .049 .044 6.037 .034 .030 .024 6.017 .013 .010 .003 6.003 5.996 .993 .990 .983 5.976 .973 .969 .962 5.955 .952 .949 .942 5.935 .932 .928 .921 5.921 .914 .910 .907 .900 5.893 .890 .886 .879 5.872 .868 .865 .858 5.851 .848 .844 .837 Inches. 9.126 .116 .111 .106 .096 9.086 .081 .076 .066 9.056 .051 .045 .035 9.025 .020 .015 .004 9.004 8.994 .989 .984 .974 8.964 .959 .954 .944 8.933 .927 .923 .913 8.902 .897 .892 .882 8.882 .871 .865 .860 .850 8.840 .835 .829 .819 8.808 .802 .798 .787 8.777 .772 .766 .755 Inches. 12. 169 .155 .148 .141 .128 12. 114 .107 .101 .088 12. 074 .068 .061 .048 12.034 .027 .020 .006 12.006 11.993 .986 .980 .966 11. 952 .946 .939 .925 11. 911 .904 .898 .884 11. 870 .863 .856 .842 11.842 .828 .821 .814 .800 11.786 .779 .772 .758 11. 744 .737 .730 .716 11. 702 .695 .688 .674 Inches. 18.253 .232 .222 .212 .192 18. 172 .162 .152 .132 18.112 .102 .091 .071 18.050 .040 .030 .009 18.009 17. 989 .979 .969 .949 17.929 .919 .908 .887 17.867 .856 .846 .826 17.805 .795 .784 .763 17. 763 .742 .731 .721 .700 17.679 .669 .658 .637 17. 616 .605 .595 .574 17.553 .543 .532 .511 5 ,? 15 0.003 .006 .010 .024 Latitude interval. Meridional distance. 1 2 3 4 5 6 7 8 9 10 Inches. 1.517 3.034 4.551 6.068 7.585 9.102 10. 619 12. 136 13.653 15. 170 Longi- tude interval. Inch. 5 'i? 15 0.003 .006 .010 .024 Latitude interval. Meridional distance. 1 2 3 4 5 6 7 8 9 10 Inches. 1.517 3.034 4.551 6.069 7.586 9.103 10. 620 12.138 13.655 15. 172 Longi- tude interval. Inch. 5 i? 15 0.003 .006 .011 .024 Latitude interval. Meridional distance. 1 2 3 4 5 6 7 8 9 10 Inches. 1.517 3.035 4.552 6.070 7.587 9.105 10. 622 12. 140 13.658 15. 175 4606108 6 82 GEOGRAPHIC TABLES AND FORMULAS. TABLE 9. Coordinates for projection of maps (scale ^^o) Continued. Latitude of parallel. Abscissas of developed parallel. Ordinates of devel- oped parallel. Longitude interval. V 5' 74' 10' 15' Longitude interval. Inch. 40 00 2.919 5.837 8.755 11.674 17. 5M 5 0.003 05 .915 .830 .745 .660 .490 71 .006 074 .913 .826 .740 .653 .479 10 .011 10 .912 .823 .734 .646 .469 15 .024 15 .908 .816 .723 .631 .447 Latitude Meridional 20 2.904 5.808 8.712 11. 616 17. 424 interval. distance. 22 X 902 804 706 .609 413 AAg 25 .900 .801 .702 .602 .403 , Inches. 30 .897 .794 .691 .588 .382 1 1.518 2 3. 035 3 4.557 35 i 2.894 5.787 8.680 11.574 17. 361 4 6.070 .892 .784 .675 .567 .351 5 7.588 40 .890 .780 .670 .560 .340 6 9.106 45 .886 .772 .659 .545 .317 7 10. 624 8 12. 143 9 13. 660 50 2.883 5.765 8.648 11.530 17.295 10 15. 178 * .881 .762 .642 .523 .285 55 60 . 879 .875 . 758 .750 . 636 .625 . 516 .501 . 273 .251 Longitude interval. Inch. 41 00 2.875 5.750 8.625 11.501 17. 251 , 05 .872 .743 .614 .486 .229 5 0.003 074 .870 .740 .609 .479 .219 7i .006 10 .868 .736 .604 .472 .208 10 .011 15 .864 .729 .594 .458 .187 15 .025 20 224 25 2.861 .859 .857 5.722 .718 .714 8.582 .577 .572 11. 443 .436 .428 17. 165 .154 .143 Latitude interval. Meridional distance. 30 .854 .707 .561 .414 .121 / Inches. 1 1.518 35 ff 45 2.850 .848 .846 .843 5.700 .696 .692 .685 8.550 .544 .539 .528 11.399 .392 .385 .370 17.099 .088 .077 .055 2 3 4 5 6 3.036 4.554 6.072 7.590 9.108 7 10.626 50 524 55 60 2.839 .837 .835 .831 5.678 .674 .670 .663 8.517 .510 .505 .494 11.355 .347 .340 .326 17. 033 .021 .011 16. 989 8 9 10 12. 145 13.663 15. 181 42 00 2.831 5.663 8.494 11. 326 16. 989 Longitude interval. " Inch. 05 .827 .655 ' .483 .311 .966 074 10 .826 .824 .652 .648 .478 .472 .304 .296 .956 .944 5 71 0.003 fVlfi 15 .820 .641 .462 .282 .923 ' 10 . UUD .011 15 .025 20 2 817 5 634 8 450 11 267 16 901 224 25 30 !sis .813 .809 .630 .626 .618 !444 .439 .428 .259 .252 .237 .889 .878 .855 Latitude interval. Meridional distance. / Inches. 35 2.805 5.611 8.417 11.222 16.833 1 1.518 .804 .608 .412 .215 .823 2 3.036 40 .802 .604 .406 .208 .812 3 4.554 45 .798 .597 .395 .192 .790 4 5 6.073 7.591 o ino 50 2.794 5.589 8.384 11. 178 16. 767 7 y ii/y 10. 627 524 55 60 .793 .791 .787 .585 .582 .574 .378 .372 .361 .170 .163 .148 .755 .745 .722 8 9 . 10 12. 147 13.666 15. 184 GEOGRAPHIC TABLES AND FORMULAS. 83 TABLE 9. Coordinates for projection of maps (scale Continued. Latitude of parallel. Abscissas of developed parallel. Ordinates of devel- oped parallel. Longitude interval. 2J' 5' 7!' 10' 15' Longitude interval. Inch. / 43 -00 05 07J 10 15 20 1* 30 35 J? 45 50 52J 55 60 44 00 05 07J 10 15 20 f 30 35 $ 45 50 52 55 60 45 00 05 07* 10 15 20 1* 30 35 % 45 50 52| 55 60 Inches. 2.787 .783 .781 .779 .776 2.772 .770 .768 .764 2.760 .758 .756 .752 2.749 .747 .745 .741 2.741 .737 .735 .733 .730 2.726 .723 .722 .718 2.714 .712 .710 .706 2.702 .700 .698 .695 2.695 .691 .689 .687 .683 2.679 .677 .675 .671 2.667 .665 .663 .660 2.655 .654 .652 .648 Inches. 5.574 .566 .562 .558 .551 5.543 .539 .535 .528 5.520 .516 .512 .505 5.498 .494 .490 .482 5.482 .474 .470 .467 .459 5.451 .447 .444 .436 5.428 .424 .420 .413 5.405 .401 .397 .390 5.390 .382 .378 .374 .366 5.358 .354 .350 .342 5.334 .330 .326 .319 5.311 .307 .303 .295 Inches. 8.361 .349 .343 .338 .326 8.314 .308 .303 .292 8.280 .274 .268 .257 8.246 .240 .235. .223 8.223 .212 .206 .200 .188 8.177 .171 .166 .154 8.142 .136 .130 .119 8.108 .102 .096 .084 8.084 .073 .067 .061 .049 8.038 .032 .026 .014 8.002 7.996 .990 .978 7.966 .960 .954 .942 Inches. 11.148 .132 .124 .117 .102 11.086 .078 .070 .055 11.040 .032 .025 .010 10.995 .987 .980 .964 10.964 .949 .941 .934 .918 10.902 .894 .887 .872 10.856 .848 .840 .825 10.810 .802 .794 .779 10. 779 .764 .756 .748 .732 10.717 .708 .701 .685 10.669 .661 .653 .638 10.622 .614 .606 .590 Inches. 16. 722 .698 .686 .675 .653 16.629 .617 .606 .583 16.560 .548 .537 .515 16. 493 .481 .470 .446 16. 446 .423 .411 .400 .377 16.354 .341 .331 .308 16.284 .272 .261 .238 16.215 .203 .192 .169 16. 169 .146 .134 .122 .098 16.075 .063 .051 .027 16.003 15.991 .980 .957 15.933 .921 .909 .885 5 ? 15 0.003 .006 .011 .025 Latitude interval. Meridional distance. 1 2 3 4 5 6 8 9 10 Inches. 1.519 3.038 4.557 6.075 7.594 9.113 10.631 12. 149 13.668 15. 187 Longitude interval. Inch. 5 ,? 15 0.003 .006 .011 .025 Latitude interval. Meridional distance. 1 2 3 4 5 6 7 8 9 10 Inches. 1.519 3.038 4.557 6.076 7.595 9.114 10. 633 12.152 13. 671 15. 190 Longitude interval. Inch. 5 $ 15 0.003 .006 .011 .025 Latitude interval. Meridional distance. 1 2 3 4 5 6 7 8 9 10 Inches. 1.519 3.038 4.557 6.077 7.596 9.115 10.635 12. 154 13.673 15. 192 84 GEOGRAPHIC TABLES AND FORMULAS. TABLE 9. Coordinates for projection of maps (scale ^5-^^) Continued. Latitude of parallel. Abscissas of developed parallel. Ordinates of devel- oped parallel. Longitude interval. 2J' 5' 7 10' 15' Longitude interval. Inch. / 46 00 05 07^ 10 15 20 22J 25 30 35 5? 45 50 52J 55 60 47 00 05 07i 10 15 20 22 25 30 35 37J 40 45 50 52* 55 60 48 00 05 07 10 15 20 22J 25 30 35 5? 45 50 52J 55 . 60 Inches. 2.648 .644 .640 .639 .635 2.631 .630 .627 .623 2.619 .617 .615 .611 2.607 .605 .603 .599 2.599 .595 .593 .591 .587 2.583 .581 .579 .575 2.570 .568 .567 .563 2.559 .557 .555 .550 2.550 .546 .544 .542 .538 2.534 .532 .530 .526 2.522 .520 .517 .513 2.509 .507 .505 .501 Inches. 5.295 .287 .281 .279 .271 5.263 .259 .255 .247 5.239 .235 .230 .223 5.214 .210 .206 .198 ' 5.198 .190 .186 .182 .174 5.166 .162 .158 .150 5.141 .137 .133 .125 5.117 .113 .109 .100 5.100 .092 .088 .084 .076 5.068 .064 .060 .051 5.043 .039 .034 .026 5.018 .014 .010 .002 Inches. 7.942 .930 .922 .918 .906 7.894 .888 .882 .870 7.858 .852 .846 .834 7.822 .816 .810 .798 7.798 .786 .780 .774 .761 7.749 .743 .737 .724 7.712 .706 .700 .688 7.676 .670 .663 .650 7.650 .638 .632 .626 .614 7.602 .596 .590 .577 7.564 .558 .552 .539 7.527 .521 .515 .502 Inches. 10.590 .574 .562 .558 .542 10. 526 .518 .510 .494 10. 478 .470 .461 .445 10. 429 .421 .413 .397 10. 397 .381 .373 .365 .348 10.332 .324 .316 .299 10. 282 .274 .266 .250 10. 234 .226 .218 .201 10.201 .185 .177 .168 .152 10.136 .128 .119 .102 10. 086 .078 .069 .052 10.036 .028 .020 .003 Inches. 15.885 .861 .844 .837 .813 15. 789 .777 .765 .741 15. 717 .705 .692 .667 15. 643 .631 .619 .595 15. 595 .571 .559 .547 .522 15. 498 .486 .474 .449 15. 423 .411 .399 .375 15.351 .339 .326 .307 15. 301 .277 .265 .252 .228 15. 204 .192 .179 .154 15. 129 .116 .103 .078 15. 054 .042 .030 .005 5 i? 15 0.003 .006 .011 .025 Latitude interval. Meridional distance. 1 2 3. 4 5 6 7 8 9 10 Inches. 1.520 3.039 4.559 6.078 7.598 9.117 10.637 12. 157 13. 677 15.196 Longitude interval. Inch. 5 i? 15 0.003 .006 .011 .025 Latitude interval. Meridional distance. / 1 2 3 4 5 6 7 8 9 10 Inches. 1.520 3.039 4.559 6.079 7.599 9.119 10.638 12. 158 13. 678 15. 197 Longitude interval. Inch. 5 i? 15 0.003 .006 .011 .025 Latitude interval. Meridional distance. 1 2 3 4 5 6 7 8 9 10 Inches. 1.520 3.04) 4.560 6.080 7.600 9.120 10. 640 12.160 13.680 15.200 GEOGRAPHIC TABLES AND FORMULAS. 85 TABLE 9. Coordinates for projection of maps (scale ) Continued. Abscissas of developed parallel. Ordinates of devel- Latitude ol Longitude interval. oped parallel. parallel. *' 5' 7*' lO' 15' Longitude interval. Inch. / Inches. Inches. Inches. Inches. Inches. / 49 00 2.501 5.002 7.502 10.003 15.005 5 0.003 05 2.496 4.993 .490 9.986 14.980 7J .006 07J .494 .989 .484 .978 .967 10 .011 10 .492 .985 .477 .970 .955 15 .025 15 .488 .976 .464 .952 .929 Latitude Meridional 20 2.484 4.968 7.452 9.936 14.904 ono interval. distance. % . 482 .480 . 964 .960 . 446 .440 . 928 .920 . o\)Z .880 / Inches. 30 .476 .952 .428 .903 .855 1 1.520 2 3.040 3 4.560 35 2.472 4.943 7.415 9.886 14.829 4 6.081 37J .470 .939 .408 .878 .816 5 7.601 40 .467 .934 .402 .869 .803 6 9.121 45 .463 .926 .389 .852 .778 7 10. 641 8 12. 162 9 13.682 50 2.459 4.918 7.377 9.836 14. 754 10 15.202 52i .457 .914 .371 .828 .742 55 .455 .910 .364 .819 .729 60 .450 .901 .352 .802 .703 86 GEOGRAPHIC TABLES AND FORMULAS. TABLE 10. Coordinates for the projection of maps (scale T [Prepared by S. S. Gannett and George T. Hawkins.] Abscissas of developed parallel. Ordinates of devel- Latitude of oped parallel. Longitude interval. parallel. 1'. 2'. 3'. 4'. 5'. Longi- tude Inch. interval. o / Inches. Inches. Inches. Inches. Inches. , 25 00 5.520 11.040 16. 560 22. 080 27.600 1 .000 05 .516 .032 .549 .065 .581 2 .002 07* .515 .029 .544 .057 .572 3 .003 10 .512 .025 .538 .050 .562 4 .006 15 .509 .018 .528 .035 .544 5 .009 20 25 S 5.505 .503 .501 11. 010 .006 .002 16. 515 .509 .503 22. 020 .012 .005 27. 525 .516 .506 Latitude interval. Meridi- onal distance 30 .497 10.995 .492 21.990 .487 i Inches. 1 6.057 35 5.494 10.988 16. 480 21. 975 27.468 2 12. 114 37* 40 45 .492 .490 .486 .984 .980 .972 .476 .470 .458 .968 .960 .945 .459 .449 .430 3 4 5 18. 171 24.228 30.285 50 5 482 10 965 16. 448 2i 930 27 411 52* !480 !921 !401 Longi- 55 .478 !957 !435 .915 .392 tude Inch. 60 .475 .950 .424 .900 .373 interval. 26 .00 5.475 10.950 16. 424 21.900 27. 373 1 .000 05 .470 .942 .412 .882 .353 2 . 002 07* .469 .937 .406 .875 .343 3 10 .467 .933 .400 .867 .333 4 006 15 .463 .925 .389 .852 .314 5 '.009 20 25* 5.459 .457 .455 10. 918 .914 .910 16. 377 .371 .365 21.835 .828 .820 27.294 .284 .275 Latitude interval. Meridi- onal distance. 30 .451 .902 .353 .805 .255 / Inches. 1 6.058 35 5.447 10.894 16. 341 21. 789 27.235 2 12. 115 37* .445 .890 .335 .780 .225 3 18. 173 40 .443 .887 .330 .773 .216 4 24.231 45 .439 .878 .318 .758 .196 5 30. 289 50 5.435 10. 870 16.306 21. 741 27. 176 52- .433 .866 .298 .732 .167 Longi- 55* .431 .863 .294 .725 .157 tude Inch. 60 .428 .855 .282 .710 .138 interval. 27 00 5.428 10.855 16. 283 21. 710 27.138 1 .000 05 .422 .848 .270 .695 .118 2 .002 07* .421 .843 .264 .686 .108 3 .003 10 .420 .839 .258 .678 .097 4 .006 15 .415 .831 .247 .662 .077 5 .010 20 22* 25 5.410 .409 .407 10.822 .818 .815 16.233 .227 .220 21.645 .636 .628 27.056 .046 .035 Latitude interval. Meridi- onal distance. 30 .403 .805 .210 .612 .015 / Inches. 1 6.058 35 , 5.399 .397 10. 798 .794 16. 198 .191 21.595 .588 26.995 .984 2 3 12. 117 18. 175 40 5 45 .395 .391 .790 .782 .185 .172 .580 .562 .974 .953 4 5 24.235 30.292 50 5.387 10. 774 16.160 21.548 26. 933 52i .384 .768 .154 .538 .922 55 .382 .765 .148 .530 .912 60 .378 .758 .135 .515 .892 GEOGRAPHIC TABLES AND FORMULAS. 87 TABLE 10. Coordinates for the projection of maps (scale TT^rnr) Continued. Abscissas of developed parallel. Ordinates of devel- Latitude of oped parallel. Longitude interval. parallel. Longi- 1'. 2'. 3'. 4'. 5'. tude Inch. interval. o / Inches. Inches. Inches. Inches. Inches. , 28 00 5.378 10.758 16.135 21.515 26. 892 1 .000 05 .374 .749 .122 .498 .871 2 .002 071 .372 .745 .116 .488 .861 3 .003 10 .370 .740 .110 .480 .850 4 .006 15 .366 .732 .098 .465 .830 5 .010 20 221 5.362 .360 10. 724 .720 16.085 .078 21.448 .439 26.810 .799 Latitude interval. Meridi- onal distance. 25 .358 .715 .072 .430 .789 30 .354 .708 .060 .415 .768 / Inches. 1 6.060 35 371 5.349 .347 10.698 .694 16.048 .041 21. 398 .388 26. 746 .735 2 3 12.120 18. 178 f)A fWJQ 40 45 .345 .341 .690 .682 .035 .022 .380 .362 .725 .703 4 5 24. zoo 30. 298 50 5.336 10.673 16.010 21.348 26.683 521 55 .334 .332 .668 .665 .004 15. 998 .339 .330 .672 .662 Longi- tude Inch. 60 .328 .657 .985 .312 .640 interval. 29 00 5.328 10.657 15.985 21.312 26.640 1 .000 05 .324 .648 .971 .295 .619 2 .002 071 .322 .643 .965 .287 .608 3 .003 10 .320 .640 .958 .278 .598 4 .006 15 .315 .630 .945 .260 .575 5 .010 20 221 25 5.310 .308 .306 10. 621 .617 .612 15.932 .925 .920 21. 242 .234 .225 26.553 .542 .532 Latitude interval. Meridi- onal distance. 30 .302 .605 .907 .209 .511 / Inches. 1 6.060 35 371 40 45 5.298 .295 .294 .289 10.596 .591 .587 .578 15.894 .886 .880 .867 21. 192 .183 .174 .156 26.490 .478 .468 .445 2 3 4 5 12. 121 18. 182 24.242 30.302 50 5.284 10.569 15.853 21. 137 26.422 521 .282 .565 .847 .130 .412 Longi- 55 .280 .560 .841 .121 .401 tude Inch. 60 .275* .552 .828 .104 .380 interval. 30 00 5.275 10.552 15.828 21. 104 26. 380 1 .000 05 .272 .543 .815 .086 .358 2 .002 071 .269 .538 .808 .077 .346 3 .003 10 .267 .534 .801 .068 .335 4 .006 15 .262 .525 .787 .050 .312 5 .010 20 221 25 5.258 .256 .254 10.516 .512 .507 15. 774 .768 .760 21.032 .024 .014 26.290 .280 .268 Latitude interval. Meridi- onal distance. 30 .249 .499 .748 20.998 .247 f Inches. I 6.061 35 371 6.245 .243 10.490 .485 15. 735 .728 20.980 .971 26.225 .213 2 3 12. 122 18.183 40 .240 .480 .721 .961 .202 4 24. 245 45 .236 .472 .708 .944 .180 5 30.305 50 5.232 10.463 15. 695 20.927 26.159 521 .229 .459 .688 .918 .147 55 .227 .454 .681 .908 .135 60 .222 .445 .667 .890 .112 88 GEOGRAPHIC TABLES AND FORMULAS. TABLE 10. Coordinates for the projection of maps (scale i^oo) Continued. Latitude of parallel. Abscissas of developed parallel. Ordinatesof devel- oped parallel. Longitude interval. Longi- 1'. 2'. 3'. 4'. 5'. tude Inch. interval. o / Inches. Inches. Inches. Inches. Inches. f 31 00 5. 222 10. 445 15. 667 20 890 26. 112 1 .000 05 .218 .435 .654 .872 .089 2 .002 07^ .216 .432 .647 .863 .079 3 .003 10 .213 .426 .640 .853 .066 4 .006 15 .209 .417 .626 .834 .043 5 .010 20 22i 25 5.204 .202 .200 10. 408 .404 .400 15. 613 .605 .598 20. 817 .807 .798 26. 021 .009 25.998 Latitude interval. Meridi- onal distance. 30 .195 .390 .585 .780 .975 t Inches. 1 6.062 85 40 45 5.190 .188 .186 .181 10.381 .376 .372 .362 15. 571 .565 .557 .544 20.762 .753 .743 .725 25. 952 .941 .929 .906 2 3 4 5 12. 124 18. 187 24.249 30. 311 50 55* 60 5.177 .174 .172 .167 10.353 .348 .344 .334 15.530 .523 .516 .502 20.706 .697 .688 .669 25. 883 .871 .860 .836 Longi- tude interval. Inch. 32 00 5.167 10.334 15.502 20. 669 25. 836 1 .000 05 .162 .325 .487 .650 .812 2 .002 (yji .160 .320 .480 .640 .800 3 .003 10 .158 .315 .473 .630 .788 4 .007 15 .153 .305 .458 .611 .764 5 .010 20 25* 5.148 .146 .143 10.296 .291 .286 15.444 .437 .430 20. 592 .582 .573 25.740 .728 .716 Latitude interval. Meridi- onal distance. 30 .139 .277 .416 .554 .693 f Inches. 1 6.063 35 5.134 .131 10.268 .263 15. 401 .394 20. 535 .526 25. 669 .659 2 3 12.127 18.190 40* 45 .129 .124 .258 .249 .387 .373 .516 .498 .645 .622 4 5 24.254 30.317 5 i 5.120 10. 239 15. 359 20.478 25.598 55* .117 .115 .234 .229 .352 .344 .469 .459 .586 .574 Longi- tude Inch. 60 .110 .220 .330 .440 .550 interval. 33 00 5.110 10.220 15.330 20. 440 25.550 1 .000 05 .105 .210 .316 .421 .526 2 .002 07- 1 - .103 .206 .308 .411 .514 3 .003 10 .100 .201 .301 .402 .502 4 .007 15 .096 .191 .287 .382 .478 5 .010 2 i 5.091 .088 10. 182 .176 15. 272 .264 20. 363 .352 25.454 .440 Latitude interval. Meridi- onal distance. 25* .086 .171 .257 .342 .428 30 .081 .162 .242 .323 .404 j Inches. 1 6.065 35 40* 45 5.076 .074 * .071 .066 10. 152 .147 .143 .132 15.228 .220 .213 .199 20. 304 .294 .285 .265 25.380 .368 .356 .331 2 3 4 5 12. 129 18. 193 24.258 30.322 50 5.061 10. 123 15.184 20.246 25.307 52i .059 .118 .177 .236 .295 55 .056 .113 .169 .226 .282 60 .052 .103 .156 . .206 .258 GEOGRAPHIC TABLES AND FORMULAS. 89 TABLE 10. Coordinates for the projection of maps (scale Tuihro) Continued. Abscissas of developed parallel. Ordinates of devel- Latitude of Longitude interval. oped parallel. parallel. Longi- 1'. 2'. 3'. 4'. 5'. tude Inch. . interval. o / Inches. Inches. Inches. Inches. Inches. t 34 00 5.052 10.103 15.155 20.206 25.258 1 .000 05 .047 .093 .140 .186 .233 2 .002 07i .044 .089 .132 .176 .220 3 .003 10 .042 .083 .125 .166 .208 4 .007 15 .037 .073 .110 .146 .183 5 .010 20 22* 25 5.032 .029 .027 10.063 .058 .053 15.095 .087 .080 20.126 .116 .106 25.158 .145 .133 Latitude interval. Meridi- onal distance. 30 .022 .043 .065 .086 .108 / Inches. 1 6.065 35 g* 5.017 .014 .012 10.033 .028 .023 15.050 .042 .035 20.066 .056 .046 25.083 .070 .058 2 3 4 12. 130 18. 198 24. 262 45 .007 .013 .020 .026 .033 5 30. 328 50 5.002 10.003 15.005 20.006 ' 25.008 52i 55 60 4.999 .997 .992 9.998 .993 .983 14.997 .990 .976 19.996 .986 .966 24. 995 .983 .958 Longi- tude interval. Inch. 35 00 4.992 9.983 14. 975 19.966 24.958 1 .000 05 .987 .973 .960 .947 .933 2 .002 07* .984 .968 .952 .936 .920 3 - .003 10 .982 .963 .945 .926 .908 4 .007 15 .976 .953 .929 .906 .882 5 .010 20 4.971 .969 9.942 .937 14. 913 .906 19.885 .874 24.856 .843 Latitude interval. Meridi- onal distance. 25* .966 .932 .898 .864 .830 30 .961 .922 .883 .844 .805 / Inches. 1 6.067 35 4.956 9.912 14.868 19. 824 24. 780 2 3 12. 133 18. 200 37i 40 45 .953 .951 .946 .907 .902 .891 .860 .853 .837 .814 .805 .783 .767 .754 .728 4 5 24! 266 30.333 * 50 4.940 9.881 14. 821 19. 762 24. 702 65* 60 .938 .935 .930 .876 .871 .861 .814 .806 .791 .752 .742 .722 .690 .677 .652 Longi- tude interval. Inch. 36 00 4.930 9.861 14. 791 19. 722 24. 652 ' 1 .000 05 .925 .850 .776 .701 .626 2 .002 .923 .845 .768 .690 .613 3 .005 10 .920 .840 .760 .680 .600 4 .007 15 .915 .830 .745 .660 .574 5 .010 20 22i 4.910 .907 9.819 .814 14. 719 .721 19. 638 .628 24.548 .535 Latitude interval. Meridi- onal distance. 26 .904 .808 .712 .617 .521 30 .899 .798 .697 .596 .495 / Inches. 1 6.067 35 37i 40 4.894 .891 .888 9.787 .782 .777 14.681 .673 .665 19. 574 .664 .554 24. 468 .465 .442 2 3 4 K " 12. 135 18. 202 24. 269 on qqfi 45 .883 .766 .649 .532 .415 oU. OOO 50 4.878 9". 756 14.633 19. 512 24.389 52| .875 .750 .626 .501 .376 55 .873 .745 .618 .490 .363 60 .868 .735 .603 .470 .338 90 GEOGRAPHIC TABLES AND FORMULAS. TABLE 10. Coordinates for the projection of maps (scale j^y^) Continued. Abscissas of developed parallel. Ordinates of devel- Latitude of oped parallel. Longitude interval. parallel. r. 2'. 3'. 4'. 5'. Longi- tude Inch. interval. o / Inches. Inches. Inches. Inches. Inches. , 37 00 4.868 9.735 14.603 19. 470 24.338 1 .000 06 .862 .724 .586 ;448 .310 2 .002 .859 .718 .578 .437 .296 3 .005 10* .856 .713 .569 .426 .282 4 .007 15 .851 .702 .553 .404 .255 5 .010 20 4.846 .843 9.691 .686 14.537 .529 19.382 .372 24. 228 .215 Latitude interval. Meridi- onal distance. 25 S .840 .680 .521 .362 .202 30 .835 .670 .505 .340 .175 / Inches. 1 6.068 35 37i 40 4.830 .827 .824 9.659 .654 .649 14. 489 .481 .473 19. 318 .308 .298 24. 148 .135 .122 2 3 4 12. 136 18. 205 24. 273 45 .819 .638 .457 .276 .095 50 4.814 9.627 ' 14.441 19.254 24.068 55 60 .811 .808 .802 .622 .616 .605 .432 .424 .407 .243 .232 .209 .054 .040 .012 Longi- tude interval. Inch. 38 00 4.802 9.605 14. 407 19. 209 24. 012 1 .000 05 .797 .594 .391 .188 23. 985 2 .002 07* .794 .589 .383 .178 .972 3 .005 10 .792 .584 .375 .167 .959 4 .007 15 .786 .673 .359 .146 .932 5 .010 20 4.781 .778 9.562 .556 14. 343 .335 19. 124 .113 23.905 .891 Latitude interval. Meridi- onal dis- tance. 25" .776 .551 .326 .102 .878 30 .770 .640 .310 .080 .850 t Inches. 1 6.069 35 40* 45 4.764 .762 .759 .754 9.529 .524 .518 .507 14. 293 .286 .277 .261 19.058 .047 .036 .015 23. 822 .809 .795 .768 2 3 4 5 12.138 18. 207 24. 277 30. 345 50 4.748 9.496 14. 244 18. 993 23.740 52* 55 60 .745 .742 .737 .490 .485 .474 ,236 .227 .211 .981 .970 .948 .726 .712 .685 Longi- tude interval. Inch. 39 00 4.737 9.474 14.211 18.948 23.685 1 .000 05 .731 .463 .194 .926 .657 2 .002 07i .728 .457 .185 .914 .642 3 .005 10 .726 .451 .177 .902 .628 4 .007 15 .720 .440 .160 .880 .600 5 .010 20 1 4.714 ' .712 9.429 .423 14. 143 .135 18. 858 .846 23. 572 .558 Latitude interval. Meridi- onal distance. 25* .709 .417 .126 .835 .544 30 .703 .407 .119 .813 .516 / Inches. 1 6.070 35 37i 40 45 4.698 .695 .692 .686 9.395 .389 .384 .373 14.093 .084 .076 .059 18.790 .779 .768 .746 23.488 .474 .460 .432 2 3 4 5 12. 140 18. 210 24.281 30.351 50 j 4.681 9.362 14.042 18. 723 23.404 .678 .356 .034 .712 .390 55 S .675 .350 .025 .700 .375 60 .669 .339 .008 .678 .347 GEOGRAPHIC TABLES AND FORMULAS. 91 TABLE 10. Coordinates for the projection of maps (scale TSTT^) Continued. Latitude of parallel. Abscissas of developed parallel. Ordinates of devel- oped parallel. Longitude interval. If. 2'. 3'. 4'. 5'. Longi- tude interval. Inch. o / 40 00 05 07i 10 15 20 22i 25 30 35 37i 40 45 50 52* 55 60 41 00 05 07| 10 15 20 22i 25 30 35 3? 40 45 50 52 55 42 00 05 07* 10 15 20 22 25 30 35 37i 40 45 50 52J 55 60 Inches. 4.669 .664 .661 .658 .652 4.647 .644 .641 .635 4.630 .627 .624 .618 4.612 .609 .606 .600 4.600 .595 .592 .589 .583 4.577 .574 .571 .566 4.560 .557 .554 .548 4.542 .539 .536 4.530 .524 .521 .518 .513 4.507 .504 .501 .495 4.489 .486 .483 .477 4.471 .468 .465 .459 Inches. 9.339 .328 .322 .316 .305 9.293 .288 .282 .271 9.259 .253 .248 .236 9.224 .219 .213 .201 9.201 .189 .183 .178 .166 9.154 .149 .143 .131 9.119 .114 .108 .0% 9.084. .078 .072 9.060 .049 .043 .037 .025 9.013 .007 .002 .990 8.978 .972 .966 .954 8.942 .936 .930 .918 Inches. 14.008 13. 991 .983 .975 .957 . 13.940 .931 .923 .906 13.889 .880 .871 .854 13.837 .828 .819 .801 13.801 .784 .775 .766 .749 13 732 .723 .714 .697 13. 679 ,670 ,661 .644 13. 626 .617 .608 13. 591 .572 ,564 .555 .537 13. 520 .511 .502 .484 13. 467 .458 .449 .431 13.413 .404 .395 .377 Inches. 18. 678 .655 .644 .632 .610 18.586 .575 .564 .542 18. 518 .507 .495 .472 18.449 .438 .426 .402 18.402 .378 .368 .355 .332 18.309 .298 .286 ,262 18. 239 .227 .215 .192 18.168 .156 .145 18. 122 .098 .086 .073 .050 18. 027 .014 .003 17. 979 17.956 .944 .932 .908 17.884 .872 .860 .836 Inches, 23. 347 .319 .305 .291 .262 23.233 .219 .205 .177 23. 148 .134 .119 .090 23.061 .047 .032 .002 23.002 22.973 .958 .944 .915 22.886 .872 .857 .828 22.798 .784 .769 .740 22.710 .695 .681 22.652 .622 .607 .592 .563 22.533 .518 .504 .474 22.445 .430 .415 .385 22.355 .340 .325 .295 1 2 3 4 5 .000 .002 ,005 .007 .010 Latitude interval. Meridi- onal distance. 1 2 3 4 5 Inches. 6.072 12. 143 18.215 24. 286 30.358 Longi- tude interval. Inch. t 1 2 3 4 5 .000 .002 .005 .007 .010 Latitude interval. Meridi- onal distance. / 1 2 3 4 5 Inches. 6.072 12. 145 18. 218 24.290 30. 362 Longi- tude interval. Inch. t 1 2 3 4 5 .000 .002 .005 .007 .010 Latitude interval. Meridi- onal distance. 1 2 3 4 5 Inches. 6.073 12. 148 18.220 24.294 30.367 92 GEOGRAPHIC TABLES AND FORMULAS. TABLE 10. Coordinates for the. projection of maps (scale y^iy^oO Continued Latitude of parallel. Abscissas of developed parallel. Ordinates of devel- oped parallel. Longitude interval. 1'. 2'. 3'. 4'. 5'. Longi- tude interval. Inch. / 43 00 05 07 10 15 20 22 25 30 35 37| 40 45 50 52i 55 60 44 00 05 07| 10 15 20 22i 25 30 35 37i 40 45 50 52i 55 60 45 00 05 07* 10 15 20 22i 25 30 35 37i 40 45 50 62| 55 60 Inches. 4.459 .453 .450 .447 .441 4.434 .431 .428 .422 4.416 .413 .410 .404 4.398 .395 .392 .386 4.386 .380 .376 .373 .367 4.361 .358 ,355 .349 4.342 .339 .336 .330 4.324 .321 .318 .312 4.312 .305 .302 .299 .293 4.287 .283 .280 .274 4.268 .264 .261 .255 4.249 .246 .242 .236 Inches. 8.918 .906 .899 .894 .882 8.869 .863 .856 .844 8.832 .826 .820 1808 8.796 .789 .784 .772 8.772 .759 .753 .747 .734 8.722 .716 .709 .697 8.685 .678 .672 .660 8.648 .642 .635 .623 8.623 .610 .604 .598 .586 8.573 .567 .560 .548 8.535 .529 .522 .510 8.497 .491 .485 .472 Inches. 13.377 .359 .349 .340 .322 13.303 .294 .285 .266 13.248 .239 .230 .212 13. 194 .184" .175 .157 13. 157 .139 .129 .120 .102 13. 083 .074 .064 .046 13. 027 .018 .009 12.990 12.971 .963 .953 .935 12.935 .916 .906 .897 .878 12. 860 .849 .841 .822 12. 803 .793 .784 .765 12.746 .737 .727 .707 Inches. 17.836 .812 .799 .787 .762 17.738 .726 .713 .688 17.664 .652 .640 .616 17. 592 .579 .567 .543 17.543 .518 .506 .494 .469 17. 444 .431 .419 .394 17. 370 .357 .345 .320 17. 295 .283 .270 .246 17.246 .221 .208 .196 .171 17.146 .134 .121 .096 17.070 .058 .045 .020 16.995 .982 .970 .944 Inches'. 22.295 .265 .249 .234 .203 22. 172 .157 .141 .110 22. 080 .065 .050 .020 21.990 .974 .959 .929 21. 929 .898 .882 .867 .836 21.805 .789 .774 .743 21. 712 .696 .681 .650 21.619 .604 .588 .558 21.558 .527 .511 .495 .464 21.433 .417 .401 .370 21. 338 .322 .306 .275 21.243 .228 .212 .180 r I 2 3 4 5 .000 .002 .005 .007 .010 Latitude interval. Meridi- onal distance. f 1 2 3 4 5 Inches. 6.075 12. 149 18. 223 24.298 30. 372 Longi- tude interval. Inch. / 1 2 3 4 5 .000 .002 .005 .007 .010 Latitude interval. Meridi- onal distance. / 1 2 3 4 5 Inches. 6.076 12. 152 18.228 24.304 30.380 Longi- tude interval. Inch: t 1 2 3 4 5 .000 .002 .005 .007 .010 Latitude interval. Meridi- onal distance. / 1 2 3 4 5 Inches. 6.077 12.154 18.231 24.308 30.385 GEOGRAPHIC TABLES AND FORMULAS. 93 TABLE 10. Coordinates for the projection of maps (scale ystUff) Continued. Latitude of parallel. Abscissas of developed parallel. Ordinates of devel- oped parallel. Longitude interval. 1'. 2'. 3'. 4'. 5'. Longi- tude interval. Inch. O ' 46 00 05 07i 10 15 20 22* 25 30 35 37i 40 45 50 52* 55 60 47 00 05 07* 10 15 20 22* 25 30 35 S 1 45 50 52* 55 60 48 00 05 07* 10 15 20 224 25 30 35 37* 40 45 50 52i 55 60 Inches. 4.236 .229 .226 .223 .216 4.210 .207 .204 .198 4.191 .188 .184 .178 4.172 .168 .165 .159 4.159 .152 .149 .146 .139 4.133 .130 .126 .120 4.113 .110 .106 .100 4.094 .090 .089 .080 4.080 .074 .071 .067 .061 4.054 .051 .048 .041 4.034 .031 .028 .021 4.014 .011 .008 .001 Inches. 8.472 .459 .452 .446 .433 8.420 .414 .408 .395 8.382 .376 .369 .356 8.343 .337 .330 .318 8.318 .305 .299 .292 .279 8.266 .259 .252 .239 8.226 .220 .213 .200 8.187 .180 .174 .161 8.160 .148 .142 .135 . . 122 8.108 .102 .095 .082 8.069 .062 .055 .042 8.029 .022 .016 .002 Inches. 12. 707 .688 .679 .669 .649 12.630 .621 .611 .593 12.573 .564 .553 .534 12. 515 .505 .4% .476 12. 476 .457 .448 .438 .418 12. 398 .389 .378 .359 12.339 .329 .319 .300 12.281 .271 .261 .241 12.241 .222 .212 .202 .182 12. 162 .153 .143 .123 12. 103 .093 .083 .063 12.043 .034 .024 .003 Inches. 16.944 .918 .905 .892 .867 16.840 .828 .815 .790 16.764 .752 .738 .712 16.687 .674 .661 .635 16.635 .610 .597 .584 .558 16.531 .518 .505 .478 16. 452 .439 -.426 .400 16. 375 .361 .348 .322 16.321 .296 .284 .270 .244 16.217 .204 .190 .164 16. 138 .124 .110 .084 16. 058 .045 .031 .004 Inches. 21. 179 .147 .131 .115 .082 21.051 .035 .019 20.988 20.955 .939 .922 .890 20.858 .842 .826 .794 20. 794 .762 .746 .730 .697 20.664 .648 .631 .598 20.565 .549 .532 .500 20.468 .451 .435 .402 20. 401 .370 .354 .337 .304 20. 271 .255 .238 .205 20. 172 .155 .138 .105 20. 072 .056 .039 .006 1 2 3 4 5 .000 .002 .005 .007 .010 Latitude interval. Meridi- onal distance. 1 2 3 4 5 Inches. 6.078 12. 157 18. 235 24. 313 30.391 ^ Longi- tude interval. Inch. 1 2 3 4 5 .000 .002 .005 .007 .010 Latitude interval. Meridi- onal distance. 1 2 3 4 5 Inches. 6.078 12. 157 18. 235 24. 315 30.392 Longi- tude interval. Inch. 1 2 3 4 5 .000 .002 .005 .007 .010 Latitude interval. Meridi- onal distance. 1 2 3 4 5 Inches. 6.080 12.160 18. 240 24. 320 30.400 94 GEOGRAPHIC TABLES AND FORMULAS. TABLE 10. Coordinates for the projection of maps (scale T^O) Continued. Abscissas of developed parallel. Ordinates of devel- Latitude of Longitude interval. oped parallel. parallel. Longi- 1'. 2'. 3'. 4'. 5'. tude Inch. interval. / Inches. Inches. Inches. Inches. Inches. , 49 00 4.001 8.002 12. 003 16.004 20.006 1 .000 05 3.995 7.989 11. 984 15. 978 19. 973 2 .002 07| .991 .982 .974 .965 .956 3 .005 10 .988 .976 .964 .952 .939 4 .007 15 .981 .962 .943 .924 .905 5 .010 20 22i 25 3.974 .971 .968 7.949 .942 .936 11.923 .914 .904 15. 898 .885 .872 19. 872 .856 .840 Latitude interval. Meridi- onal distance. 30 .961 .922 .883 .844 .805 ' Inches. \ 6.081 35 3.954 7.908 11.863 15.817 19. 771 2 12 162 37i 40 45 .951 .948 .941 .902 .895 .882 .853 .843 .823 .804 .790 .764 .755 .738 .705 3 4 5 18! 243 24. 324 30.405 50 3.934 7.869 11.803 15.738 19. 672 52i .931 .862 .793 .724 .655 55 .928 .855 .783 .710 .638 60 .921 .842 .762 .683 .604 GEOGRAPHIC TABLES AND FOEMULAS. 95 TABLE 11. Areas of quadrilaterals of earth's surface of 1 extent in latitude and longitude. From Smithsonian Geographical Tables.] Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. / o / / 00 30 1 00 1 30 4, 752. 33 4, 752. 16 4, 751. 63 4, 750. 75 22 00 22 30 23 00 23 30 4, 414. 67 4, 399. 30 4, 383. 60 4, 367. 57 44 00 44 30 45 00 45 30 3,440.98 3, 412. 26 3, 383. 27 3,354.01 2 00 2 30 3 00 3 30 4, 749. 52 4,747.93 4,746.00 4, 743. 71 24 00 24 30 25 00 25 30 4, 351. 21 4, 334. 52 4, 317. 51 4, 300. 17 46 00 46 30 47 00 47 30 3, 324. 49 3, 294. 71 3,264.68 3, 234. 39 4 00 4 30 5 00 5 30 4, 741. 07 4,738.08 4, 734. 74 4,731.04 26 00 26 30 27 00 27 30 4, 282. 50 4, 264. 51 4, 246. 20 4, 227. 56 48 00 48 30 49 00 49 30 3, 203. 84 3, 173. 04 3,141.99 3, 110. 69 6 00 6 30 7 00 7 30 4, 727. 00 4, 722. 61 4, 717. 86 4, 712. 76 28 00 28 30 29 00 29 30 4, 208. 61 4, 189. 33 4, 169. 74 4, 149. 83 50 00 50 30 51 00 51 30 3, 079. 15 3,047.37 3, 015. 34 2, 983. 08 8 00 8 30 9 00 9 30 4, 707. 32 4, 701. 52 4, 695. 38 4, 688. 89 30 00 30 30 31 00 31 30 4, 129. 60 4, 109. 06 4, 088. 21 4, 067. 05 52 00 52 30 53 00 53 30 2, 950. 58 2, 917. 85 2, 884. 88 2, 851. 68 10 00 10 30 11 00 11 30 4, 682. 05 4, 674. 86 4, 667. 32 4, 659. 43 32 00 32 30 33 00 33 30 4, 045. 57 4, 023. 79 4, 001. 69 3, 979. 30 54 00 54 30 55 00 55 30 2, 818. 27 2, 784. 62 2, 750. 76 2, 716. 67 12 00 12 30 13 00 13 30 4, 651. 20 4, 642. 63 4, 633. 71 4,624.44 34 00 34 30 35 00 35 30 3, 956. 59 3, 933. 59 3, 910. 28 3, 886. 67 56 00 56 30 57 00 57 30 2.682.37 2, 647. 85 2, 613. 13 2, 578. 19 14 00 14 30 15 00 15 30 4, 614. 82 4, 604. 87 4, 594. 57 4,583.92 36 00 36 30 37 00 37 30 3, 862. 76 3, 838. 56 3,814.06 3, 789. 26 58 00 58 30 59 00 59 30 2, 543. 05 2, 507. 70 2, 472. 16 2, 436. 42 16 00 16 30 17 00 17 30 4, 572. 94 4, 561. 61 4, 549. 94 4, 537. 93 38 00 38 30 39 00 39 30 3, 764. 18 3, 738. 80 3, 713. 14 3, 687. 18 60 00 60 30 61 00 61 30 2, 400. 48 2, 364. 34 2,328.02 2, 291. 51 18 00 18 30 19 00 19 30 4, 525. 59 4, 512. 90 4, 499. 87 4, 486. 51 40 00 40 30 41 00 41 30 3, 660. 95 3, 634. 42 3, 607. 62 3, 580. 54 62 00 62 30 63 00 63 30 2, 254. 82 2, 217. 94 2, 180. 89 2, 143. 66 20 00 20 30 21 00 21 30 4,472.81 4, 458. 78 4, 444. 41 4,429.71 42 00 42 30 43 00 43 30 3, 553. 17 3, 525. 54 3, 497. 62 3, 469. 44 64 00 64 30 65 00 65 30 2, 106. 26 2, 068. 68 2, 030. 94 1, 993. 04 96 GEOGRAPHIC TABLES AND FORMULAS. TABLE 11. Areas of quadrilaterals of earth's surface of 1 extent in latitude and longitude Continued. [From Smithsonian Geographical Tables.] Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. o / / o / 66 00 66 30 67 00 67 30 1, 954. 97 1, 916. 75 1, 878. 37 1, 839. 84 76 00 76 30 77 00 77 30 1, 164. 49 1, 123. 75 1, 082. 91 1, 041. 99 86 00 86 30 87 00 87 30 336. 02 294.08 252. 11 210. 12 68 00 68 30 69 00 69 30 1, 801. 16 1,762.33 1, 723. 36 1, 684. 24 78 00 78 30 79 00 79 30 1, 000. 99 959.90 918. 73 877.49 88 00 88 30 89 00 89 30 168. 12 126. 10 84.07 42.04 70 00 70 30 71 00 ' 71 30 1, 645. 00 1, 605. 62 1, 566. 10 1,526.46 80 00 80 30 81 00 81 30 836. 18 794. 79 753. 34 711.83 90 00 00.00 72 00 72 30 73 00 73 30 1, 486. 70 1, 446. 81 1, 406. 81 1, 366. 69 82 00 82 30 83 00 83 30 670. 27 628. 64 586. 97 545. 24 74 00 74 30 75 00 75 30 1,326.46 1, 286. 12 1, 245. 68 1, 205. 13 84 00 84 30 85 00 85 30 503. 47 461. 66 419. 81 377.93 GEOGRAPHIC TABLES AND FORMULAS, 97 TABLE 12. Areas of quadrilaterals of earth's surface of 30 f extent in latitude and longitude. [From Smithsonian Geographical Tables. | Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. / o / / 00 15 30 45 1, 188. 10 1,188.08 1, 188. 05 1,188.00 11 00 11 15 11 30 11 45 1, 166. 84 1, 165. 86 1, 164. 86 1, 163. 85 22 00 22 15 22 30 22 45 1, 103. 68 1, 101. 77 1, 099. 84 1,097.88 1 00 1 15 1 30 1 45 1,187.92 1, 187. 82 1, 187. 70 1J87.56 12 00 12 15 12 30 12 45 1, 162. 81 1, 161. 75 1, 160. 67 1, 159. 56 23 00 23 15 23 30 23 45 1, 095. 91 1,093.92 1,091.90 1,089.87 2 00 2 15 2 30 2 45 1, 187. 39 1, 187. 20 1, 186. 99 1,J86.76 13 00 13 15 13 30 ! 13 45 ,158.44 , 157. 29 , 156. 12 , 154. 93 24 00 24 15 24 30 24 45 1, 087. 81 1,085.74 1, 083. 64 1, 081. 52 3 00 3 15 3 30 3 45 1, 186. 51 1, 186. 24 1, 185. 95 1, 185. 62 14 00 14 15 14 30 14 45 , 153. 72 , 152. 48 , 151. 23 , 149. 95 25 00 25 15 25 30 25 45 1, 079. 39 1, 077. 23 1, 075. 05 1,072.85 4 00 4 15 4 30 4 45 1, 185. 28 1, 184. 92 , 184. 53 , 184. 13 15 00 15 15 15 30 15 45 , 148. 65 , 147. 33 , 145. 99 , 144. 63 26 00 26 15 26 30 26 45 1, 070. 64 1, 068. 40 1, 066. 14 1, 063. 86 5 00 5 15 5 30 5 45 , 183. 70 , 183. 24 , 182. 77 , 182. 28 16 00 16 15 16 30 16 45 , 143. 25 , 141. 84 , 140. 41 , 138. 96 27 00 27 15 27 30 27 45 1, 061. 56 1, 059. 24 1, 056. 90 1, 054. 54 6 00 6 15 6 30 6 45 1, 181. 76 1, 181. 22 1, 180. 66 1, 180. 08 17 00 17 15 17 30 17 45 , 137. 60 , 136. 00 1,104.49 1, 132. 96 28 00 28 15 28 30 28 45 1, 052. 16 1, 049. 76 1,047.34 1,044.90 7 00 7 15 7 30 7 45 1, 179. 48 1, 178. 85 1, 178. 20 1, 177. 53 18 00 18 15 18 30 18 45 1,131.41 1, 129. 83 1, 128. 24 1, 126. 62 29 00 29 15 29 30 29 45 1, 042. 44 1, 039. 97 1, 037. 47 1,034.95 8 00 8 15 8 30 8 45 1, 176. 84 1, 176. 13 1, 175. 39 1, 174. 63 19 00 19 15 19 30 19 45 1, 124. 98 1, 123. 32 1,121.64 1, 119. 93 30 00 30 15 30 30 30 45 1, 032. 41 1,029.85 1,027.27 1,024.68 9 00 9 15 9 30 9 45 1, 173. 86 1, 173. 06 1, 172. 23 1, 171. 39 20 00 20 15 20 30 20 45 1,118.21 1,116.47 1, 114. 71 1, 112. 92 31 00 31 15 31 30 31 45 1,022.06 1,019.43 1,016.77 1, 014. 10 10 00 10 15 10 30 10 45 1,170.52 1, 169. 63 1, 168. 73 1, 167. 80 21 00 21 15 21 30 21 45 1, 111. 11 1, 109. 28 1,107.44 1,105.57 32 00 32 15 32 30 32 45 1,011.40 1, 008. 69 1, 005. 96 1,003.20 40001 08 7 98 GEOGRAPHIC TABLES AND FORMULAS. TABLE 12. Areas of quadrilaterals of earth's surface of 30' extent in latitude and longi- tude Continued. [From Smithsonian Geographical Tables.] Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. o / / / 33 00 1,000.43 44 00 860. 25 55 00 687. 70 33 15 997.64 44 15 856. 67 55 15 683. 44 33 30 994. 83 44 30 853. 07 55 30 679. 17 33 45 992.00 44 45 849. 46 55 45 674. 89 34 00 989. 16 45 00 845. 82 56 00 670. 60 34 15 986. 29 45 15 842. 18 56 15 666. 29 34 30 983. 41 45 30 838. 51 56 30 661. 97 34 45 980. 50 45 45 834. 83 56 45 657. 64 35 00 977. 58 46 00 831. 13 57 00 653. 29 35 15 974.64 46 15 827. 42 57 15 648. 93 35 30 971. 68 46 .30 823. 68 57 30 644. 55 35 45 968. 70 46 45 819. 94 57 45 640. 17 36 00 965. 70 47 00 816. 18 58 00 635. 77 36 15 962. 68 47 15 812.40 58 15 631.36 36 30 959. 65 47 30 808. 60 58 30 626. 93 36 45 956. 60 . 47 45 804. 79 58 45 622. 49 37 00 953. 52 48 00 800. 97 59 00 ! 618.05 37 15 950. 43 48 15 797. 13 59 15 ! 613.59 37 30 947. 32 48 30 793. 27 59 30 j 609.11 37 45 944.21 48 45 789. 39 59 45 604. 62 38 00 941. 05 49 00 785. 50 60 00 600. 13 38 15 937. 88 49 15 781. 60 60 15 595. 62 38 30 934. 71 49 30 777. 68 60 30 591. 09 38 45 931. 51 49 45 773. 74 60 45 586. 56 39 00 928. 29 50 00 769. 79 61 00 582. 01 39 15 925. 06 50 15 765. 83 61 15 577. 45 39 30 921. 80 50 30 761. 85 61 30 i 572.88 39 .45 918. 53 50 45 757. 85 61 45 ; 568.30 i I 40 00 915. 25 51 00 753.84 62 00 i 563.71 40 15 911. 94 51 15 749. 82 62 15 559. 11 40 30 908. 61 51 30 745. 78 62 30 554. 49 40 45 905. 27 51 45 741. 72 62 45 549. 86 41 00 901. 91 52 00 737. 65 63 00 545. 23 41 15 898. 54 52 15 733. 57 63 15 540. 58 41 30 895. 14 52 30 729. 47 63 30 535. 92 41 45 891. 73 52 45 725. 36 63 45 531. 25 42 00 888. 30 53 00 721. 23 64 00 526.57 42 15 884. 85 53 15 717. 08 64 15 521. 88 42 30 881. 39 53 30 712. 93 64 30 517. 17 42 45 877. 91 53 45 708. 76 64 45 512. 46 43 00 874. 41 54 00 704. 57 65 00 507. 74 43 15 870. 90 54 15 700. 38 65 15 503. 01 43 30 867. 37 54 30 696. 16 65 30 498. 26 43 45 863. 82 54 45 691. 94 65 45 493. 51 GEOGRAPHIC TABLES AND FORMULAS. 99 TABLE 12. Areas of quadrilaterals of earth's surface of SO' extent in latitude and longi- tude Continued. [From Smithsonian Geographical Tables.] Middle latitude of quadrilat- eral. Area in square miles. Middle latitude of quadrilat- eral. Area in square miles. Middle latitude of quadrilat- eral. Area in square miles. / 66 00 66 15 66 30 66 45 488. 75 483. 97 479. 19 474. 40 / 74 00 74 15 74 30 74 45 331. 62 326. 58 321. 53 316. 48 / 82 00 82 15 82 30 82 45 167. 57 162. 37 157. 16 151. 95 67 00 67 15 67 30 67 '45 469. 60 464.78 459. 96 455. 13 75 00 75 15 *75 30 75 45 311. 42 306. 36 301. 28 296. 21 83 00 83 15 83 30 83 45 146. 74 141. 53 136. 31 131. 09 68 00 68 15 68 30 68 45 450. 29 445.45 440. 59 435.72 76 00 76 15 76 30 76 45 291. 12 286.04 280. 94 275.84 84 00 84 15 84 30 84 45 125. 87 120.64 115. 42 110. 18 69 00 69 15 69 30 69 45 430. 84 425. 96 421.06 416. 16 77 00 77 15 77 30 77 45 270. 73 265.62 260. 50 255. 38 85 00 85 15 85 30 85 45 104.95 99.72 94.48 89.25 70 00 70 15 70 30 70 45 411. 25 406.34 401. 41 396. 47 78 00 78 15 78 30 78 45 250. 25 245. 12 239. 98 234. 83 86 00 86 15 86 30 86 45 84.01 78.76 73.52 68.27 71 00 71 15 71 30 71 45 391. 53 386.58 381.62 376.65 79 00 79 15 79 30 79 45 229.68 224. 53 219. 37 214. 21 87 00 87 15 87 30 87 45 63.03 57. 78 52.53 47.28 72 00 72 15 72 30 72 45 371. 68 366.70 361. 71 356. 71 80 00 80 15 80 30 80. 45 209. 05 203. 88 198. 70 193. 52 88 00 88 15 88 30 88 45 42.03 36.78 31.53 26.27 73 00 73 15 73 30 73 45 351. 71 346.69 * 341.68 336. 65 81 00 81 15 81 30 81 45 188. 34 183. 15 177. 96 172. 77 89 00 89 15 89 30 89 45 21.02 15.76 10.51 5.26 100 GEOGRAPHIC TABLES AND FORMULAS. TABLE 13. Areas of quadrilaterals of earth's surface of 15' extent in latitude and longitude. [From Smithsonian Geographical Tables.] Middle latitude of quadrilateral. Area in square miles. Middle latitude of quadrilateral. Area in square miles. Middle latitude of quadrilateral. Area in square miles. / // 07 30 15 00 22 30 30 00 297. 02 297. 02 297. 02 297. 01 / // 5 37 30 5 45 00 5 52 30 6 00 00 295. 63 295. 57 295. 51 295. 44 / // 11 07 30 11 15 00 11 22 30 11 30 00 291. 59 291. 47 291. 34 291. 22 37 30 45 00 52 30 1 00 00 297.01 297.00 296. 99 296. 98 6 07 30 6 15 00 6 22 30 6 30 00 295. 37 295. 31 295. 24 295.17 11 37 30 11 45 00 11 52 30 12 00 00 291.09 290. 96 290. 83 290. 70 1 07 30 1 15 00 1 22 30 1 30 00 296.97 296. 96 296. 94 296. 93 6 37 30 6 45 00 6 52 30 7 00 00 295. 09 295. 02 294. 95 294. 87 12 07 30 12 15 00 12 22 30 12 30 00 290. 57 290. 44 290. 30 290. 17 1 37 30 1 45 00 1 52 30 2 00 00 296. 91 296. 89 296. 87 296. 85 7 07 30 7 15 00 7 22 30 7 30 00 294. 79 294. 71 294. 63 294. 55 12 37 30 12 45 00 12 52 30 13 00 00 290. 03 289. 89 289. 75 289. 61 2 07 30 2 15 00 2 22 30 2 30 00 296. 82 296. 80 296. 77 296. 75 7 37 30 7 45 00 7 52 30 8 00 00 294. 47 294. 39 294. 30 294. 21 13 07 30 13 15 00 13 22 30 13 30 00 289. 47 289. 33 289. 18 289. 03 2 37 30 2 45 00 2 52 30 3 00 00 296. 72 296. 69 296. 66 296. 63 8 07 30 8 15 00 8 22 30 8 30 00 294. 12 294. 03 293. 94 293. 85 13 37 30 13 45 00 13 52 30 14 00 00 288. 88 288. 73 288. 58 288. 43 3 07 30 3 15 00 3 22 30 3 30 00 296. 60 296. 56 296. 53 296. 49 8 37 30 8 45 00 8 52 30 9 00 00 293. 75 293. 66 293. 56 293. 47 14 07 30 14 15 00 14 22 30 14 30 00 288. 28 288. 12 287. 96 287. 81 3 37 30 3 45 00 3 52 30 4 00 00 296. 45 296. 41 296. 36 296. 32 9 07 30 9 15 00 9 22 30 9 30 00 293. 37 293. 27 293. 16 293. 06 14 37 30 14 45 00 14 52 30 15 00 00 287. 65 287. 49 287. 33 287. 17 4 07 30 4 15 00 4 22 30 4 30 00 296. 28 296. 23 296. 18 296. 13 9 37 30 9 45 00 9 52 30 10 00 00 292. 95 292. 85 292. 74 292. 63 15 07 30 15 15 00 15 22 30 15 30 00 287. 00 286. 83 286. 67 286. 50 4 37 30 4 45 00 4 52 30 5 00 00 296. 08 296. 03 295. 98 295. 93 10 07 30 10 15 00 10 22 30 10 30 00 292. 52 292. 41 292.30 292. 19 15 37 30 15 45 00 15 52 30 16 00 00 286. 33 286. 16 285. 99 285. 82 5 07 30 5 15 00 5 22 30 5 30 00 295. 87 295. 81 295. 75 295. 69 10 37 30 10 45 00 10 52 30 11 00 00 292.07 291.95 291. 83 291. 71 16 07 30 16 15 00 16 22 30 16 30 00 285. 64 285. 46 285. 28 285. 10 GEOGRAPHIC TABLES AND FORMULAS. 101 TABLE 13. Areas of quadrilaterals of earth's surface of 15 f extent in latitude and longi- tude Continued. [From Smithsonian Geographical Tables.] Middle latitude of quadrilateral. Area in square miles. Middle latitude of quadrilateral. Area in square miles. Middle latitude of quadrilateral. Area in square miles. / // 16 37 30 16 45 00 16 52 30 X7 00 00 284. 92 284. 74 284. 56 284.38 / // 22 07 30 22 15 00 22 22 30 22 30 00 275. 68 275. 44 275. 20 274.96 / // 27 37 30 27 45 00 27 52 30 28 00 00 263. 93 263. 64 263. 34 263. 04 17 07 30 17 15 00 17 22 30 17 30 00 ' 284. 19 284.00 283. 81 283. 62 22 37 30 22 45 00 22 52 30 23 00 00 274. 72 274.47 274. 22 273. 98 28 07 30 28 15 00 28 22 30 28 30 00 262. 74 262. 44 262. 14 261. 84 17 37 30 17 45 00 17 52 30 18 00 00 283. 43 283. 24 283. 05 282. 86 23 07 30 23 15 00 23 22 30 23 30 00 273. 73 273. 48 273. 23 272. 98 28 37 30 28 45 00 28 52 30 29 00 00 261. 53 261. 23 260. 92 260. 61 18 07 30 18 15 00 18 22 30 18 30 00 282.66 282.46 282. 26 282. 06 23 37 30' 23 45 00 23 52 30 24 00 00 272. 72 272. 47 272. 21 271. 95 29 07 30 29 15 00 29 22 30 29 30 00 260. 30 259. 99 259.68 259. 37 18 37 30 18 45 00 18 52 30 19 00 00 281.86 281. 66 281. 45 281. 25 24 07 30 24 15 00 24 22 30 24 30 00 371.69 271.44 271. 17 270. 91 29 37 30 29 45 00 29 52 30 30 00 00 259. 05 258. 74 258. 42 258, 10 19 07 30 19 15 00 19 22 30 19 30 00 281.04 280. 83 280. 62 280.41 24 37 30 24 45 00 24 52 30 25 00 00 270.65 270. 38 270. 11 269. 85 30 07 -30 30 15 00 30 22 30 30 30 00 257. 78 257. 46 357. 14 256. 82 19 37 30 19 45 00 19 52 30 20 00 00 280. 20 279.99 279. 77 279. 55 25 07 30 25 15 00 25 22 30 25 30 00 269. 58 269. 31 269.04 268. 76 30 37 30 30 45 00 30 52 30 31 00 00 256. 49 256. 17 255. 84 255. 52 20 07 30 20 15 00 20 22 30 20 30 00 279.34 279. 12 278. 90 278. 68 25 37 30 25 45 00 25 52 30 26 00 00 268. 49 268. 21 267. 94 267. 66 31 07 30 31 15 00 31 22 30 31 30 00 255.19 254. 86 254. 53 254. 19 20 37 30 20 45 00 20 52 30 21 00 00 278. 46 278. 23 278.00 277. 78 26 07 30 26 15 00 26 22 30 26 30 00 267. 38 267. 10 266. 82 266.54 31 37 30 31 45 00 31 52 30 32 00 00 253. 86 253. 53 253. 19 252. 85 21 07 30 21 15 00 21 22 30 21 30 00 277.55 277. 32 277.09 276. 86 26 37 30 26 45 00 26 52 30 27 00 00 266. 25 265. 97 265. 68 265. 39 32 07 30 32 15 00 32 22 30 32 30 00 252. 51 252. 17 251.83 251. 49' 21 37 30 21 45 00 21 52 30 22 00 00 276. 63 276. 39 276. 16 275. 92 27 07 30 27 15 00 27 22 30 27 30 00 265. 10 264.81 264.52 264. 23 32 37 30 32 45 00 32 52 30 33 00 00 251. 15 250. 80 250. 45 250. 11 102 GEOGRAPHIC TABLES AND FORMULAS. TABLE 13. Areas of quadrilaterals of earth's surface of 15' extent in latitude and longi- tude Continued. [From Smithsonian Geographical Tables.] Middle latitude of quadrilateral. Area in square miles. Middle latitude of quadrilateral. Area in square miles. Middle latitude of quadrilateral. Area in square miles. o / // 33 07 30 33 15 00 33 22 30 33 30 00 249. 76 249. 41 249. 06 248. 71 / // 38 37 30 38 45 00 38 52 30 39 00 00 233. 28 232. 88 232. 48 232. 07 o / // 44 07 30 44 15 00 44 22 30 44 30 00 214. 61 214. 17 213. 72 213. 27 33 37 30 33 45 00 33 52 30 34 00 00 248. 36 248. 00 247. 65 247. 29 39 07 30 39 15 00 39 22 30 39 30 00 231. 67 231. 27 230. 86 230. 45 44 37' 30 44 45 00 44 52 30 45 00 00 212. 82 212.37 211.91 211. 46 34 07 30 34 15 00 34 22 30 34 30 00 246. 93 246. 57 246. 21 245. 85 39 37 30 39 45 00 39 52 30 40 00 00 230. 04 229. 63 229. 22 228. 81 45 07 30 45 15 00 45 22 30 45 30 00 211.00 210. 55 210. 09 209. 63 34 37 30 34.45 00 34 52 30 35 00 00 245. 49 245. 13 244. 76 244. 40 40 07 3tf 40 15 00 40 22 30 40 30 00 228. 40 227. 99 227. 57 227. 15 45 37 30 45 45 00 45 52 30 46 00 00 209.17 208. 71 208. 25 207. 78 35 07 30 35 15 00 35 22 30 35 30 00 244. 03 243. 66 243. 29 242. 92 40 37 30 40 45 00 40 52 30 41 00 00 226. 73 226. 32 225. 90 225. 48 46 07 30 46 15 00 46 22 30 46 30 00 207. 32 206. 86 206. 39 205. 92 35 37 30 35 45 00 35 52 30 36 00 00 242. 55 242. 18 241. 80 241. 43 41 07 30 41 15 00 41 22 30 41 30 00 225. 06 224. 64 224. 21 223. 79 46 37 30 46 45 00 46 52 30 47 00 00 205. 45 204. 99 204. 52 204. 05 36 07 30 36 15 00 36 22 30 36 30 00 241. 05 240. 67 240. 29 239. 91 41 37 30 41 45 00 41 52 30 42 00 00 223. 36 222. 93 222. 50 222. 08 47 07 30 47 15 00 47 22 30 47 30 00 203. 57 203. 10 202. 63 202.15 36 37 30 36 45 00 36 52 30 37 00 00 239. 53 239. 15 238. 77 238. 38 42 07 30 42 15 00 42 22 30 42 30 00 221. 65 221. 21 220. 78 220. 35 47 37 30 47 45 00 47 52 30 48 00 00 201. 67 201. 20 200. 72 200.24 37 07 30 37 15 00 37 22 30 37 30 00 237. 99 237. 61 237.22 236. 83 42 37 30 42 45 00 42 52 30 43 00 00 219. 91 . 219. 48 219. 04 218. 60 48 07 30 48 15 00 48 22 30 48 30 00 199. 76 199. 28 198. 80 198. 32 37 37 30 37 45 00 37 52 30 38 00 00 236. 44 236. 05 235. 66 235. 26 43 07 30 43 15 00 43 22 30 43 30 00 218. 16 217.73 217. 28 216. 84 48 37 30 48 45 00 48 52 30 49 00 00 197. 83 197. 35 196. 86 196. 38 38 07 30 38 15 00 38 22 30 38 30 00 234. 87' 234. 47 234. 07 233. 68 43 37 30 43 45 00 43 52 30 44 00 00 216. 40 215. 96 215. 51 215. 06 49 07 30 49 15 00 49 22 30 49 30 00 195. 89 195. 40 194. 91 194. 42 GEOGRAPHIC TABLES AND FORMULAS. 103 13. Areas of quadrilaterals of earth's surface of 15 f extent in latitude and longi- tude Continued. [From Smithsonian Geographical Tables.] Middle latitude of quadrilateral. Area in square miles. Middle latitude of quadrilateral. Area in square miles. Middle latitude of quadrilateral. Area in square miles. / // 49 37 30 49 45 00 49 52 30 50 00 00 193. 93 193.44 192. 94 192. 45 / // 55 07 30 55 15 00 55 22 30 55 30 00 171. 39 170. 86 170. 33 169. 79 / // 60 37 30 60 45 00 60 52 30 61 00 00. 147. 21 146. 64 146. 07 145. 50 50 07 30 50 15 00 50 22 30 50 30 00 191.95 191. 46 190. 96 190. 46 55 37 30 55 45 00 55 52 30 56 00 00 169. 26 168. 72 168. 19 167.65 61 07 30 61 15 00 61 22 30 61 30 00 144. 93 144. 36 143. 79 143. 22 50 37 30 50 45 00 50 52 30 51 00 00 189. 96 189.46 188. 96 188. 46 56 07 30 56 15 00 56 22 30 56 30 00 167. 11 166. 57 166. 03 165. 49 61 37 30 61 45 00 61 52 30 62 00 00 142. 65 142. 08 141.50 140. 93 51 07 30 51 15 00 51 22 30 51 30 00 187. 96 187. 46 186. 95 186. 45 56 37 30 56 45 00 56 52 30 57 00 00 164.95 164.41 163. 87 163. 32 62 07 30 62 15 00 62 22 30 62 30 00 140. 35 139. 78 139. 20 138. 62 51 37 30 51 45 00 51 52 30 52 00 00 185.94 185.43 184.92 184.41 57 07 30 57 15 00 57 22 30 57 30 00 162. 78 162. 23 161.68 161. 14 62 37 30 62 45 00 62 52 30 63 00 00 138. 04 137. 47 136. 89 136. 31 52 07 30 52 15 00 52 22 30 52 30 00 183.90 183.39 182. 88 182. 37 57 37 30 57 45 00 57 52 30 58 00 00 160.59 160.04 159. 49 158. 94 63 07 30 63 15 00 63 22 30 63 30 00 ^ 135. 73 135. 15 134. 56 133. 98 52 37 30 52 45 00 52 52 30 53 00 00 181. 85 181. 34 180. 82 180. 31 58 07 30 58 15 00 58 22 30 58 30 00 158. 39 157. 84 157. 29 156. 73 63 37 30 63 45 00 63 52 30 64 00 00 133. 40 132. 81 132. 23 131.64 53 07 30 53 15 00 53 22 30 53 30 00 179. 79 179. 27 178. 75 178. 23 58 37 30 58 45 00 58 52 30 59 00 00 156. 18 155. 62 155. 07 154. 51 64 07 30 64 15 00 64 22 30 64 30 00 131.06 130. 47 129. 88 129. 29 53 37 30 53 45 00 53 52 30 54 00 00 177. 71 177. 19 176.67 176. 14 59 07 30 59 15 00 59 22 30 59 30 00 153. 96 153. 40 152. 84 152. 28 64 37 30 64 45 00 64 52 30 65 00 00 128. 70 128. 12 127. 53 126. 94 54 07 30 54 15 00 54 22 30 54 30 00 175. 62 175. 10 174. 57 174.04 59 37 30 59 45 00 59 52 30 60 00 00 151. 72 151. 16 150. 60 150. 03 65 07 30 65 15 00 65 22 30 65 30 00 126. 34 125. 75 125. 16 124. 57 54 37 30 54 45 00 54 52 30 55 00 00 173. 51 172.99 172. 46 171.93 60 07 30 60 15 00 60 22 30 60 30 00 149. 47 148. 91 148. 34 147. 77 65 37 30 65 45 00 65 52 30 66 00 00 123. 97 123. 38 122. .78 122. 19 104 GEOGRAPHIC TABLES AND FORMULAS. TABLE 13. Areas of quadrilaterals of earth's surface of 15 f extent in latitude and longi- tude Continued. [From Smithsonian Geographical Tables.] Middle latitude of quadrilateral. Area in square miles. Middle latitude of quadrilateral. Area in square miles. Middle latitude of quadrilateral. Area in square miles. / // 66 07 30- 66 15 00 66 22 30 66 30 00 121.59 120. 99 120. 40 119. 80 o / // 71 37 30 71 45 00 71 52 30 72 00 00 94.78 94.16 93.54 92.92 / // 77 07 30 77 15 00 77 22 30 77 30 00 67.04 66.41 65.77 65.13 66 37 30 66 45 00 66 52 30 67 00 00 119. 20 118. 60 118.00 117.40 72 07 30 72 15 00 72 22 30 72 30 00 92. 30 91.68 91.05 90.43 77 37 30 77 45 00 77 52 30 78 00 00 64.49 63.85 63.20 62.56 67 07 30 67 15 00 67 22 30 67 30 00 116. 80 116.20 115. 59 114. 99 72 37 30 72 45 00 72 52 30 73 00 00 89.80 89.18 88. 55 87.93 78 07 30 78 15 00 78 22 30 78 30 00 61.92 61.28 60.64 60.00 67 37 30 67 45 00 67 52 30 68 00 00 114. 39 113. 78 113. 18 112. 57 73 07 30 73 15 00 73 22 30 73 30 00 87.30 86.67 86.05 85.42 78 37 30 78 45 00 78 52 30 79 00 00 59.35 58.71 58.06 57.42 68 07 30 68 15 00 68 22 30 68 30 00 111.97 111. 36 110. 76 110. 15 73 37 30 73 45 00 73 52 30 74 00 00 84.79 84.16 83.53 82.91 79 07 30 79 15 00 79 22 30 79 30 00 56.78 56.13 55.49 54.84 68 37 30 68 45 00 68 52 30 69 00 00 109. 54 108. 93 108. 32 107. 71 74 07 30 74 15 00 74 22 30 74 30 00 82.28 81.65 81.01 80.38 79 37 30 79 45 00 79 52 30 80 00 00 54.20 53.55 52.91 52.26 69 07 30 69 15 00 69 22 30 69 30 00 107. 10 106. 49 105. 88 105. 27 74 37 30 74 45 00 74 52 30 75 00 00 79.75 79.12 78.49 77.86 80 07 30 80 15 00 80 22 30 80 30 00 51.62 50.97 50.32 49.68 69 37 30 69 45 00 69 52 30 70 00 00 104. 65 104. 04 103. 43 102. 81 75 07 30 75 15 00 75 22 30 75 30 00 77.22 76.59 75.95 75.32 80 37 30 80 45 00 80 52 30 81 00 00 49.03 48.38 47.73 47.08 70 07 30 70 15 00 70 22 30 70 30 00 102. 20 101.59 . 100.97 100.35 75 37 30 75 45 00 75 52 30 76 00 00 74.69 74.05 73.42 72.78 81 07 30 81 15 00 81 22 30 81 30 00 46.44 45.79 45.14 44.49 70 37 30 70 45 00 70 52 30 71 00 00 99.74 99.12 98.50 97.88 76 07 30 76 15 00 76 22 30 76 30 00 72. 14 71.51 70.87 70.24 81 37 30 81 45 00 81 52 30 82 00 00 43.84 43.19 42.54 41.89 71 07 30 71 15 00 71 22 30 71 30 00 97.26 96.65 96.03 95.41 76 37 30 76 45 00 76 52 30 77 00 00 69.60 68.96 68.32 67.68 82 07 30 82 15 00 82 22 30 82 30 00 41.24 40.59 39.94 39.29 GEOGRAPHIC TABLES AND FORMULAS. 105 TABLE 13. Areas of quadrilaterals of earth's surface of 15' extent in latitude and longi- tude Continued. [From Smithsonian Geographical Tables.] Middle latitude of quadrilateral. Area in square miles. Middle latitude of quadrilateral. Area in square miles. Middle latitude of quadrilateral. Area in square miles. o / // / // / // 82 37 30 82 45 00 82 52 30 83 00 00 38.64 37.99 37.34 36.69 85 07 30 85 15 00 85 22 30 85 30 00 25.58 24.93 24.27 23.62 87 37 30 87 45 00 87 52 30 88 00 00 12.48 11.82 11.16 10.51 83 07 30 83 15 00 83 22 30 83 30 00 36.03 35. 38 34.73 34.08 85 37 30 85 45 00 85 52 30 86 00 00 22.97 22.31 21.66 21.00 88 07 30 88 15 00 88 22 30 88 30 00 9.85 9.20 8.54 7.88 83 37 30 83 45 00 83 52 30 84 00 00 33.42 32.77 32.12 31.47 86 07* 30 86 15 00 86 22 30 86 30 00 20.35 19.69 19.04 18.38 88 37 30 88 45 00 88 52 30 89 00 00 7.22 6.57 5.91 5.26 84 07 30 84 15 00 84 22 30 84 30 00 30.81 30. 16 29.51 28.86 86 37 30 86 45 00 86 52 30 87 00 00 17.72 17.07 16.41 15.76 89 07 30 89 15 00 89 22 30 89 30 00 4.60 3.94 3.28 2.63 84 37 30 84 45- 00 84 52 30 85 00 00 28.20 27.54 26.89 26.24 87 07 30 87 15 00 87 22 30 87 30 00 15.10 14.44 13.79 . 13. 13 '89 37 30 89 45 00 89 52 30 1.97 1.31 0.66 106 GEOGRAPHIC TABLES AND FORMULAS. TABLE 14. Areas of quadrilaterals of earth's surface of 10' extent in latitude and longitude. [From Smithsonian Geographical Tables.] Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadri lateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. o / 05 15 25 35 132. 01 132.01 132. 01 132. 00 / 7 25 7 35 7 45 7 55 130. 93 130. 88 130. 84 130. 79 o / 14 45 14 55 15 05 15 15 127. 77 127. 67 127. 58 127. 48 45 55 1 05 1 15 132.00 131.99 131. 99 131.98 8 05 8 15 8 25 8 35 130. 73 130. 68 130. 63 130.57 15 25 15 35 15 45 15 55 ' 127.38 127. 28 127. 18 127. 08 1 25 1 35 1 45 1 55 131.97 131. 96 131.95 131. 94 8 45 8 55 9 05 9 15 130. 51 130. 46 130. 40 130. 34 16 05 - 16 15 16 25 16 35 126.98 126. 87 126. 77 126.66 2 05 2 15 2 25 2 35 131. 93 131.91 131. 90 131. 88 9 25 9 35 9 45 9 55 130. 28 130. 22 130. 15 130. 09 16 45 16 55 17 05 17 15 126.55 126. 44 126. 33 126.22 2 45 2 55 3 05 3 15 131. 86 131. 84 131. 82 131. 80 10 05 10 15 10 25 10 35 130. 02 129. 96 129. 89 129. 82 17 25 17 35 17 45 17 55 126. 11 126. 00 125. 88 125. 77 3 25 3 35 3 45 3 55 131. 78 131. 76 131. 74 131. 71 10 45 10 55 11 05 11 15 129. 76 129.68 129. 61 129.54 18 05 18 15 18 25 18 35 125. 65 125. 54 125. 42 125. 30 4 05 4 15 4 25 4 35 131. 68 131. 66 131. 63 131.60 11 25 11 35 11 45 11 55 129. 47 129. 39 129. 32 129. 24 18 45 18 55 19 05 "19 15 125. 18 125. 06 124. 94 124. 81 4 45 4 55 5 05 5 15 131.57 131. 54 131. 50 131.47 12 05 12 15 12 25 12 35 129. 16 129. 08 129. 00 128. 92 19 25 19 35 19 45 19 55 124. 69 124. 56 124. 44 124. 31 5 25 5 35 5 45 5 55 131. 44 131. 40 131. 36 131. 33 12 45 12 55 13 05 13 15 128. 84 128.76 128. 67 128. 59 20 05 20 15 20 25 20 35 124. 18 124. 05 123. 92 123. 79 6 05 6 15 6 25 6 35 131. 29 131. 25 131.21 131.16 13 25 13 35 13 45 13 55 128. 50 128. 41 128. 33 128. 24 20 45 20 55 21 05 21 15 123. 66 123. 52 123. 39 123. 25 6 45 6 55 7 05 7 15 131. 12 131. 07 131. 03 130. 98 14 05 14 15 14 25 14 35 128. 14 128. 05 127. 96 127. 87 21 25 21 35 21 45 21 55 123. 12 122. 98 122. 84 122. 70 GEOGRAPHIC TABLES AND FORMULAS. 107 TABLE 14. Areas of quadrilaterals of earth's surface of 10' extent in latitude and longi- tude Continued. [From Smithsonian Geographical Tables.] Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. ! / / o / 22 05 122. 56 29 25 . 115. 37 36 45 106. 29 22 15 122. 42 29 35 115. 18 36 55 106. 06 22 25 122. 28 29 45 114.99 37 05 105. 83 22 35 122. 13 29 55 114. 81 37 15 105. 60 22 45 121. 99 30 05 114. 62 37 25 105. 37 22 55 121.84 30 15 114. 43 37 35 105. 14 23 05 121. 69 30 25 114. 24 37 45 104. 91 23 15 121. 55 30 35 114. 04 37 55 104.68 23 25 121.40 30 45 113. 85 38 05 104.44 23 35 121. 25 30 55 113. 66 38 15 104. 21 23 45 121. 10 31 05 113. 47 38 25 103. 97 23 55 120. 94 31 15 113. 27 38 35 103. 74 24 05 120. 79 31 25 113.07 38 45 103. 50 24 15 120. 64 31 35 112. 88 38 55 103. 26 24 25 120. 48 31 45 112. 68 39 05 103. 02 24 35 120. 33 31 55 112. 48 39 15 102. 78 24 45 120. 17 32 05 112.28 39 25 102. 54 24 55 120. 01 32 15 112. 08 39 35 102. 30 25 05 119. 85 32 25 111. 87 39 45 102. 06 25 15 119. 69 32 35 111.67 39 55 101. 82 25 25 119. 53 32 45 111.47 40 05 101. 57 25 35 119. 37 32 55 111.26 40 15 101.33 25 45 119. 21 33 05 111.06 40 25 101.08 25 55 119.04 33 15 110. 85 40 35 100.83 26 05 118. 87 33 25 110.64 40 45 100.59 26 15 118.71 33 35 110.43 40 55 100.34 26 25 118.54 33 45 110. 22 41 05 100. 09 26 35 118. 37 33 55 110. 01 41 15 99.84 26 45 118. 21 34 05 109.80 41 25 99.59 26 55 118.04 34 15 109. 59 41 35 99.33 27 05 117. 87 34 25 109. 37 41 45 99.08 27 15 117. 69 34 35 109.16 41 55 98.83 27 25 117.52 34 45 108. 94 42 05 98.57 27 35 117.35 34 55 108. 73 42 15 98.32 27 45 117.17 35 05 108. 51 42 25 98.06 27 55 116.99 35 15 108. 29 42 35 97.80 28 05 116.82 35 25 108. 07 42 45 97.55 28 15 116.64 35 35 107. 85 42 55 97.29 28 25 116. 46 35 45 107. 63 43 05 97. 03 28 35 i 116.28 35 55 107. 41 43 15 96.77 28 45 116. 10 36 05 107. 19 43 25 96.50 28 55 115. 92 36 15 106. 96 43 35 96.24 29 05 115. 73 36 25 106.74 43 45 95.98 29 15 115. 55 36 35 106. 51 43 55 95.71 108 GEOGRAPHIC TABLES AND FORMULAS. TABLE 14. Areas of quadrilaterals of earth's surface of 10' extent in latitude and longi- tude Continued. [From Smithsonian Geographical Tables.] Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. o / 44 05 44 15 44 25 44 35 95.45 95.19 94.92 94.65 / 50 45 50 55 51 05 51 15 84.21 83.91 83.61 83.31 / 57 25 57 35 57 45 57 55 71.78 71.46 71.13 70.80 -44 45 44 55 45 05 45 15 94.38 94.11 93.84 93.58 51 25 51 35 51 45 51 55 83.01 82.71 82.41 82.11 58 05 58 15 58 25 58 35 70.48 70.15 69.82 69.49 45 25 45 35 45 45 45 55 93.30 93.03 92.76 92.48 52 05 52 15 52 25 52 35 81.81 81.51 81.20 80.90 58 45 58 55 59 05 59 15 69. 17 68.84 68.51 68.18 46 05 46 15 46 25 46 35 92.21 91.94 91.66 91.38 52 45 52 55 53 05 53 15 80.60 80.29 79.98 79.68 59 25 59 35 59 45 59 55 67.84 67.51 67.18 66.85 46 45 46 55 47 05 47 15 91.10 90.82 90.55 90.27 53 25 53 35 53 45 53 55 79.37 79.06 78.75 78.44 60 05 ,60 15 60 25 60 35 66.51 66.18 65.84 65.51 47 25 47 35 47 45 47 55 89.99 89.70 89.42 89.14 . 54 05 54 15 54 25 54 35 78.13 77.82 77.51 77.19 60 45 60 55 61 05 61 15 65.17 64.84 64.50 64.16 48 05 48 15 48 25 48 35 88.85 88.57 88.28 88.00 54 45 54 55 55 05 55 15 76.88 76.57 76.25 75.94 61 25 61 35 61 45 61 55 63.82 63.48 63.14 62.80 48 45 48 55 49 05 49 15 87.71 87.42 87.13 86.84 55 25 55 35 55 45 55 55 75.62 75.30 74.99 74.67 62 05 62 15 62 25 62 35 62.46 62.12 61.78 61.44 49 25' 49 35 49 45 49 55 86.55 86.26 85.97 85.68 56 05 56 15 56 25 56 35 74.35 74.03 73.71 73.39 62 45 62 55 63 05 63 15 61.10 60.75 60.41 60.06 50 05 50 15 50 25 50 35 85.39 85.09 84.80 84.50 56 45 56 55 57 05 57 15 73.07 72.75 72.43 72.10 63 25 63 35 63 45 63 55 59.72 59.37 59.03 58.68 GEOGRAPHIC TABLES AND FORMULAS. 109 TABLE 14. Areas of quadrilaterals of earth's surface of 10' extent inlalitude and longi- tude Continued. [From Smithsonian Geographical Tables.] Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. o / 64 05 64 15 64 25 64 35 58.33 57.99 57.64 57.29 o / 70 45 70 55 71 05 71 15 44.05 43.69 43.32 42.95 / 77 25 77 35 77 45 77 55 29.13 28.76 28.37 27.99 64 45 64 55 65 05 65 15 56.94 56.59 56.24 55.89 71 25 71 35 71 45 71 55 42.58 42.22 41.85 41.48 78 05 78 15 78 25 78 35 27.62 27.24 26.85 26.47 65 25 65 35 65 45 65 55 55.54 55.19 54.83 54.48 72 05 72 15 72 25 72 35 41.11 40.74 40.37 40.00 78 45 78 55 79 05 79 15 26.09 25.71 25.33 24.95 66 05 66 15 66 25 66 35 54.13 53.78 53.42 53.06 72 45 72 55 73 05 73 15 39.63 . 39.26 38.89 38.52 79 25 79 35 79 45 79 55 24.57 24.18 23.80 23.42 66 45 66 55 67 05 67 15 52.71 52.35 52.00 51.64 73 25 73 35 73 45 73 55 38. 15 37.78 37. 41 37.03 80 05 80 15 80 25 80 35 23.04 22.65 22.27 21.89 67 25 67 35 67 45 67 55 51.28 50.93 50.57 50.21 74 05 74 15 74 25 74 35 36.66 36.29 35.91 35.54 80 45 80 55 81 05 81 15 21.50 21.12 20.73 20.35 68 05 68 15 68 25 68 35 49.85 49.49 49.13 48.77 74 45 74 55 75 05 75 15 35.17 04.79 34.42 34.04 81 25 81 35 81 45 81 55 . 19.97 19.58 19.20* 18.81 68 45 68 55 69 05 69 15 48.41 48.05 47.69 47.33 75 25 75 35 75 45 75 55 33.66 33.29 32.91 32.53 82 05 82 15 82 25 82 35 18.43 18.04 17.65 17.27 69 25 69 35 69 45 69 -55 46.97 46.60 46.24 45.88 76 05 76 15 76 25 76. 35 32.16 31.78 31.40 31.03 82 45 82 55 83 05 83 15 16.88 16.50 16.11 15.73 70 05 70 15 70 25 70 35 45.51 45.15 44.78 44.42 76 45 76 55 77 05 77 15 30.65 30.27 29.89 29.51 83 25 83 35 83 45 83 55 15.34 14.95 14.57 14.18 110 GEOGRAPHIC TABLES AND FORMULAS. TABLE 14. Areas of quadrilaterals of earth's surface of 10' extent in latitude and longi- tude Continued . [From Smithsonian Geographical Tables.] Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. o / / / 84 05 13.79 86 05 9.14 88 05 4.47 84 15 13.40 86 15 8.75 88 15 . 4.09 84 25 13.02 86 25 8.36 88 25 3.70 84 35 12.63 86 35 7.97 88 35 3.31 84 45 12.24 86 45 7.59 88 45 2.92 84 55 11. 86 86 55 7.20 88 55 2.53 85 05 11.47 87 05 6.81 89 05 2.14 85 15 11.08 87 15 6.42 89 15 1.75 85 25 10.69 87 25 6.03 89 25 1.36 85 35 10.30 87 35 5.64 89 35 0.97 85 45 9.92 87 45 5.25 89 45 0.58 85 55 9.53 87 55 4.86 89 55 0.19 GEOGRAPHIC TABLES AND FORMULAS. TABLE 15. For conversion of arc into time. Ill o h. m. o 60 61 62 63 64 65 66 67 68 69 h. m. o 120 121 122 123 124 125 126 127 128 129 h. m. o h. m. h. m. o h. m. ' m. s. " s. 1 2 3 4 5 6 7 8 9 4 8 012 16 20 24 28 032 36 4 4 4 4 8 4 12 4 16 4 20 4 24 4 28 4 32 4 36 8 8 4 8 8 8 12 8 16 8 20 8 24 828 8 32 8 36 180 181 182 183 184 185 186 187 188 189 12 12 4 12 8 12 12 12 16 12 20 12 24 12 28 12 32 12 36 240 241 242 243 244 245 246 247 248 249 16 16 4 16 8 16 12 16 16 16 20 16 24 16 28 16 32 16 36 300 301 302 303 304 305 306 307 308 309 20 20 4 20 8 20 12 20 16 20 20 20 24 20 28 20 32 20 36 1 2 3 4 5 6 7 8 9 4 8 12 16 20 24 28 32 36 1 2 3 4 5 6 7 8 9 0.000 0.067 0.133 0.200 0.267 0.333 0.400 0.467 0.533 0.600 10 40 70 440 130 8 40 190 12 40 250 16 40 310 20 40 10 40 10 0.667 11 12 13 14 15 16 17 18 19 44 048 52 056 1 1 4 1 8 1 12 1 16 71 72 73 74 75 76 77 78 79 4 44 4 48 452 4 56 5 5 4 5 8 5 12 5 16 131 132 133 134 185 136 137 138 139 844 8 48 852 8 56 9 9 4 9 8 9 12 9 16 191 192 193 194 195 196 197 198 199 1244 12 48 12 52 12 56 13 13 4 13 8 13 12 13 16 251 252 253 254 255 256 257 258 259 260~ 16 44 16 48 16 52 16 56 17 17 4 17 8 17 12 17 16 311 312 313 314 315 316 317 318 319 20 44 20 48 20 52 20 56 21 21 4 21 8 21 12 21 16 11 12 13 14 15 16 17 18 19 44 048 52 56 1 1 4 1 8 i 12 1 16 11 12 13 14 15 16 17 18 19 0.733 0.800 0.867 0.933 1.000 1.067 1.133 1.200 1.267 20 1 20 80 5 20 140 141 142 143 144 145 146 147 148 149 9 20 |200 13 20 17 20 320 21 20 20 1 20 20 1.333 21 22 23 24 25 26 27 28 29 ~30~ 31 3'2 33 M 35 36 37 38 39 1 24 1 28 1 32 1 36 1 40 1 44 1 48 1 52 1 56 81 82 83 S4 s:, 86 87 88 89 524 5 28 5 32 5 36 5 40 544 5 48 5 52 556 9 24 9 28 9 32 9 36 9 40 944 9 48 9 52 9 56 201 202 203 204 205 206 207 208 209 13 24 13 28 13 32 13 36 13 40 1344 13 48 1352 13 56 261 262 263 264 265 266 267 268 269 17 24 17 28 17 32 17 36 17 40 17 44 17 48 17 52 17 56 321 322 323 324 325 326 327 328 329 330 21 24 21 28 21 32 21 36 21 40 21 44 21 48 21 52 21 56 21 22 23 24 25 26 27 38 29 1 24 1 28 1 32 1 36 1 40 1 44 1 48 1 52 1 56 21 22 23 24 25 26 27 28 29 ~80~ 1.400 1.467 1.533 1.600 1.667 1.733 1.800 1.867 1.933 2 90 6 150 10 210 14 270 18 22 30 2 2.000 2 4 2 8 2 12 2 16 2 20 2 24 2 28 2 32 2 36 91 92 93 94 95 % 97 98 99 6 4 6 8 6 12 6 16 6 20 6 24 6 28 6 32 6 36 151 152 153 154 155 156 157 158 159 160~ 10 4 10 8 10 12 10 16 10 20 10 24 10 28 10 32 1036 211 212 213 214 215 216 217 218 219 220~ 14 4 14 8 14 12 14 16 14 20 14 24 14 28 14 32 1436 271 272 273 274 275 276 277 278 279 280~ 18 4 18 8 18 12 18 16 18 20 18 24 18 28 18 32 18 36 331 332 333 334 335 336 337 338 339 22 4 22 8 22 12 22 16 2220 22 24 22 28 22 32 22 36 31 32 33 34 35 36 37 38 39 ~4P~ 2 4 2 8 2 12 2 16 2 20 2 24 2 28 2 32 2 36 31 32 33 34 35 36 37 38 39 2.067 2.133 2 200 2.267 2.333 2.400 2.467 2.533 2.600 40 2 40 100 6 40 10 40 14 40 18 40 .'{40 22 40 2 40 40 2.667 41 42 43 44 45 46 47 48 49 244 2 48 2 52 2 56 3 3 4 3 8 3 12 3 16 101 102 103 104 105 106 107 108 109 6 44 6 48 6 52 6 56 7 7 4 7 8 7 12 7 16 161 162 163 164 165 166 167 168 169 10 44 1048 10 52 10 56 11 11 4 11 8 11 12 11 16 221 222 223 224 225 226 227 228 229 14 44 14 48 1452 14 56 15 15 4 15 8 15 12 15 16 281 282 283 284 285 zst; 287 288 289 18 44 1848 18 52 18 56 19 19 4 19 8 19 12 19 16 341 342 343 344 345 346 347 348 349 2244 22 48 22 52 2256 23 23 4 23 8 23 12 23 16 41 42 43 44 45 46 47 48 49 2 44 2 48 2 52 2 56 3 3 4 3 8. 3 12 3 16 41 42 43 44 45 46 47 48 49 2.733 2.800 2,867 2.933 3.000 3.067 3.133 3.200 3.267 50 3 20 110 7 20 170 11 20 230 1520 290 1920 350 23 20 50 320 50 3.333 51 M 53 54 55 56 57 58 59 3 24 3 28 3 32 3 36 340 3 44 3 48 3 52 3 56 111 112 113 114 115 116 117 118 119 7 24 7 28 7 32 7 36 740 7 44 748 7 52 7 56 171 172. 173 174 175 176 177 178 179 11 24 11 28 11 32 11 36 11 40 11 44 11 48 11 52 11 56 231 232 233 234 235 236 237 238 239 15 24 15 28 15 32 15 36 15 40 15 44 15 48 15 52 15 56 291 292 293 294 295 296 297 298 299 19 24 1928 19 32 19 36 19 40 19 44 19 48 19 52 19 56 351 352 353 354 355 356 357 358 359 23 24 23 28 23 32 23 36 23 40 23 44 2348 23 52 23 56 61 52 53 54 55 56 57 58 59 3 24 3 28 3 32 3 36 3 40 3 44 3 48 3 62 '3 56 51 52 53 54 55 56 57 58 59 3.400 3.467 3.533 3.600 3.667 3.733 3.800 3.867 3.933 60 4 120 8 180 12 240 16 300 .20 360 24 60 4 60 4.000 112 GEOGRAPHIC TABLES AND FORMULAS. TABLE 16. For conversion of time into arc. Hours of time into arc. Time. Arc. Time. Arc. Time. Arc. , Time. Arc. Time. Arc. Time. Arc. hrs. o hrs. hrs. hrs. o hrs o hrs. 1 15 5 75 9 135 13 195 1 7 255 21 315 2 30 6 90 10 150 14 210 18 270 22 330 3 45 7 105 11 165 15 225 19 285 23 345 4 60 8 120 12 180 16 240 20 300 24 360 Minutes of time into arc. Seconds of time into arc. m. o / m. o / m o / s. s. s. 1 15 21 5 15 41 10 15 1 15 21 5 15 41 10 15 2 30 22 5 30 42 10 30 2 30 22 5 30 42 10 30 3 45 23 5 45 43 10 45 3 45 23 5 45 43 10 45 4 1 24 6 44 11 4 1 24 6 44 11 5 1 15 25 6 15 45 11 15 5 1 15 25 6 15 45 11 15 6 1 30 26 6 30 46 11 30 6 1 30 26 6 30 46 11 30 7 1 45 27 6 45 47 11 45 7 1 45 27 6 45 47 11 45 8 2 28 7 48 12 8 2 28 7 48 12 9 2 15 29 7 15 49 12 15 9 2 15 29 7 15 49 12 15 10 2 30 30 7 30 50 12 30 10 2 30 30 7 30 50 12 30 11 2 45 31 7 45 51 12 45 11 2 45 31 7 45 51 12 45 12 3 32 8 52 13 12' 3 32 8 52 13 13 3 15 33 8 15 53 13 15 13 3 15 33 8 15 53 13 15 14 3 30 34 8 30 54 13 30 14 3 30 34 8 30 54 13 30 15 3 45 35 8 45 55 13 45 15 3 45 35 8 45 55 13 45 16 4 36 9 56 14 16 4 36 9 56 14 17 4 15 37 9 15 57 14 15 17 4 15 37 9 15 57 14 15 18 4 30 38 9 30 58 14 30 18 4 30 38 9 30 58 14 30 19 4 45 39 9 45 59 14 45 19 4 45 39 9 45 59 14 45 20 5 40 10 60 15 20 5 40 10 60 15 Hundredths of a second of time into arc. Hundredths of a second .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 of time. // n n n n n ii ii 0.00 0.00 0.15 0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 .10 1.50 1.65 1.80 1.95 2.10 2.25 2.40 2.55 2.70 2.85 .20 3.00 3.15 3.30 3.45 3.60 3.75 3,90 4.05 4.20 4.35 .30 4.50 4.65 4.80 4.95 5.10 5.25 5.40 5.55 5.70 5.85 .40 6.00 6.15 6.30 6.45 6.60 6.75 6.90 7.05 7.20 7.35 0.50 7.50 7.65 7.80 7.95 8.10 8.25 8.40 8.55 8.70 8.85 .60 9.00 9.15 9.30 9.45 9.60 9.75 9.90 10.05 10.20 10.35 .70 10.50 10.65 10.80 10.95 11.10 11.25 11.40 11.55 11.70 11.85 .80 12.00 12.15 12.30 12.45 12.60 12.75 12.90 13.05 13.20 13.35 .90 13.50 13.65 13.80 13.95 14.10 14.25 14.40 14.55 14.70 14.85 GEOGRAPHIC TABLES AND FORMULAS. TABLE 17. For conversion of mean time into sidereal time. 113 . m m 1 m 2 m 3 h m s 000 h m s 6 5 15 h m s 12 10 29 h m s 18 15 44 1 s m s 0.00 00 0.50 m s 3 3 1 2 3 4 5 6 B 9 06 5 12 10 18 16 24 21 30 26 36 31 42 37 48 42 54 47 6 11 20 6 17 25 6 23 30 6 29 36 6 35 41 6 41 46 6 47 51 6 53 56 702 12 16 34 12 22 40 12 28 45 12 34 50 12 40 55 12 47 1 12 53 6 12 59 11 13 5 16 18 21 49 18 27 54 18 33 59 18 40 5 18 46 10 18 52 15 18 58 20 19 4 26 19 10 31 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 4 7 . 11 15 18 22 26 29 33 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 3 6 3 10 3 14 3 17 3 21 3 25 3 28 3 32 3 35 10 1 52 767 13 11 21 19 16 36 0.10 37 0.60' 3 39 11 12 13 14 15 16 17 18 19 6 58 13 3 19 8 25 13 31 19 37 24 43 29 1 49 34 1 55 40 7 12 12 7 18 17 7 24 23 7 30 28 7 36 33 7 42 38 7 48 44 7 54 49 8 54 13 17 27 13 23 32 13 29 37 13 35 42 10 41 48 13 47 53 13 53 58 14 3 14 6 9 19 22 41 19 28 47 19 34 52 19 40 57 19 47 2 19 53 7 19 59 13 20 5 18 20 11 23 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 40 44 47 51 55 58 1 2 1 6 1 9 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 3 43 3 46 3 50 3 54 3 57 4 1 4 5 4 8 4 12 20 2 1 45 8 6 59 14 12 14 20 17 28 0.20 1 13 0.70 4 16 21 22 23 24 25 26 27 28 29 2 7 50 2 13 55 2 20 1 2 26 6 2 32 11 2 38 16 2 44 22 2 50 27 2 56 32 8 13 5 8 19 10 8 25 15 8 31 20 8 37 26 8 43 31 8 49 36 8 55 41 9 1 47 14 18 19 14 24 24 14 30 30 14 36 35 14 42 40 14 48 45 14 54 51 15 56 15 7 1 20 23 34 20 29 39 20 35 44 20 41 49 20 47 55 20 54 21 5 21 6 10 21 12 16 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 1 17 1 20 1 24 1 28 1 31 1 35 1 39 1 42 1 46 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 4 19 4 23 4 27 4 30 4 34 4 38 4 41 4 45 4 49 30 3 2 37 9 7 52 15 13 6 21 18 21 0.30 1 50 , 0.80 4 52 31 32 33 34 35 36 37 38 39 3 8 43 3 14 48 3 20 53 3 26 58 3 33 3 3 39 9 3 45 14 3 51 19 3 57 24 9 13 57 9 20 2 9 26 8 9 32 13 9 38 18 9 44 23 9 50 28 9 56 34 10 2 39 15 19 12 15 25 17 15 31 22 15 37 27 15 43 33 15 49 38 15 55 43 16 1 48 16 7 54 21 24 26 21 30 31 21 36 37 21 42 42 21 48 47 21 54 52 22 58 22 7 3 22 13 8 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 1 53 1 57 2 1 2 4 2 8 2 11 2 15 2 19 2 22 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 4 56 4 59 5 3 5 7 5 10 5 14 5 18 5 21 5 25 40 4 3 30 10 8 44 16 13 59 22 19 13 0.40 2 26 0.90 5 29 41 42 43 44 45 46 47 48 49 4 9 35 4 15 40 4 21 45 4 27 51 4 33 56 4 40 1 4 46 6 4 52 12 4 58 17 10 14 49 10 20 55 10 27 10 33 5 10 39 10 10 45 16 10 51 21 10 57 26 11 3 31 16 20 4 16 26 9 16 32 14 16 38 20 16 44 25 16 50 30 16 56 35 17 2 41 17 8 46 22 25 19 22 31 24 22 37 29 22 43 34 22 49 39 22 55 45 23 1 50 23 7 55 23 14 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 2 30 2 33 2 37 2 41 2 44 2 48 2 52 2 55 2 59 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 5 32 5 36 5 40 5 43 5 47 5 51 5 54 5 58 6 2 50 5 4 22 11 9 37 17 14 51 23 20 6 o.:,o '3 3 | 1.00 6 5 51 52 53 54 55 56 57 58 59 5 10 27 5 16 33 5 22 38 5 28 43 5 34 48 5 40 54 5 46 59 5 53 4 5 59 9 11 15 42 11 21 47 11 27 52 11 33 58 11 40 3 11 46 8 11 52 13 11 58 19 12 4 24 17 20 56 17 27 2 17 33 7 17 39 12 17 45 17 17 51 23 17 57 28 18 3 33 18 9 38 23 26 11 23 32 16 23 38 21 23 44 27 23 50 32 23 56 37 24 2 42 24 8 48 24 14 53 Example: Let the given mean time be 14 57"> 32 . 56. The table gives nrstforl4'>54 n >51 2 27" then for 2 41.56 0.44 2 27.44 The sum 14" 57" 32 '. 56+2" 27'. 44=15>> 0> 0- is the required sidereal time. 60 6 5 15 12 10 29 18 15 44 24 20 58 4606108- 114 GEOGRAPHIC TABLES AND FORMULAS. TABLE 18. For conversion of sidereal time into mean time. s m m 1 m 2 m 3 h m s 000 h m s 6 6 15 h m s 12 12 29 h m s 18 18 44 s 0.00 m s s 0.50 m s 3 3 1 2 3 4 5 6 7 8 9 066 12 12 18 19 24 25 30 31 36 37 42 44 48 50 54 56 6 12 21 6 18 27 6 24 33 6 30 40 6 36 46 6 42 52 6 48 58 6 55 4 7 1 11 12 18 35 12 24 42 12 30 48 12 36 54 12 43 12 49 7 12 55 13 13 1 19 13 7 25 18 24 50 18 30 56 18 37 2 18 43 9 18 49 15 18 55 21 19 1 27 19 7 34 19 13 40 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 4 7 11 15 18 22 26 29 33 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 3 7 3 10 3 14 3 18 3 21 3 25 3 29 3 32 3 36 10 112 7 7 17 13 13 31 19 19 46 0.10 37 0.60 3 40 11 12 13 14 15 16 17 18 19 7 9 13 15 19 21 25 27 31 34 37 40 43 46 49 52 55 59 7 13 23 7 19 29 7 25 36 7 31 42 7 37 48 7 43 54 7 50 1 7 56 7 8 2 13 13 19 38 13 25 44 13 31 50 13 37 56 13 44 3 13 50 9 13 56 15 14 2 21 14 8 28 19 25 52 19 31 59 19 38 5 19 44 11 19 50 17 19 56 23 20 2 30 20 8 36 20 14 42 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0:19 40 44 43 51 55 59 1 2 1 6 1 10 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 3 43 3 47 3 51 3 54 3 58 4 2 4 5 4 9 4 13 20 225 8 8 19 14 14 34 20 20 48 0.20 1 13 0.70 4 16 21 22 23 24 25 26 27 28 29 2 8 11 2 14 17 2 20 24 2 26 30 2 32 36 2 38 42 2 44 49 2 50 55 2 57 1 8 14 26 8 20 32 8 26 88 8 32 44 8 38 51 8 44 57 - 8 51 3 8 57 9 9 3 16 14 20 40 14 26 46 14 32 53 14 38 59 14 45 5 14 51 11 14 57 18 15 3 24 15 9 30 20 26 55 20 33 1 20 39 7 20 45 13 20 51 20 20 57 26 21 3 32 21 9 38 21 15 45 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 1 17 1 21 1 24 1 28 1 32 1 35 1 39 1 43 1 46 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 4 20 4 24 4 27 4 31 4 35 4 38 4 42 4 46 4 49 30 337 9 9 22 15 15 36 21 21 51 0.30 1 50 0.80 4 53 31 32 33 34 35 36 37 38 39 3 9 14 3 15 20 3 21 26 3 27 32 3 33 38 3 39 45 3 45 51 3 51 57 3 58 3 9 Ib 28 9 21 34 9 27 41 9 33 47 9 39 53 9 45 59 9 52 5 9 58 12 10 4 18 15 21 43 15 27 49 15 33 55 15 40 1 15 46 8 15 52 14 15 58 20 16 4 26 16 10 33 21 27 57 21 34 3 21 40 10 21 46 16 21 52 22 21 58 28 22 4 35 22 10 41 22 16 47 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 1 54 1 57 2 1 2 5 2 8 2 12 2 16 2 19 2 23 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 4 57 5 5 4 5 8 5 11 5 15 5 19 5 22 5 26 40 4 4 10 10 10 24 16 16 39 22 22 53 0.40 2 26 0.90 5 30 41 42 43 44 45 46 47 48 49 4 10 16 4 16 22 4 22 28 4 28 35 4 34 41 4 40 47 4 46 53 4 53 4 59 6 10 16 30 10 22 37 10 28 43 10 34 49 10 40 55 10 47 2 10 53 8 10 59 14 11 5 20 16 22 45 16 28 51 16 34 57 16 41 4 16 47 10 16 53 16 16 59 22 17 5 29 17 11 35 22 29 22 35 6 22 41 12 22 47 18 22 53 24 22 59 31 23 5 37 23 11 43 23 17 49 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 2 30 2 34 2 37 2 41 2 45 2 48 2 52 2 56 2 59 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 5 33 5 37 5 41 5 44 5 48 5 52 5 55 5 59 6 3 50 5 5 12 11 11 27 17 17 41 23 23 56 0.50 30 o 1.00 6 6 51 52 53 54 55 56 57 58 59 5 11 18 5 17 25 5 23 31 5 29 37 5 35 43 6 41 50 5 47 56 5 54 2 608 11 17 33 11 23 39 11 29 45 11 35 52 11 41 58 11 48 4 11 54 10 12 17 12 6 23 17 23 47 17 29 54 17 36 17 42 6 17 48 12 17 54 19 18 25 18 6 31 18 12 37 23 30 2 23 36 8 23 42 14 23 48 21 23 54 27 24 33 24 6 39 24 12 46 24 18 52 Example: Given 15 h O m s . The table gives first for 14* 57"" 18" 2~27 then for 2 42 0.44 The 15h()m 15 2 27.44 difference > _ 2m 278.44 = 14^ 57-" 32".56 required mean time. 60 6 ' 6 15 12 12 29 18 18 44 24 24 58 is the GEOGRAPHIC TABLES AND FORMULAS. TABLE 19. For inlerconversion of feet and decimals of a mile. 115 Feet. Miles. Feet. Miles. Feet. Miles. Feet. Miles. 53 .01 1373 .26 2693 .51 4013 .76 106 .02 1426 .27 2746 .52 4066 .77 158 .03 1478 .28 2798 .53 4118 .78 211 .04 1531 .29 2851 .54 4171 .79 264 .05 1584 .30 2904 .55 4224 .80 317 .06 1637 .31 2957 .56 4277 .81 370 .07 1690 .32 3010 .57 4330 .82 422 .08 1742 .33 3062 .58 4382 .83 475 .09 1795 .34 3115 .59 4435 .84 528 .10 1848 .35 3168 .60 4488 .85 581 .11 1901 .36 3221 .61 4541 .86 634 .12 1954 .37 3274 .62 4594 .87 686 .13 2006 .38 3326 .63 4646 .88 739 .14 2059 .39 3379 .64 4699 .89 792 .15 2112 .40 3432 .65 4752 .90 845 .16 2165 .41 3485 .66 4805 .91 898 .17 2218 .42 3538 .67 4858 .92 950 .18 2270 .43 3590 .68 4910 .93 1003 .19 2323 .44 3643 .69 4963 .94 1056 .20 2376 .45 3696 .70 5016 .95 1109 .21 2429 .46 3749 .71 5069 .96 1162 .22 2482 .47 3802 .72 5122 .97 1214 .23 2534 .48 3854 .73 5174 .98 1267 .24 2587 .49 3907 .74 5227 .99 1320 .25 2640 .50 3960 .75 5280 1.00 116 GEOGBAPHIC TABLES AND FOKMULAS. TABLE 20. Converting wheel revolutions into hundredths of a mile. [Prepared .by J. H. Jennings.] [Scale divisions outside; revolutions inside.] CIRCUMFERENCE OF WHEEL, 9.5 FEET. 1 2 3 4 5 6 7 8 9 10 6 11 17 22 28 33 39 44 50 56 10 61 67 72 78 83 89 94 100 105 111 20 117 122 128 133 139 144 150 155 161 167 30 172 178 183 189 194 200 205 211 216 222 40 228 233 239 244 250 255 261 266 272 278 50 283 289 294 300 305 311 316 322 328 333 60 339 344 350 355 361 366 372 378 383 389 70 394 400 405 411 416 422 428 433 439 444 80 450 455 461 466 472 478 483 489 494 500 90 506 511 516 522 528 533 539 544 550 555 CIRCUMFERENCE OF WHEEL, 9.6 FEET. 1 2 3 4 5 6 7 8 9 10 5 11 16 22 27 33 38 44 50 55 10 60 66 72 77 82 88 93 99 105 110 20 116 121 126 132 137 143 148 154 159 165 30 171 177 182 188 193 199 204 209 215 220 40 225 231 236 242 247 253 258 ! 264 270 275 50 281 286 292 297 303 308 314 319 325 330 60 336 341 347 352 358 363 369 374 380 385 70 391 396 402 407 413 418 424 429 435 440 80 446 451 457 462 468 473 479 484 490 495 90 501 506 512 517 523 528 534 539 544 550 CIRCUMFERENCE OF WHEEL, 9.7 FEET. 1 2 3 4 5 6 7 8 9 10 5 11 16 22 27 33 38 44 49 54 10 60 65 71 76 81 87 92 98 103 109 20 114 120 125 131 136 142 147 152 158 163 30 169 174 179 185 190 196 201 206 212 218 40 223 228 234 239 245 250 256 261 267 272 50 '"277 283 288 294 299 305 310 316 321 326 60 331 337 342 348 353 359 364 370 376 381 70 386 392 397 403 408 414 419 424 429 435 80 441 446 451 457 462 468 473 479 484 490 90 495 500 506 511 517 522 528 533 539 544 GEOGRAPHIC TABLES AND FORMULAS. 117 TABLE 20. Converting wheel revolutions into hundredths of a mile Continued. CIRCUMFERENCE OF WHEEL, 9.8 FEET. 1 2 3 4 5 6 7 8 9 10 5 11 16 22 27 32 38 43 49 54 10 59 65 70 75 81 86 91 97 102 108 M 113 119 124 129 135 140 145 151 156 162 30 167 172 178 183 189 194 199 205 211 216 40 221 226 231 237 242 248 253 259 265 270 50 275 280 286 291 296 302 307 313 318 324 60 329 334 339 345 350 356 361 366 372 377 70 383 388 .394 400 405 410. 415 421 426 431 80 437 442 447 453 458 464 469 474 480 485 *90 490 496 501 506 512 517 522 528 533 539 CIRCUMFERENCE OF WHEEL, 9.9 FEET. 1 2 3 4 5 6 7 8 9 10 6 11 16 21 27 32 37 43 48 53 10 59 64 69 75 80 85 91 96 101 107 20 112 117 122 128 133 138 144 149 155 160 30 165 170 176 181 186 192 197 203 208 213 40 219 224 229 235 240 245 251 256 261 267 50 272 277 282 288 293 298 304 309 314 320 60 325 330 336 341 346 352 357 362 368 373 70 378 384 389 394 400 405 410 416 421 426 80 432 437 442 448 453 458 464 469 474 480 90 485 490 496 501 506 512 517 522 528 533 CIRCUMFERENCE OF WHEEL, 10 FEET. 1 2 3 4* 5 6 7 8 9 10 5 11 16 21 26 32 37 42 48 53 10 58 63 69 75 80 85 90 96 101 106 20 111 116 121 127 132 137 143 148 153 158 30 164 169 174 180 185 190 195 201 206 211 40 217 222 227 232 238 243 248 253 259 264 50 269 275 280 285 290 296 301 306 311 317 60 322 327 333 338 343 349 354 359 364 370 70 375 380 385 391 396 401 406 412 417 422 80 428 433 438 444 449 454 459 465 470 475 90 481 486 491 496 502 507 512 517 523 528 118 GEOGRAPHIC TABLES AND FORMULAS. TABLE 20. Converting wheel revolutions into hundredths of a mile Continued. CIRCUMFERENCE OF .WHEEL, 10.1 FEET. 1 2 3 4 5 6 7 8 9 10 5 10 16 21 26 31 36 41 47 52 10 58 63 68 73 79 84 89 94 100 105 20 110 115 121 126 131 136 142 147 152 157 30 162 167 173 178 183 188 193 199 204 209 40 214 220 226 231 236 241 247 252 257 262 50 267 272 277 282 288 293 298 303 308 314 60 319 324 329 334 340 345 350 355 361 366 70 371 376 381 386 392 397 402 408 413 418 80 424 429 434 439 445 450 455 460 466 471 90 476 481 486 492 497 502 507 513 518 523 CIRCUMFERENCE OF WHEEL, 10.2 FEET. 1 2 3 4 5 6 7 8 9 10 5 10 16 21 26 31 36 41 47 52 10 57 62 67 73 78 83 88 93 98 104 20 109 114 119 124 130 135 140 145 150 155 30 . 161 166 171 176 181 186 191 197 202 207 40 212 218 224 229 234 239 244 249 254 259 50 264 269 275 280 285 290 295 300 306 311 60 316 321 326 332 337 342 347 352 357 363 70 368 373 378 383 388 394 399 404 409 414 80 419 425 430 435 440 446 451 456 461 466 90 471 476 481 487 492 497 503 508 513 518 CIRCUMFERENCE OF WHEEL, 10.3 FEET. 1 2 3 4 5 6 7 8 9 10 5 10 15 20 26 31 36 41 46 51 10 56 62 67 72 77 82 87 92 97 103 20 108 113 118 123 128 133 138 144 149 154 30 159 164 169 174 180 185 190 195 200 204 40 209 214 219 224 230 235 240 245 250 256 50 262 267 272 277 282 287 292 297 303 308 60 313 318 323 328 333 338 344 349 354 359 70 364 369 374 380 385 390 395 400 405 410 80 416 421 426 431 436 441 446 451 457 462 90 467 472 477 482 487 492 498 503 508 513 GEOGRAPHIC TABLES AND FORMULAS. 119 TABLE 20. Converting ivheel revolutions into hundredths of a mile Continued. CIRCUMFERENCE OF WHEEL, 10.4 FEET. 1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 30 36 41 46 51 10 56 61 66 71 76 81 86 91 97 102 20 107 112 117 122 127 132 137 142 147 152 30 157 163 168 173 178 183 188 193 198 203 40 208 213 218 223 228 233 238 244 249 254 50 259 264 269 274 279 284 289 295 300 305 60 310 315 320 325 330 335 340 345 350 356 70 361 366 371 376 k 381 386 391 396 401 406 80 411 416 421 426 432 437 442 447 452 457 90 462 467 472 478 483 488 493 498 503 508 1 CIRCUMFERENCE OF WHEEL, 10.5 FEET. 1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 30 35 40 45 50 10 55 60 65 70 75 80 85 90 95 101 20 106 111 116 121 126 131 136 141 146 151 30 156 161 166 171 176 181 186 191 196 201 40 206 211 216 221 226 231 236 241 246 251 50 257 262 267 272 277 282 287 292 297 302 60 307 312 317 322 327 332 337 342 347 352 70 357 362 367 372 377 382 387 392 397 402 80 407 .412 417 422 428 433 438 443 448 453 90 458 463 468 473 478 483 488 493 498 503 CIRCUMFERENCE OF WHEEL, 10.6 FEET. 1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 30 35 40 45 50 10 55 60 65 70 75 80 85 90 95 100 20 105 110 115 120 125 130 135 140 144 149 30 154 159 164 169 174 179 184 189 194 199 40 204 209 214 219 224 229 234 239 244 249 50 254 259 264 269 274' 279 284 289 294 299 60 304 309 314 319 324 329 334 339 344 349 70 354 359 364 369 374 379 384 389 393 398 80 403 408 413 418 423 428 433 438 443 448 90 453 458 463 468 473 478 483 488 493 498 120 GEOGRAPHIC TABLES AND FORMULAS. TABLE 20. Converting wheel revolutions into hundredth* of a mile Continued. CIRCUMFERENCE OF WHEEL, 10.7 FEET. 1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 30 35 40 44 49 10 54 59 64 69 74 79 84 89 94 99 20 104 109 114 119 123 128 133 138 143 148 30 153 158 163 168 173 178 183 188 193 198 40 203 207 212 217 222 227 232 237 242 247 50 252 257 262 267 272 277 282 287 291 296 60 301 306 311 316 321 326 331 336 341 346 70 351 356 361 366 371 375 380 385 390 395 80 400 405 410 415 420 425 430 435 440 .445 90 450 454 459 464 469 474 479 484 489 494 CIRCUMFERENCE OF WHEEL, 10.8 FEET. 1 2 3 4 5 6 7 8 9 10 5 10 15 20 24 29 34 39 44 49 10 54 59 64 68 73 78 83 88 93 98 20 103 108 113 118 122 127 132 137 142 147 30 152 156 161 166 171 176 181 186 191 196 40 200 205 210 215 220 225 230 235 I 240 244 i 50 249 254 259 264 269 274 279 283 288 293 60 298 303 308 313 318 323 328 332 t 337 341 70 346 351 356 361 366 371 376 381 386 391 80 396 401 406 411 416 421 425 430 435 440 90 445 450 455 460 464 469 474 479 484 489 CIRCUMFERENCE OF WHEEL, 10.9 FEET. 1 2 3 4 5 6 7 8 9 10 5 10 15 19 24 29 34 39 44 48 10 53 58 63 68 73 78 82 87 92 97 20 102 107 111 116 121 126 131 136 141 145 30 150 155 160 165 170 175 179 184 189 193 40 197 202 207 212 217 222 227 232 237 242 50 247 252 257 261 '266 271 276 281 286 290 60 295 300 305 310 315 319 324 329 334 339 70 344 349 353 358 363 368 373 378 383 387 80 392 397 402 407 411 416 421 426 431 436 90 440 445 450 455 460 465 469 474 479 484 GEOGRAPHIC TABLES AND FORMULAS. 121 TABLE 20. Converting wheel revolutions into hundredths of a mile Continued. CIRCUMFERENCE OF WHEEL, 11.0 FEET. 1 .1 1 5 6 7 8 9 10 5 10 14 19 24 29 33 38 43 48 10 53 57 62 67 72 76 81 86 91 96 20 101 106 110 115 119 124 129 134 139 144 30 149 154 158 163 168 173 178 182 187 192 40 197 202 206 211 216 221 225 230 235 240 50 245 250 254 259 263 268 273 278 283 288 60 293 298 302 307 312 317 321 326 331 336 70 341 346 350 355 360 365 369 374 379 384 80 389 394 398 403 408 413 417 422 427 432 90 437 442 446 451 456 461 465 470 475 480 CIRCUMFERENCE OF WHEEL, 11.1 FEET. 1 * 8 4 5 6 7 8 9 10 5 10 14 19 24 29 33 38 43 48 10 52 57 62 66 71 76 81 85 90 95 20 100 104 109 114 119 124 129 133 138 143 30 147 152 157 161 166 171 176 180 185 190 40 195 200 205 209 214 219 224 229 233 238 50 243 248 252 257 262 267 271 276 281 286 60 290 295 300 305 309 314 319 324 328 333 70 338 343 347 352 357 362 367 371 376 381 80 386 390 395 400 405 409 414 419 424 428 90 433 438 443 447 452 457 462 466 471 476 CIRCUMFERENCE OF WHEEL, 11.2 FEET. 1 g 5 6 7 8 9 10 5 9 14 19 24 28 33 38 42 47 10 52 57 62 66 71 76 80 84 89 94 20 99 104 108 113 117 122 127 132 137 141 30 146 151 155 160 165 169 174 179 184 188 40 193 198 203 207 212 217 222 226 231 236 50 240 245 250 255 259 264 269 274 278 283 60 287 292 297 302 307 312 316 321 326 330 70 334 339 344 348 353 358 363 367 372 377 80 382 386 391 396 400 405 410 415 419 424 90 429 434 438 443 447 452 456 461 466 471 122 GEOGRAPHIC TABLES AND FORMULAS. TABLE 20. Converting wheel revolutions into hundredths of a mile Continued. CIRCUMFERENCE OF WHEEL, 11.3 FEET. 1 2 3 4 7 8 9 10 5 9 14 19 23 28 33 37 42 47 10 51 56 61 65 70 74 79 83 88 93 20 98 103 108 112 117 122 126 131 135 140 30 145 150 154 159 164 168 173 1Z8 183 187 40 191 196 200 205 210 215 220 224 229 234 50 238 243 248 252 257 261 266 271 276 280 60 285 290 294 299 304 308 313 318 322 327 70 332 336 341 346 350 355 360 364 370 374 80 378 383 387 392 397 402 406 411 416 420 90 425 430 434 439 444 448 453 458 462 467 CIRCUMFERENCE OF WHEEL, 11.4 FEET. 1 2 3 4 5 6 7 8 9 10 5 9 14 18 23 28 32 37 42 46 10 50 56 60 65 69 74 79 83 88 93 20 97 102 107 111 116 120 125 129 134 139 30 143 148 152 157 162 167 171 176 180 185 40 190 195 199 204 208 213 217 222 227 231 50 236 241 245 250 255 259 264 269 273 278 60 282 287 291 296 301 306 310 315 319 324 70 329 333 338 343 347 352 357 361 366 370 80 - 375 380 384 389 394 398 403 407 412 417 90 421 426 431 435 440 445 449 454 458 463 CIRCUMFERENCE OF WHEEL, 11.5 FEET. 1 2 3 4 5 6 7 8 9 10 5 9 14 18 23 28 32 37 41 46 10 50 55 59 63 68 72 77 82 87 92 20 96 101 105 110 114 119 124 128 133 138 30 142 147 151 156 161 165 170 174 179 184 40 188 193 197 202 207 211 216 220 225 229 50 234 239 243 248 252 257 262 266 271 275 60 280 285 289 294 298 303 308 312 317 321 70 326 331 335 340 344 349 353 358 363 367 80 372 377 381 386 390 395 399 404 409 413 90 418 422 427 432 436 441 445 450 454 459 GEOGRAPHIC TABLES AND FORMULAS. 123 TABLE 2Q. Comerling wheel revolutions into hundredths of a mile Continued. CIRCUMFERENCE OF WHEEL, 11.6 FEET. 1 2 3 4 5 6 7 8 9 10 5 9 14 18 23 27 32 36 41 46 10 50 55 59 64 68 73 77 82 87 91 20 96 100 104 109 114 118 123 127 132 136 30 141 146 150 155 159 164 168 173 178 182 40 187 191 196 200 205 209 214 218 223 227 M 232 237 241 246 250 255 259 264 269 273 60 278 282 287 291 296 300 305 309 314 318 70 323 328 332 337 341 346 350 355 360 364 80 369 373 378 382 387 391 396 400 405 410 90 414 419 423 428 432 437 441 446 450 455 CIRCUMFERENCE OF WHEEL, 11.7 FEET. 1 2 3 4 5 6 7 8 9 10 5 9 13 18 23 27 32 36 41 45 10 50 54 59 63 68 72 77 81 86 90 20 95 99 104 108' 113 117 122 126 131 135 30 140 144 149 153 158 162 167 171 176 180 40 185 189 194 198 203 207 212 217 221 225 50 230 235 239 244 248 253 257 262 266 271 60 275 280 284 289 293 298 302 307 311 316 70 320 325 329 334 338 343' 347 352 *356 361 80 365 370 374 379 383 388 392 397 401 406 90 410 415 419 424 428 433 437 442 446 451 CIRCUMFERENCE OF WHEEL, 11.8 FEET. 1 2 3 4 5 6 7 8 9 10 4 9 13 18 22 27 32 36 40 45 10 49 53 58 62 67 72 76 80 85 89 20 94 "98 103 107 112 116 121 125 130 134 30 139 143 148 152 157 161 165 170 174 179 40 183 187 192 197 201 206 210 215 219 223 50 228 232 237 241 246 250 255 259 264 268 60 273 277 282 286 291 295 300 304 309 313 70 317 321 326 330 335 339 344 348 353 358 80 362 367 372 376 380 385 389 393 398 402 90 407 411 416 420 425 429 434 438 443 447 124 GEOGRAPHIC TABLES AND FORMULAS. TABLE 20. Converting wheel revolutions into hundredths of a mile Continued. CIRCUMFERENCE OF WHEEL, 11.9 FEET. 1 2 3 4 6 7 8 9 10 4 9 13 18 22 27 31 '35 40 44 10 49 53 58 62 67 71 76 80 84 89 20 93 98 102 107 111 115 120 124 129 133 30 138 142 146 151 155 160 164 169 173 178 40 182 187 191 195 200 204 209 213 218 222 50 226 231 235 240 244 249 253 258 262 266 60 271 275 280 284 289 293 298 302 306 311 70 315 320 324 329 333 338 342 346 350 355 80 360 364 369 373 377 382 386 391 395 399 90 404 409 413 417 422 426 431 435 440 444 CIRCUMFERENCE OF WHEEL, 12 FEET. 1 2 3 4 5 6 7 8 9 10 4 9 13 18 22 26 31 35 40 44 10 48 53 57 62 66 70 75 . 79 84 88 20 91 96 100 104 109 ' 113 118 122 128 132 30 136 141 145 150 154 158 163 168 172 176 40 180 185 189 194 198 202 207 211 ; 216 220 50 224 229 233 238 242 246 251 255 260 264 60 268 273 277 281 286 290 295 299 304 308 70 312 317 321 326 330 334 339 343 348 352 80 356 361 365 370 374 378 383 388 392 396 90 400 405 409 414 418 422 427 431 436 440 CIRCUMFERENCE OF WHEEL, 12.1 FEET. 1 2 3 4 5 6 7 8 9 10 4 9 13 17 22 26 31 35 39 44 10 48 53 57 61 66 70 75 79 83 87 20 91 96 100 105 109 113 118 122 126 131 30 135 139 144 148 153 157 161 165 170 174 40 178 183 187 192 196 201 205 209 214 218 50 222 227 231 235 240 244 249 253 257 262 60 266 270 275 279 283 288 292 296 301 305 70 310 314 318 323 327 331 336 340 344 349 80 353 358 362 366 370 375 379 384 388 392 90 397 401 405 410 414 419 423 427 432 436 GEOGRAPHIC TABLES AND FORMULAS. 125 TABLE 20. Converting wheel revolutions into hundredth* of a mile Continued. CIRCUMFERENCE OF WHEEL, 12.2 FEET. i | 3 4 5 6 7 8 9 10 4 9 13 17 22 26 30 35 39 43 10 48 52 56 61 65 69 74 78 82 87 20 91 95 100 104 108 113 117 121 126 130 30 134 138 143 147 151 156 160 165 169 173 40 ITS 182 186 191 195 199 204 208 212 .216 50 221 225 230 234 238 243 247 251 256 260 60 264 268 273 277 281 286 290 294 299 303 70 307 312 316 320 325 329 333 338 342 346 80 351 356 359 364 368 372 377 381 385 390 1*0 395 399 404 408 412 417 421 425 429 433 After measuring wheel use nearest tenth for size of wheel. 126 GEOGRAPHIC TABLES AND FORMULAS. TABLE 21. Five-place logarithms of natural numbers, [Fractional change in a number corresponding to a change in its logarithm.] Computed from the formula, N ' fi //=modulus of common logarithms = 0.43429448. For A log N = 1 unit in A^ N For A log N = 4 units in A.ZV IT (in round numbers) Fourth place rA* , Fifth place Fifth place Sixth place Sixth place Seventh place . . Seventh place GEOGRAPHIC TABLES AND FORMULAS. TABLE 21. Five-place logarithms of natural numbers Continued. 127 N. L. 1 2 3 4 56789 00 000 30 103 47 712 60 206 69 897 77 815 84 510 90 309 95 424 1 2 3 4 5 6 7 8 9 00 000 04 139 07 918 11 394 14 613 30 103 32 222 34 242 36 173 38 021 47 712 49 136 50 515 51 851 53 148 60 206 61 278 62 325 63 347 64 345 69 897 70 757 71 600 72 428 73 239 77 815 78 533 79 239 79 934 80 618 84 510 85 126 85 733 86 332 86 923 90 309 90 849 91 381 91 908 92 428 95 424 95 904 96 379 % 848 97 313 17 609 20 412 23 045 25 527 27 875 39 794 41 497 43 136 44 716 46 240 54 407 55 630 56 820 57 978 59 106 65 321 66 276 67 210 68 124 69 020 74 036 74 819 75 587 76 343 77 085 81 291 81 954 82 607 83 251 83 885 87 506 88 081 88 649 89 209 89 763 92 942 93 450 93 952 94 448 94 939 97 772 98 227 98 677 99 123 99 564 10 00 000 00 432 00 860 01 284 01 703 02 119 02 531 02 938 03 342 03 743 11 12 13 14 15 16 17' 18 19 04 139 04 532 04 922 05 308 05 690 07 918 08 279 08 636 08 991 09 342 11 394 11 727 12 057 12 385 12 710 14 613 14 922 15 229 15 534 15 836 17 609 17 898 18 184 18 469 18 752 20 412 20 683 20 952 21 219 21 484 23 045 23 300 23 553 23 805 24 055 25 527 25 768 26 007 26 245 26 482 27 875 28 103 28 330 28 556 28 780 06070 06446 06819 07188 07555 09 691 10 037 10 380 10 721 11 059 13 033 13 354 13 672 13 988 14 301 16 137 16 435 16 732 17 026 17 319 19 033 19 312 19 590 19 866 20 140 21 748 22 Oil 22 272 22 531 22 789 24 304 24 551 24 797 25 042 25 285 26 717 26 951 27 184 27 416 27 646 29 003 29 226 29 447 29 667 29 885 ' 20 30 103 30 320 30 535 30 750 30 963 31 175 31 387 31 597 31 806 32 015 21 22 23 24 25 26 27 28 29 32 222 32 428 32 634 32 838 33 041 34 242 34 439 34 635 34 830 35 025 36 173 36 361 36 549 36 736 36 922 38 021 38 202 38 382 38 561 38 739 39 794 39 967 40 140 40 312 40 483 41 497 41 664 41 830 41 9% 42 160 43 136 43 297 43 457 43 616 43 775 44 716 44 871 45 025 45 179 45 332 46 240 46 389 46 538 46 687 46 835 33 244 33 445 33 646 33 846 34 044 35 218 35 411 35 603 35 793 35 984 37 107 37 291 37 475 37 658 37 840 38 917 39 094 39 270 39 445 39 620 40 654 40 824 40 993 41 162 41 330 42 325 42 488 42 651 42 813 42 975 43 933 44 091 44 248 44 404 44 560 45 484 45 637 45 788 45 939 46 090 46 982 47 129 47 276 47 422 47 567 30 47 712 47 857 48 001 48 144 48 287 48 430 48 572 48 714 48 855 48 996 31 32 33 34 35 36 37 38 39 49 136 49 276 49 415 49 554 49 693 50 515 50 651 50 786 50 920 51 055 51 851 51 983 52 114 52 244 52 375 53 148 53 275 53 403 53 529 53 656 54 407 54 531 54 654 54 777 54 900 55 630 55 751 55 871 55 991 56 110 56 820. 56 937 57 054 67 171 57 287 57 978 58 092 58 206 58 320 58 433 59 106 59 218 59 329 59 439 59 550 49 831 49 969 50 106 50 243 50 379 51 188 51 322 51 455 51 587 51 720 52 504 52 634 52 763 52 892 53 020 53 782 53 908 64 033 54 158 54 283 55 023 55 145 55 267 55 388 55 509 56 229 56 348 66 467 56 585 56 703 57 403 57 519 57 634 57 749 57 864 58 546 68 659 58 771 58 883 58 995 59 660 69 770 59 879 59 988 60 097 40 60 206 60 314 60 423 60 531 60 638 60 745 60 853 60 959 61 066 61 172 41 42 43 44 45 46 47 48 49 61 278 61 384 61 490 61 595 61 700 62 325 62 428 62 531 62 634 62 737 63 347 63 448 63 548 63 649 63 749 64 345 64 444 64 542 64 640 64 738 65 321 65 418 65 514 65 610 65 706 66 276 66 370 66 464 66 558 66 652 67 210 67 302 67 394 67 486 67 578 68 124 68 215 68 305 68 395 68 485 69 020 69 108 69 197 69 285 69 373 61 805 61 909 62 014 62 118 62 221 62 839 62 941 63 043 63 144 63 246 63 849 63 949 64 048 64 147 64 246 64 836 64 933 65 031 65 128 65 225 65 801 65 896 65 992 66 087 66 181 66 745 66 839 66 932 67 025 67 117 67 669 67 761 67 852 67 943 68 034 68 574 68 664 68 753 68 842 68 931 69 461 69 548 69 636 69 723 69 810 50 69 897 69 984 70 070 70 157 70 243 70 329 70 415 70 501 70 586 70 672 N. L. 1 2 3 4 56789 1' = 2 : 3 = 4 = = 60" S. 4. 68 557 T. 4. 68 557 = 120 4. 68 557 4. 68 557 = 180 4. 68 557 4. 68 557 = 240 4.68557 4.68558- 5' = 300" S. 4. 68 557 T. 4. 68 558 6 = 360 4. 68 557 4. 68 558 7 = 420 4. 68 557 4. 68 568 8 = 480 4. 68 657 4. 68 558 128 GEOGRAPHIC TABLES AND FORMULAS. TABLE 21. Five-place logarithms of natural numbers Continued. N. L. 1 2 3 4 56789 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 69 897 69 984 70 070 70 157 70 243 70 329 70* 415 70 501 70 586 70 672 70 757 70 842 70 927 71 012 71 096 71 600 71 684 71 767 71 850 71 933 72 428 72 509 72 591 72 673 72 754 73 239 73 320 73 400 73 480 73 560 74 036 74 115 74 194 74 273 74 351 74 819 74 896 74 974 75 051 75 128 75 587 75 664 75 740 75 815 75 891 76 343 76 418 76 492 76 567 76 641 77085 77159 77232 77305 77379 71 181 71 265 71 349 71 433 71 517 72 016 72 099 72 181 72 263 72 346 72 835 72 916 72 997 73 078 73 159 73 640 73 719 73 799 73 878 73 957 74 429 74 507 74 586 74 663 74 741 75 205 75 282 75 358 75 435 75 511 75 967 76 042 76 118 76 193 76 268 76 716 76 790 76 864 76 938 77 012 77 452 77 525 77 597 77 670 77 743 77 815 77 887 77 960 78 032 78 104 78 176 78 247 78 319 78 390 78 462 78 533 78 604 78 675 78 746 78 817 79 239 79 309 79 379 79 449 79 518 79 934 80 003 80 072 80 140 80 209 80 618 80 686 80 754 80 821 80 889 81 291 81 358 81 425 81 491 81 558 81 954 82 020 82 086 82 151 82 217 82 607 82 672 82 737 82 802 82 866 83 251 83 315 83 378 83 442 83 506 83 885 83 948 84 Oil 84 073 84 136 78 888 78 958 79 029 79 099 79 169 79 588 79 657 79 727 79 7% 79 865 80 277 80 346 80 414 80 482 80 550 80 956 81 023 81 090 81 158 81 224 81 624 81 690 81 757 81 823 81 889 82 282 82 347 82 413 82 478 82 543 82 930 82 995 83 059 83 123 83 187 83 569 83 632 83 69*5 83 759 83 822 84 198 84 261 84 323 84 386 84 448 84 510 84 572 84 634 84 696 84 757 84 819 84 880 84 942 85 003 85 065 85 126 85 187 85 248 85 309 85 370 85 733 85 794 85 854 85 914 85 97,4 86 332 86 392 86 451 86 510 86 570 86 923 86 982 87 040 87 099 87 157 87 506 87 664 87 622 87 679 87 737 88 081 88 138 88 195 88 252 88 309 88 649 88 705 88 762 88 818 88 874 89 209 89 265 89 321 89 376 89 432 89 763 89 818 89 873 89 927 89 982 85 431 85 491 85 552 85 612 85 673 86 034 86 094 86 153 86 213 86 273 86 629 86 688 86 747 86 806 86 864 87 216 87 274 87 332 87 390 87 448 87 795 87 852 87 910 87 967. 88 024 88 366 88 423 88 480 88 536 88 593 88 930 88 986 89 042 89 098 89 154 89 487 89 542 89 597 89 653 89 708 90 037 90 091 90 146 90 200 90 255 90 309 90 363 90 417 90 472 90 526 90 580 90 634 90 687 90 741 90 795 90 849 90 902 90 956 91 009 91 062 91 381 91 434 91 487 91 540 91 593 91 908 91 960 92 012 92 065 92 117 92 428 92 480 92 531 92 583 92 634 92 942 92 993 93 044 93 095 93 146 93 450 93 500 93 551 93 601 93 651 93 952 94 002 94 052 94 101 94 151 94 448 94 498 94 547 94 59 94 645 94 939 94 988 95 036 95 085 95 134 91 116 91 169 91 222 91 275 91 328 91 645 91 698 91 751 91 803 91 855 92 169 92 221 92 273 92 324 92 376 92 686 92 737 92 788 92 840 92 891 93 197 93 247 93 298 93 349 93 399 93 702 93 752 93 802 93 852 93 902 94 201 94 250 94 300 94 349 94 399 94 694 94 743 94 792 94 841 94 890 95 182 95 231 95 279 95 328 95 376 95 424 95 472 95 521 95 569 95 617 95 665 95 713 95 761 95 809 95 856 95 904 95 952 95 999 96 047 96 095 96 379 96 426 96 473 96 520 96 567 96 848 96 895 96 942 96 988 97 035 97 313 97 359 97 405 97 451 97 497 97 772 97 818 97 864 97 909 97 955 98 227 98 272 98 318 98 363 98 408 98 677 98 722 98 767 98 811 98 856 99 123 99 167 99 211 99 255 99 300 99 564 99 607 99 651 99 695 99 739 96 142 96 190 96 237 96 284 96 332 96 614 96 661 96 708 96 755 96 802 97 081 97 128 97 174 97 220 97 267 97 543 97 589 97 635 97 681 97 727 98 000 98 046 98 091 98 137 98 182 98 453 98 498 _ 98 543 98 588 98 632 98 900 98 945 98 989 99 034 99 078 99 344 99 388 99 432 99 476 99 520 99 782 99 826 99 870 99 913 99 957 00 000 00 043 00 087 00 130 00 173 00 217 00 260 00 303 00 346 00 389 v. L. 1 2 3 4 56789 9' = 540" S. 4. 68 557 T. 4. 68 558 13' = 780" S. 4. 68 557 T. 4. 68 558 10 = 600 4. 68 557 4. 68 558 14 -= 840 4. 68 557 4. 68 558 11 = 660 4. 68 557 4. 68 558 15 = 900 4. 68 557 4. 68 558 12 = 720 4. 68 557 4. 68 558 16 = 960 4. 68 557 4. 68 558 GEOGRAPHIC .TABLES AND FORMULAS. TABLE 21. Five-place logarithms of natural numbers Continued. 129 N. L. 1 2 3 4 56789 P. P. 100 00 000 043 087 130 173 217 260 303 346 389 101 432 475 518 56 604 647 689 732 775 817 44 43 42 102 103 860 903 945 988 *030 01 284 326 368 410 452 *072 *115 #157 *199 *242 494 536 578 620 662 1 2 4,4 4,3 4,2 8,8 8,6 8,4 104 105 106 70S 745 787 828 870 02 119 160 202 243 284 531 572 612 653 694 912 953 995 *036 #078 325 366 407 449 490 735 776 816 857 898 3 4 5 6 13,2 12,9 12,6 17,6 17,2 16,8 22,0 21,5 21,0 26,4 25,8 25,2 107 108 109 938 979 *019 *060 *100 03 342 383 423 463 503 743 782 822 862 902 *14l *181 *222 *262 *302 543 583 623 663 703 941 981 #021 *060 *100 7 8 9 30,8 30,1 29,4 35,2 34,4 33,6 39,6 38,7 37,8 110 04 139 179 218 258 297 336 376 415 454 493 111 112 113 532 571 610 650 689 922 961 999 *038 #077 05 308 346 385 423 461 727 766 805 844 883 #115 #154 *192 #231 *269 500 538 576 614 652 1 2 41 40 39 4,1 4,0 3,9 8,2 8,0 7,8 114 115 116 690 729 767 805 843 06 070 108 145 183 221 446 483 521 558 595 881 918 956 994 *032 258 2% 333 371 408 633 670 707 744 781 3 4 5 6 12,3 12,0 11,7 16,4 16,0 15,6 20,5 20,0 19,5 24,6 24,0 23,4 117 118 819 856 893 930 967 07 188 225 262 298 335 *004 #041 *078 *115 #151 372 408 445 482 518 7 8 9 28,7 28,0 27,3 32,8 32,0 31,2 36 9 36 35 1 119 556 591 628 664 700 737 773 809 846 882 120 918 954 990 *027 *063 ,099 *135 *171 *207 #243 121 08 279 314 350 386 422 458 493 529 565 600 38 37 36 122 636 672 707 743 778 814 849 884 920 955 1 38 37 36 123 991 *026 *061 *096 *132 *167 *202 *237 *272 *307 2 7,6 7,4 7,2 3 Ily4 11 1 10 8 124 125 126 09 342 377 412 447 482 691 726 760 795 830 10 037 072 106 140 175 517 552 587 621 656 864 899 934 968 *003 209 243 278 312 346 4 5 6 15,2 14,8 14,4 19,0 .18,5 18,0 22,8 22,2 21,6 127 ' 128 129 380 415 449 483 517 721 756 789 823 857 11 059 093 126 160 193 551 685 619 653 687 890 924 958 992 *025 227 261 294 327 361 7 8 9 26,6 25,9 25,2 30,4 29,6 28,8 34,2 33,3 32,4 130 394 428 461 494 528 661 594 628 661 694 131 727 760 793 826 860 893 926 959 992 *024 35 34 33 132 133 12 057 090 123 156 189 385 418 450 483 516 222 254 287 320 352 548 581 613 646 678 1 2 3,5 3,4 3,3 7,0 6,8 6,6 134 135 136 710 743 775 808 840 13 033 066 098 130 162 354 386 418 450 481 872 905 937 969 *001 194 226 258 290 322 513 545 577 609 640 3 4 5 6 10,5 10,2 9,9 14,0 13,6 13,2 17,5 17,0 16,5 21,0 20,4 19,8 137 138 672 704 735 767 799 988 *019 *051 *082 #114 830 862 893 925 956 *145 *176 *208 *239 #270 7 8 9 24,5 23,8 23,1 28,0 27,2 26,4 31,5 30 6 29 7 139 14 301 333 364 395 426 457 489 520 551 582 140 613 644 675 706 737 768 799 829 860 891 141 922 953 983 *014 #045 #076 *106 *137 *168 *198 32 31 30 142 143 15 229 259 290 320 351 534 564 594 625 655 381 412 442 473 503 685 715 746 776 806 1 2 3,2 3,1 3,0 6,4 6,2 6,0 3 9,6 9 3 9,0 144 145 146 836 866 897 927 957 16 137 167 197 227 256 435 465 495 524 554 987 *017 *047 *077 #107 286 316 346 376 406 584 613 643 673 702 4 5 6 12,8 12,4 12,0 16,0 15,5 15,0 19,2 18,6 18,0 147 148 149 732 761 791 820 850 17 026 056 085 114 143 319 348 377 406 435 879 909 938 967 997 173 202 231 260 289 464 493 522 551 580 7 8 9 22,4 21,7 21,0 25,6 24,8 24,0 28,8 27,9 27,0 150 609 638 667 696 725 754 782 811 840 869 X. L. 1 2 3 4 56789 P. P. 16' = 960" S. 4. 68 557 T. 4. 68 558 21' = 1260" S. 4. 68 557 T. . 68 558 17 = 1020 4. 68 557 4. 68 558 22 = 1320 4. 68 557 4. 68 558 18 = 1080 4. 68 557 4. 68 558 23 = 1380 4. 68 557 . 68 558 19 = 1140 4. 68 557 4. 68 558 24 = 1440 4. 68 557 < . 68 558 20 = 1200 4. 68 557 4. 68 558 25 = 1500 4. 68 557 .68 558 4606108 9 130 GEOGEAPHIC TABLES AND FOEMULAS. TABLE 21. Five-place logarithms of natural numbers Continued. N. L. 1 2 3 4 56789 P. P. 150 17 609 638 667 696 725 754 782 811 840 869 151 152 898 926 955 984 *013 18 184 213 241 270 298 *041 *070 *099 *127 *156 327 355 384 412 441 29 28 163 469 498 526 554 583 611 639 667 696 724 1 2,9 2,8 2 5,8 5,6 154 752 780 808 837 865 893 921 949 977 *005 3 8,7 8,4 155 19 033 061 089 117 145 173 201 229 257 285 4 11,6 11,2 156 312 340 368 396 424 451 479 507 535 562 5 14,5 14,0 6 17,4 16,8 157 590 618 645 673 700 728 756 783 811 838 7 20,3 19,6 158 866 893 921 948 976 *003 *030 #058 *085 *112 8 23,2 22,4 159 20 140 167 194 222 249 276 303 330 358 385 9 26,1 25,2 160 412 439 466 493 520 548 575 602 629 656 161 683 710 737 763 790 817 844 871 898 925 O7 .)<: 162 163 952 978 *005 *032 #059 21 219 245 272 299 325 *085 *112 *139 *165 *192 352 378 405 431 458 1 - 2,7 2,6 2 6,4 5,2 164 484 511 537 564 590 617 643 669 696 722 3 8,1 7,8 165 748 775 801 827 854 880 906 932 958 985 4 10,8 10,4 166 22 Oil 037 063 089 115 141 167 194 220 246 5 13,5 13,0 6 16,2 15,6 167 272 298 324 350 376 401 427 453 479 505 7 18,9 18,2 168 531 557 583 608 634 660 686 712 737 763 8 21,6 20,8 169 789 814 840 866 891 917 943 968 994 *019 9 24,3 23,4 170 23 045 07C 096 121 147 172 198 223 249 274 171 300 325 350 376 401 426 452 477 502 528 172 173 553 578 603 629 654 805 830 855 880 905 679 704 729 754 779 930 955 980 *005 *030 1 2,6 2 5,0 174 24 055 080 105 130 155 180 204 229 254 279 3 7,5 175 304 329 353 378 403 428 452 477 502 527 4 10,0 176 551 576 601 625 650 674 699 724 748 773 5 12,5 6 15,0 177 178 797 822 846 871 895 25 042 066 091 115 139 920 944 969 993 *018 164 188 212 237 261 7 17,5 8 20,0 179 285 310 334 358 382 406 431 455 479 503 9 22,5 180 627 551 575 600 624 648 672 696 720 744 181 182 183 768 792 816 840 864 26 007 031 055 079 102 245 269 293 316 340 888 912 935 959 983 126 150 174 198 221 364 387 411 435 458 1 24 23 2,4 2,3 2 4,8 4,6 184 482 505 529 553 576 600 623 647 670 694 3 7,2 6,9 185 186 717 741 764 788 811 951 975 998 *021 *045 834 858 881 905 928 *068 *091 #114 #138 *161 4 5 9,6 9,2 12,0 11,5 6 14,4 13,8 187 27 184 207 231 254 277 300 323 346 370 393 7 16,8 16,1 188 416 439 462 485 508 531 554 577 600 623 8 19,2 18,4 189 646 669 692 715 738 761 784 807 830 852 9 21,6 20,7 190 875 898 921 944 967 989 #012 #035 *058 *081 191 28 103 126 149 171 194 217 240 262 285 307 22 21 192 330 353 375 398 421 443 466 488 511 533 193 556 578 601 623 646 668 691 713 735 758 1 2,2 2,1 2 4,4 4,2 194 780 803 825 847 870 892 914 937 959 981 3 6,6 6,3 195 29 003 026 048 070 092 115 137 159 181 203 4 8,8 8,4 196 226 248 270 292 314 336 358 380 403 425 5 11,0 10,5 6 13,2 12,6 197 447 469 491 513 535 557 579 601 623 645 7 15,4 14,7 198 667 688 710 732 754 776 798 820 842 863 8 17,6 16,8 199 885 907 929 951 973 994 *016 *038 *060 *081 9 19,8 18,9 200 30 103 125 146 168 190 211 233 255 276 298 ' N. L. 1 2 3 4 56789 P. P. 25' = 1500" S. 4. 68 657 T. 4. 68 558 30' = 1800" S. 4. 68 557 T. 4. 68 559 26 = 1560 4. 68- 557 4. 68 558 31 = 1860 4. 68 557 4. 68 559 27 = 1620 4. 68 557 4. 68 558 32 = 1920 4. 68 557 4. 68 559 28 = 1680 4. 68 557 4. 68 558 33 = 1980 4. 68 557 4. 68 559 29 - 1740 4. 68 557 4. 68 558 34 = 2040 4. 68 557 4. 68 669 GEOGRAPHIC TABLES AND FORMULAS. TABLE 21. Five-place logarithms of natural numbers Continued. 131 N. L. 1 2 3 4 5 6789 P. P. 200 30 103 125 146 168 190 211 233 255 276 298 201 329 341 363 384 406 428 449 471 492 514 22 21 202 535 557 578 600 621 643 664 685 707 728 1 22 21 203 7jk) 771 792 814 835 856 878 899 920 942 2 4^4 4,2 3 66 63 204 205 963 984 #006 *027 *048 31 175 197 218 239 260 *069 *091 *112 #133 #154 281 302 323 34 366 4 8,8 8,4 5 11,0 10,5 206 387 408 429 450 471 492 513 534 555 676 6 13,2 12,6 207 208 209 597 618 639 660 681 806 827 848 869 890 32 015 035 056 077 098 702 723 744 765 785 911 931 952 973 994 118 139 160 181 201 7 15,4 14,7 8 17,6 16,8 9 19,8 18,9 210 222 243 263 284 305 325 346 366 387 408 211 428 449 469 490 519 531 562 572 593 613 20 212 634 654 675 695 715 736 756 777 797 818 1 on 213 838 858 879 899 919 940 960 980 #001 #021 JL 2 i*f\J 4,0 214 215 33 041 062 082 102 122 244 264 284 304 325 18 163 183 20? 224 365 385 405 425 3 4 5 6,0 8,0 10,0 216 445 465 486 506 526 646 566 586 606 626 6 12,0 217 218 646 666 686 706 726 846 866 885 905 925 746 945 766 786 806 826 965 985 *005 #025 7 8 g 14,0 16,0 ifl n 219 34 044 064 084 104 124 143 163 183 203 223 220 242 262 282 301 321 341 361 380 400 420 221 439 459 479 498 518 537 557 577 596 616 19 222 635 655 674 694 713 733 753 772 792 811 1 1 Q 223 830 850 869 889 908 928 947 967 986 #005 2 3,8 224 225 35 025 044 064 083 102 218 238 257 276 295 315 141 160 180 199 334 353 372 392 3 4 5 5,7 7,6 9 5 226 411 430 449 468 488 607 526 545 564 583 6 J,tF 11/4 227 228 603 622 641 660 679 793 813 832 851 870 698 889 717 736 755 774 908 927 946 965 7 8 9 13,3 15,2 17.1 229 984 #003 #021 *040 #069 #078 #097 #116 *135 *154 230 36 173 192 211 229 248 267 286 305 324 342 231. 232 361 380 399 418 436 549 568 586 605 624 455 642 474 493 511 530 661 680 698 717 18 1 1.8 233 736 754 773 791 810 829 847 866 884 903 2 3,6 234 922 940 959 977 996 *014 #033 #051 #070 *088 3 4 5,4 7,2 235 37 107 125 144 162 181 199 218 236 254 273 5 9,0 236 291 310 328 346 365 383 401 420 438 457 6 10,8 237 475 493 511 530 548 566 585 603 621 639 7 g 12,6 14,4 238 239 658 676 694 712 731 840 858 876 894 912 749 931 767 785 803 822 949 967 985 *003 9 240 38 021 039 057 075 093 112 130 148 166 184 241 202 220 238 266 274 292 310 328 346 364 17 242 382 399 417 435 '453 471 489 507 525 543 1 1-7 243 561 578 596 614 632 650 668 686 703 721 2 3,4 244 739 757 775 792 810 828 846 863 881 899 3 4 5,1 6,8 245 917 934 952 970 987 *005 *023 *041 #058 #076 5 8,5 246 39 094 111 129 146 164 182 199 217 235 252 6 10,2 247 279 287 305 322 340 358 375 393 419 428 7 g 11,9 13,6 248 249 445 463 480 498 515 620 637 655 672 690 533 707 650 568 585 602 724 742 759 777 9 15,3 250 794 811 829 846 863 881 898 915 933 950 N. L. 1 2 3 4 5 6789 P. P. 33' = 1980" S. 4. 68 557 T. 4. 68 559 38' = 2280" S. 4. 68 557 T. 4. 68 559 34 = 2040 4. 68 557 4. 68 559 39 = 2340 4. 68 557 4. 68 559 35 = 2100 4. 68 567 4. 68 669 40 = 2400 4. 68 557 4. 68 559 36 = 2160 4. 68 557 4. 68 569 41 = 2460 4. 68 566 4. 68 560 37 = 2220 4. 68 557 4. 68 559 42 = 2520 4. 68 556 4. 68 560 132 GEOGRAPHIC TABLES AND FORMULAS. TABLE 21. Five-place logarithms of natural numbers Continued. N. L. 1 2 3 4 56789 P. P. 250 39 794 811 829 846 863 881 898 915 933 950 251 967 985 *002 *019 *037 #054 *071 *088 *106 *123 18 252 40 140 157 175 192 209 226 243 261 278 295 1 1,8 253 312 329 346 364 381 398 415 432 449 466 2 3,6 3 5,4 254 483 500 518 535 552 569 58G 603 620 637 4 7,2 255 654 671 688 705 722 739 756 773 790 807 5 9,0 256 824 841 858 875 892 909 926 943 960 976 6 10,8 7 12,6 257 258 993 #010 *027 *044 *061 41 162 179 196 212 229 *078 *095 *111 *128 #145 246 263 280 296 313 "8 9 14,4 16,2 259 330 347 363 380 397 414 430 447 464 481 260 497 514 531 547 564 581 597 614 631 647 261 664 681 697 714 731 747 764 780 797 814 17 262 830 847 863 880 896 913 929 946 963 979 1 1/7 263 996 #012 *029 *045 *062 *078 *095 *m *127 *144 2 3,4 264 42 160 177 193 210 226 243 259 275 292 308 3 4 5,1 6,8 265 266 325 341 357 374 390 488 504 521 537 553 406 423 439 455 472 570 586 602 619 635 5 6 8,5 10,2 267 651 667 684 700 716 732 749 765 781 797 7 3 11,9 13,6 268 269 81? 830 846 862 878 975 991 #008 *24 #040 894 911 927 943 959 *056 *072 *088 *104 #120 9 15,3 270 43 136 152 169 185 201 217 233 249 265 281 271 297 313 329 345 361 377 393 409 425 441 16 272 457 473 489 505 521 537 553 569 584 600 273 616 632 648 664 680 696 712 727 743 759 1 1,6 2 3/2 274 775 791 807 823 838 854 870 886 902 917 3 4,8 275 933 949 965 981 996 #012 *028 *044 *059 *075 4 6/4 276 44 091 107 122 138 154 170 185 201 217 232 5 8,0 (j 9,6 277 248 264 279 295 311 326 342 358 373 389 7 11,2 278 404 420 436 451 467 483 498 514 529 545 8 12,8 279 560 576 592 607 623 638 654 669 685 700 9 14,4 280 716 731 747 762 778 793 809 824 840 855 281 871 886 902 917 932 948 963 979 994 *010 282 45 025 040 056 071 086 10? 117 133 148 163 15 283 179 194 209 225 240 255 271 286 301 317 1 1,5 2 3,0 284 285 . 332 347 362 378 393 484 500 515 530 545 408 423 439 454 469 561 576 591 606 621 3 4 4,5 6,0 286 637 652 667 682 697 712 728 743 758 773 5 7,5 287 788 803 818 834 849 864 879 894 909 924 6 7 9,0 10,5 288 289 939 954 969 984 *000 46 090 105 120 135 150 *015 *030 *045 #060 #075 165 180 195 210 225 8 9 12,0 13,5 290 240 255 270 285 300 315 330 345 359 374 291 389 404 419 434 449 464 479 494 509 523 292 293 538 553 568 583 598 687 702 716 731 746 613 627 642 657 672 761 776 790 805 820 1 14 1,4 294 835 850 864 879 894 909 923 938 953 967 2 2,8 295 982 997 *012 *026 *041 *056 *070 *085 *100 *114 3 4,2 296 47 129 144 159 173 188 202 217 232 246 261 4 5 5/6 7,0 297 276 290 305 31? 334 349 363 378 392 407 6 8,4 298 422 436 451 465 480 494 509 524 538 553 7 9,8 299 567 582 596 611 625 640 654 669 683 698 8 11,2 9 12,6 300 712 727 741 756 770 784 799 813 828 842 N. L. 1 2 3 4 56789 P. P. 41' = 2460" S. 4. 68 556 T. 4. 68 560 46' = 2760" S. 4. 68 556 T. 4. 68 560 42 = 2520 4. 68 556 4. 68 560 47 = 2820 4. 68 556 4. 68 560 43 = 2580 4. 68 556 4. 68 560 48 =. 2880 4. 68 556 4. 68 560 44 = 2640 4. 68 556 4. 68 560 49 = 2940 4. 68 556 4. 68 560 45 = 2700 4. 68 556 4. 68 560 50 = 3000 4. 68 556 4. 68 561 GEOGRAPHIC TABLES AND FORMULAS. TABLE 21. Five-place logarithms of natural numbers Continued. 138 N. L. 12 3 4 5 6789 P.P. 300 47 712 727 741 756 770 784 799 813 828 842 301 857 871 885 900 914 929 943 958 972 986 302 48 001 015 029 044 058 073 087 101 116 130 303 144 159 173 187 202 216 230 244 259 273 304 287 302 316 330 344 359 373 387 401 416 15 306 430 444 458 473 487 501 515 530 544 558 1 1,5 306 572 586 601 615 629 643 657 671 686 700 2 3,0 3 4,5 307 714 728 742 756 770 785 799 813 827 841 4 6,0 308 855 869 883 897 911 926 940 954 968 982 5 7,5 309 996 #010 *024 *038 *052 *066 *080 *094 #108 #122 6 7 9,0 10 S 310 49 136 150 164 178 192 206 220 234 248 262 8 -LU/0 12,0 311 312 276 290 304 318 332 415 429 443 457 471 3 360 374 388 402 499 513 527 541 9 13/0 313 554 568 582 596 610 624 638 651 665 679 314 693 707 721 734 748 762 776 790 803 817 315 831 845 859 872 886 900 914 927 941 955 14. 316 969 982 996 *010 *024 #037 *051 #065 *079 *092 1 1/4 317 50 106 120 133 147 161 174 188 202 215 229 1 2,8 318 243 256 270 284 297 311 325 338 352 365 3 4,2 319 379 393 406 420 433 447 461 474 488 501 4 5 5,6 7,0 320 515 529 542 556 569 583 596 610 623 637 6 8,4 321 651 664 678 691 705 718 732 745 759 772 8 11/2 322 786 799 813 826 840 853 866 880 893 907 9 12,6 323 920 934 947 961 974 987 #001 *014 *028 #041 324 51 055 068 081 095 108 12J 135 148 162 175 325 326 188 202 215 228 242 322 335 348 362 375 255 388 268 282 295 308 402 415 428 441 327 455 468 481 495 508 521 534 548 561 574 13 328 587 601 614 627 640 654 667 680 693 706 1 1,3 329 720 733 746 759 772 786 799 812 825 838 2 2/6 q Q 330 851 865 878 891 904 917 930 943 957 970 4 o/y 5/2 331 332 983 996 #009 *022 *035 52 114 127 140 153 166 *048 *061 #075 *088 *101 179 192 205 218 231 5 6 6/6 7,8 9/1 333 244 257 270 284 297 310 323 336 349 362 8 10/4 334 375 388 401 414 427 440 453 466 479 492 9 11,7 335 504 517 530 543 556 569 582 595 608 621 336 634 647 660 673 686 699 711 724 737 750 337 763 776 789 802 815 827 840 853 866 879 338 339 892 905 917 930 943 53 020 033 046 058 071 956 084 969 982 994 *007 097 110 122 135 12 340 148 161 173 186 199 212 224 237 250 263 1 1.2 2 2,4 341 275 288 301 314 326 339 352 364 377 390 3 3,6 342 343 403 415 428 441 453 529 542 555 567 580 466 693 479 491 504 517 605 618 631 643 4 5 4,8 6,0 6 7,2 344 656 668 681 694 706 719 732 744 757 769 7 8,4 345 346 782 794 807 820 832 908 920 933 945 958 845 970 857 870 882 895 983 995 *OOS *020 8 9 9,6 10,8 347 348 54 033 045 058 070 083 158 170 183 195 208 095 220 108 120 133 145 233 245 258 270 349 283 295 307 320 332 345 357 370 382 394 350 407 419 432 444 456 469 481 494 506 518 N. L. 1 2 3 4 5 6,7 8 9 P. P. 50' = 3000" S. 4. 68 556 T. 4. 68 561 55' = 3300" S.4. 68 556 T.4. 68 561 51 = 3060 4. 68 556 4. 68 561 56 = 3360 4. 68 55? 4. 38 561 52 = 3120 4. 68 556 4. 68 561 57 = 3420 4. 68 555 4. 68 561 53 = 3180 4. 68 556 4. 68 561 58 = 3480 4. 68 555 4. 68 562 54 =* 3240 4. 68 556 4. 68 561 59 = 3540 4. 68 555 4. 68 562 134 GEOGRAPHIC TABLES AND FORMULAS. TABLE 21. Five-place logarithms of natural numbers Continued. N. L. 1 2 3 4 56789 P.P. 350 54 407 419 432 444 456 469 481 494 506 518 351 352 531 543 555 568 580 654 667 679 691 704 593 605 617 630 642 716 728 741 753 765 353 777 790 802 814 827 839 851 864 876 888 13 354 900 913 925 937 949 962 974 986 998 *011 355 55 023 035 047 060 072 084 096 108 121 133 O 356 145 157 169 182 194 206 218 230 242 255 3 2,b 3,9 357 267 279 291 303 315 328 340 352 364 376 4 5,2 358 388 400 413 425 437 449 461 473 485 497 5 6,5 359 509 522 534 546 558 570 582 594 606 618 6 7 7,8 9,1 360 630 642 654 666 678 691 703 715 . 727 739 8 10,4 9 11,7 361 751 763 775 787 799 811 823 835 847 859 362 871 883 895 907 919 931 943 955 967 979 363 991 *003 #015 *027 #038 *050 *062 *074 *086 #098 364 365 56 110 122 134 146 158 229 241 253 265 277 170 182 194 205 217 289 301 312 324 336 1 O 366 348 360 372 384 3% 407 419 431 443 455 IB 1 1/2 367 467 478 490 502 514 526 538 549 561 573 2 2,4 368 369 585 597 608 620 632 703 714 726 738 750 644 656 667 679 691 761 773 785 797 808 3 4 3,6 4,8 370 5 6 6,0 7,2 820 832 844 855 867 879 891 902 914 926 371 937 949 961 972 984 996 *008 *019 *031 #043 7 8,4 O A 372 57 054 066 078 089 101 113 124 136 148 159 y/t> 10 ft 373 171 183 194 206 217 229 241 252 264 276 -iU/o 374 287 299 310 322 334 345 357 368 380 392 375 376 403 415 426 438 449 519 530 542 553 565 461 473 484 496 507 576 588 600 611 623 377 634 646 657 669 680 692 703 715 726 738 11 378 749 761 772 784 795 807 818 830 841 852 1 1/1 379 864 875 887 898 910 921 933 944 955 967 2 2,2 O Q 380 978 990 *001 *013 *024 *035 *047 *058 *070 *081 4 o/o 4,4 381 58 092 104 115 127 138 149 161 172 184 195 5 5,5 A A 382 206 218 229 240 252 263 274 286 297 309 O,O 383 320 331 343 354 365 377 388 399 410 422 8 8,8 384 386 386 433 444 456 467 478 546 557 569 580 591 659 670 681 692 704 490 501 512 524 535 602 614 625 636 647 715 726 737 749 760 9 9,9 387 771 782 794 805 816 827 838 850 861 872 388 883 894 906 917 928 939 950 961 973 984 1 f\ 389 995 *006 *017 *028 *040 *051 #062 *073 *084 #095 J.U i n 390 59 106 118 129 140 151 162 173 184 195 207 . 2 J./U 2,0 391 218 229 240 251 262 273 284 295 306 318 3 4 3,0 392 393 329 340 351 362 373 439 450 461 472 483 384 395 406 417 428 494 506 517 528 539 5 6 5^0 6,0 394 550 561 572 583 594 605 616 627 638 649 7 7,0 o fi 395 660 671 682 693 704 715 726 737 748 759 o/U q n 396 770 780 791 802 813 824 835 846 857 868 y/u 397 879 890 901 912 923 934 945 956 966 977 398 988 999 *010 *021 #032 *043 *054 ,066 *076 *086 399 60 097 108 119 130 141 152 163 173 184 195 400 206 217 228 239 249 260 271 282 293 304 s. L. 1 2 3 4 56789 P.P. OP 58' = 3480" S. 4. 68 555 T. 4. 68 562 1 3' = 3780" S. 4. 68 555 T. 4. 68 562 59 = 3540 4. 68 555 4. 68 562 14= 3840 4. 68 555 4. 68 563 10= 3600 4. 68 555 4. 68 562 15= 3900 4. 68 555 4. 68 563 11= 3660 " 4. 68 555 4. 68 562 16= 3960 4. 68 555 4. 68 563 12= 3720 4. 68 555 4. 68 562 17= 4020 4. 68 555 4. 68 563 GEOGKAPHIC TABLES AJSTD FORMULAS. 135 TABLE 21. Five-place logarithms of natural numbers Continued. N. L. 1 2 3 4 5 6789 P . P. 400 60 206 217 228 239 249 260 271 282 293 304 401 314 325 336 347 358 369 379 390 401 412 402 423 433 444 455 466 477 487 498 509 520 403 531 541 552 563 574 584 595 606 617 627 404 638 649 660 670 681 692 703 713 724 735 405 746 756 767 778 788 799 810 821 831 842 406 853 863 874 885 895 906 917 927 938 949 11 407 959 970 981 991 *002 #013 *023 *034 *045 *055 1 1/1 408 61 066 077 087 098 109 119 130 140 151 162 2 2,2 409 172 183 194 204 215 225 236 247 257 268 3 3,3 410 278 289 300 310 321 331 342 352 363 374 4 5 4,4 5,5 411 384 395 405 416 426 437 448 458 469 479 6 6,6 412 413 490 500 511 521 532 595 606 616 627 637 542 648 553 563 574 584 658 669 679 690 7 8 9 7,7 8,8 9,9 414 415 700 711 721 731 742 805 815 826 836 847 752 857 763 773 784 794 868 878 888 899 416 909 920 930 941 951 962 972 982 993 *003 417 62 014 024 034 045 055 066 076 086 097 107 418 118 128 138 149 159 170 180 190 201 211 419 221 232 242 252 263 273 284 294 304 315 420 325 335 346 356 366 377 387 397 408 418 421 428 439 449 459 469 480 490 500 511 521 10 422 423 531 542 552 562 572 634 644 655 665 675 583 685 593 603 613 624 696 706 716 726 1 2 1/0 2,0 3 3,0 424 737 747 757 767 778 788 798 808 818 829 4 4,0 425 839 849 859 870 880 890 900 910 921 931 5 5,0 426 941 951 961 972 982 992 *002 #012 *022 *033 6 6,0 7 7,0 427 63 043 053 063 073 083 094 104 114 124 134 8 8,0 428 144 155 165 175 185 195 205 215 225 236 9 9,0 429 246 256 266 276 286 296 306 317 327 337 430 347 357 367 377 387 397 407 417 428 438 431 448 458 468 478 488 498 508 518 528 538 432 548 558 568 579 589 599 609 619 629 639 433 649 659 669 679 689 699 709 719 729 739 434 749 759 769 779 789 799 809 819 829 839 435 849 859 869 879 889 899 909 919 929 939 436 949 959 969 979 988 998 *008 #018 *028 *038 9 437 64 048 058 068 078 088 098 108 118 128 137 1 0,9 438 147 157 167 177 187 197 207 217 227 237 2 1,8 439 246 256 266 276 286 2% 306 316 -326 335 3 4 2,7 3,6 440 345 355 365 375 385 395 404 414 424 434 5 6 4,5 5,4 441 444 454 464 473 483 493 503 513 523 532 7 6,3 442 443 542 552 562 572 582 640 650 660 670 680 591 689 601 611 621 631 699 709 719 729 8 9 7,2 8,1 444 445 738 748 758 768 777 836 846 856 865 875 11 797 807 816 826 895 904 914 924 446 933 943 953 963 972 982 992 #002 *011 *021 447 65 031 040 050 060 070 079 089 099 108 118 448 128 137 147 157 167 176 186 196 205 215 449 225 234 244 254 263 273 283 292 302 312 450 321 331 341 350 360 369 379 389 398 408 N. L. 1 2 3 4 5 6789 P. P. 1 6' = 3960" S. 4. 68 555 T. 4. 68 563 1 11'= 4260" S. 4. 68 554 T. .68 564 1 7 = 4020 4. 68 555 4. 68 563 1 12 = 4320 4. 68 554 . 68 564 1 8 = 4080 4. 68 555 4. 68 563 1 13 = 4380 4. 68 554 . 68 564 1 9 = 4140 4. 68 555 4. 68 563 1 14 = 4440 4. 68 554 . 68 664 1 10 = 4200 4. 68 554 4. 68 563 1 15 = 4500 4. 68 554 . 68 564 136 GEOGRAPHIC TABLES AND FORMULAS. TABLE 21. Five-place logarithms of natural numbers Continued. N. L. 1 2 3 4 5 6789 P.P. 450 65 321 331 341 350 360 369 379 389 398 408 451 418 427 437 447 456 466 475 485 495 504 452 514 523 533 543 552 562 371 581 591 600 453 610 619 629 639 648 658 667 677 686 696 464 706 715 725 734 744 753 763 772 782 792 455 801 811 820 830 839 849 *58 868 877 887 456 896 906 916 925 935 944 954 963 973 982 10 457 992 #001 *011 *020 *030 *039 *049 *058 *068 *077 1 1,0 458 66 087 096 106 115 124 134 L43 153 162 172 2 2,0 459 181 191 200 210 219 229 238 247 257 266 3 3,0 460 276 285 295 304 314 323 332 342 351 361 4 4,0 5 5,0 461 370 380 389 398 408 417 427 436 445 455 6 6,0 462 464 474 483 492 502 511 321 530 539 549 7 7,0 463 558 567 577 586 596 605 614 624 633 642 8 8,0 9 9,0 464 465 652 661 671 680 689 745 755 764 773 783 699 708 717 727 736 792 801 811 820 829 466 839 848 857 867 876 885 894 904 913 922 467 932 941 950 960 969 978 987 997 *006 *015 468 67 025 034 043 052 062 071 080 089 099 108 469 117 127 136 145 154 164 173 182 191 201 470 210 219 228 237 247 256 265 274 284 293 471 302 311 321 330 339 348 357 367 376 385 9 472 473 394 403 413 422 431 486 495 504 514 523 440 449 459 468 477 532 541 550 560 569 1 0,9 2 1,8 3 2,7 474 678 587 596 605 614 624 633 642 651 660 4 3,6 475 669 679 688 697 706 715 724 733 742 752 5 4,5 476 761 770 779 788 797 806 S15 825 834 843 6 5,4 7 6,3 477 852 861 870 879 888 897 906 916 925 934 8 7,2 478 943 952 961 970 979 988 997 *006 *015 *024 9 8,1 479 68 034 043 052 061 070 079 088 '097 '106 '115 480 124 133 142 151 160 169 178 187 196 205 481 482 215 224 233 242 251 305 314 323 332 341 260 269 278 287 296 350 359 368 377 386 483 395 404 413 422 431 440 449 458 467 476 484 485 494 502 511 520 629 538 547 556 565 485 674 583 592 601 610 619 628 637 646 655 486 664 673 681 690 699 708 717 726 735 744 8 487 753 762 771 780 789 797 806 815 824 833 1 0,8 2 1,6 488 842 851 860 869 878 886 895 904 913 922 489 931 940 949 958 966 975 984 993 *002 t 011 4 3^2 490 69 020 028 037 046 055 064 073 082 090 099 5 4,0 6 4,8 491 108 117 126 135 144 152 161 170 179 188 7 5,6 492 197 205 214 223 232 241 249 258 267 276 8 6,4 493 285 294 302 311 320 329 338 346 355 364 9 7,2 494 373 381 390 399 408 417 425 434 443 452 495 461 469 478 487 496 504 513 522 531 539 496 548 557 566 674 583 592 601 609 618 627 497 636 644 653 662 671 679 688 697 705 714 498 499 723 732 740 749 758 810 819 827 836 845 767 854 775 784 793 801 862 871 880 888 500 897 906 914 923 932 940 949 958 966 975 N. L. 1 2 3 4 5 6789 P. P. 1 15'= 4600" S. 4. 68 564 T. 4. 68 564 1 16 = 4560 4. 68 564 4. 68 565 1 20'= 4800" S. 4. 68 554 T. 4. 68 566 1 21 = 4860 4. 68 553 4. 68 566 1 17 = 4620 4. 68 554 4. 68 565 1 22 = 4920 4. 68 553 4. 68 566 1 18 = 4680 4. 68 554 4. 68 565 1 23 = 4980 4. 68 553 4. 68 566 1 19 = 4740 4. 68 554 4. 68 565 1 24 = 5040 4. 68 653 4. 68 566 GEOGRAPHIC TABLES AND FORMULAS. TABLE 21. Five-place logarithms of natural numbers Continued. 137 N. L. 1 2 3 4 5 6789 P. P. 500 69 897 906 914 923 932 940 949 958 966 975 501 984. 992*001 *010 *018 *027* 036 *044 *053 *062 502 70 070 079 088 096 105 114 122 131 140 148 503 157 165 174 183 191 200 209 217 226 234 504 243 252 260 269 278 286 295 303 312 321 505 506 329 338 346 355 364 415 424 432 441 449 372 458 381 389 398 406 467 475 484 492 507 508 501 509 518 526 535 586 595 603 612 621 544 629 552 561 569 578 638 646 655 663 9 509 672 680 689 697 706 714 723 731 740 749 1 2 0,9 1/8 510 757 766 774 783 791 800 808 817 825 834 3 2,7 511 512 4 5 6 3,6 4/5 5,4 842 851 859 868 876 927 935 944 952 961 885 893 902 910 919- 969 978 986 995 *003 513 71 012 020 029 037 046 054 063 071 079 088 7 6,3 514 096 105 113 122 130 139 147 155 164 172 8 9 7,2 8,1 515 516 181 189 198 206 214 265 273 282 290 299 223 307 231 240 248 257 315 324 332 341 517 518 349 357 366 374 383 433 441 450 458 466 391 475 399 408 416 425 483 492 500 508 619 517 525 533 542 550 559 567 575 684 592 520 6CO 609 617 625 634 642 650 659 667 675 521 522 623 684 692 700 709 717 767 775 784 792 800 a50 858 867 875 883 725 809 892 734 742 750 759 817 825 834 842 900 908 917 925 1 2 8 0,8 1,6 524 933 941 950 958 966 975 983 991 999 *008 3 4 2,4 3,2 525 72 016 024 032 041 049 057 066 074 082 090 5 4,0 526 099 107 115 123 132 140 148 156 165 173 6 4,8 7 5,6 527 181 189 198 206 214 222 230 239 247 265 8 6,4 528 529 263 272 280 288 296 346 354 362 370 378 304 387 313 321 329 337 395 403 411 419 9 7,2 530 428 436 444 452 460 469 477 485 493 501 531 509 518 526 534 542 550 558 567 575 583 532 533 591 599 607 616 624 673 681 689 697 705 632 713 640 648 656 665 722 730 738 746 534 754 762 770 779 787 795 803 811 819 827 635 536 835 843 852 860 868 916 925 933 941 949 876 957 884 892 900 908 965 973 981 989 7 537 997 *006 *014 *022 *030 *038 *046 *054 *062 *070 1 0,7 538 73 078 086 094 102 111 119 127 135 143 151 2 1/4 539 159 167 175 183 191 199 207 215 223 231 3 2,1 540 239 247 255 263 272 280 288 296 304 312 5 3,5 541 320 328 336 344 352 360 368 376 384 392 6 4,2 542 400 408 416 424 432 440 448 456 464 472 7 4,9 C f 543 480 488 496 504 512 520 528 536 544 552 9 0,0 6,3 544 560 568 576 584 592 600 608 616 624 632 545 640 648 656 664 672 679 687 695 703 711 646 719 727 735 743 751 759 767 775 783 791 547 799 807 815 823 830 838 846 854 862 870 548 878 886 894 902 910 918 926 933 941 949 549 957 965 973 981 989 997* 005 *013 *020 *028 550 74 036 044 052 060 068 076 084 092 099 107 N. L. 1 2 3 4 5 6789 P. P. 1 23'= 4980" S. 4. 68 553 T. 4. 68 566 1 28'= 5280" S. 4. 68 553 T. 4. 68 567 1 24 = 5040 4. 68 553 4. 68 566 1 29 = 5340 ' 4. 68 553 4. 68 667 1 25 = 5100 4. 68 553 4. 68 566 1 30 = 5400 4. 68 553 4. 68 567 1 26 = 5160 4. 68 553 4. 68 567 1 31 = 5460 4. 68 552 4. 68 668 1 27 = 5220 4. 68 653 4. 68 567 1 32 = 5520 4. 68 552 4. 68 668 138 GEOGRAPHIC TABLES AND FORMULAS. TABLE 21. Five-place logarithms of natural numbers Continued. N. L. 1 2 3 4 5 6789 P. P. 550 74 036 044 052 060 068 076 084 092 099 107 551 115 123 131 139 147 155 162 170 178 186 552 553 194 202 210 218 225 273 280 288 296 304 233 241 249 257 265 312 320 327 335 343 554 565 556 351 359 367 374 382 429 437 445 453 461 607 515 523 531 539 390 398 406 414 421 468 476 484 492 500 547 554 562 570 578 557 586 593 601 609 617 663 671 679 687 695 624 632 640 648 656 702 710 718 726 733 559 741 749 757 764 772 780 788 796 803 811 560 819 827 834 842 850 858 865 873 881 889 561 896 904 912 920 927 935 943 950 958 966 562 974 981 989 997 *005 *012 * 320 *028 *035 *043 8 563 75 051 059 066 074 082 089 097 105 113 120 1 0,8 2 1,6 564 128 136 143 151 159 166 174 182 189 197 3 2,4 565 205 213 220 228 236 243 251 259 266 274 4 3,2 566 282 289 297 305 312 320 328 335 343 351 5 4,0 6 4,8 567 568 358 366 374 381 389 435 442 450 458 465 397 404 412 420 427 473 481 488 496 504 8 5,6 6,4 569 611 519 526 634 542 549 557 565 572 580 9 7,2 570 687 595 603 610 618 626 633 641 648 656 571 664 671 679 686 694 702 709 717 724 732 572 573 740 747 755 762 770 815 823 831 838 846 778 785 793 800 808 853 861 868 876 884 574 891 899 906 914 921 929 937 944 952 959 575 967 974 982 989 997 *005 *( 312 *020 *027 *035 576 76 042 050 057 065 072 080 087 095 103 110 577 118 125 133 140 148 155 163 170 178 185 578 579 193 200 208 215 223 268 275 283 290 298 230 238 245 253 260 305 313 320 328 335 580 343 350 358 365 373 380 388 395 403 410 581 582 418 425 433 440 448 492 500 507 515 522 456 462 470 477 485 530 537 545 552 559 7 583 567 574 582 589 597 604 612 619 626 634 1 0,7 2 1/4 584 585 641 649 656 664 671 716 723 730 738 745 678 686 693 701 708 753 760 768 775 782 3 4 2,1 2,8 586 790 797 805 812 819 827 834 842 849 856 5 3,5 6 4,2 587 588 864 871 879 886 893 938 945 953 960 967 901 908 916 923 930 975 982 989 997 *004 7 8 4,9 5,6 589 77 012 019 026 034 041 048 056 063 070 078 9 6,3 590 085 093 100 107 115 122 129 137 144 151 591 159 166 173 181 188 195 203 210 217 225 592 232 240 247 254 262 269 276 283 291 298 593 305 313 320 327 335 342 349 357 364 371 594 ' 595 379 386 393 401 408 452 459 466 474 481 415 422 430 437 444 488 495 503 510 517 596 525 532 539 54fc 554 561 568 576 583 590 597 597 605 612 619 627 634 641 648 656 663 598 670 677 685 692 699 706 714 721 728 735 599 743 750 757 764 772 779 786 793 801 808 600 815 822 830 837 844 851 859 866 873 880 N. L. 1 2 3 4 5 6789 P.P. 1 31' = 5460" S. 4. 68 552 T. 4. 68 568 1 36' = 5760" S. 4. 68 562 T. 4. 68 569 1 32 = 5520 4. 68 552 4. 68 568 1 37 = 5820 4. 68 552 4. 68 569 1 33 = 6580 4. 68 552 4. 68 568 1 38 = 5880 4. 68 552 4. 68 669 1 34 = 5640 4. 68 552 4. 68 568 1 39 = 5940 4. 68 551 4. 68 569 1 35 = 5700 4. 68 552 4. 68 669 1 40 = 6000 4. 68 551 4. 68 570 GEOGRAPHIC TABLES AND FORMULAS. TABLE 21. Five-place logarithms of natural numbers Continued. 139 N; L. 1 2 3 4 5 6789 P P. 600 77 815 822 830 837 844 851 859 866 873 880 601 887 895 902 909 916 924 931 938 945 952 602 960 967 974 981 988 9% * 003 *010 $017 *025 603 78 032 039 046 053 061 068 075 082 089 097 604 104 111 118 125 132 140 147 154 161 168 605 176 183 190 197 204 211 219 226 233 240 606 247 254 262 269 276 283 290 297 305 312 8 607 608 319 326 333 340 347 390 398 405 412 419 355 426 362 369 376 383 433 440 447 455 1 2 0,8 1,6 609 462 469 476 483 490 497 504 512 519 526 3 2,4 610 633 540 547 554 561 569 576 583 590 597 4 5 3,2 4,0 611 612 604 611 618 625 633 675 682 689 696 704 640 711 647 654 661 668 718 725 732 739 6 7 4,8 5,6 613 746 753 760 767 774 781 789 796 803 810 8 9 6,4 7,2 614 817 824 831 838 845 852 859 866 873 880 615 888 895 902 909 916 923 930 937 944 951 616 958 965 972 979 986 993 *000 *007 *014 *021 617 79 029 036 043 050 057 064 071 078 085 092 618 099 106 113 120 127 134 141 148 155 162 619 169 176 183 190 197 204 211 218 225 232 620 239 246 253 260 267 274 281 288 295 302 621 309 316 323 330 337 344 351 358 365 372 7 622 379 386 393 400 407 414 421 428 435 442 I 7 623 449 456 463 470 477 484 491 498 505 511 2 1/4 624 518 625 532 539 546 653 560 567 574 581 3 A 2,1 v 625 588 595 602 609 616 623 630 637 644 650 5 &r& 3 5 626 667 664 671 678 685 692 699 706 713 720 6 OfO 4,2 627 727 734 741 748 754 761 768 775 782 789 7 ' g 4,9 56 628 7% 808 810 817 824 831 837 844 851 858 cf/D 6 ^ 629 865 872 879 886 893 900 906 913 920 927 o/o 630 934 941 948 956 962 969 975 982 989 996 631 80 003 010 017 024 030 037 044 051 058 065 632 633 072 079 085 092 099 140 147 154 161 168 106 175 113 120 127 134 182 188 195 202 634 209 216 223 229 236 243 250 257 264 271 635 277 284 291 298 305 312 318 325 332 339 636 346 353 359 366 373 380 387 393 400 407 6 637 414 421 428 434 441 448 455 462 468 475 1 0,6 638 482 489 496 502 509 516 523 530 536 543 2 1,2 639 550 557 564 570 577 584 591 598 604 611 3 1/8 640 618 626 632 638 646 652 669 665 672 679 4 5 2,4 3,0 641 686 693 699 706 713 720 726 733 740 747 6 3,6 642 643 754 760 767 774 781 821 828 835 841 848 794 801 80 814 862 868 875 882 7 8 9 4,2 4,8 5,4 644 889 895 902 909 916 922 929 936 943 949 645 646 956 963 969 976 983 81 023 030 037 043 050 990 057 996 #003 *010 *017 064 070 077 084 647 090 097 104 111 117 124 131 137 144 151 648 158 164 171 178 184 191 198 204 211 218 649 224 231 238 245 251 258 265 271 278 285 650 291 298 305 311 318 325 331 338 345 351 N. L. 1 2 3 4 5 6789 P P. 40 7 = 6000" S. 4. 68 551 T. 4. 68 570 1 45' = 6300" S. 4. 68 551 T . 4. 68 571 41 = 6060 4. 68 551 4. 68 570 1 46 = 6360 4. 68 551 4. 68 571 42 = 6120 4. 68 551 4. 68 570 1 47 = 6420 4. 68 5i?0 4. 68 572 43 = 6180 4. 68 561 4. 68 570 1 48 =. 6480 4. 68 5$0 4. 68 572 44 = 6240 4. 68 661 4. 68 671 1 49 = 6540 4. 68 550 4. 68 572 140 GEOGRAPHIC TABLES AND FORMULAS. TABLE 21. Five-place logarithms of natural numbers Continued. N. L. 1 2 3 4 5 6789 P. P. 650 81 291 298 305 311 318 325 531 338 345 351 651 652 653 358 365 371 378 385 425 431 438 445 451 491 498 505 511 518 391 398 405 411 418 458 465 471 478 485 525 531 538 544 551 664 558 564 571 578 584 591 598 604 611 617 655 666 624 631 637 644 651 690 697 704 710 717 657 664 671 677 684 723 730 737 743 750 657 658 757 763 770 776 783 823 829 836 842 849 790 796 803 809 816 856 862 869 875 882 659 889 895 902 908 915 921 928 935 941 948 660 954 961 968 974 981 987 < )94 #000 *007 *014 661 82 020 027 033 040 046 053 ( )60 066 073 079 7 662 086 092 099 105 112 119 i 125 132 138 145 663 151 158 164 171 178 184 191 197 204 210 1 0,7 2 1,4 664 217 223 230 236 243 249 256 263 269 276 3 2,1 665 282 289 295 302 308 315 : J21 328 334 341 4 2,8 666 347 354 360 367 373 380 387 393 400 406 5 3,5 6 4,2 667 413 419 426 432 439 445 452 458 465 471 7 4,9 668 478 484 491 497 604 510 , )17 523 530 536 8 6,6 669 543 549 556 662 569 575 582 588 595 601 9 6,3 670 607 614 620 627 633 640 ( >46 653 659 666 671 672 672 679 685 692 698 737 743 750 756 763 705 711 718 724 730 769 776 782 789 795 673 802 808 814 821 827 834 840 847 853 860 674 866 872 879 885 892 898 905 911 918 924 675 930 937 943 950 956 963 9 975 982 988 676 995 #001 *008 #014 *020 *027*< )33 #040 #046 #052 677 83 059 065 072 078 085 091 097 104 110 117 678 123 129 136 142 149 155 L61 168 174 181 679 187 193 200 206 213 219 ' 225 232 238 245 680 251 257 264 270 276 283 289 296 302 308 681 315 321 327 334 340 347 353 359 366 372 6 682 683 378 385 391 398 404 442 448 455 461 467 410 417 423 429 436 474 480 487 493 499 1 0,6 2 1,2 684 506 512 518 525 531 537 544 550 556 563 3 1,8 4 2,4 685 569 575 582 588 594 601 607 613 620 626 5 3,0 686 632 639 645 651 658 664 670 677 683 689 6 3,6 687 696 702 708 715 721 727 734 740 746 753 7 4,2 8 48 688 689 759 765 771 778 784 822 828 835 841 847 790 797 803 809 816 853 860 866 872 879 9 5,4 690 885 891 897 904 910 916 83 929 935 942 691 948 954 960 967 973 979 < J85 992 998 *004 692 693 84 Oil 017 023 029 036 073 080 086 092 098 042 048 055 061 '067 105 111 117 123 130 694 136 142 148 155 161 167 173 180 186 192 695 198 205 211 217 223 230 ' 236 242 248 255 696 261 267 273 280 286 292 298 305 311 317 697 323 330 336 342 348 354 361 367 373 379 698 386 392 398 404 410 417 123 429 435 442 699 448 454 460 466 473 479 485 491 497 504 700 510 516 522 528 535 541 547 553 559 566 N. L. 1 2 3 4 5 6789 P. P. 1 48' =? 6480" S. 4. 68 550 T. 4. 68 572 10 53/ = 6780" S. 4. 68 550 T. 4. 68 573 1 49 = 6540 4. 68 550 4. 68 572 1 54 = 6840 4. 68 650 4. 68 573 1 50 = 6600 4. 68 550 4. 68 572 1 55 = 6900 4. 68 649 4. 68 574 1 51 = 6660 4. 68 550 4. 68 673 1 66 = 6960 4. 68 549 4. 68 674 1 52 = 6720 4. 68 650 4. 68 573 1 57 = 7020 4. 68 549 4. 68 574 GEOGRAPHIC TABLES AND FORMULAS. TABLE 21. Five-place logarithms of natural numbers Continued. 141 N. L. 1 2 3 4 5 6 7 8 9 P.P. 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 . 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 760 84 510 516 522 528 535 541 547 553 559 566 7 1 0/7 2 1/4 3 2,1 4 2,8 5 3,5 6 4,2 7 4,9. 8 5,6 9 6,3 B 1 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 1 0,5 2 1,0 3 1,5 4 2,0 5 2,5 6 3,0 7 3,5 8 4,0 9 4,5 572 578 584 590 597 634 640 646 652 658 696 702 708 714 720 757 763 770 776 782 819 825 831 837 844 880 887 893 899 905 942 948 954 960 967 85 003 009 016 022 028 065 071 077 083 089 603 609 61& 621 628 665 671 677 683 689 726 733 739 745 751 788 794 800 807 813 850 856 862 868 874 911 917 924 930 936 973 979 985 991 997 034 040 046 052 058 095 101 107 114 120 126 132 138 144 150 156 163 169 175 181 187 193 199 205 211 248 254 260 266 272 309 315 321 327 333 370 376 382 388 394 431 437 443 449 455 491 497 503 509 616 552 558 564 570 576 612 618 625 631 637 673 679 685 691 697 217 224 230 236 242 278 285 291 297 303 339 345 352 358 364 400 406 412 418 42 461 467 473 479 485 522 528 534 540 646 582 588 594 600 606 643 649 65^ 661 667 703 709 715 721 727 733 739 745 751 757 763 769 775 781 788 794 800 806 812 818 854 860 866 872 878 914 920 926 932 938 974 980 986 992 998 86 034 040 046 052 058 094 100 106 112 118 153 159 165 171 177 213 219 225 231 237 273 279 285 291 297 824 830 836 842 848 884 890 896 902 908 944 950 956 962 968 *004 *010 #016 #022 *028 064 070 076 082 088 124 130 136 141 147 183 189 195 201 207 243 249 255 261 267 303 308 314 320 326 332 338 344 350 356 362 368 374 380 386 392 398 404 410 416. 451 457 463 469 475 510 516 522 528 534 570 576 581 587 593 629 635 641 646 652 688 694 700 705 711 7*7 753 759 764 770 806 812 817 823 829 864 870 876 882 888 421 427 433 439 445 481 487 493 499 504 540 546 552 558 564 599 605 611 617 623 658 664 670 676 682 717 723 729 735 741 776 782 788 794 800 835 841 847 853 859 894 900 906 911 917 923 929 935 941 947 953 958 964 970 976 982 988 994 999 *005 87 040 046 052 058 064 099 105 111 116 122 157 163 169 175 181 216 221 227 233 239 274 280 286 291 297 332 338 344 349 355 390 396 402 408 413 448 454 460 466 471 *011 *017 #023 *029 #035 070 075 081 087 093 128 134 140 146 151 186 192 198 204 210 245 251 256 262 268 303 309 315 320 326 361 367 373 379 384 419 425 431 437 442 477 483 489 495 500 506 512 518 523 529 535 541 547 552 558 N. L. 1 2 3 4 56789 P.P. lo 56' = 6960" S. 4. 68 549 T. 4. 68 574 2 1' = 7260" S. 4. 68 549 T. 4. 68 575 1 57 = 7020 4. 68 549 4. 68 574 22= 7320 4. 68 548 4. 68 576 1 58 = 7080 4. 68 549 4. 68 575 23= 7380 4. 68 548 4. 68 576 1 59 = 7140 4. 68 549 4. 68 575 24= 7440 4. 68 548 4. 68 576 2 = 7200 4. 68 549 4. 68 575 25= 7500 4. 68 548 4. 68 577 142 GEOGRAPHIC TABLES AND FORMULAS. TABLE 21. Five-place logarithms of natural numbers Continued. N. L. 1 2 3 4 56789 P. P. 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 - 797 798 799 800 87 506 512 518 523 529 535 541 547 552 558 6 1 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 1 0,5 2 1,0 3 1,5 4 2,0 5 2,5 6 3,0 7 3,5 8 4,0 9 4,5 564 570 576 581 587 622 628 633 639 645 679 685 691 697 703 737 743 749 754 760 795 800 806 812 818 852 858 864 869 875 910 915 921 927 933 967 973 978 984 990 88 024 030 036 041 047 593 599 604 610 616 651 656 662 668 674 708 714 720 726 731 766 772 777 783 789 823 829 835 841 846 881 887 892 898 904 938 944 950 955 961 996 *001 *007 *013 *018 053 058 064 070 076 081 087 093 098 104 110 116 121 127 133 138 144 150 156 161 195 201 207 213 218 252 258 264 270 275 309 315 321 326 332 366 372 377 383 389 423 429 434 440 446 480 485 491 497 502 536 542 547 553 559 593 598 604 610 615 167 173 17 184 190 224 230 235 241 247 281 287 292 298 304 338 343 349 355 360 395 400 406 412 417 451 457 463 468 474 508 513 519 625 530 564 570 576 581 587 621 627 632 638 643 649 655 660 666 672 677 683 689 694 700 705 711 717 722 728 762 767 773 779 784 818 824 829 835 840 874 880 885 891 897 930 936 941 947 953 986 992 997 *003 *009 89 042 048 053 059 064 098 104 109 115 120 154 159 165 170 176 734 739 745 750 756 790 795 801 807 812 846 852 857 863 868 902 908 913 919 925 958 964 969 975 981 *014 *020 *025 *031 *037 070 076 081 087 092 126 131 137 143 148 182 187 193 198 204 209 215 221 226 232 237 243 248 254 260 265 271 276 282 287 321 326 332 337 343 376 382- 387 393 398 432 437 443 448 454 487 492 498 504 509 542 548 553 559 564 597 603 609 614 620 653 658 664 669 675 708 713 719 724 730 293 298 304 310 315 348 354 360 365 371 404 409 415 421 426 459 465 470 476 481 515 520 526 531 537 570 575 581 586 592 625 631 636 642 647 680 686 691 697 702 735 741 746 752 757 763 768 774 779 785 790 796 801 807 812 818 823 829 834 840 873 878 883 889 894 927 933 938 944 949 982 988 993 998 #004 90 037 042 048 053 059 091 097 102 108 113 146 151 157 162 168 200 206 211 217 222 255 260 266 271 276 845 851 856 862 867 900 905 911 916 922 955 960 966 971 977 *009 #015 *020 #026 #031 064 069 075 080 086 119 124 129 135 140 173 179 184 189 195 227 233 238 244 249 282 287 293 298 304 309 314 320 .325 331 336 342 347 352 358 N. L. 1 2 3 4 56789 P.P. 2 5'= 7500" S. 4. 68 548 T. 4. 68 577 2 10'= 7800" S. 4. 68 547 T. 4. 68 578 2 6 = 7560 4. 68 548 4. 68 577 2 11 = 7860 4. 68 547 4. 68 579 27 = 7620 4. 68 548 4. 68 577 2 12 = 7920 4. 68 547 4. 68 579 2 8 = 7680 4. 68 547 4. 68 578 2 13 = 7980 4. 68 547 4. 68 579 29 = 7740 4. 68 547 4. 68 578 2 14 = 8040 4. 68 546 4. 68 579 GEOGRAPHIC TABLES AND FORMULAS. TABLE 21. Five-place logarithms of natural numbers Continued. 143 N. L. 1 2 3 4 56789 P.P. 800 90 309 314 320 325 331 336 342 347 352 358 801 802 363 369 374 380 385 417 423 428 434 439 390 396 401 407 412 445 450 455 461 466 803 472 477 482 488 493 499 504 509 515 520 804 526 531 536 542 547 553 558 563 569 574 805 580 585 590 596 601 607 612 617 623 628 806 634 639 644 650 655 660 666 671 677 682 807 687 693 698 703 709 714 720 725 730 736 808 741 747 752 757 763 768 773 779 784 789 809 795 800 806 811 816 822 827 832 838 843 810 849 854 859 865 870 875 881 886 891 897 811 902 907 913 918 924 929 934 940 945 950 6 812 966 961 966 972 977 982 988 993 998 *004 1 0,6 813 91 009 014 020 025 030 036 041 046 052 057 2 1,2 814 062 068 073 078 084 089 094 100 105 110 3 1,8 4 2,4 815 116 121 126 132 137 142 148 153 158 164 5 3,0 816 169 174 180 185 190 196 201 206 212 217 6 3,6 817 222 228 233 238 243 249 264 269 265 270 7 4,2 8 4,8 818 275 281 286 291 297 302 307 312 318 323 9 6,4 819 328 334 339 344 350 355 360 365 371 376 820 381 387 392 397 403 408 413 418 424 429 821 434 440 445 450 455 461 466 471 477 482 822 823 487 492 498 503 508 540 545 551 656 561 614 519 524 529 535 566 572 577 682 587 824 825 826 593 598 603 609 614 645 651 656 661 666 698 703 709 714 719 619 624 630 635 640 672 677 682 687 693 724 730 735 740 745 827 828 829 751 756 761 766 772 803 808 814 819 824 855 861 866 871 876 777 782 787 793 798 829 834 840 845 850 882 887 892 897 903 830 908 913 918 924 929 934 939 944 950 965 831 960 965 971 976 981 986 991 997 *002 *007 832 833 92 012 018 023 028 033 065 070 075 080 085 038 044 049 054 059 091 096 101 106 111 1 0,5 2 1,0 3 1,5 834 117 122 127 132 137 143 148 153 158 163 4 2,0 835 169 174 179 184 189 195 200 205 210 215 5 2,5 836 221 226 231 236 241 247 252 267 262 267 6 3,0 7 3,5 837 273 278 283 288 293 298 304 309 314 319 8 4,0 838 324 330 335 340 345 350 355 361 366 371 9 4,5 839 376 381 387 392 397 402 407 412 418 423 840 428 433 438 443 449 454 459 464 469 474 841 480 485 490 495 500 605 511 516 521 526 842 531 536 542 647 552 657 562 567 572 578 843 583 588 593 598 603 609 614 619 624 629 844 634 639 645 650 655 660 665 670 675 681 845 686 691 696 701 706 711 716 722 727 732 846 737 742 747 752 758 763 768 773 778 783 847 848 788 793 799 804 809 840 845 850 855 860 814 819 824 829 834 865 870 875 881 886 849 891 896 901 906 911 916 921 927 932 937 850 942 947 952 957 962 967 973 978 983 988 N. L. 1 2 3 4 56789 P. P. 2 13' = 7980" S. 4. 68 547 T. 4. 68 579 2 18'=8280" 8. 4. 68 546 T. . 68 581 2 14 = 8040 4. 68 546 4. 68 579 2 19 =8340 4. 68 546 . 68 581 2 15 = 8100 4. 68 546 4. 68 580 2 20 =8400 4. 68 64$ 68 582 2 16 =8160 4. 68 546 4. 68 580 2 21 -8460 4. 68 54 . 68 582 2 17 = 8220 4. 68 546 4. 68 580 2 22 =8520 4. 68 545 .68 582 144 GEOGRAPHIC TABLES AND FORMULAS. TABLE 21. Five-place logarithms of natural numbers Continued. N. L. 1 2 3 4 5 6789 P P. 850 92 942 947 952 957 962 967 973 978 983 988 851 852 993 998 *003 *008 *013 93 044 049 054 059 064 $018 *024 ^029 *034 *039 069 075 080 085 090 853 095 100 105 110 115 120 125 131 136 141 854 146 151 156 161 166 171 176 181 186 192 855 197 202 207 212 217 222 227 232 237 242 856 247 252 258 263 268 273 278 283 288 293 6 857 298 303 308 313 318 323 328 334 339 344 1 0,6 858 349 354 359 364 369 374 579 384 389 394 2 1/2 859 399 404 409 414 420 425 430 435 440 445 3 4 1,8 2,4 860 450 455 460 465 470 475 480 485 490 495 5 3,0 861 500 505 510 515 520 526 531 536 541 546 6 7 3,6 4,2 862 551 556 561 566 571 576 )81 586 591 596 4 8 863 601 606 611 616 621 626 631 636 641 646 9 4,o 5,4 864 651 656 661 666 671 676 682 687 692 697 865 702 707 712 717 722 727 732 737 742 747 866 752 757 762 767 772 777 782 787 792 797 867 802 807 812 817 822 827 832 837 842 847 868 852 857 862 867 872 877 882 887 892 897 869 902 907 912 917 922 927 932 937 942 947 870 952 957 962 967 972 977 982 987 992 997 871 94 002 007 012 017 022 027 032 037 042 047 5 872 052 057 062 067 072 077 082 086 091 096 1 0,5 873 101 106 111 116 121 126 131 136 141 146 2 1/0 874 151 156 161 166 171 176 181 186 191 1% 3 4 1/5 2,0 875 201 206 211 216 221 226 ' 231 236 240 245 5 2,5 876 250 255 260 265 270 275 280 285 290 295 6 3,0 877 300 305 310 315 320 325 330 335 340 345 7 g 3,5 4,0 878 349 354 359 364 369 374 I 579 384 389 394 9 4,5 879 399 404 409 414 419 424 429 433 438 443 880 448 453 458 463 468 473 478 483 488 493 881 498 503 507 512 517 522 527 532 537 542 882 547 552 557 562 567 571 576 581 586 591 883 596 601 606 611 616 621 626 630 635 640 884 645 650 655 660 665 670 675 680 685 689 885 694 699 704 709 714 719 ' 724 729 734 738 886 ' 743 748 753 758 763 768 773 778 783 787 4 887 792 797 802 807 812 817 822 827 832 836 1 0,4 888 841 846 851 856 861 866 871 876 880 885 2' 0,8 889 890 895 900 905 910 915 919 924 929 934 3 1,2 890 939 944 949 954 959 963 968 973 978 983 4 5 1,6 2,0 891 892 893 988 993 998 *002 *007 95 036 041 046 051 056 085 090 095 100 105 #012 *017 *022 *027 *032 061 066 071, 075 080 109 114 119 124 129 6 7 8 9 2,4 2,8 3,2 3,6 894 134 139 143 148 153 158 ] L63 168 173 177 895 182 187 192 197 202 207 ', 211 216 221 226 896 231 236 240 245 250 255 260 265 270 274 897 279 284 289 294 299 303 308 313 318 323 898 328 332 337 342 347 352 J57 361 366 371 899 376 381 386 390 395 400 405 410 415 419 900 424 429 434 439 444 448 453 458 463 468 N. L. 1 2 3 4 5 6789 P. P. 2 21' = 8460" S. 4. 68 545 T. 4. 68 582 2 26' = 8760" S. 4. 68 544 T 4. 68 584 2 22 = 8520 4. 68 545 4. 68 582 2 27 =8820 4. 68544 4. 68 584 2 23 = 8580 4. 68 545 4. 68 583 2 28 = 8880 4. 68 544 4. 68 584 2 24 = 8640 4. 68 545 4. 68 583 2 29 = 8940 4. 68 544 4. 68 585 2 25 = 8700 4. 68 545 4. 68 583 2 30 = 9000 4. 68 544 4. 68 585 GEOGKAPH1C TABLES AND FORMULAS. TABLE 21. Five-place logarithms of natural numbers Continued. 145 X. L. 1 2 3 4 56789 P. P. 900 95 424 429 434 439 444 448 453 458 463 468 901 902 472 477 482 487 492 521 525 530 535 540 497 501 506 511 516 545 550 554 559 564 903 569 574 578 583 588 593 598 602 607 612 904 617 622 626 631 636 641 646 650 655 660 905 665 670 674 679 684 689 694 698 703 708 906 713 718 722 727 732 737 742 746 751 756" 907 761 766 770 775 780 785 789 794 799 804 908 809 813 818 823 828 832 837 842 847 852 909 856 861 866 871 875 880 885 890 895 899 910 904 909 914 918 923 928 933 938 942 947 911 952 957 961 966 971 976 980 985 990 995 912 913 999 *004 *009 *014 #019 % 047 052 057 061 066 #023 *028 *033 *038 *042 071 076 080 085 090 5 1 0,5 2 1,0 914 095 099 104 109 114 118 123 128 133 137 3 1,5 915 142 147 162 156 161 166 171 175 180 185 4 2,0 916 190 194 199 204 209 213 218 223 227 232 5 2,5 917 237 242 246 251 256 261 265 270 275 280 6 3,0 7 3,5 918 919 284 289 294 298 303 332 336 341 346 350 308 313 317 322 327 355 360 365 369 374 8 4,0 9 4,5 920 379 384 388 393 398 402 407 412 417 421 921 426 431 435 440 445 450 454 459 464 468 922 923 473 478 483 487 492 520 525 530 534 539 497 501 506 511 515 544 548 553 558 562 924 567 572 577 581 586 591 595 600 605 609 925 614 619 624 628 633 638 642 647 652 656 926 661 666 670 675 680 685 689 694 699 703 927 928 708 713 717 722 727 755 759 764 769 774 731 736 741 745 750 778 783 788 792 797 929 802 806 811 816 820 825 830 834 839 844 930 848 853 858 862 867 872 876 881 886 890 931 895 900 904 909 914 918 923 928 932 937 932 942 946 951 956 960 965 970 974 979 984 4 933 988 993 997 *002 *007 ,,,011 *016 *021 #025 *030 1 0,4 934 97 035 039 044 (M9 053 058 063 067 072 077 2 0,8 935 081 086 090 095 100 104 109 114 118 123 936 128 132 137 142 146 151. 155 160 165 169 5 2,0 937 174 179 183 188 192 197 202 206 211 216 6 2,4 938 220 225 230 234 239 243 248 253 257 262 939 267 271 276 280 285 290 294 299 304 308 9 3,6 940 313 317 322 327 331 336 340 345 350 354 941 359 364 368 373 377 382 387 391 396 400 942 943 405 410 414 419 424 451 456 460 465 470 428 433 437 442 447 474 479 483 488 493 944 497 502 506 511 516 520 525 529 534 539 945 543 548 552 557 562 566 571 575 580 585 946 589 594 598 603 607 612 617 621 626 630 947 948 949 635 640 644 649 653 681 685 690 695 699 727 731 736 740 745 658 663 667 672 676 704 708 713 717 722 749 754 759 763 768 950 772 777 782 786 791 795 800 804 809 813 X. L. 1 2 3 4 56789 P. P. 2 30' = 9000" S. 4. 68 544 T. 4. 68 585 2 35' = 9300" S. 4. 68 543 T. 4. 68 587 2 31 = 9060 4. 68 544 4. 68 585 2 36 = 9360 4. 68 543 4. 68 587 2 32 = 9120 4. 68 543 4. 68 586 2 37 = 9420 4. 68 542 4. 68 588 2 33 = 9180 4. 68 543 4. 68 586 2 38 = 9480 4. 68 542 4. 68 588 2 34 = 9240 4. 68 643 4. 68 587 2 39 = 9640 4. 68 642 4. 68 588 4606108 10 146 GEOGEAPHIC TABLES AND FOEMULAB. TABLE 21. Five-place logarithms of natural numbers Continued. N. L. 1 2 3 4 5 6789 P.P. 950 97 772 777 782 786 791 795 300 804 809 813 951 818 823 827 832 836 841 845 850 855 859 952 953 864 868 873 877 882 909 914 918 923 928 886 891 896 900 905 932 937 941 946 950 954 955 959 964 968 973 978 982 987 991 996 955 956 98 000 005 009 014 019 046 050 055 059 064 023 028 032 037 041 068 073 078 082 087 957 091 096 100 105 109 114 118 123 127 132 958 137 141 146 150 155 159 164 168 173 177 * 959 182 186 191 195 200 204 209 214 218 223 960 227 232 236 241 245 250 254 259 263 268 961 272 277 281 286 290 295 299 304 308 313 5 962 318 322 327 331 336 340 345 349 354 358 1 0,5 963 363 367 372 376 381 385 390 394 399 403 2 1,0 964 965 408 412 417 421 426 453 457 462 466. 471 430 435 439 444 448 475 480 484 489 493 3 1,5 4 2,0 5 2,5 966 498 502 607 511 516 520 325 529 534 538 6 3,0 967 543 547 552 556 561 565 570 574 579 583 7 3,5 8 4,0 968 969 588 592 597 601 605 632 637 641 646 650 610 614 619 623 628 655 659 664 668 673 9 4,5 970 677 682 686 691 695 700 704 709 713 717 971 722 726 731 735 740 744 749 753 758 762 972 767 771 776 780 784 789 793 798 802 807 973 811 816 820 825 829 834 838 843 817 851 974 856 860 865 869 874 878 383 887 892 896 975 976 900 905 909 914 918 945 949 954 958 963 923 927 932 936 941 967 972 976 981 985 977 978 989 994 998 *003 *007 99 034 038 043 047 052 *012 #016 *021 *025 *029 056 061 065 069 074 979 078 083 087 092 096 100 105 109 114 118 980 123 127 131 136 140 145 149 154 158 162 981 167 171 176 180 185 189 193 198 202 207 4 982 983 211 216 220 224 229 255 260 264 269 273 233 238 242 247 251 277 282 286 291 295 1 0,4 2 0,8 984 300 304 308 313 317 322 326 330 335 339 3 1,2 985 344 348 352 357 361 366 370 374 379 383 4 1,6 986 388 392 396 401 405 410 114 419 423 427 5 2,0 6 2,4 987 988 989 432 436 441 445 449 476 480 484 489 493 520 624 628 533 537 454 458 463 467 471 498 502 506 511 515 542 546 550 555 559 7 2,8 8 3,2 9 3,6 990 564 568 572 577 581 685 590 594 599 603 991 607 612 616 621 625 629 634 638 642 647 992 651 656 660 664 669 673 677 682 686 691 993 695 699 704 708 712 717 721 726 730 734 994 739 743 747 752 756 760 765 769 774 778 995 782 787 791 795 800 804 308 813 817 822 9% 826 830 835 839 843 848 852 856 861 865 997 870 874 878 883 887 891 896 900 904 909 998 913 917 922 926 930 935 939 944 948 952 999 957 961 965 970 974 978 983 987 991 996 1000 00 000 004 009 013 017 022 026 030 035 039' N. L. 1 2 3 4 5 6789 P.P. 2 38' 9480" S. 4. 68 642 T. 4. 68 588 2 43'= 9780" S. 4. 68 541 T. 4. 68 590 2 39 - 9540 4. 68 642 4. 68 588 2 44 = 9840 4. 68 641 4. 68 590 2 40 = 9600 4. 68 542 4. 68 589 2 45 = 9900 4. 68 541 4. 68 591 2 41 = 9660 4. 68 542 4. 68 589 2 46 = 9960 4. 68 541 4. 68 591 2 42 =9720 4. 68 541 4. 68 590 2 47 =10020 4. 68 540 4. 68 592 GEOGRAPHIC TABLES AND FORMULAS. 147 Formula for using quantities S and T: log sin a = log a" + S. log tan a = log a" + T. log cot a = a. c. log a" -fa. c. log 7! log a" = log sin a S = log tan # T 7 . log cos a = log (90 - a)" + A log cot a = log (90 - <*)" + T 7 . log tan a = a. c. log (90 - a}" + a. c. log T. log (90 a)" = log cos a 8= log cot a T. 148 GEOGRAPHIC TABLES AND FORMULAS. TABLE 22. Five-place logarithms of circular functions, expressed in arc and time. O h m. s. ' L. Sin. d. L. T'ang. c. d. L. Cotg. L. Cos. 4 8 12 16 1 2 3 4 6. 46 373 6. 76 476 6.94 085 7. 06 579 30103 17609 12494 9691 6. 46 373 6. 76 476 6. 94 085 7. 06 579 30103 17609 12494 9691 3. 53 627 3. 23 524 3. 05 915 2. 93 421 0.00 000 0.00 000 0.00 000 0.00 000 0. 00 000 60 59 58 57 56 60 56 52 48 44 20 24 28 32 36 5 6 7 8 9 7. 16 270 7.24 188 7. 30 882 7.36 682 7.41 797 7918 6694 5800 5115 4576 7. 16 270 7. 24 188 7. 30 882 7. 36 682 7.41 T97 7918 6694 5800 5115 4576 2.83 730 2. 75 812 2.69 118 2. 63 318 2. 58 203 0.00 000 0.00 000 0.00 000 0.00 000 0.00 000 55 54 53 52 51 59 40 36 32 28 24 40 44 48 52 56 10 11 12 13 14 7. 46 373 7. 50 512 7. 54 291 7.57 767 7. 60 985 4139 3779 3476 3218 2997 7.46 373 7. 50 512 7.54 291 7.57 767 7. 60 986 4139 3779 3476 3219 2996 2. 53 627 2. 49 488 2. 45 709 2. 42 233 2. 39 014 0.00 000 0.00 000 0.00 000 0.00 000 0.00 000 50 49 48 47 46 59 20 16 12 8 4 1 4 8 12 16 15 16 17 18 19 7. 63 982 7.66 784 7. 69 417 7.71 900 7. 74 248 2802 2633 2483 2348 2227 7.63 982 7.66 785 7.69 418 7.71 900 7. 74 248 2803 2633 2482 2348 2228 2. 36 018 2.33 215 2. 30 582 2. 28 100 2. 25 752 0.00 000 0.00 000 9. 99 999 9.99 999 9. 99 999 45 44 43 22 41 59 56 52 48 44 1 20 24 28 32 36 20 21 22 23 24 7. 76 475 7. 78 594 7.80 615 7. 82 545 ' 7.84 393 2119 2021 1930 1848 7.76 476 7. 78 595 7. 80 615 7.82 546 7. 84 394 2119 2020 1931 1848 1773 2. 23 524 2. 21 405 2. 19 385 2.17 454 2. 15 606 9. 99 999 9. 99 999 9. 99 999 9.99 999 9.99 999 40 39 38 37 36 58 40 36 32 28 24 1 40 44 48 52 56 25 26 27 28 29 7. 86 166 7.87 870 7. 89 509 7.91 088 7.92 612 1704 1639 1579 1524 1472 1 7. 86 167 7. 87 871 7. 89 510 7.91 089 7. 92 613 1704 1639 1579 1524 1473 2. 13 833 2. 12 129 2. 10 490 2. 08 911 2. 07 387 9. 99 999 9.99 999 9. 99 999 9. 99 999 9. 99 998 35 34 33 32 31 58 20 16 12 8 4 2 4 8 12 16 30 31 32 33 34 7. 94 084 7. 95 508 7.% 887 7. 98 223 7.99 520 1424 1379 1336 1297 IOCQ 7. 94 086 7. 95 510 7. 96 889 7. 98 225 7. 99 522 1424 1379 1336 1297 2. 05 914 2. 04 490 2.03 111 2.01 775 2. 00 478 9. 99 998 9. 99 998 9. 99 998 9. 99 998 9. 99 998 30 29 28 27 26 58 56 . 52 48 44 2 20 24 28 32 36 35 36 37 38 39 8. 00 779 8. 02 002 8.03 192 8. 04 350 8. 05 478 1223 1190 1158 1128 8. 00 781 8.02 004 8.03 194 8.04 353 8. 05 481 1223 1190 1159 1128 1. 99 219 1. 97 996 1. 96 806 1.95 647 1. 94 519 9. 99 998 9. 99 998 9. 99 997 9. 99 997 9. 99 997 25 24 23 22 21 57 40 36 32 28 24 2 40 44 48 52 56 40 41 42 43 44 8. 06 578 8.07 650 8. 08 696 8.09 718 8.10 717 1072 1046 1022 999 8. 06 581 8. 07 653 8. 08 700 8.09 722 8. 10 720 1072 1047 1022 998 1. 93 419 1. 92 347 1.91 300 1.90 278 1.89 280 9. 99 997 9. 99 997 9. 99 997 9. 99 997 9. 99 996 20 19 18 17 16 57 20 16 12 8 4 3 4 8 12 16 45 46 47 48 49 8. 11 693 8. 12 647 8. 13 581 8. 14 495 8. 15 391 954 934 914 896 8.11 696 8. 12 651 3.13 585 8. 14 500 8. 15 395 955 934 915 895 1.88 304 1. 87 349 1. 86 415 1. 85 500 1.84 605 9.99 996 9. 99 996 9. 99 996 9. 99 996 9.99 9% 15 14 13 12 11 57 56 52 48 44 3 20 24 28 32 36 50 51 52 53 54 3. 16 268 8.17 128 8.17 971 8. 18 798 8. 19 610 860 843 827 812 7Q7 8. 16 273 8. 17 133 8. 17 976 8. 18 804 8.19 616 860 843 828 812 1.83 727 1. 82 867 1.82 024 1.81 196 1. 80 384 9. 99 995 9. 99 99 9.99 995 9. 99 995 9.99 995 10 9 8 7 6 56 40 36 32 28 24 3 40 44 48 52 56 55 56 57 58 59 8. 20 407 8.21 189 8.21 958 8.22 713 8. 23 456 782 769 755 743 70n 8. 20 413 8.21 195 8.21 964 8.22 720 8. 23 462 782 769 756 742 1. 79 587 1. 78 805 1.78 036 1.77 280 1. 76 538 9. 99 994 9. 99 994 9. 99 994 9. 99 994 9. 99 994 5 4 3 2 1 56 20 16 12 8 4 4 60 8. 24 186 8. 24 192 1.75 808 9 99 993 56 L. Cos. d. |L. Cotg. C. d. L. Tang. L. Sin. ' m. s. 89 GEOGRAPHIC TABLES AND FORMULAS. 149 TABLE 22. Five-place logarithms of circular functions, etc. Continued. m. s. ' L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. 4 4 8 12 16 1 2 3 4 8. 24 186 8. 24 903 8. 25 609 8.26 304 8. 26 988 717 706 695 684 8.24 192 8. 24 910 8. 25 616 8. 26 312 8.26 996 718 706 696 684 1.75 808 1.75 090 1. 74 384 1.73 688 1.73 004 9. 99 993 9. 99 993 9. 99 993 9.99 993 9. 99 992 60 59 58 57 56 56 56 52 48 44 4 20 24 28 32 36 5 6 8 9 8.27 661 8.28 324 8. 28 977 8.29 621 8.30 255 663 653 644 634 8.27 669 8.28 332 8. 28 986 8.29 629 8. 30 263 663 654 643 634 1. 72 331 1. 71 668 1.71 014 1. 70 371 1. 69 737 9. 99 992 9. 99 992 9. 99 992 9. 99 992 9. 99 991 55 54 53 52 51 55 40 36 32 28 24 4 40 44 48 52 M 10 11 12 13 14 8. 30 879 8. 31 495 8. 32 103 8.32 702 8.33 292 616 608 599 590 8.30 888 8.31 505 8.32 112 8. 32 711 8. 33 302 617 607 599 591 1. 69 112 1. 68 495 1.67 888 1. 67 289 1. 66 698 9.99 991 9. 99 991 9. 99 990 9.99 990 9.99 990 50 49 48 47 46 55 20 16 12 8 4 5 4 8 12 16 15 16 17 18 19 8. 33 875 8. 34 450 8. 35 018 8. 35 578 8. 36 131 575 568 560 553 8.33 886 8. 34 461 8.35 029 8.35 590 8. 36 143 575 568 561 553 1.66 114 1. 65 539 1.64 971 1. 64 410 1. 63 857 9.99 990 9. 99 989 9.99 989 9. 99 989 9. 99 989 45- 44 43 42 41 55 56 52 48 44 5 20 24 28 32 36 20 21 22 23 24 8.36 678 8. 37 217 8. 37 750 8.38 276 8. 38 796 539 533 526 520 8.36 689 8. 37 229 8.37 762 8.38289 8.38 809 540 533 527 520 1. 63 311 1.62 771 1.62 238 1.61 711 1.61 191 9. 99 988 9.99 988 9.99 9S8 9. 99 987 9. 99 987 40 39 38 37 36 54 40 36 32 28 24 5 40 44 48 52 56 25 26 27 28 29 8. 39 310 8. 39 818 8. 40 320 8. 40 816 8.41 307 508 502 496 491 8. 39 323 8. 39 832 8. 40 334 8. 40 830 s. 11 u-jl 509 502 496 491 1. 60 677 1.60 168 1. 59 666 1.59 170 1.58 679 9. 99 987 9.99 986 9. 99 986 9. 99 986 9. 99 985 35 34 33 32 31 54 20 16 12 8 4 6 4 8 12 10 30 31 32 33 34 8.41 792 8. 42 272 8. 42 746 8. 43 216 8.43 680 480 474 470 464 S.-ll W)7 8. 42 287 8. 42 762 8. 43 232 8. 43 6% 480 475 47.0 464 1,58 193 1.57 713 1.57 238 1.56 768 1.56 304 9. 99 985 9.99 985 9. 99 984 9. 99 984 9. 99 984 30 29 28 27 26 54 56 52 48 44 6 20 24 28 32 36 35 36 37 38 39 8. 44 139 8. 44 594 8. 45 044 8. 45 489 8.45930 455 450 445 441 8. 44 156 8. 44 611 8. 45 061 8. 45 507 8.45 948 455 450 446 441 1.55 844 1.55 389 1.54 939 1. 54 493 1.54 052 9. 99 983 9. 99 983 9. 99 983 9. 99 982 9. 99 982 25 24 23 22 21 53 40 36 32 28 24 6 40 44 48 52 56 40 41 42 43 44 8.46 366 8.46 799 8.47 226 8.47 650 8. 48 069 433 427 424 419 8.46 385 8. 46 817 8. 47 245 8. 47 669 8. 48 089 432 428 424 420 1.53 615 1. 53 183 1.52 755 1. 52 331 1.51 911 9. 99 982 9. 99 981 9. 99 981 9. 99 981 9. 99 980 20 19 18 17 16 53 20 16 12 8 4 7 4 8 12 16 45 46 47 48 49 8. 48 485 8. 48 896 8. 49 304 8.49 708 8.50 108 411 408 404 400 8.48 505 8.48 91? 8. 49 325 8. 49 729 8. 50 130 412 408 404 401 1.51 495 1.51 083 1.50 675 1.50 271 1. 49 870 9. 99 980 9. 99 979 9. 99 979 9.99 979 9. 99 978 15 14 13 12 11 53 56 52 48 44 7 20 24 28 32 36 50 51 52 53 54 8.50 504 8. 50 897 8.51 287 8.51 673 8.52 055 393 390 386 382 8. 50 527 8.50 920 8.51 310 8.51 6% 8. 52 079 393 390 386 383 1. 49 473 1.49 080 1.48 690 1.48 304 1. 47 921 9. 99 978 9. 99 977 9. 99 977 9. 99 977 9. 99 976 10 9 8 7 6 52 40 36 32 28 24 7 40 44 48 62 56 55 56 57 58 f,'J 8. 52 434 8. 52 810 8.53 183 8.53 552 8. 53 919 376 373 369 367 8. 52 459 8.52 835 8. 53 208 8.53 5^8 8. 53 945 376 373 370 367 1.47 541 1.47 165 1.46 792 1.46 422 1. 46 055 9. 99 976 9. 99 975 9. 99 975 9. 99 974 9. 99 974 5 4 3 2 1 52 20 16 12 8 4 8 60 8.54 282 8.54 308 1.45 692 9. 99 974 52 L.Cos. d. L. Cotg. c. d. L. Tang. L. Sin. i m. s. 88 5 h 150 GEOGRAPHIC TABLES AND FOEMULAS. TABLE 22. Five-place logarithms of circular functions, etc. Continued. O h 2 m. s. ' L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. 8 4 8 12 16 1 2 3 4 8. 54 282 8.54 642 8. 54 999 8.55 354 8.55 705 360 357 355 351 040 8.54 308 8. 54 669 8. 55 027 8. 55 382 8. 55 734 361 358 355 352 040 1. 45 692 1. 45 331 1.44 973 1. 44 618 1. 44 266 9.99 974 9. 99 973 9. 99 973 9. 99 972 9. 99 972 60 59 58 57 56 52 56 52 48 44 8 20 24 28 32 36 5 6 7 8 9 8. 56 054 8. 56 400 8. 56 743 8. 57 084 8. 57 421 346 343 341 337 qoc 8. 56 083 8. 56 429 8.56 773 8.57 114 8. 57 452 346 344 341 338 OOfi 1.43 917 1.43 571 1. 43 227 1. 42 886 1.42 548 9. 99 971 9. 99 971 9. 99 970 9. 99 970 9. 99 969 55 54 53 52 51 51 40 36 32 28 24 8 40 44 48 52 56 10 11 12 13 14 8.57 757 8. 58 089 8.58 419 8. 58 747 8. 59 072 332 330 328 325 000 8.57 788 8.58 121 8. 58 451 8. 58 779 8.59 105 333 380 328 326 000 1.42 212 1.41 879 1.41 549 1. 41 221 1. 40 895 9. 99 969 9. 99 968 9. 99 968 9. 99 967 9. 99 967 50 49 48 47 46 51 20 16 12 8 4 9 4 8 12 16 15 16 17 18 19 8. 59 395 8. 59 715 8. 60 033 8.60 349 8. 60 662 320 318 316 313 8. 59 428 8. 59 749 8. 60 068 8.60 384 8. 60 698 321 319 316 314 1. 40 572 1. 40 251 1. 39 932 1. 39 616 1. 39 302 9. 99 967 9. 99 966 9. 99 966 9. 99 965 9. 99 964 45 44 43 42 41 51 56 52 48 44 9 20 24 28 32 36 20 21 22 23 24 8. 60 973 8.61 282 8. 61 589 8.61 894 8. 62 196 309 307 305 302 8. 61 009 8.61 319 8. 61 626 8.61 931 8. 62 234 310 307 305 303 1. 38 991 1. 38 681 1.38 374 1. 38 069 1.37 766 9. 99 964 9. 99 963 9. 99 963 9. 99 962 9. 99 962 40 39 38 37 36 50 40 36 32 28 24 9 40 44 48 52 56 25 26 27 28 29 8. 62 497 8. 62 795 8. 63 091 8.63 385 8. 63 678 298 296 294 293 290 8. 62 535 8. 62 834 8. 63 131 8. 63 426 8. 63 718 299 297 295 292 291 1. 37 465 1. 37 166 1. 36 869 1.36 574 1. 36 282 9. 99 961 9. 99 961 9. 99 960 9. 99 960 9. 99 959 35 34 33 32 31 50 20 16 12 8 4 10 4 8 12 16 30 31 32 33 34 8. 63 968 8. 64 256 8. 64 543 8. 64 827 8. 65 110 288 287 284 283 001 8. 64 009 8. 64 298 8.64 585 8. 64 870 8. 65 154 289 287 285 284 001 1. 35 991 1. 35 702 1. 35 415 1.35 130 1. 34 846 9. 99 959 9. 99 958 9.99 958 9. 99 957 9. 99 956 30 29 28 27 26 50 56 52 48 44 10 20 24 28 32 36 35 36 37 38 39 8. 65 391 8. 65 670 8. 65 947 8. 66 223 8. 66 497 279 277 276 274 272 8. 65 4&5 8.65 715 8. 65 993 8. 66 269 8. 66 543 280 278 276 274 273 1.34 565 1.34 285 1. 34 007 1. 33 731 1.33 457 9. 99 956 9. 99 955 9. 99 955 9. 99 954 9. 99 954 25 24 23 22 21 49 40 36 32 28 24 10 40 44 48 52 56 40 41 42 43 44 8. 66 769 8. 67 039 8. 67 308 8. 67 575 8. 67 841 270 269 267 266 263 8. 66 816 8. 67 087 8. 67 356 8. 67 624 8. 67 890 271 269 268 266 264 1.33 184 1. 32 913 1. 32 644 1. 32 376 1. 32 110 9. 99 953 9. 99 952 9. 99 952 9. 99 951 9. 99 951 20 19 18 17 16 49 20 16 12 8 4 11 4 8 12 16 45 46 47 48 49 8. 68 104 8. 68 367 8. 68 627 8. 68 886 8. 69 144 263 260 259 258 256 8. 68 154 8. 68 417 8. 68 678 8. 68 938 8. 69 196 263 261 260 258 257 1.31 846 1.31 583 1. 31 322 1.31 062 1.30804 9. 99 950 9. 99 949 9. 99 949 9. 99 948 9. 99 948 15 14 13 12 11 49 56 52 48 44 11 20 24 28 32 36 50 51 52 53 54 8. 69 400 8. 69 654 8. 69 907 8. 70 159 8. 70 409 254 253 252 250 249 8. 69 453 8. 69 708 8. 69 962 8. 70 214 8. 70 465 255 254 252 251 249 1.30 547 1.30 292 1.30 038 1. 29 786 1. 29 535 9. 99 947 9. 99 946 9. 99 946 9. 99 945 9. 99 944 10 9 8 7 6 48 40 36 32 28 24 11 40 44 48 52 56 55 56 57 68 59 8. 70 658 8.70 905 8.71 151 8.71 395 8. 71 638 247 246 244 243 242 8. 70 714 8. 70 962 8. 71 208 8. 71 453 8.71 697 248 246 245 244 243 1.29 286 1.29 038 1.28 792 1. 28 547 1. 28 303 9. 99 944 9. 99 943 9. 99 942 9. 99 942 9.99 941 5 4 3 2 1 48 20 16 12 8 4 12 60 8.71 880 8. 71 940 1.28 060 9. 99 940 48 L. Cos. d. L. Cotg. c.d. L.Tang. L. Sin. / m. s. 87 GEOGRAPHIC TABLES AND FORMULAS. 151 TABLE 22. five-place logarithms of circular functions, etc. Continued. 0* 3 m. s. ' L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. 12 4 8 12 16 1 2 3 4 8.71 880 8. 72 120 8. 72 359 8. 72 597 8.72 834 240 239 238 237 8.71 940 8. 72 181 8. 72 420 8. 72 659 . 8. 72 896 241 239 239 237 1. 28 060 1.27 819 1.27 580 1. 27 341 1.27 104 9.99 940 9. 99 940 9. 99 939 9. 99 938 9. 99 938 60 59 58 57 56 48 56 52 48 44 12 20 24 28 32 36 5 6 7 8 9 8. 73 069 8. 73 303 8.73 535 8. 73 767 8. 73 997 234 232 232 230 8. 73 132 8. 73 366 8.73 600 8. 73 832 8. 74 063 234 234 232 231 1.26 868 1.26634 1. 26 400 1. 26 168 1. 25 937 9. 99 937 9. 99 936 9. 99 936 9. 99 935 9. 99 934 55 54 53 52 51 47 40 36 . 32 28 24 12 40 44 48 52 56 10 11 12 13 14 8. 74 226 8. 74 454 8.74 680 8.74 906 8.75 130 228 226 226 224 8. 74 292 8. 74 521 8. 74 748 8. 74 974 8. 75 199 229 227 226 225 1. 25 708 1.25 479 1. 25 252 1.25 026 1. 24 801 9.99 934 9. 99 933 9. 99 932 9. 99 932 9. 99 931 50 49 48 47 46 47 20 16 12 8 4 13 4 8 12 16 15 16 17 18 19 8.75 353 8. 75 575 8. 75 795 8. 76 015 8.76 234 222 220 220 219 8. 75 423 8. 75 645 8. 75 867 8. 76 087 8.76 306 222 222 220 219 1. 24 577 1.24 355 1. 24 133 1. 23 913 1.23 694 9. 99 930 9. 99 929 9.99 929 9.99 928 9. 99 927 45 44 43 42 41 47 56 52 48 44 13 20 24 28 32 36 20 21 22 23 24 8. 76 451 8. 76 667 8.76 883 8. 77 097 8.77 310 216 216 214 213 8. 76 525 8. 76 742 8. 76 958 8. 77 173 8. 77 387 217 216 215 214 1.23 475 1.23258 1.23 042 1.22 827 1. 22 613 9. 99 926 9. 99 926 9. 99 925 9.99 924 9.99 923 40 39 38 37 36 46 40 36 32 28 24 13 40 44 48 52 56 25 26 27 28 29 8. 77 522 8. 77 733 8. 77 943 8. 78 152 8.78 360 211 210 209 208 8.77600 8. 77 811 8. 78 022 8. 78 232 8. 78 441 211 211 210 209 ono 1. 22 400 1. 22 189 1.21 978 1.21 768 1. 21 559 9. 99 923 9.99 922 9.99 921 9.99 920 9.99 920 35 34 33 32 31 46 20 16 12 8 4 14 4 8 12 16 30 31 32 33 34 8.78 568 8. 78 774 8. 78 979 8.79 183 8.79 386 206 205 204 203 8. 78 649 8. 78 855 8. 79 061 8. 79 266 8. 79 470 206 206 205 204 1.21 351 1.21 145 1.20 939 1.20 734 1.20 530 9.99 919 9. 99 918 9. 99 917 9. 99 917 9. 99 916 30 29 28 27 26 46 56 52 48 44 14 20 24 28 32 36 35 36 37 38 39 8.79 588 8. 79 789 8.79 990 ' 8.80 189 8.80 388 201 201 199 199 8. 79 673 8. 79 875 8. 80 076 8. 80 277 8. 80 476 202 201 201 199 1.20327 1.20 125 1. 19 924 1. 19 723 1.19 524 9. 99 915 9. 99 914 9. 99 913 9. 99 913 9. 94 912 25 24 23 22 21 45 40 36 32 28 24 14 40 44 48 52 56 40 41 42 43 44 8.80 585 8. 80 782 8. 80 978 8.81 173 8.81 367 197 196 195 194 8. 80 674 8.80872 8.81 068 8.81 264 8.81 459 198 196 196 195 1. 19 326 1. 19 128 1. 18 932 1. 18 736 1.18 541 9. 99 911 9. 99 910 9.99 909 9.99 909 9. 99 908 20 19 18 17 16 45,20 16 12 8 4 15 4 8 12 16 45 46 47 48 49 8.81 560 8.81 752 8. 81 944 8.82 134 8. 82 324 192 192 190 190 8.81 653 8.81 846 8. 82 038 8. 82 230 8. 82 420 193 192 192 190 1. 18 347 1. 18 154 1. 17 962 1. 17 770 1. 17 580 9.99 907 9.99 906 9.99 905 9. 99 904 9.99 904 15 14 13 12 11 45 56 52 48 44 15 20 24 28 32 36 50 51 52 53 54 8. 82 513 8. 82 701 8.82 888 8. 83 075 8.83 261 188 187 187 186 8. 82 610 8. 82 799 8.82 987 8.83 175 8.83 361 189 188 188 186 1. 17 390 1. 17 201 1. 17 013 1. 16 825 1. 16 639 9. 99 903 9.99 902 9. 99 901 9. 99 900 9. 99 899 10 9 8 7 6 44 40 36 32 28 24 15 40 44 48 52 56 55 56 57 58 59 8. 83 446 8.83 630 8. 83 813 8.83 9% 8.84 177 184 183 183 181 8.83 547 8.83 732 8. 83 916 8.84 100 8.84 282 185 .184 184 182 1. 16 453 1.16 268 1. 16 084 1.15 900 1. 15 718 9. 99 898 9. 99 898 9. 99 897 9. 99 896 9. 99 895 5 4 3 2 1 44 20 16 12 8 4 16 60 8.84 358 8.84 464 1. 15 636 9. 99 894 44 L. Cos. d. L. Cotg. c. d. L. Tang. L. Sin. / m. s. 152 GEOGRAPHIC TABLES AND FORMULAS. TABLE 22. Five-place logarithms of circular functions, etc. Continued. O h 4 m. s. > L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. 16 4 8 12 16 1 2 3 4 8.84 358 8. 84 539 8.84 718 8. 84 897 8.85 075 181 179 179 178 177 177 176 175 175 173 8.84464 8.84 646 8. 84 826 8.85 006 8.85 185 182 180 180 179 178 177 177 176 176 174 174 174 172 172 171 171 170 169 169 168 167 167 166 165 165 165 163 163 163 161 162 160 160 160 159 158 158 157 157 156 155 155 155 153 154 153 152 152 151 151 150 150 149 148 149 147 147 147 146 146 1. 15 536 1. 15 354 1.15 174 1. 14 994 1. 14 815 9. 99 894 9. 99 893 9. 99 892 9. 99 891 9. 99 891 60 59 58 57 56 44 56 52 48 44 16 20 24 28 32 36 5 6 7 8 9 8.85 252 8. 85 429 8. 85 605 8. 85 780 8. 85 955 8. 85 363 8.85 540 8. 85 717 8. 85 893 8. 86 069 1. 14 637 1. 14 460 1. 14 283 1. 14 107 1. 13 931 9. 99 890 9. 99 889 9. 99 888 9. 99 887 9. 99 886 55 54 53 52 51 43 40 36 32 28 24 16 40 44 48 52 56 10 11 12 13 14 8. 86 128 8.86 301 8. 86 474 8.86 645 8. 86 816 173 173 171 171 171 169 169 169 167 168 166 166 165 164 164 8. 86 243 8. 86 417 8.86 591 8. 86 763 8. 86 935 1. 13 757 1. 13 583 1. 13 409 1. 13 237 1.13 065 9.99 885 9. 99 884 9. 99 883 9. 99 882 9. 99 881 50 49 48 47 46 43 20 16 12 8 4 17 4 8 12 16 ]5 16 17 18 19 8. 86 987 8. 87 156 8. 87 325 8. 87 494 8. 87 661 8.87 106 8.87 277 8. 87 447 8.87 616 8.87 785 1. 12 894 1. 12 723 1.12 553 1. 12 384 1. 12 215 9. 99 880 9. 99 879 9. 99 879 9. 99 878 9.99 877 45 44 43 42 41 43 56 52 48 44 17 20 24 28 32 36 20 21 22 23 24 8. 87 829 8. 87 995 8.88 161 8. 88 326 8.88 490 8.87 953 8.88 120 8.88 287 8.88 453 8. 88 618 1. 12 047 1. 11 880 1.11 713 1. 11 547 1. 11 382 9. 99 876 9. 99 875 9. 99 874 9. 99 873 9. 99 872 40 39 38 37 36 35 34 33 32 31 42 40 36 32 28 24 17 40 44 48 52 56 25 26 27 28 29 8.88 654 8. 88 817 8. 88 980 8.89 142 8. 89 304 163 163 162 162 160 8. 88 783 8. 88 948 8. 89 111 8. 89 274 8. 89 437 1. 11 217 1. 11 052 1. 10 889 1. 10 726 1. 10 563 9. 99 871 9.99 870 9. 99 869 9. 99 868 9. 99 867 42 20 16 12 8 4 18 4 8 12 16 30 31 32 33 34 8. 89 464 8. 89 625 8.89 784 8.89 943 8. 90 102 161 159 150 159 158 8. 89 598 8. 89 760 8. 89 920 8. 90 080 8.90 240 1. 10 402 1.10 240 1. 10 080 1. 09 920 1. 09 760 9. 99 866 9. 99 865 9. 99 864 9. 99 863 9. 99 862 30 29 28 27 26 42 56 52 48 44 18 20 24 28 32 36 35 36 37 38 39 8.90 260 8. 90 417 8. 90 574 8.90 730 8.90 885 157 157 156 155 155 155 154 153 153 152 152 151 151 150 150 149 149 148 147 147 147 146 146 145 145 8. 90 399 8. 90 557 8. 90 715 8. 90 872 8.91 029 1.09 601 1. 09 443 1. 09 285 1.09 128 1. 08 971 9. 99 861 9. 99 860 9. 99 859 9. 99 858 9. 99 857 25 24 23 22 21 41 40 36 32 28 24 18 40 44 48 52 56 40 41 42 43 44 8. 91 040 8.91 195 8.91 349 8.91 502 8.91 655 8.91 185 8. 91 340 8.91 495 8.91 650 8.91 803 1. 08 815 1.08 660 1.08 505 1. 08 350 1. 08 .197 9.99 856 9. 99 855 9.99 854 9. 99 853 9. 99 852 20 19 18 17 16 41 20 16 12 8 4 19 4 8 12 16 45 46 47 48 49 8.91 807 8.91 959 8.92 110 8.92 261 8.92 411 8.91 957 8. 92 110 8. 92 262 8. 92 414 8.92 565 1. 08 043 1. 07 890 1. 07 738 1. 07 586 1. 07 4a5 9.99 851 9. 99 850 9. 99 848 9. 99 847 9. 99 846 15 14 13 12 11 41 56 52 48 44 19 20 24 28 32 36 50 51 52 53 54 8.92 561 8.92 710 8. 92 859 8. 93 007 8.93 154 8.92 716 8. 92 866 8.93 016 8. 93 165 8. 93 313 1. 07 284 1.07 134 1.06 984 1.06 835 1.06 687 9. 99 845 9,99 844 9.99 843 9. 99 842 9.99841 10 9 8 7 6 40 40 36 32 28 24 19 40 44 48 52 56 55 56 57 58 59 8. 93 301 8. 93 448 8. 93 594 8. 93 740 8.93 885 8. 93 462 8. 93 609 8. 93 756 8. 93 908 8. 94 049 1.06 538 1. 06 391 1.06 244 1. 06 097 1. 05 951 9. 99 840 9.99 839 9. 99 838 9. 99 837 9.99 836 5 4 3 2 1 40 20 16 12 8 4 20 60 8.94 030 8.94 195 1. 05 805 9.99 834 40 L. Cos. d. L. Cotg. c. d. L. Tang. L. Sin. i m. s. 85 C 5 h GEOGRAPHIC TABLES AND FORMULAS. 153 TABLE 22. Five-place logarithms of circular functions, etc. Continued. O h 5 m. s. / L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. 20 4 8 12 16 1 2 3 4 8.94 030 8. 94 174 8. 94 317 8. 94 461 8.94 603 144 143 144 142 143 8. 94 195 8. 94 340 8.94485 8. 94 630 8. 94 773 145 145 145 143 144 1.05 805 1.05 660 1. 05 515 1.05 370 1. 05 227 9. 99 834 9. 99 833 9. 99 832 9. 99 831 9. 99 830 60 59 58 57 56 40 56 52 48 44 20 20 24 28 32 36 5 6 7 8 9 8. 94 746 8. 94 887 8. 95 029 8.95 170 8. 95 310 141 142 141 140 140 8. 94 917 8. 95 060 8. 95 202 8. 95 344 8. 95 486 143 142 142 142 141 1.05 083 1.04 940 1.04 798 1. 04 656 1.04 514 9. 99 829 9.99828 9. 99 827 9.99 825 9. 99 824 55 54 53 52 51 39 40 36 32 28 24 20 40 44 48 52 56 10 11 12 13 14 8.95 450 8. 95 589 8. 95 728 8. 95 867 8.% 005 139 139 139 138 138 8. 95 627 8. 95 767 8. 95 908 8.% 047 8. 96 187 140 141 139 140 138 1. 04 373 1.04233 1. 04 092 1.03 953 1. 03 813 9. 99 823 9. 99 822 9. 99 821 9. 99 820 9. 99 819 50 49 48 47 46 39 20 16 12 8 4 21 4 8 12 16 15 16 17 18 19 8. 96 143 8.96 280 8. 96 417 8.96 553 8.% 689 137 137 136 136 136 8. 96 325 8.96 464 8.96 602 8. 96 739 8. % 877 139 138 137 138 136 1. 03 675 1.03 536 1. 03 398 1. 03 261 1. 03 123 9.99 817 9. 99 816 9. 99 815 9. 99 814 9.99813 45 44 43 42 41 39 56 52 48 44 21 20 24 28 32 36 20 21 22 23 24 8.% 825 8.96 960 8.97 095 8.97 229 8.97 363 135 135 134 134 133 8. 97 013 8. 97 150 8. 97 285 8. 97 421 8.97556 137 135 136 135 135 1. 02 987 1.02 850 1.02 715 1.02 579 1. 02 444 9. 99 812 9. 99 810 9.99 809 9. 99 808 9.99807 40 39 38 37 36 38 40 36 32 28 24 21 40 44 48 52 56 25 26 27 28 29 8. 97 496 8.97 629 8. 97 762 8.97 894 8.98026 133 133 132 132 131 8. 97 691 8. 97 825 8.97 959 8.98 092 8. 98 225 134 134 133 133 133 1.02 309 1.02 175 1.02 041 1. 01 908 1.01 775 9.99 806 9. 99 804 9.99 803 9. 99 802 9. 99 801 35 34 33 32 31 38 20 16 12 8 4 22 4 8 12 16 30 31 32 33 34 8.98 157 8.98 288 8. 98 419 8. 98 549 8. 98 679 131 131 130 130 129 8.98 358 8. 98 490 8.98 622 8. 98 753 8.98 884 132 132 131 131 131 1.01 642 1.01 510 1.01 378 1.01 247 1.01 116 9. 99 800 9. 99 798 9. 99 797 9.99 7% 9.99 795 30 29 28 27 26 38 56 52 48 44 22 20 24 28 32 36 35 36 37 38 39 8.98 808 8. 98 937 8.99 066 8.99 194 8. 99 322 129 129 128 128 128 8.99015 8. 99 145 8. 99 275 8.99 405 8. 99 534 130 130 130 129 128 1.00 985 1.00 855 1.00 72$ L 00 466 9. 99 793 9. 99 792 9. 99 791 9.99 790 9. 99 788 25 24 23 22 21 37 40 36 32 28 24 22 40 44 48 52 56 40 41 42 43 44 8.99 450 8. 99 577 8. 99 704 8.99 830 8.99 956 127 127 126 126 126 8.99 662 8.99 791 8. 99 919 9.00 046 9. 00 174 129 128 127 128 127 1.00 338 1.00 209 1.00 081 0. 99 954 0. 99 826 9. 99 787 9. 99 786 9.99 785 9. 99 783 9. 99 782 20 19 18 17 16 37 20 16 12 8 4 23 4 8 12 16 45 46 47 48 49 9. 00 082 9.00 207 9. 00 332 9.00 456 9.00 581 125 125 124 125 123 9. 00 301 9. 00 427 9. 00 553 9. 00 679 9.00 805 126 126 126 126 125 0. 99 699 0. 99 573 0. 99 447 0. 99 321 0. 99 195 9. 99 781 9. 99 780 9. 99 778 9. 99 777 9. 99 776 15 14 13 12 11 37 56 52 48 44 23 20 24 28 32 36 50 51 52 53 54 9.00 704 9.00 828 9. 00 951 9. 01 074 9.01 196 124 123 123 122 122 9. 00 930 9. 01 055 9.01 179 9. 01 303 9.01427 125 124 124 124 123 0. 99 070 0. 98 945 0. 98 821 0. 98 697 0.98573 9. 99 775 9. 99 773 9. 99 772 9.99 771 9. 99 769 10 9 8 7 6 36 40 36 32 28 24 23 40 44 48 52 56 55 56 57 58 59 9. 01 318 9.01 440 9.01 561 9.01 682 9.01 803 122 121 121 121 120 9.01 550 9.01 673 9.01 796 9. 01 918 9. 02. 040 123 123 122 122 122 0. 98 450 0. 98 327 0.98204 0. 98 082 0. 97 960 9. 99 768 9.99 767 9.99 765 9. 99 764 9.99 763 5 4 3 2 1 36 20 16 12 8 4 24 60 9.01 923 9.02 162 0.97 838 9.99 761 36 L. Cos. d. L. Cotg. c.d. L. Tang. L. Sin. / m. s. 84 154 GEOGRAPHIC TABLES AND FORMULAS. TABLE 22. Five-place logarithms of circular functions, etc. Continued. & 6 m. s. / L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. 24 4 , 8 12 16 1 2 3 4 9. 01 923 9.02043 9.02 163 9. 02 283 9. 02 402 . 120 120 120 119 118 9. 02 162 9.02 283 9. 02 404 9. 02 525 9. 02 645 121 121 121 120 121 0.97 838 0.97 717 0. 97 596 0. 97 475 0.97 355 9. 99 761 9. 99 760 9. 99 759 9. 99 757 9. 99 756 60 59 58 57 56 36 56 52 48 44 24 20 24 28 32 36 5 6 7 8 9 9. 02 520 9. 02 639 9.02 757 9. 02 874 9. 02 992 119 118 117 118 117 9.02 766 9.02 885 9.03 005 9. 03 124 9. 03 242 119 120 119 118 119 0.97 234 0. 97 115 0. 96 995 0.96 876 0. 96 758 9. 99 755 9. 99 753 9. 99 752 9. 99 751 9. 99 749 55 54 53 52 51 35 40 36 32 28 24 24 40 44 48 52 56 10 11 12 13 14 9,03 109 9. 03 226 9. 03 342 9. 03 458 9. 03 574 117 116 116 116 116 9. 03 361 9. 03 479 9. 03 597 9. 03 714 9.03 832 118 118 117 118 116 0. 96 639 0. 96 521 0. 96 403 0.% 286 0.96 168 9. 99 748 9. 99 747 9.99 745 9.99 744 9. 99 742 50 49 48 47 46 35 20 16 12 8 4 25 4 8 12 16 15 16 17 18 19 9.03 690 9. 03 805 9.03 920 9.04 034 9. 04 149 115 115 114 115 113 9. 03 948 9. 04 065 9. 04 181 9. 04 297 9.04 413 117 116 116 116 115 0. 96 052 0.95 935 0. 95 819 0. 95 703 0. 95 587 9. 99 741 9. 99 740 9.99 738 9. 99 737 9. 99 736 45 44 43 42 41 35 56 52 48 44 25 20 24 28 32 36 20 21 22 23 24 9. 04 262 9. 04 376 9.04 490 9.04 60? 9.04 715 114 114 113 112 113 9. 04 528 9.04 643 9.04 758 9. 04 873 9. 04 987 115 115 115 114 114 0. 95 472 0. 95 357 0. 95 242 0. 95 127 0. 95 013 9. 99 734 9. 99 733 9. 99 731 9. 99 730 9.99 728 40 39 38 37 36 34 40 36 32 28 24 25 40 44 48 52 56 25 26 27 28 29 9. 04 828 9. 04 940 9. 05 052 9. 05 164 9. 05 275 112 112 112 111 111 9. 05 101 9. 05 214 9.05 328 9. 05 441 9.05 553 113 114 113 112 113 0. 94 899 0.94 786 0. 94 672 0. 94 559 0.94 447 9. 99 727 9. 99 726 9.99 724 9. 99 723 9. 99 721 35 34 33 32 31 34 20 16 12 8 4 26 4 8 12 16 80 31 32 33 34 9.05 386 9. 05 497 9. 05 607 9. 05 717 9. 05 827 111 110 110 110 110 9. 05 666 9. 05 778 9. 05 890 9.06 002 9.06 113 112 112 112 111 111 0.94 334 0. 94 222 0. 94 110 0. 93 998 0.93 887 9. 99 720 9.99 718 9. 99 717 9. 99 716 9. 99 714 80 29 28 27 26 34 56 52 48 44 26 20 24 28 32 36 35 36 37 38 39 9. 05 937 9.06 046 9.06 155 9.06 264 9.06 372 109 109 109 108 109 9. 06 224 9. 06 335 9. 06 445 9.06 556 9. 06 666 111 110 111 110 109 0. 93 776 0. 93 665 0. 93 555 0. 93 444 0. 93 334 9. 99 713 9. 99 711 9.99 710 9. 99 708 9. 99 707 25 24 23 22 21 33 40 36 32 28 24 26 40 44 48 52 56 40 41 42 43 44 9.06 481 9. 06 589 9. 06 696 9.06 804 9.06 911 108 107 108 107 107 9. 06 775 9.06 885 9.06 994 9. 07 103 9. 07 211 110 109 109 108 109 0.93 22 0. 93 115 0. 93 006 0. 92 897 0. 92 789 9. 99 705 9.99 704 9. 99 702 9. 99 701 9. 99 699 20 19 18 17 16 33 20 16 12 8 4 27 4 8 12 16 45 46 47 48 49 9.07 018 9.07 124 9. 07 231 9. 07 337 9. 07 442 106 107 106 105 106 9.07 320 9. 07 428 9.07 536 9. 07 643 9.07 751 108 108 107 108 107 0.92 680 0. 92 572 0.9*2 464 0. 92 357 0. 92 249 9. 99 698 9.99 696 9. 99 695 9. 99 693 9. 99 692 15 14 13 12 11 33 56 52 48 44 27 20 24 28 32 36 50 51 52 53 54 9. 07 548 9. 07 653 9.07 758 9. 07 863 9. 07 968 105 105 105 105 104 9. 07 858 9.07 964 9. 08 071 9. 08 177 9. 08 283 106 107 106 106 106 0.92 142 0. 92 036 0.91 929 0.91 823 0. 91 717 9. 99 690 9. 99 689 9. 99 687 9. 99 686 9. 99 684 10 9 8 7 6 32 40 .36 32 28 24 27 40 44 48 52 56 55 56 57 58 59 9. 08 072 9.08 176 9. 08 280 9. 08 383 9. 08 486 104 104 103 103 103 9.08 389 9.08 495 9.08 600 9. 08 705 9. 08 810 106 105 105 105 104 0.91 611 0.91 505 0. 91 400 0. 91 295 0. 91 190 9. 99 683 9. 99 681 9. 99 680 9. 99 678 9. 99 677 5 4 3 2 1 32 20 16 12 8 4 28 60 9.08 589 9. 08 914 0. 91 086 9. 99 675 32 L. Cos. d. L. Cotg. c. d. L. Tang. L. Sin. ' m. s. 83 5 h GEOGEAPHIC TABLES AND FORMULAS. 155 TABLE 22. five-place logarithms of circular functions, etc. Continued. Ah ijro m. s. ' L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. 28 4 8 12 16 ?> 2 3 4 9. 08 589 9.08 692 9.08 795 9. 08 897 9.08 999 103 103 102 102 102 9. 08 914 9. 09 019 9. 09 123 9. 09 227 9.09 330 105 104 104 103 104 0. 91 086 0. 90 981 0. 90 877 0. 90 773 0. 90 670 9.99 675 9. 99 674 9.99 672 9.99 670 9. 99 669 60 59 58 57 56 32 56 52 48 44 28 20 24 28 32 36 5 6 7 8 9 9. 09 101 9.09 202 9.09 304 9.09 405 9.09506 101 102 101 101 100 9. 09 434 9.09 537 9.09 640 9.09 742 9.09 845 103 103 102 103 102 0.90 566 0.90 463 0.90 360 0. 90 258 0.90 155 9. 99 667 9.99 666 9. 99 664 9.99 663 9. 99 661 55 54 53 52 51 31 40 36 32 28 24 28 40 44 48 52 56 10 11 12 13 14 9.09 606 9.09 707 9.09807 9.09 907 9. 10 006 101 100 100 99 100 9. 09 947 9. 10 049 9. 10 150 9. 10 252 9. 10 353. 102 101 102 101 101 0.90053 0. 89 951 0. 89 a50 0. 89 748 0. 89 647 9.99 659 9.99 658 9. 99 656 9. 99 655 9". 99 653 50 59 48 47 46 31 20 16 12 8 4 29 4 8 12 16 15 16 17 18 19 9. 10 106 9. 10 205 9.10 304 9.10 402 9. 10 501 99 99 98 99 98 9. 10 454 9.10 555 9.10 656 9. 10 756 9.10 856 101 101 100 100 100 0. 89 546 0. 89 445 0. 89 344 0.89 244 0.89 144 9. 99 651 9.99 650 9. 99 648 9.99 647 9.99 645 45 44 43 42 41 31 56 52 48 44 29 20 24 28 32 36 20 21 22 23 24 9. 10 599 9. 10 697 9. 10 795 9. 10 893 9.10 990 98 98 98 97 97 9. 10 956 9.11 056 9. 11 155 9. 11 254 9.11 353 100 99 99 99 99 0. 89 044 0.88 944 0.88 845 0.88 746 0.88 647 9. 99 643 9. 99 642 9-. 99 640 9. 99 638 9. 99 637 40 39 38 37 36 30 40 36 32 28 24 29 40 44 48 52 56 25 26 27 28 29 9.11 087 9. 11 184 9.11 281 9. 11 377 9. 11 474 97 97 96 97 % 9. 11 452 9.11 551 9. 11 649 9. 11 747 9.11 845 99 98 98 98 98 0.88 548 0.88 449 0. 88 351 0.88 253 0.88 155 9.99 635 9.99 633 9. 99 632 9. 99 630 9. 99 629 35 34 33 32 31 30 20 16 12 8 4 30 4 8 12 16 30 31 32 33 34 9.11 570 9.11 666 9.11 761 9. 11 857 9.11 952 96 95 96 95 95 9.11 943 9.12 040 9. 12 138 9. 12 235 9. 12 332 97 98 97 97 96 0. 88 057 0.87 960 0.87 862 0.87 765 0.87 668 9. 99 627 9.99 625 9.99 624 9. 99 622 9.99 620 30 29 28 27 26 30 56 52 48 44 30 20 24 28 32 36 35 36 37 38 39 9. 12 047 9. 12 142 9. 12 236 9. 12 331 9. 12 425 95 94 95 94 94 9. 12 428 9.12 525 9. 12 621 9. 12 717 9. 12 813 97 96 96 96 96 0. 87 572 0. 87 475 0. 87 379 0. 87 283 0. 87 187 9. 99 618 9.99 617 9. 99 615 9. 99 613 9.99 612 25 24 23 22 21 29 40 36 32 28 24 30 40 44 48 52 56 40 41 42 43 44 9. 12 519 9. 12 612 9. 12 706 9. 12 799 9. 12 892 93 94 93 93 93 9.12 909 9.13 004 9.13 099 9. 13 194 9. 13 289 95 95 95 95 95 0. 87 091 0.86 996 0. 86 901 0.86 806 0. 86 711 9. 99 610 9.99 608 9. 99 607 9.99 605 9. 99 603 20 19 18 17 16 29 20 16 12 8 4 31 4 8 12 16 45 46 47 48 49 9. 12 985 9. 13 078 9. 13 171 9. 13 263 9.13 355 93 93 92 92 92 9.13 384 9.13 478 9. 13 573 9. 13 667 9. 13 761 94 95 94 94 93 0. 86 616 0.86 522 0.86 427 0. 86 333 0. 86 239 9.99 601 9.99 600 9. 99 598 9. 99 596 9.99 595 15 14 13 12 11 29 56 52 48 44 31 20 24 28 32 36 50 51 52 53 54 9. 13 447 9. 13 539 9. 13 630 9. 13 722 9. 13 813 92 91 92 91 91 9.13 854 9. 13 948 9.14 041 9. 14 134 9. 14 227 94 93 93 93 93 0.86 146 0.86 052 0.85 959 0.85 866 0.85 773 9. 99 593 9. 99 591 9. 99 589 9.99 588 9.99 586 10 9 8 7 6 28 40 36 32 28 24 31 40 44 48 52 56 55 56 57 58 59 9.13 904 9.13 994 9. 14 085 9. 14 175 9. 14 266 90 91 90 91 90 9. 14 320 9. 14 412 9.14 504 9. 14 697 9. 14 688 92 92 93 91 92 0.85 680 0.85 588 0.85 4% 0.85 403 0.85 312 9.99 584 9.99 582 9.99 581 9. 99 579 9. 99 677 5 4 3 2 1 28 20 16 12 8 4 32 60 9. 14 356 9. 14 780 0.86 220 9.99 575 28 L. Cos. d. L. Cotg. c.d. L. Tang. L. Sin. i m. s. 156 GEOGRAPHIC TABLES AND FOKMULA.8. TABLE 22. Five-place logarithms of circular functions, etc. Continued. O h 8 m. s. / L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. 32 4 8 12 16 1 2 3 4 9.14 356 9. 14 445 9. 14 535 9. 14 624 9. 14 714 89 90 89 90 89 9. 14 780 9. 14 872 9. 14 963 9. 15 054 9. 15 145 92 91 91 91 91 0. 85 220 0. 85 128 0. 85 037 0. 84 946 0.84 855 9. 99 575 9. 99 574 9. 99 572 9. 99 570 9. 99 568 60 59 58 57 56 28 56 52 48 44 32 20 24 28 32 36 5 6 7 8 9 9. 14 803 9. 14 891 9. 14 980 9. 15 069 9. 15 157 88 89 89 88 88 9. 15 236 9. 15 327 9. 15 417 9. 15 508 9. 15 598 91 90 91 90 90 0.84 764 0. 84 673 0. 84 583 0. 84 492 0. 84 402 9. 99 566 9.99 565 9. 99 563 9. 99 561 9. 99 559 55 54 53 52 51 27 40 36 32 28 24 32 40 44 48 52 56 10 11 12 13 14 9. 15 245 9. 15 333 9. 15 421 9. 15 508 9. 15 596 88 88 87 88 87 9. 15 688 9. 15 777 9. 15 867 9. 15 956 9. 16 046 89 90 89 90 89 0. 84 312 0. 84 223 0. 84 133 0. 84 044 0. 83 954 9. 99 557 9.99 556 9.99 554 9. 99 552 9. 99 550 50 49 48 47 46 27 20 16 12 8 4 33 4 8 12 16 15 16 17 18 19 9.15 683 9.15 770 9. 15 857 9. 15 944 9. 16 030 87 87 87 86 86 9. 16 135 9. 16 224 9. 16 312 9. 16 401 9. 16 489 89 88 89 88 88 0.83 865 0. 83 776 0. 83 688 0.83 599 0. 83 511 9. 99 548 9. 99 546 9. 99 545 9.99 543 9. 99 541 45 44 43 42 41 27 56 52 48 44 33 20 24 28 32 36 20 21 22 23 24 9.16 116 9. 16 203 9. 16 289 9. 16 374 9. 16 460 87 86 85 86 85 9. 16 577 9.16 665 9. 16 753 9. 16 841 9. 16 928 88 88 88 87 88 0. 83 423 0. 83 335 0. 83 247 0. 83 159 0. 83 072 9. 99 539 9. 99 537 9. 99 535 9. 99 533 9. 99 532 40 39 38 37 36 26 40 36 32 28 24 33 40 44 48 52 56 25 26 27 28 29 9.16 545 9. 16 631 9. 16 716 9. 16 801 9.16 886 86 85 85 85 84 9. 17 016 9. 17 103 9. 17 190 9. 17 277 9. 17 363 87 87 87 86 87 0. 82 984 0. 82 897 0. 82 810 0.82 723 0.82 637 9. 99 530 9. 99 528 9. 99 526 9. 99 524 9. 99 522 35 34 33 32 31 26 20 16 12 8 4 34 4 8 12 16 30 31 32 33 34 9. 16 970 9. 17 055 9. 17 139 9. 17 223 9. 17 307 85 84 84 84 84 9. 17 450 9. 17 536 9. 17 622 9. 17 708 9. 17 794 86 86 86 86 86 0. 82 550 0. 82 464 0. 82 378 0. 82 292 0. 82 206 9. 99 520 9. 99 518 9. 99 517 9. 99 515 9. 99 513 30 29 28 27 26 26 56 62 48 44 34 20 24 28 32 36 35 36 37 38 39 9. 17 391 9. 17 474 9. 17 558 9. 17 641 9. 17 724 83 84 83 83 83 9.17 88Q 9. 17 965 9. 18 051 9.18 136 9. 18 221 85 86 85 85 85 0. 82 120 0. 82 035 0. 81 949 0.81 864 0.81 779 9. 99 511 9. 99 509 9.99 507 9. 99 505 9. 99 503 25 24 23 22 21 25 40 36 32 28 24 34 40 44 48 52 56 40 41 42 43 44 9. 17 807 9. 17 890 9. 17 973 9. 18 055 9. 18 137 83 83 82 82 83 9. 18 306 9. 18 391 9. 18 475 9.18 560 9. 18 644 85 84 85 84 84 0.81 694 0. 81 609 0. 81 525 0. 81 440 0. 81 356 9. 99 501 9. 99 499 9. 99 497 9. 99 495 9. 99 494 20 19 18 17 16 25 20 16 12 8 4 35 4 8 12 16 45 46 47 48 49 9. 18 220 9. 18 302 9. 18 383 9. 18 465 9. 18 547 82 81 82 82 81 9. 18 728 9. 18 812 9. 18 896 9.18 979 9. 19 063 84 84 83 84 83 0.81 272 0.81 188 0.81 104 0. 81 021 0. 80 937 9. 99 492 9.99 490 9. 99 488 9. 99 486 9. 99 484 15 14 13 12 11 25 56 52 48 44 35 20 24 28 32 36 50 51 52 53 54 9. 18 628 9. 18 709 9. 18 790 9. 18 871 9. 18 95? 81 81 81 81 81 9. 19 146 9. 19 229 9. 19 312 9. 19 395 9. 19 478 83 83 83 83 83 0. 80 854 0. 80 771 0.80 688 0. 80 605 0. 80 522 9. 99 482 9. 99 480 9. 99 478 9. 99 476 9. 99 474 10 9 8 7 6 24 40 36 32 28 24 35 40 44 48 52 56 55 56 57 58 59 9. 19 033 9.19 113 9.19 193 9. 19 273 9. 19 353 80 80 80 80 80 9. 19 561 9. 19 643 9. 19 725 9. 19 807 9. 19 889 82 82 82 82 82 ' 0. 80 439 0. 80 357 0.80 275 0. 80 193 0. 80 111 9. 99 472 9.99 470 9.99 468 9. 99 466 9. 99 464 5 4 3 2 1 24 20 16 12 8 4 36 60 9. 19 433 9. 19 971 0. 80 029 9. 99 462 24 L. Cos. d. L. Cotg. c. d. L. Tang. L. Sin. ' m. s. 81 C 5 h GEOGRAPHIC TABLES AND FORMULAS. 157 TABLE 22. Five-place logarithms of circular functions, etc. Continued. O h 9 m. s. ' L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. 36 4 8 12 16 1 2 3 4 9. 19 433 9. 19 513 9. 19 592 9. 19 672 9. 19 751 80 79 80 79 79 9. 19 971 9. 20 053 9.20 134 9. 20 216 9. 20 297 82 81 82 81 81 0. 80 029 0. 79 947 0. 79 866 0. 79 784 0. 79 703 9. 99 462 9. 99 460 9. 99 458 9.99 156 9.99 454 60 59 58 57 56 24 56 52 48 44 36 20 24 28 32 36 5 6 7 8 9 9.19 830 9.19 909 9. 19 988 9. 20 067 9.20 145 79 79 79 78 78 9. 20 378 9. 20 459 9.20 540 9. 20 621 9. 20 701 81 81 81 80 81 0. 79 622 0. 79 541 0. 79 460 0. 79 379 0. 79 299 9.99 452 9. 99 450 9. 99 448 9.99 446 9.99 444 55 54 53 52 51 23 40 36 32 28 24 36 40 44 48 52 56 10 11 12 13 14 9. 20 223 9.20 302 9.20 380 9.20 458 9.20 535 79 78 78 77 78 9.20 782 9. 20 862 9. 20 942 9.21 022 9.21 102 80 80 80 80 80 0. 79 218 0. 79 138 0. 79 058 0. 78 978 0. 78 898 9. 99 442 9. 99 440 9. 99 438 9. 99 436 9. 99 434 50 49 48 47 46 23 20 16 12 8 4 37 4 8 12 16 15 16 17 18 19 9. 20 613 9. 20 691 9. 20 768 9.20 845 9.20 922 78 77 77 77 77 9.21 182 9.21 261 9.21 341 9.21 420 9.21 499 79 80 79 79 79 0. 78 818 0. 78 739 0. 78 659 0.78 580 0. 78 501 9. 99 432 9. 99 429 9. 99 427 9.99 425 9.99423 45 44 43 42 41 23 56 52 48 44 37 20 24 28 32 36 20 21 22 23 24 9.20999 9. 21 076 9.21 153 9.21 229 9.21 306 77 77 76 77 76 9.21 578 9.21 657 9.21 736 9.21 814 9. 21 893 79 79 78 79 78 0. 78 422 0. 78 343 0. 78 264 0. 78 186 0.78 107 9. 99 421 9.99 419 9.99417 9. 99 415 9. 99 413 40 39 38 37 36 22 40 36 32 28 24 37 40 44 48 52 56 25 26 27 28 29 9.21 382 9.21 458 9.21 534 9. 21 610 9.21 685 76 76 76 75 76 9. 21 971 9.22 049 9.22 127 9.22 205 9.22 283 78 78 78 78 78 0.78029 0. 77 951 0. 77 873 0. 77 795 0. 77 717 9.99 411 9.99 409 9. 99 407 9. 99 404 9.99 402 35 34 33 32 31 22 20 16 12 8 4 38 4 8 12 16 30 31 32 33 34 9.21 761 9.21 836 9.21 912 9.21 987 9.22 062 75 76 75 75 75 9.22 361 9.22 438 9.22 516 9.22 593 9.22 670 77 78 77 77 77 0. 77 639 0. 77 562 0. 77 484 0. 77 407 0. 77 330 9.99 400 9.99 398 9. 99 396 9.99 394 9.99 392 30 29 28 26 22 56 52 % 38 20 24 28 32 36 35 36 37 38 39 9. 22 137 9.22 211 9.22 286 9.22 361 9.22 435 74 75 75 74 74 9.22 747 9.22 824 9. 22 901 9.22 977 9.23054 77 77 76 77 76 0. 77 253 0.77 176 0. 77 099 0. 77 023 0. 76 946 9.99 390 9.99 388 9.99 385 9. 99 383 9.99 381 25 24 23 22 21 21 40 36 32 28 24 38 40 44 48 52 56 40 41 42 43 44 9.22 509 9.22 583 9.22 657 9.22 731 9.22 805 74 74 74 74 73 9.23 130 9.23 206 9.23 283 9. 23 359 9. 23 435 76 77 76 76 75 0. 76 870 0. 76 794 0. 76 717 0. 76 641 0. 76 565 9.99 379 9. 99 377 9.99 375 9. 99 372 9. 99 370 20 19 18 17 16 21 20 16 12 8 4 39 4 8 12 16 45 46 47 48 49 9. 22 878 9.22 952 9.23 025 9. 23 098 9.23 171 74 73 73 73 73 9.23 510 9. 23 586 9. 23 661 9.23 737 9. 23 812 76 75 76 75 75 0. 76 490 0. 76 414 0. 76 339 0. 76 263 0. 76 188 9.99 368 9. 99 366 9. 99 364 9. 99 362 9. 99 359 15 14 13 12 11 21 56 52 48 44 39 20 24 28 32 86 50 51 52 53 54 9.23 244 9.23 317 9.23 390 9.23 462 9.23 535 73 73 72 73 72 9.23 887 9.23 962 9.24 037 9. 24 112 9.24 186 75 75 75 74 0. 76 113 0. 76 038 0. 75 963 0. 75 888 0. 75 814 9.99 357 9.99 355 9. 99 353 9.99 351 9.99 348 10 9 8 7 6 20 40 36 32 28 24 39 40 44 48 52 56 K 56 57 58 59 9.23 607 9. 23 679 9.23 752 9.23 823 9.23 895 72 73 71 72 72 9.24 261 9.24 335 9.24 410 9. 24 484 9.24 558 74 75 74 74 74 0. 75 739 0.75 665 0. 75 590 0. 75 516 0. 75 442 9. 99 346 9.99 344 9. 99 342 9. 99 340 9. 99 337 5 4 2 1 20 20 16 12 8 4 40 60 9.23 967 9.24 632 0. 75 368 9.99 335 20 L.COS. d. L. Cotg. c.d. L. Tang. L. Sin. ' m. s. 80 158 GEOGKAPHIC TABLES AND FORMULAS. TABLE 22. Five-place logarithms of circular functions, etc. Continued. O h 10 m. s. L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. d. 40 4 8 12 16 1 2 4 9.23 967 9.24 039 9. 24 110 9. 24 181 9. 24 253 72 71 71 72 9. 24 632 9. 24 706 9. 24 779 9. 24 853 9. 24 926 74 73 74 73 74. 0.75 368 0. 75 294 0. 75 221 0. 75 147 0. 75 074 9.99 335 9. 99 333 9. 99 331 9. 99 328 9. 99 326 2 2 3 2 60 59 58 57 56 20 56 52 48 44 40 20 24 28 32 36 5 6 7 8 9 9. 24 324 9. 24 395 9. 24 466 9. 24 536 9. 24 607 71 71 70 71 9.25 000 9. 25 073 7. 25 146 9. 25 219 9. 25 292 73 73 73 73 70 0. 75 000 0. 74 927 0.74 854 0. 74 781 0. 74 708 9. 99 324 9. 99 322 9. 99 319 9. 99 317 9. 99 315 2 3 2 2 55 54 53 52 51 19 40 36 32 28 24 40 40 44 48 52 56 10 11 12 13 14 9. 24 677 9. 24 748 9. 24 818 9.24 888 9. 24 958 71 70 70 70 9. 25 365 9. 25 437 9. 25 510 9. 25 582 9. 25 655 72 73 72 73 79 0. 74 635 0. 74 563 0. 74 490 0. 74 418 0. 74 345 9. 99 313 9.99 310 9. 99 308 9. 99 306 9.99 304 3 2 2 2 50 49 48 47 46 19 20 16 12 8 4 41 4 8 12 16 15 16 17 18 19 9. 25 028 9. 25 098 9.25 168 9. 25 237 9.25 307 70 70 69 70 9.25 727 9.25 799 9. 25 871 9. 25 943 9.26 015 72 72 72 72 0. 74 273 0. 74 201 0. 74 129 0. 74 057 0. 73 985 9.99 301 9. 99 299 9. 99 297 9. 99 294 9.99 292 2 2 3 2 45 44 43 42 41 19 56 52 48 44 41 20 24 28 32 36 20 21 22 23 24 9.25376 9. 25 445 9. 25 514 9.25 583 9. 25 652 69 69 69 69 9. 26 086 9. 26 158 9. 26 229 9. 26 301 9. 26 372 72 71 72 71 0. 73 914 0. 73 842 0. 73 771 0. 73 699 0. 73 628 9. 99 290 9. 99 288 9. 99 285 9.99 283 9. 99 281 2 3 2 2 40 39 38 37 36 18 40 36 32 28 24 41. 40 44 48 52 56 25 26 27 28 29 9. 25 721 9. 25 790 9.25 858 9. 25 927 9. 25 995 69 68 69 68 GO 9. 26 443 9.26 514 9. 26 585 9. 26 655 9. 26 726 71 71 70 71 0. 73 557 0. 73 486 0. 73 415 0. 73 345 0. 73 274 9.99 278 9. 99 276 9. 99 274 9. 99 271 9. 99 269 2 2 3 2 35 34 33 32 31 18 20 16 12 8 4 42 4 8 12 16 30 31 32 33 34 9.26 063 9. 26 131 9. 26 199 9. 26 267 9. 26 335 68 68 68 68 68 9.26 797 9.26 867 9.26 937 9.27 008 9. 27 078 70 70 71 70 0. 73 203 0. 73 133 0. 73 063 0.72 992 0. 72 922 9. 99 267 9.99 264 9. 99 262 9. 99 260 9.99 257 3 2 2 3 30 29 28 27 26 18 56 52 48 44 42 20 24 28 32 36 35 36 37 38 39 9. 26 403 9. 26 470 9.26 538 9.26 605 9.26 672 67 68 67 67 fi7 9.27 148 9. 27 218 9.27 288 9. 27 357 9.27 427 70 70 69 70 0. 72 852 0. 72 782 0. 72 712 0. 72 643 0. 72 573 9. 99 255 9. 99 2o2 9.99 250 9. 99 248 9.99 245 3 2 2 3 25 24 23 22 21 17 40 36 32 28 24 42 40 44 48 52 56 40 41 42 43 44 9. 26 739 9.26 806 9. 26 873 9. 26 940 9.27 007 67 67 67 67 9. 27 496 9.27 566 9. 27 635 9.27 704 9. 27 773 70 69 69 69 0.72 504 0. 72 434 0. 72 365 0. 72 296 0. 72 227 9. 99 243 9. 99 241 9. 99 238 9. 99 236 9.99 233 2 3 2 3 20 19 18 17 16 17 20 16 12 8 4 43 4 8 12 16 45 46 47 48 49 9. 27 073 9. 27 140 9.27 206 9. 27 273 9.27 339 67 66 67 66 9.27 842 9.27 911 9. 27 980 9. 28 049 9. 28 117 69 69 69 68 0.72 158 0. 72 089 0. 72 020 0. 71 951 0. 71 883 9. 99 231 9. 99 229 9. 99 226 9. 99 224 9.99 221 2 3 2 3 15 14 13 12 11 17 56 52 48 44 43 20 24 28 32 36 50 51 52 53 54 9.27 405 9. 27 471 9.27 537 9. 27 602 9.27 668 66 66 65 66 9.28 186 9.28 254 9.28 323 9.28 391 9. 28 459 68 69 68 68 0.71 814 0.71 746 0. 71 677 0.71 609 0. 71 541 9.99 219 9.99 217 9. 99 214 9. 99 212 9. 99 209 2 3 2 3 10 9 8 7 6 16 40 36 32 28 24 43 40 44 48 52 56 55 56 57 58 59 9.27 734 9. 27 799 9. 27 864 9. 27 930 9. 27 995 65 65 66 65 9. 28 527 9. 28 595 9. 28 662 9. 28 730 9, 28 798 68 67 68 68 0. 71 473 0.71 405 0.71 338 0. 71 270 0.71 202 9. 99 207 9.99 204 9. 99 202 9. 99 200 9. 99 197 3 2 2 3 5 4 3 2 1 16 20 16 12 8 4 44 60 9.28 060 9.28 865 0.71 135 9.99 195 16 L. Cos. d. L. Cotg. c. d. L. Tang. L. Sin. d. ' m. s. 79 GEOGRAPHIC TABLES AND FORMULAS. 159 TABLE 22. Five-place logarithms of circular functions, etc. Continued. O h 11 m. s. ' L. Sin. d. L. Tang. c.d. L. Cotg. L. Cos. d. 44 4 8 12 16 1 2 3 4 9.28 060 9.28 125 9.28 190 9.28254 9. 28 319 . 65 65 64 65 9.28 865 9.28 933 9.29 000 9.29 067 9.29 134 68 67 67 67 0. 71 135 0.71 067 0.71 000 0.70 933 0. 70 866 9.99 196 9.99 192 9. 99 190 9.99 187 9. 99 185 3 2 3 2 60 59 58 57 56 16 0. 56 52 48 44 44 20 24 28 32 36 5 6 7 8 9 9.28 384 9.28 448 9. 28 512 9.28 577 9.28 641 64 64 65 64 9. 29 201 9.29 268 9.29 335 9.29402 9.29 468 67 67 67 66 0. 70 799 0. 70 732 0. 70 665 0. 70 598 0. 70 532 9.99 182 9.99 180 9. 99 177 9. 99 175 9. 99 172 2 3 2 3 55 54 53 52 51 15 40 36 32 28 24 44 40 44 48 52 56 10 11 12 13 14 9.28 705 9. 28 769 9.28 833 9.28 896 9.28 960 64 64 63 64 9.29 535 9. 29 601 9.29 668 9. 29 734 9.29 800 66 67 66 66 0. 70 465 0. 70 399 0. 70 332 0. 70 266 0. 70 200 9. 99 170 9.99 167 9.99 165 9. 99 162 9.99 160 3 2 3 2 50 49 48 47 46 15 20 16 12 8 4 45 4 8 12 16 15 16 17 18 19 9.29 024 9.29087 9. 29 150 9.29 214 9. 29 277 63 63 64 63 9. 29 866 9.29 932 9. 29 998 9.30 064 9. 30 130 66 66 66 66 fifi 0. 70 134 0.70068 0.70 002 0. 69 936 0. 69 870 9. 99 157 9. 99 155 9. 99 152 9.99 150 9. 99 147 2 3 2 3 45 44 43 42 41 15 56 52 48 44 45 20 24 28 32 36 20 21 22 23 24 9.29 340 9. 29 403 9.29 466 9.29 529 9.29591 63 63 63 62 9.30 195 9. 30 261 9. 30 326 9.30 391 9. 30 457 66 65 65 66 fiS 0.69 805 0. 69 739 0. 69 674 0.69 609 0. 69 543 9.99 145 9. 99 142 9. 99 140 9. 99 137 9. 99 135 3 2 3 2 40 39 38 37 36 14 40 36 32 28 24 45 40 44 48 52 56 25 26 27 28 29 9.29 654 9.29 716 9.29 779 9. 29 841 9.29 903 62 63 62 62 fiS 9. 30 522 9.30587 9.30 652 9. 30 717 9.30782 65 65 65 65 fi4 0. 69 478 0.69413 0. 69 348 0. 69 283 0. 69 218 9. 99 132 9.99 130 9. 99 127 9.99 124 9.99 122 2 3 3 2 35 34 33 32 31 14 20 16 12 8 4 46 4 8 12 16 30 31 32 33 34 9.29966 9.30 028 9.30 090 9.30 151 9. 30 213 62 62 61 62 9.30 846 9. 30 911 9. 30 975 9. 31 040 9.31 104 65 64 65 64 0. 69 154 0. 69 089 0. 69 025 0.68 960 0.68 896 9.99 119 9. 99 117 9. 99 114 9. 99 112 9.99 109 2 3 2 3 30 29 28 27 26 14 56 52 48 44 46 20 24 28 32 36 35 36 37 38 39 9. 30 275 9.30 336 9. 30 398 9.30459 9. 30 621 61 62 61 62 9.31 168 9.31 233 9.31 297 9. 31 361 9. 31 425 65 64 64 64 0. 68 832 0. 68 767 0.68 703 0. 68 639 0.68 575 9. 99 106 9. 99 104 9. 99 101 9. 99 099 9.99 096 2 3 2 3 25 24 23 22 21 13 40 36 32 28 24 46 40 44 48 52 56 40 41 42 43 44 9.30 582 9.30 643 9. 30 704 9. 30 765 9.30826 61 61 61 61 9. 31 489 9.31 552 9.31 616 9.31 679 9.31 743 63 64 63 64 0. 68 511 0. 68 448 0. 68 384 0. 68 321 0. 68 257 9. 99 093 9. 99 091 9. 99 088 9.99 086 9.99 083 2 3 2 3 20 19 18 17 16 13 20 16 12 8 4 47 4 8 12 16 45 46 47 48 49 9.30 887 9. 30 947 9. 31 008 9.31 068 9.31 129 60 61 60 61 9.31 806 9.31 870 9.31 933 9.31 996 9.32059 64 63 63 63 0. 68 194 0.68 130 0. 68 067 0.68 004 0. 67 941 9. 99 080 9. 99 078 9. 99 075 9. 99 072 9. 99 070 2 3 3 2 15 14 13 12 11 13 56 52 48 44 47 20 24 28 32 36 50 51 52 53 54 9.31 189 9.31 250 9.31 310 9.31 370 9. 31 430 61 60 60 60 9.32122 9. 32 185 9. 32 248 9. 32 311 9. 32 373 63 63 63 62 0. 67 878 0. 67 815 0. 67 752 0.67 689 0. 67 627 9.99 067 9.99 064 9.99 062 9. 99 059 9. 99 056 3 2 3 3 10 9 8 7 6 12 40 36 32 28 24 47 40 44 48 52 56 55 56 67 58 59 9. 31 490 9. 31 549 9.31 609 9.31 669 9.31 728 59 60 60 59 9:32 436 9. 32 498 9. 32 561 9. 32 623 9.32685 62 63 62 62 0.67 564 0. 67 502 0.67 439 0.67 377 0. 67 315 9.99 054 9. 99 051 9. 99 048 9.99 046 9. 99 043 3 3 2 3 5 4 3 2 1 12 20 16 12 8 4 48 60 9. 31 788 9. 32 747 0. 67 253 9.99 040 12 L. Cos. d. L. Cotg. c.d. L. Tang. L. Sin. d. ' m. s. 78 5 h 160 GEOGRAPHIC TABLES AND FOKMULAS. .TABLE 22. Five-place logarithms of circular functions, etc. Continued. O h 12 m. s. / L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. d. 48 4 8 12 16 1 3 4 9.31 788 9. 31 847 9.31 907 9. 31 966 9. 32 025 59 60 59 59 59 59 59 59 58 59 59 58 58 59 58 58 58 58 58 58 58 57 58 57 58 57 57 58 57 57 57 56 57 57 57 56 57 56 56 57 56 56 56 56 56 56 55 56 55 56 9.32 747 9. 32 810 9. 32 872 9. 32 933 9. 32 995 63 62 61 62 62 62 61 62 61 62 61 61 61 61 61 61 61 61 60 61 60 61 60 60 61 60 60 60 60 60 59 60 60 59 60 59 59 59 60 59 59 59 59 58 59 59 58 59 58 59 58 58 58 58 58 58 58 58 58 57 0. 67 253 0.67 190 0. 67 128 0. 67 067 0.67 005 9. 99 040 9. 99 038 9. 99 035 9. 99 032 9. 99 030 2 3 3 2 3 3 2 3 3 3 2 3 3 3 2 3 3 3 2 3 3 3 2 3 3 60 59 58 57 56 12 56 52 48 44 48 20 24 28 32 36 5 6 7 8 9 9. 32 084 9. 32 143 9. 32 202 9. 32 261 9. 32 319 9. 33 057 9.33 119 9. 33 180 9. 33 242 9. 33 303 0. 66 943 0. 66 881 0. 66 820 0.66 758 0. 66 697 9. 99 027 9. 99 024 9. 99 022 9. 99 019 9. 99 016 55 54 53 52 51 11 40 36 32 28 24 48 40 44 48 52 56 10 11 12 13 14 9. 32 378 9. 32 437 9. 32 495 9. 32 553 9. 32 612 9. 33 365 9. 33 426 9. 33 487 9. 33 548 9.33 609 0. 66 635 0. 66 574 0. 66 513 0. 66 452 0.66 391 9. 99 013 9.99 Oil 9. 99 008 9.99 005 9. 99 002 50 49 48 47 46 11 20 16 12 8 4 49 4 8 12 16 15 16 17 18 19 9. 32 670 9. 32 728 9. 32 786 9. 32 844 9. 32 902 9. 33 670 9.33 731 9. 33 792 9. 33 853 9. 33 913 0. 66 330 0. 66 269 0. 66 208 0. 66 147 0.66 087 9.99 000 9.98997 9. 98 994 9.98 991 9. 98 989 45 44 43 42 41 11 56 52 48 44 49 20 24 28 32 36 20 21 22 23 24 9. 32 960 9. 33 018 9. 33 075 9. 33 133 9. 33 190 9. 33 974 9. 34 034 9. 34 095 9. 34 155 9. 34 215 0. 66 026 0. 65 966 0. 65 905 0.65 845 0. 65 785 9. 98 986 9. 98 983 9. 98 980 9. 98 978 9. 98 975 40 39 38 37 36 10 40 36 32 28 24 49 40 44 48 52 56 25 26 27 28 29 9. 33 248 9. 33 305 9. 33 362 9. 33 420 9. 33 477 9.34276 9. 34 336 9. 34 396 9. 34 456 9.34516 0. 65 724 0. 65 664 0. 65 604 0. 65 544 0. 65 484 9. 98 972 9. 98 969 9. 98 967 9.98 964 9. 98 961 3 2 3 3 3 3 2 3 3 3 3 3 2 3 3 3 3 2 3 35 34 33 32 31 10 20 16 12 8 4 50 4 8 12 16 30 31 32 33 34 9.33 534 9. 33 591 9. 33 647 9. 33 704 9. 33 761 9. 34 576 9. 34 635 9. 34 695 9. 34 755 9. 34 814 0. 65 424 0. 65 365 0. 65 305 0. 65 245 0. 65 186 9. 98 958 9. 98 955 9. 98 953 9. 98 950 9. 98 947 30 29 28 27 26 10 56 52 48 44 50 20 24 28 32 36 35 36 37 38 39 9. 33 818 9. 33 874 9.33 931 9. 33 987 9. 34 043 9. 34 874 9. 34 933 9.34 992 9.35051 9. 35 111 0. 65 126 0. 65 067 0. 65 008 0. 64 949 0. 64 889 9.98 944 9. 98 941 9.98 938 9. 98 936 9. 98 933 25 24 23 22 21 9 40 36 32 28 24 50 40 44 48 52 56 40 41 42 43 44 9. 34 100 9. 34 156 9. 34 212 9. 34 268 9. 34 324 9.35 170 9. 35 229 9.35 288 9. 35 347 9. 35 405 0. 64 830 0.64 771 0. 64 712 0. 64 653 0. 64 595 9. 98 930 9. 98 927 9. 98 924 9. 98 921 9. 98 919 20 19 18 17 16 9 20 16 12 8 4 51 4 8 12 16 45 46 47 48 49 9. 34 380 9. 34 436 9. 34 491 9. 34 547 9. 34 602 9.35464 9. 35 523 9.35 581 9. 35 640 9.35 698 0. 64 536 0.64 477 0. 64 419 0.64 360 0.64 302 9. 98 916 9. 98 913 9. 98 910 9. 98 907 9. 98 904 3 3 3 3 3 15 14 13 12 11 9 56 52 48 44 51 20 24 28 32 36 50 51 52 53 54 9.34 658 9. 34 713 9. 34 769 9. 34 824 9. 34 879 55 56 55 55 55 9. 35 757 9. 35 815 9. 35 873 9. 35 931 9. 35 989 0. 64 243 0. 64 185 0.64 127 0. 64 069 0. 64 Oil 9. 98 901 9. 98 898 9. 98 896 9. 98 893 9. 98 890 3 2 3 3 3 3 3 3 3 8 10 9 8 7 6 8 40 36 32 28 24 51 40 44 48 52 56 55 56 57 58 59 9. 34 934 9. 34 989 9.35 044 9. 35 099 9. 35 154 55 55 55 55 55 9. 36 047 9.36 105 9.36 163 9. 36 221 9. 36 279 0. 63 953 0. 63 895 0. 63 837 0. 63 779 0. 63 721 9. 98 887 9. 98 884 9. 98 881 9. 98 878 9. 98 875 5 4 3 2 1 8 20 16 12 8 4 52 60 9.35209 9.36 336 0. 63 664 9. 98 872 8 L. Cos. d. L. Cotg. c. d. L. Tang. L. Sin. d. t m. s. 77 GEOGRAPHIC TABLES AND FORMULAS. 161 TABLE 22. Five-place logarithms of circular functions, etc. Continued. O h 13 m. s. ' L. Sin. d. L. Tang. c.d. L. Cotg. L. Cos. d. 52 4 8 12 16 1 2 3 4 9.35 209 9. 35 263 9. 35 318 9. 35 373 9. 35 427 54 55 55 54 54 9.36 336 9. 36 394 9. 36 452 9.36 509 9.36 566 58 58 57 57 58 0. 63 664 0.63 606 0. 63 548 0. 63 491 0. 63 434 9. 98 872 9. 98 869 9. 98 867 9. 98 864 9. 98 861 3 2 3 3 3 60 59 58 57 56 8 56 52 48 44 52 20 24 28 32 36 5 6 7 8 9 9. 35 481 9. 35 536 9. 35 590 9.35 644 9.35 698 55 54 54 54 64 9. 36 624 9. 36 681 9. 36 738 9. 36 795 9.36 852 57 57 57 57 57 0. 63 376 0. 63 319 0. 63 262 0. 63 205 0. 63 148 9. 98 858 9.98855 9. 98 852 9.98 849 9. 98 846 3 3 3 3 8 55 54 53 52 51 7 40 36 32 28 24 52 40 44 48 52 56 10 11 12 13 14 9. 35 752 9.35806 9.35 860 9. 35 914 9.35 968 54 54 54 54 54 9.36 909 9.36 966 9.37 023 9. 37 080 9.37 137 57 57 57 57 56 0. 63 091 0. 63 034 0. 62 977 0. 62 920 0. 62 863 9. 98 843 9.98 840 9. 98 837 9. 98 834 9. 98 831 3 3 3 3 3 50 49 48 47 46 7 20 16 12 8 4 53 4 8 12 16 15 16 17 18 19 9.36 022 9. 36 075 9.36 129 9.36 182 9.36 236 53 54 53 54 53 9. 37 193 9. 37 250 9. 37 306 9. 37 363 9. 37 419 57 56 57 56 57 0. 62 807 0. 62 750 0. 62 694 0. 62 637 0. 62 581 9. 98 828 9. 98 825 9. 98 822 9. 98 819 9. 98 816 3 3 3 3 3 45 44 43 42 41 7 56 52 48 44 53 20 24 28 32 36 20 21 22 23 24 9. 36 289 9.36 342 9.36 395 9. 36 449 9.36 502 63 53 54 53 53 9. 37 476 9. 37 532 9.37 588 9. 37 644 9.37 700 56 56 56 56 66 0. 62 524 0. 62 468 0. 62 412 0. 62 356 0.62 300 9. 98 813 9. 98 810 9. 98 807 9. 98 804 9. 98 801 3 3 3 3 3 40 39 38 37 36 6 40 36 32 28 24 53 40 44 48 52 56 25 26 27 28 29 9.36 556 9. 36 608 9. 36 660 9.36 713 9.36 766 53 52 53 53 53 9. 37 756 9. 37 812 9.37 868 9. 37 924 9. 37 980 56 56 56 56 55 0. 62 244 0. 62 188 0. 62 132 0. 62 076 0.62 020 9. 98 79$ 9. 98 795 9. 98 792 9. 98 789 9.98 786 3 3 3 3 3 35 34 33 32 31 6 20 16 12 8 4 54 4 8 12 16 30 31 32 33 34 9. 36 819 9. 36 871 9.36 924 9. 36 976 9.37 028 52 53 52 52 53 9.38 035 9.38 091 9. 38 147 9.38 202 9.38 257 56 56 55 55 56 0.61 965 0.61 909 0. 61 853 0.61 798 0. 61 743 9. 98 783 9. 98 780 9. 98 777 9. 98 774 9. 98 771 3 3 3 3 3 30 29 28 27 26 6 56 52 48 44 54 20 24 28 32 36 35 36 37 38 39 9. 37 081 9.37 133 9.37 185 9. 37 237 9.37 289 52 52 52 52 52 9. 38 313 9.38 368 9. 38 423 9. 38 479 9. 38 534 55 56 66 55 55 0.61 687 0.61 632 0. 61 577 0. 61 521 0.61 466 9. 98 768 9.98 765 9.98 762 9. 98 759 9.98 756 3 3 3 3 a 25 24 23 22 21 6 40 36 32 28 24 54 40 44 48 52 56 40 41 42 43 44 9. 37 341 9. 37 393 9.37 445 9. 37 497 9. 37 549 52 52 52 52 51 9.38 589 9.38 644 9. 38 699 9.38 754 9.38 808 55 55 56 54 55 0.61 411 0.61 356 0.61 301 0. 61 246 0.61 192 9. 98 753 9. 98 750 9.98 746 9. 98 743 9. 98 740 3 4 3 3 3 20 19 18 17 16 5 20 16 12 8 4 55 4 8 12 16 45 46 47 48 49 9.37 600 9. 37 652 9. 37 703 9. 37 765 9.37 806 52 51 52 51 62 9.38 863 9. 38 918 9. 38 972 9. 39 027 9. 39 082 55 64 65 55 54 0. 61 137 0. 61 082 0. 61 028 0. 60 973 0. 60 918 9. 98 737 9. 98 734 9. 98 731 9. 98 728 9. 98 725 3 3 3 3 3 15 14 13 12 11 5 56 52 48 44 55 20 24 28 32 36 50 51 52 53 54 9.37 858 9.37 909 9.37 960 9. 38 Oil 9.38 062 51 61 51 51 51 9.39 136 9. 39 190 9. 39 245 9.39 299 9. 39 353 54 55 54 54 54 0. 60 864 0. 60 819 0. 60 755 0. 60 701 0.60 647 9.98 722 9. 98 719 9. 98 715 9. 98 712 9. 98 709 3 4 3 3 3 10 9 8 7 6 4 40 36 32 28 24 55 40 44 48 52 56 55 56 57 58 59 9. 38 113 9.38 164 9. 38 215 9. 38 266 9. 38 317 51 51 51 51 51 9. 39 407 9. 39 461 9. 39 515 9. 39 569 9. 39 623 64 54 54 54 54 0. 60 593 0. 60 539 0.60 485 0. 60 431 0. 60 377 9. 98 706 9.98 703 9. 98 700 9. 98 697 9. 98 694 3 3 3 3 4 5 4 3 2 1 4 20 16 12 8 4 56 60 9.38 368 9. 39 677 0. 60 323 9. 98 690 4 L. Cos. d. L. Cotg. c.d. L. Tang. L. Sin. d. ' m. s. 4606108 11 76 162 GEOGRAPHIC TABLES AND FORMULAS. TABLE 22. Five-place logarithms of circular functions, etc. Continued. O h 14 m. s. ' L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. d. 56 4 8 12 16 1 2 3 4 9. 38 368 9. 38 418 9. 38 469 9. 38 519 9. 38 570 50 51 50 51 9. 39 677 9. 39 731 9.39 785 9. 39 838 9. 39 892 54 54 53 54 0. 60 323 0. 60 2G9 0. 60 215 0. 60 162 0. 60 108 9. 98 690 9. 98 687 9.98 684 9. 98 681 9. 98 678 3 3 3 3 60 59 58 57 56 4 56 52 48 44 56 20 24 28 32 36 5 6 8 9 9.38 620 9. 38 670 9.38 721 9.38 771 9.38 82 L 50 51 50 50 50 9. 39 945 9. 39 999 9. 40 052 9.40 106 9. 40 159 54 53 54 53 53 0. 60 055 0.60 001 0. 59 948 0. 59 894 0. 59 841 9. 98 675 9. 98 671 9. 98 668 9. 98 665 9. 98 662 4 3 3 3 55 54 53 52 51 3 40 36 32 28 24 56 40 44 48 52 56 10 11 12 13 14 9. 38 87J 9. 38 921 9. 38 971 9. 39 021 9. 39 071 50 50 50 50 50 9.40 212 9. 40 266 9. 40 319 9. 40 372 9.40 425 54 53 53 53 KO 0.59 788 0. 59 734 0. 59 681 0.59 628 0. 59 575 9. 98 659 9. 98 656 9. 98 652 9. 98 649 9. 98 646 3 4 3 3 50 49 48 47 46 3 20 16 12 8 4 57 4 8 12 16 15 16 17 18 19 9. 39 121 9. 39 170 9.39 220 9. 39 270 9. 39 319 49 50 50 49 KA 9. 40 478 9.40 531 9.40 584 9. 40 636 9. 40 689 53 53 52 53 ^q 0. 59 522 0. 59 469 0. 59 416 0. 59 364 0. 59 311 9. 98 643 9. 98 640 9. 98 636 9. 98 633 9. 98 630 3 4 3 3 45 44 43 42 41 3 56 52 48 44 57 20 24 28 32 36 20 21 22 23 24 9.39 369 j ' 9. 39 418 9. 39 467 9. 39 517 9. 39 566 49 49 50 49 49 9. 40 742 9. 40 795 9. 40 847 9.40 900 9. 40 952 53 52 53 52 53 0. 59 258 0. 59 205 0. 59 153 0. 59 100 0.59 048 9. 98 627 9. 98 623 9. 98 620 9. 98 617 9. 98 614 4 3 3 3 40 39 38 37 36 2 40 36 32 28 24 57 40 44 48 52 56 25 26 27 28 29 9. 39 615 9. 39 664 9. 39 713 9. 39 762 9. 39 811 49 49 49 49 49 9.41 005 9.41 057 9. 41 109 9.41 161 9. 41 214 52 52 52 53 52 0. 58 995 0.58 943 0. 58 891 0. 58 839 0. 58 786 9. 98 610 9. 98 607 9. 98 604 9. 98 601 9. 98 597 3 3 3 4 35 34 33 32 31 2 20 16 12 8 4 , 58 4 8 12 16 30 31 32 33 34 9. 39 860 9.39909 9. 39 958 9.40 006 9.40 055 49 49 48 49 48 9. 11 266 9.41 318 9. 41 370 9. 41 422 9. 41 474 52 52 52 52 52 0. 58 734 0.58 682 0.58 630 0. 58 578 0. 58 526 9. 98 594 9.98 591 9.98 588 9. 98 584 9. 98 581 3 3 4 3 30 29 28 27 26 2 56 52 48 44 58 20 24 28 32 36 35 36 37 38 39 9. 40 103 9. 40 152 9.40 200 9. 40 249 9.40 297 49 48 49 48 49 9.41 526 9.41 578 9.41 629 9. 41 681 9.41 733 52 51 52 52 51 0. 58 474 0. 58 422 0. 58 371 0. 58 319 0. 58 267 9. 98 578 9. 98 574 9. 98 571 9. 98 568 9.98 565 4 3 3 3 25 24 23 22 21 1 40 36 32 28 24 58 40 44 48 52 56 40 41 42 43 44 9. 40 346 9.40394 9. 40 442 9. 40 490 9. 40 538 48 48 48 48 48 9. 41 784 9.41 836 9. 41 887 9.41 939 9.41 990 52 51 52 51 51 0.58 216 0.58 164 0. 58 113 0. 58 061 0. 58 010 9.98 561 9. 98 558 9. 98 555 9. 98 551 9. 98 548 3 3 4 3 3 20 19 18 17 16 1 20 16 12 8 4 59 4 8 12 16 45 46 47 48 49 9. 40 586 9. 40 634 9. 40 682 9.40 730 9.40 778 48 48 48 48 47 9. 42 041 9. 42 093 9.42 144 9.42 195 9. 42 246 52 51 51 51 51 0. 57 959 0. 57 907 0. 57 866 0.57 805 0. 57 754 9.98 545 9.98 541 9. 98 538 9. 98 535 9. 98 531 4 3 3 4 3 15 14 13 12 11 1 56 52 48 44 59 20 24 28 32 36 50 51 52 53 54 9.40825 9. 40 873 9. 40 921 9.40 968 9.41 016 48 48 47 48 47 9. 42 297 9.42 348 9. 42 399 9.42 450 9. 42 501 51 51 51 51 51 0. 57 703 0.57 652 0.57 601 0. 57 550 0. 57 499 9. 98 528 9. 98 525 9. 98 521 9. 98 518 9.98 515 3 4 3 3 4 10 9 8 6 40 36 32 28 24 59 40 44 48 52 56 55 56 57 58 59 9.41 063 9.41 111 9.41 158 9.41 205 9.41 252 48 47 47 47 48 9.42 552 9. 42 603 9. 42 653 9.42 704 9. 42 755 51 50 51 51 50 0.57 448 0.57 397 0.57 347 0. 57 296. 0. 57 245 9. 98 511 9. 98 508 9. 98 505 9. 98 501 9. 98 498 3 3 4 3 4 5 4 3 2 1 20 16 12 8 4 60 60 9.41 300 9.42 805 0. 57 195 9. 98 494 L. Cos. d. L. Cotg. c. d. L. Tang. L. Sin. d. / m. s. 75 5 h GEOGRAPHIC TABLES AND FORMULAS. 163 TABLE 22. Five-place logarithms of circular functions, etc. Continued. l h 15 m. s. L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. d. 4 8 12 16 1 2 3 4 9.41 300 9.41 347 9. 41 394 9.41 441 9. 41 488 47 47 47 47 9. 42 805 9.42 856 9.42 906 9. 42 957 9.43007 51 50 51 50 0. 57 195 0. 57 144 0. 57 094 0. 57 043 0.56 993 9. 98 494 9. 98 491 9.98488 9. 98 484 9. 98 481 3 3 4 3 60 59 58 57 56 60 56 52 48 44 20 24 28 32 36 5 6 7 8 9 9.41 535 9.41 582 9.41 628 9.41 675 9.41 722 47 46 47 47 9. 43 057 9. 43 108 9. 43 158 9. 43 208 9. 43 258 51 50 50 50 0.56 943 0. 56 892 0.56 842 0.56 792 0.56 742 9. 98 477 9. 98 474 9. 98 471 9. 98 467 9. 98 464 3 3 4 3 55 54 53 52 51 59 40 36 32 28 24 40 44 48 53 56 10 11 12 13 14 9.41 768 9. 41 815 9. 41 861 9.41 908 9.41 954 47 46 47 46 9. 43 308 9. 43 358 9. 43 408 9. 43 458 9.43508 50 50 50 50 0.56 692 0. 56 642 0.56 592 0.56 542 0. 56 492 9.98460 9. 98 457 9.98 453 9. 98 450 9. 98 447 3 4 3 3 50 49 48 47 46 59 20 16 12 8 4 1 4 8 12 16 15 16 17 18 19 9.42 001 9. 42 047 9. 42 093 9.42 140 9. 42 186 46 46 47 46 9.43 558 9.43 607 9.43 657 9. 43 707 9.43 756 49 50 50 49 0. 56 442 0. 56 393 0.56 343 0. 56 293 0. 56 244 9.98443 9. 98 440 9. 98 436 9. 98 433 9. 98 429 3 4 3 4 45 44 43 42 41 59 56 52 48 44 1 20 24 28 32 36 20 21 22 23 24 9.42 232 9. 42 278 9. 42 324 9. 42 370 9. 42 416 46 46 46 46 9.43 806 9. 43 855 9.43 905 9. 43 954 9.44 004 49 50 49 50 0.5C 194 0.56 145 0. 56 095 0. 56 046 0. 55 996 '.. '.IS 426 9. 98 422 9. 98 419 C. 98 415 9. <*5. 412 4 3 4 3 40 39 38 37 36 58 40 36 32 28 24 1 40 44 48 52 56 25 26 27 28 29 9. 42 461 9. 42 507 9.42 553 9. 42 599 9. 42 644 46 46 46 45 9.44053 9. 44 102 9. 44 151 9.44 201 9.44 250 49 49 50 49 0. 55 947 0. 55 898 0. 55 849 0.55 799 0. 55 750 9.98409 9. 98 405 9. 98 402 9. 98 398 9. 98 395 4 3 4 3 35 34 33 32 31 58 20 16 12 8 4 2 I 8 12 16 30 31 32 33 34 9. 42 690 9. 42 735 9. 42 781 9. 42 826 9. 42 872 45 46 45 46 9.44 299 9.44 348 9.44 397 9. 44 446 9. 44 495 49 49 49 49 0. 55 701 0. 55 652 0.55 603 0. 55 554 0. 55 505 9. 98 391 9. 98 388 9.98 384 9. 98 381 9. 98 377 3 4 3 4 30 29 28 27 26 58 56 52 48 44 2 20 24 28 32 36 35 36 37 38 39 9. 42 917 9. 42 962 9. 43 008 9. 43 053 9. 43 098 45 46 45 45 9. 44 544 9. 44 592 9.44 641 9.44 690 9. 44 738 48 49 49 48 0. 55 456 0. 55 408 0. 55 359 0. 55 310 0. 55 262 9. 98 373 9.98 370 9.98 366 9.98 363 9. 98 359 3 4 3 4 25 24 23 22 21 57 40 36 32 28 24 2 40 44 48 52 56 40 41 42 43 44 9. 43 143 9. 43 188 9. 43 233 9. 43 278 9.43 323 45 45 45 45 9. 44 787 9.44 836 9.44 884 9. 44 933 9. 44 981 49 48 49 48 0. 55 213 0. 55 164 0. 55 116 0. 55 067 0.55 019 9. 98 356 9. 98 352 9. 98 349 9. 98 345 9. 98 342 4 3 4 3 20 19 18 ' 17 16 57 20 16 12 8 4 3 4 8 12 16 45 46 47 48 49 9. 43 367 9.43 412 9. 43 457 9.43502 9. 43 546 45 45 45 44 9.45 029 9. 45 078 9.45 126 9.45 174 9. 45 222 49 48 48 48 0.54 971 0.54 922 0.54 874 0. 54 826 0. 54 778 9. 98 338 9.98 334 9. 98 331 9.98 327 9. 98 324 4 3 4 3 15 14 13 12 11 57 56 52 48 44 3 20 24 28 32 36 50 51 52 53 54 9. 43 591 9.43 635 9.43 680 9.43 724 9. 43 769 44 45 44 45 9.45271 9.45 319 9.45 367 9.45 415 9. 45 463 48 48 48 48 0. 54 729 0. 54 681 0. 54 633 0.54 585 0. 54 537 9. 98 320 9. 98 317 9. 98 313 9. 98 309 9. 98 306 3 4 4 3 10 9 8 7 6 56 40 36 32 28 24 3 40 44 48 52 56 :>:. 56 57 58 59 9. 43 813 9. 43 857 9. 43 901 9. 43 946 9.43 990 44 44 45 44 9.45 511 9. 45 559 9. 45 606 9. 45 654 9. 45 702 48 47 48 48 0. 54 489 0. 54 441 0. 54 394 0.54 346 0. 54 298 9. 98 302 9. 98 299 9. 98 295 9.98 291 9. 98 288 3 4 4 3 5 4 3 2 1 56 20 16 12 8 4 4 60 9. 44 034 9. 45 750 0.54 250 9. 98 284 56 L. Cos. d. L. Cotg. c. d. L. Tang. L. Sin. d. ' m. s. 74 c 164 GEOGRAPHIC TABLES AND FORMULAS. TABLE 22. Five-place logarithms of circular functions, etc. Continued. l h 16 m. s. ' L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. d. 4 4 8 12 16 1 2 3 4 9. 44 034 9. 44 078 9. 44 122 9. 44 166 9. 44 210 44 44 44 44 43 9.45 750 9. 45 797 9. 45 845 9.45 892 9.45 940 47 48 47 48 47 0.54 250 0. 54 203 0.54 155 0. 54 108 0. 54 060 9. 98 284 9. 98 281 9. 98 277 9. 98 273 9. 98 270 3 4 4 3 4 60 59 58 57 56 56 56 52 48 44 4 20 24 28 32 36 5 6 7 8 9 9. 44 253 9.44 297 9. 44 341 9.44 385 9.44 428 44 44 44 43 44 9. 45 987 9.46 035 9. 46 082 9. 46 130 9.46 177 48 47 48 47 47 0. 54 013 0. 53 965 0. 53 918 0. 53 870 0. 53 823 9. 98 266 9. 98 262 9.98 259 9. 98 255 9. 98 251 4 3 4 4 3 55 54 53 52 51 55 40 36 32 28 24 4 40 44 48 52 56 10 11 12 13 14 9. 44 472 9. 44 516 9. 44 559 9. 44 602 9. 44 646 44 43 43 44 43 9. 46 224 9. 46 271 9. 46 319 9. 46 366 9.46 413 47 48 47 47 47 0. 53 776 0. 53 729 0. 53 681 0. 53 634 0. 53 587 9. 98 248 9. 98 244 9.98 240 9. 98 237 9. 98 233 4 4 3 4 4 50 49 48 47 46 55 20 16 12 8 4 5 4 8 12 16 15 16 17 18 19 9.44 689 9. 44 733 9. 44 776 9. 44 819 9. 44 862 44 43 43 43 43 9. 46 460 9.46 507 9. 46 554 9. 46 601 9. 46 648 47 47 47 47 46 0. 53 540 0. 53 493 0. 53 446 0. 53 399 0. 53 352 9. 98 229 9. 98 226 9. 98 222 9. 98 218 9. 98 215 3 4 4 3 4 45 44 43 42 41 55 56 52 48 44 5 20 24 28 82 36 _>o 21 22 23 24 9.44 905 9. 44 948 9.44 992 9. 45 035 9. 45 077 43 44 43 42 43 9. 46 694 9.46 741 9. 46 788 9. 46 835 9. 46 881 47 47 47 46 47 0. 53 306 0. 53 259 0. 53 212 0. 53 165 0. 53 119 9. 98 211 9. 98 207 9. 98 204 9. 98 200 9. 98 1% 4 3 4 4 4 40 39 38 37 36 54 40 36 32 28 24 5 40 44 48 52 56 25 26 27 28 29 9. 45 120 9.45 163 9.45 206 9. 45 249 9. 45 292 43 43 43 43 42 9.46 928 9. 46 975 9.47 021 9.47 068 9.47 114 47 46 47 46 46 0. 53 072 0. 53 025 0. 62 979 0. 52 932 0. 52 886 9.98 192 9.98 189 9.98 185 9.98 181 9.98 177 3 4 4 4 s 35 34 33 32 31 54 20 16 12 8 4 6 4 8 12 16 30 31 32 33 34 9. 45 334 9. 45 377 9. 45 419 9. 45 462 9.45 504 43 42 43 42 43 9.47 160 9. 47 207 9. 47 253 9.47 299 9. 47 346 47 46 46 47 46 0. 52 840 0. 52 793 0.52 747 0. 52 701 0. 02 654 9. 98 174 9.98 170 9. 98 166 9.98 162 9. 98 159 4 4 4 3 4 30 29 28 27 26 54 56 52 48 44 6 20 24 28 32 36 35 36 37 38 39 9. 45 547 9.45 589 9. 45 632 9. 45 674 9. 45 716 42 43 42 42 42 9. 47 392 9.47 438 9. 47 484 9. 47 530 9. 47 576 46 46 46 46 46 0. 52 608 0. 62 562 0. 52 516 0. 52 470 0. 52 424 9. 98 155 9. 98 151 9. 98 147 9. 98 144 9. 98 140 4 4 3 4 4 25 24 23 22 21 53 40 36 32 28 24 6 40 44 48 52 56 40 41 42 43 44 9.45 758 9. 45 801 9. 45 843 9. 45 885 9. 45 927 43 42 42 42 42 9. 47 622 9.47 668 9.47 714 9.47 760 9.47 806 46 46 46 46 46 0. 52 378 0. 52 332 0. 52 286 0. 52 240 0. 52 194 9. 98 136 9.98 132 9. 98 129 9.98 125 9. 98 121 4 3 4 4 4 20 19 18 17 16 53 20 16 12 8 4 7 4 8 12 16 45 46 47 48 49 9. 45 969 9.46 Oil 9.46 053 9. 46 095 9. 46 136 42 42 42 41 42 9 47 852 9. ? 897 9 47 943 9. 47 989 9. 4^ 035 45 46 46 46 45 0. 52 148 0.52 103 0.52 057 0.52 Oil 0.51 965 9.98 117 9. 98 113 9.98 110 9. 98 106 9.98 102 4 3 4 4 4 15 14 13 12 11 53 56 52 48 44 7 20 24 28 32 36 50 51 52 53 54 9.46 178 9. 46 220 9. 46 262 9. 46 303 9. 46 345 42 42 41 42 41 9. 48 080 9.48 126 9. 58 171 9. 48 217 9. 48 262 46 45 46 45 45 0.51 920 0.51 874 0.51 829 0.51 783 0.51 738 9. 98 098 9.98 094 9. 98 090 9. 98 087 9. 98 083 4 4 3 4 4 10 9 8 6 52 40 36 32 28 24 7 40 "44 48 52 56 55 56 57 58 59 9.46 386 9. 46 428 9. 46 469 9. 4"6 511 9. 46 552 42 41 42 41 42 9. 48 307 9.48 353 9.48 398 9. 48 443 9. 48 489 46 45 45 46 45 0.51 693 0.51 647 0. 51 602 0.51 557 0.51 511 9. 98 079 9. 98 075 9. 98 071 9. 98 067 9. 98 063 4 4 4 4 3 5 4 3 1 52 20 16 12 8 4 8 60 9. 46 694 9. 48 534 0.51 466 9. 98 060 ,T2 L. Cos d. L. Cotg. c.d. L. Tang L. Sin. d. ' m. s. 73 GEOGRAPHIC TABLES AND FORMULAS. 165 TABLE 22. Five-place logarithms of circular functions, etc. Continued. l h 17 m. s. ' L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. a. 8 4 8 12 16 1 2 3 4 9. 46 594 9.46 635 9.46 676 9. 46 717 9.46 758 41 41 41 41 42 9.48 534 9.48 579 9. 48 624 9.48 669 9. 48 714 45 45 45 45 45 0.51 466 0.51 421 0.51 376 0.51 331 0. 51 286 9. 98 060 9. 98 056 9.98 052 9. 98 048 9. 98 044 4 4 4 4 4 60 59 58 57 56 52 56 52 48 44 8 20 24 28 32 36 5 6 7 8 9 9.46 800 9. 46 841 9. 46 882 9.46 923 9.46 964 41 41 41 41 41 9. 48 759 9.48 804 9. 48 849 9. 48 894 9. 48 939 45 45 45 45 45 0. 61 241 0.51 196 0.51 151 0. 51 106 0. 51 061 9. 98 040 9. 98 036 9. 98 032 9. 98 029 9. 98 025 4 4 3 4 4 55 54 53 52 51 51 40 36 32 28 24 8 40 44 48 52 56 10 11 12 13 14 9.47 005 9.47 045 9.47 086 9.47 127 9.47 168 40 41 41 41 41 9. 48 984 9. 49 029 9. 49 073 9.49 118 9. 49 163 45 44 45 45 44 0.51 016 0. 50 971 0. 50 927 0. 50 882 0.50 837 9. 98 021 9.98017 9. 98 013 9. 98 009 9.98 005 4 4 4 4 4 50 49 48 47 46 51 20 16 12 8 4 9 4 8 12 16 15 16 17 18 19 9. 47 209 9. 47 249 9. 47 290 9.47 330 9.47 371 40 41 40 41 40 9.49 207 9. 49 252 9. 49 296 9.49 341 9.49 385 45 44 45 44 45 0. 50 793 0. 50 748 0.50 704 0. 50 659 0. 50 615 9. 98 001 9. 97 997 9. 97 993 9.97 989 9.97 986 4 4 4 3 4 45 44 43 42T 41 51 56 52 48 44 9 20 24 28 32 36 20 21 22 23 24 9. 47 411 9. 47 452 9. 47 492 9. 47 533 9. 47 573 41 40 41 40 40 9. 49 430 9. 49 474 9. 49 519 9.49 563 9. 49 607 44 45 44 44 45 0. 50 570 0. 50 526 0. 50 481 0. 50 437 0. 50 393 9. 97 982 9. 97 978 9. 97 974 9. 97 970 9. 97 966 4 4 4 4 4 40 39 38 37 36 50 40 36 32 28 24 9 40 44 48 52 56 25 26 27 28 29 9. 47 613 9.47 654 9.47 694 9. 47 734 9. 47 774 41 40 40 40 40 9.49 652 9.49 696 9. 49 740 9. 49 784 9. 49 828 44 44 44 44 44 0. 50 348 0. 50 304 0.50 260 0. 50 216 0. 50 172 9. 97 962 9. 97 958 9. 97 954 9. 97 950 9. 97 946 4 4 4 4 4 35 34 33 32 31 50 20 16 12 8 4 10 4 8 12 16 30 31 32 33 34 9.47 814 9.47 854 9. 47 894 9. 47 934 9.47 974 40 40 40 40 40 9. 49 872 9.49 916 9. 49 960 9.50 004 9.50048 44 44 44 44 44 0.50 128 0.50 084 0. 50 040 0. 49 996 0. 49 952 9.97 942 9. 97 938 9.97 934 9.97 930 9. 97 926 4 4 4 4 4 30 29 28 27 25 50 50 52 48 44 10 20 24 28 32 36 35 36 37 38 39 9. 48 014 9.48 054 9.48 094 9.48 133 9.48 173 40 40 39 40 40 9.50 092 9.50 136 9.50 180 9.50 223 9.50 267 44 44 43 44 44 0. 49 908 0.49 864 0. 49 820 0.49 777 0.49 733 9. 97 922 9. 97 918 9. 97 914 9. 97 910 9.97 906 4 4 4 4 4 25 24 23 22 21 I'.i Hi 36 32 28 24 10 40 44 48 52 56 40 41 42 43 44 9.48 213 9. 48 252 9.48 292 9. 48 332 9.48371 39 40 40 39 40 9.50311 9.50 355 9. 50 398 9.50 442 9.50 485 44 43 44 43 44 0.49 689 0. 49 645 0. 49 602 0.49 558 0. 49 515 9. 97 902 9. 97 898 9. 97 894 9.97 890 9. 97 886 4 20 19 18 17 16 49 20 16 12 8 1 11 4 8 12 16 45 46 47 48 49 9.48 411 9. 48 450 9. 48 490 9.48 529 9.48 568 39 40 39 39 39 9.50 529 9. 50 572 9.50 616 9. 50 659 9. 50 703 44 44 43 44 43 0. 49 471 0. 49 428 0. 49 384 0. 49 341 0. 49 297 9. 97 882 9. 97 878 9. 97 874 9. 97 870 9. 97 866 4 5 1f> 14 13 12 11 49 56 52 48 44 11 20 24 28 32 36 50 51 52 53 54 9. 48 607 9. 48 647 9.48 686 9. 48 725 9.48 764 40 39 39 39 39 9.50 746 9. 50 789 9. 50 833 9.50876 9. 50 919 43 44 43 43 43 0. 49 254 0. 49 211 0.49 167 0.49 124 0. 49 081 9. 97 861 9. 97 857 9. 97 853 9. 97 849 9. 97 845 4 4 4 4 10 9 8 7 6 IS .10 36 32 28 24 11 40 44 48 52 56 55 56 57 58 59 9.48 803 9. 48 842 9. 48 881 9.48 920 9. 48 959 39 39 39 39 39 9.50 962 9.51 005 9. 51 048 9. 51 092 9. 51 135 43 43 44 43 43 0. 49 038 0. 48 995 0. 48 952 0. 48 908 0. 48 865 9. 97 841 9. 97 837 9. 97 833 9. 97 829 9. 97 825 4 4 4 4 5 4 3 2 1 48 20 16 12 8 4 12 60 9. 48 998 9.51 178 0. 48 822 9.97 821 48 L. Cos. d. L. Cotg. c.d. L. Tang. L. Sin. d. ' m. s. 72 166 GEOGRAPHIC TABLES AND FORMULAS. TABLE 22. Five-place logarithms of circular functions, etc, Continued. l h 18 m. s. t L. Sin. d. L. Tang. c.d. L. Cotg. L. Cos. d. 12 4 8 12 16 1 2 3 4 9. 48 998 9. 49 037 9.49 076 9. 49 115 9. 49 153 39 39 39 38 39 9. 51 178 9.51 221 9. 51 264 9. 51 306 9.51 349 43 43 42 43 43 0. 48 822 0.48 779 0. 48 736 0. 48 694 0. 48 651 9. 97 821 9. 97 817 9. 97 812 9. 97 808 9. 97 804 4 5 4 4 4 60 59 58 57 56 48 56 52 48 44 12 20 24 28 32 36 5 6 7 8 9 9.49 192 9. 49 231 9. 49 269 9. 49 308 9. 49 347 39 38 39 39 38 9. 51 392 9. 51 435 9.51 478 9.51 520 9. 51 563 43 43 42 43 43 0. 48 608 0. 48 565 0. 48 522 0. 48 480 0. 48 437 9.97 800 9.97 796 9. 97 792 9. 97 788 9. 97 784 4 4 4 4 5 55 54 53 52 51 47 40 36 32 28 24 12 40 44 48 52 56 10 11 12 13 14 9.49 385 9. 49 424 9. 49 462 9. 49 500 9. 49 539 39 38 38 39 38 9. 51 606 9.51 648 9. 51 691 9.51 734 9.51 776 42 43 43 42 43 0. 48 394 0. 48 352 0.48 309 0. 48 266 0. 48 224 9. 97 779 9. 97 775 9. 97 771 9. 97 767 9. 97 763 4 4 4 4 4 50 49 48 47 46 47 20 16 12 8 4 13 4 8 12 16 15 16 17 ^18 19 9. 49 577 9. 49 615 9. 49 654 9. 49 692 9. 49 730 38 39 38 38 38 9.51 819 9. 51 861 9. 51 903 9.51 946 9. 51 988 42 42 43 42 43 0. 48 181 0.48 139 0. 48 097 0. 48 054 0. 48 012 9. 97 759 9. 97 754 9. 97 750 9.97 746 9. 97 742 5 4 4 4 4 45 44 43 42 41 47 56 52 - 48 44 13 20 24 28 32 36 20 21 22 23 24 9. 49 768 9. 49 806 9. 49 844 9. 49 882 9. 49 920 38 38 38 38 38 9. 52 031 9. 52 073 9. 52 115 9. 52 157 9.52 200 42 42 42 43 42 0. 47 969 0. 47 927 0. 47 885 0. 47 843 0. 47 800 9. 97 738 9.97 734 9. 97 729 9. 97 725 9. 97 721 4 5 4 4 4 40 39 38 37 36 46 40 36 32 28 24 13 40 44 48 52 56 25 26 27 28 29 9. 49 958 9. 49 996 9. 034 '.). f 072 9. 50 110 38 38 38 38 38 9. 52 242 9. 52 284 9. 52 326 9. 52 368 9. 52 410 42 42 42 42 42 0.47 758 0. 47 716 0.47 674 0. 47 632 0.47 590 9. 97 717 9. 97 713 9. 97 708 9. 97 704 9. 97 700 4 5 4 4 4 35 34 33 32 31 46 20 16 12 8 4 14 4 8 12 16 30 81 32 33 34 9. 50 148 9. 50 185 9. 50 223 9. 50 261 9. 50 298 37 38 38 37 38 9. 52 452 9. 52 494 9. 52 536 9. 52 578 9. 52 620 42 42 42 42 41 0. 47 548 0.47 506 0. 47 464 0.47 422 0. 47 380 9. 97 696 9. 97 691 9.97 687 9.97 683 9. 97 679 5 4 4 4 5 30 29 28 27 26 46 56 52 48 44 14 20 21 28 32 36 35 36 37 38 39 9. 50 336 9. 50 374 9. 50 411 9. * 449 9. 50 486 38 37 38 37 37 9. 52 661 9. 52 703 9.52 745 9. 52 787 9. 52 829 42 42 42 42 41 0. 47 339 0. 47 297 0. 47 255 0.47 213 0.47 171 .>. it? <;: i 9. 97 670 9. 97 666 9. 97 662 9. 97 657 4 4 4 5 4 25 24 23 22 21 45 40 36 32 28 24 14 40 44 48 52 56 40 41 42 43 44 9. 50 523 9. 50 561 9. 50 598 9. 50 635 9. 50 673 38 37 37 38 37 9. 52 870 9. 52 912 9. 52 95? 9.52 995 9. 53 037 42 41 42 42 41 0. 47 130 0.47 088 0.47 047 0. 47 C05 0. 46 963 9.97 653 9.97 649 9. 97 645 9. 97 640 9. 97 636 4 4 5 4 4 20 19 18 17 16 45 20 16 12 8 4 15 4 8 12 16 45 46 47 48 49 9. 50 710 9. 50 747 9. 50 784 9. 50 821 9.50858 37 37 37 37 38 9.53 078 9.53 120 9. 53 161 9. 53 202 9. 53 244 42 41 41 42 41 0. 46 922 0. 46 880 0. 46 839 0.46 798 0. 46 756 9. 97 632 9.97 628 9. 97 623 9. 97 619 9. 97 615 4 5 4 4 5 15 14 13 12 11 45 56 52 48 44 15 20 24 28 32 36 50 51 52 53 54 9. 50 896 9. 50 933 9. 50 970 9. 51 007 9. 51 043 37 37 37 36 37 9. 53 285 9. 53 327 9. 53 368 9.53 409 9.53450 42 41 41 41 42 0. 46 715 0. 46 673 0. 46 632 0. 46 591 0. 46 550 9. 97 610 9. 97 606 9. 97 602 9. 97 597 9. 97 593 4 4 5 4 4 10 9 8 7 6 44 40 36 32 28 24 15 40 44 48 52 56 55 56 57 58 59 9.51 080 9. 51 117 9.51 154 9. 51 191 9. 51 227 37 37 37 36 37 9. 53 492 9. 53 533 9. 53 5 4 9. 53 615 9. 53 656 41 41 41 41 41 0. 46 508 0.46467 0. 46 426 0. 46 385 0. 46 344 9. 97 589 9. 97 584 9. 97 580 9. 97 576 9. 97 571 5 4 4 5 4 5 4 3 2 1 44 20 16 12 8 4 16 60 9. 51 264 9. 53 697 0. 46 303 9.97 567 44 L. Cos. d. L. Cotg. c.d. L. Tang. L. Sin. d. / m. s. 71 GEOGRAPHIC TABLES AND FORMULAS. 167 TABLE 22. Five-place logarithms of circular functions, etc. Continued. l h 19 m. s. ' L. Sin. d. L. Tang. c.d. L. Cotg. L. Cos. d. 16 4 8 12 16 1 2 3 4 9. 51 264 9. 51 301 9. 51 338 9. 51 374 9. 51 411 37 37 36 37 36 9. 53 697 9.53 738 9. 53 779 9.53 820 9. 53 861 41 41 41 41 41 0. 46 303 0. 46 262 0.46 221 0. 46 180 0. 46 139 9. 97 567 9. 97 563 9. 97 558 9. 97 554 9. 97 550 4 5 4 4 5 60 59 58 57 56 44 56 52 48 44 16 20 24 28 32 36 5 6 7 8 9 9.51 447 9. 51 484 9. 51 520 9.51 557 9.51 593 37 36 37 36 36 9.53 902 9. 53 943 9. 53 984 9. 54 025 9.54065 41 41 41 40 41 0.46 098 0. 46 057 0. 46 016 0. 45 975 0.45 935 9.97 545 9. 97 541 9. 97 536 9. 97 532 9. 97 528 4 5 4 4 5 55 54 53 52 51 43 40 36 32 28 24 16 40 44 48 52 56 10 11 12 13 14 9.51 629 9.51 666 9.51 702 9. 51 738 9.51 774 37 36 36 36 37 9.54 106 9. 54 147 9.54 187 9. 54 228 9. 54 269 41 40 41 41 40 0.45 894 0. 45 853 0. 45 813 0. 45 772 0. 45 731 9. 97 523 9. 97 519 9. 97 515 9. 97 510 9.97 506 4 4 5 4 5 50 49 48 47 46 43 20 16 12 8 4 17 4 8 12 16 15 16 17 18 19 9. 51 811 9.51 847 9. 51 883 9.51 919 9.51 956 36 36 36 36 36 9.54 309 9.54 350 P. 54 390 9. 54 431 9. 54 471 41 40 41 40 41 0. 45 691 0.45 650 0.45 610 0.45 569 0. 45 529 ' 9. 97 501 9.97 497 9. 97 492 9. 97 488 9. 97 484 4 5 4 4 5 45 44 43 42 41 43 56 52 48 44 17 20 24 28 32 36 20 21 22 23 24 9.51 9C1 9. 52 027 9. 52 063 9. 52 099 9. 52 135 36 36 36 36 36 9. 54 512 9.54 552 9. 54 593 9. 54 633 9. 54 67? 40 41 40 40 41 0. 45 488 0. 45 448 0. 45 407 0. 45 367 0. 45 327 9. 97 479 9. 97 475 9. 97 470 9. 97 466 9. 97 461 4 5 4 5 4 40 39 38 37 36 42 40 36 32 28 24 17 40 44 48 52 56 26 26 27 28 29 9.52 171 9. 52 207 9. 52 242 9. 52 278 9. 52 314 36 35 36 36 36 9.54 714 9.54 754 9. 54 794 9. 54 835 9. 54 875 40 40 41 40 40 0. 45 286 0. 45 246 0. 45 206 0.45 165 o.-ir, I'jA 9. 97 457 9. 97 453 9. 97 448 9. 97 444 9. 97 439 4 5 4 5 4 35 34 33 32 31 42 20 16 12 8 4 18 4 8 12 16 30 31 32 33 34 9.52 350 9.52 385 9. 52 421 9. 52 456 9. 52 492 35 36 35 36 35 9. 54 915 9.54 95!? 9. 54 995 9. 55 0.35 9.55 075 40 40 40 40 40 0.45 085 0. 45 045 0. 45 005 0. 44 965 0.44 925 9. 97 435 9. 97 430 9. 97 426 9. 97 421 9. 97 417 5 4 5 4 5 30 29 28 27 26 42 56 52 48 44 18 20 24 28 32 36 35 36 37 38 39 ( .l. .V_> r,-J7 9.52 563 9.52 598 9. 52 634 9. 52 669 36 35 36 35 36 9.55115 9.55 155 9.55 19^ 9. 55 235 9. 55 275 40 40 40 40 40 0. ii sxfi 0. 44 845 0. 44 805 0. 44 765 0. 44 725 9.97 412 9.97 408 9. 97 403 9. 97 399 9. 97 394 4 5 4 5 4 25 24 23 22 21 41 40 36 32 28 24 18 40 44 48 52 56 40 41 42 43 44 9. 52 705 9. 52 74Q 9.52 775 9. 52 811 9. 52 846 35 35 36 35 35 9.55 315 9. 55 355 9. 55 395 9.55434 9. 55 474 40 40 39 40 40 0.44 r,s.-> 0.44 645 0. 44 605 0. 44 566 0. 44 526 9.97 390 9. 97 385 9.97 381 9. 97 376 9. 97 372 5 4 5 4 5 20 19 18 17 16 41 20 16 12 8 1 19 4 8 12 16 45 46 47 48 49 9. 52 881 9.52 916 9. 52 951 9. 52 986 9.53 021 35 35 35 35 35 9.55 514 9.55554 9. 55 593 9.55 633 9.55673 40 39 40 40 39 0.44 486 0. 44 446 0. 44 407 0.44 367 0. 44 327 9. 97 367 9.97 363 9. 97 358 9. 97 353 9. 97 349 4 5 5 4 5 15 14 13 12 11 41 56 52 48 44 19 20 24 28 32 36 50 51 52 53 54 9. 53 056 9.53 092 9. 53 126 9. 53 161 9. 53 196 36 34 35 35 35 9.55 712 9. 55 752 9. 55 791 9. 55 831 9. 55 870 40 39 40 39 40 0.44288 0. 44 248 0.44 209 0.44 169 0. 44 130 9. 97 344 9. 97 340 9. 97 335 9. 97 331 9. 97 326 4 5 4 5 4 10 9 8 7 6 40 40 36 32 28 24 19 40 44 48 52 56 55 56 57 58 59 '.. .",:; -i:>,\ 9.53 266 9.53 301 9.53 336 9. 53 370 36 35 35 34 35 9. 55 910 9.55949 9. 55 989 9.56 028 9.56 067 39 40 39 39 40 0.44 090 0. 44 051 0.44 Oil 0.43 972 0.43 933 9. 97 322 9. 97 317 9. 97 312 9. 97 308 9. 97 303 5 5 4 5 4 5 4 3 2 1 40 20 16 12 8 4 20 60 9.53 405 9.56 107 0. 43 893 9. 97"299 40 L. Cos. d. L. Cotg. c.d. L. Tang. L. Sin. d. / m. s. 70 168 GEOGRAPHIC TABLES AND FORMULAS. TABLE 22. Five-place logarithms of circular functions, etc. Continued. l h 20 m. s. ' L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. d. 20 4 8 12 16 1 2 3 4 9. 53 405 9. 53 440 9. 53 475 9.53 509 9.53 544 35 35 34 35 34 35 34 35 34 35 34 34 35 34 34 35 34 34 34 34 34 34 34 34 34 34 34 34 34 34 33 34 34 33 34 34 33 34 33 34 33 34 33 34 33 33 34 33 33 33 34 33 33 33 33 33 33 33 33 33 9. 56 107 9.56 146 9.56 185 9. 56 224 9.56 264 39 39 39 40 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 38 39 39 39 38 39 39 38 39 38 39 38 39 38 39 38 38 39 38 38 39 38 36 38 38 39 38 38 38 38 38 38 38 38 38 38 38 37 38 38 38 0. 43 893 0. 43 854 0. 43 815 0. 43 776 0. 43 736 9. 97 299 9. 97 294 9. 97 289 9. 97 285 9. 97 280 5 5 4 5 4 5 5 4 5 5 4 5 5 4 5 5 4 5 5 4 5 5 4 5 5 4 5 5 5 4 5 5 4 5 5 5 4 5 5 5 4 5 5 5 5 4 5 5 5 5 4 5 5 5 5 60 59 58 57 56 40 56 52 48 44 20 20 24 28 32 36 5 6 7 8 9 9. 53 578 9.53 613 9. 53 647 9.53 682 9. 53 716 9. 56 303 9. 56 342 9. 56 381 9. 56 420 9.56459 0.43 697 0. 43 658 0.43 619 0.43 580 0.43 541 9. 97 276 9.97 271 9. 97 266 9. 97 262 9. 97 257 55 54 53 52 51 39 40 36 32 28 24 20 40 44 48 52 56 10 11 12 13 14 9.53 751 9. 53 785 9. 53 819 9. 53 854 9.53 888 9. 56 498 9. 56 537 9. 56 576 9. 56 615 9.56 654 0.43 502 0. 43 463 0. 43 424 0.43 385 0. 43 346 9. 97 252 9. 97 248 9. 97 243 9. 97 238 9. 97 234 60 49 48 47 46 39 20 16 12 8 4 21 4 8 12 16 15 16 17 18 19 9.53 922 9. 53 957 9. 53 991 9.54 025 9.54059 9.56 693 9. 56 732 9. 56 771 9. 56 810 9. 56 849 0. 43 307 0. 43 268 0. 43 229 0.43 190 0.43 151 9. 97 229 9. 97 224 9. 97 220 9. 97 215 9. 97 210 45 44 43 42 41 39 56 52 48 44 21 20 24 28 32 36 20 21 22 23 24 9.54 093 9. 54 127 9. 54 161 9. 54 195 9. 54 229 9. 56 887 9.56 926 9. 56 965 9.57 004 9.57 042 0.43 113 0. 43 074 0. 43 035 0.42 996 0.42 958 9. 97 206 9. 97 201 9. 97 196 9.97 192 9.97 187 40 39 38 37 36 38 40 36 32 28 24 21 40 44 48 52 56 25 26 27 28 29 9. 54 263 9.54 297 9. 54 331 9.54 365 9. 54 399 9.57 081 9. 57 120 9.57 158 9. 57 197 9.57 22) 0.42 919 0. 42 880 0.42 842 0. 42 803 0.42 765 9.97 182 9.97 178 9. 97 173 9.97 168 9.97 163 35 34 33 32 31 38 20 16 12 8 4 22 4 8 12 16 30 31 32 33 34 9. 54 433 9. 54 466 9.54500 9. 54 534 9. 54 567 J. 57 274 9. 57 312 9.57 351 9. 57 389 9.57 428 0. 42 726 0. 42 688 0. 42 649 0. 42 611 0. 42 572 9. 97 159 9.97 154 9. 97 149 9.97 145 9. 97 140 30 29 28 27 26 38 56 52 48 44 22 20 24 28 32 36 35 36 37 38 , 39 9. 54 601 9.54 635 9. 54 668 9. 54 702 9. 54 735 9. 57 466 9. 57 504 9. 57 543 9. 57 581 9. 57 619 0. 42 534 0. 42 496 0. 42 457 0.42 419 0. 42 381 9. 97 135 9.97 130 9.97 126 9. 97 121 9. 97 116 25 24 23 22 21 37 40 36 32 28 24 22 40 44 48 52 56 40 41 42 43 44 9. 54 769 9.54 802 9. 54 836 9. 54 869 9.54 903 9. 57 658 9. 57 696 9. 57 734 9.57 772 9. 57 810 0. 42 342 0. 42 304 0. 42 266 0. 42 228 0. 42 190 9.97 111 9. 97 107 9.97 102 9. 97 097 9.97 092 20 19 18 17 16 37 20 16 12 8 4 23 4 8 12 16 45 46 47 48 49 9. 54 936 9. 54 969 9. 55 003 9.55 036 9.55069 9. 57 849 9. 57 887 9. 57 925 9. 57 963 9.58 001 0. 42 151 0.42 113 0.42 075 0. 42 037 0.41 999 9. 97 087 9. 97 083 9. 97 078 9. 97 073 9.97 068 15 14 13 12 11 37 56 52 48 44 23 20 24 28 32 36 50 51 52 53 54 9. 55 102 9. 55 136 9. 55 169 9. 55 202 9. 55 235 9.58 039 9.58 077 9. 58 115 9.58 153 9.58 191 0. 41 961 0. 41 923 0.41 885 0.41 847 0.41 809 9. 97 063 9. 97 059 9. 97 054 9. 97 049 9.97 044 10 9 8 7 6 36 40 36 32 28 24 23 40 44 48 52 56 65 56 57 58 59 9. 55 268 9. 55 301 9. 55 334 9. 55 367 9.55400 9. 58 229 9. 58 267 9. 58 304 9. 58 342 9.58380 0.41 771 0.41 733 0.41 696 0. 41 658 0. 41 620 9. 97 039 9. 97 035 9. 97 030 9. 97 025 9. 97 020 4 5 5 5 *, 5 4 3 2 1 86 20 16 12 8 4 24 60 9. 55 433 9. 58 418 0.41 582 9. 97 015 36 L. Cos. d. L. Cotg. c. d. L. Tang. L. Sin. d. / m. s 69 GEOGRAPHIC TABLES AND FORMULAS. 169 TABLE 22. Five-place logarithms of circular functions, etc. Continued. l h 21 m. s. ' L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. d. 24 4 8 12 16 1 2 3 4 9.55 433 9.55 466 9.55499 9.55 532 9.55 564 33 33 33 32 33 33 33 32 33 33 9.58 418 9.58 455 9.58 493 9. 58 531 9.58 569 37 38 38 38 37 38 37 38 38 37 38 37 38 37 37 38 37 38 37 37 37 38 37 37 37 37 38 37 37 37 37 37 37 37 37 37 37 36 37 37 37 37 36 37 37 37 36 37 37 36 37 36 37 36 37 36 37 36 37 36 0.41 582 0.41 545 0. 41 507 0.41 469 0.41 431 9. 97 015 9. 97 010 9.97 005 9. 97 001 9. 96 996 5 5 4 5 5 5 5 5 5 5 4 5 5 5 5 5 5 5 5 5 5 5 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 5 5 5 5 5 5 60 59 58 57 56 36 56 52 48 44 24 20 24 28 32 36 5 6 7 8 9 9.55 597 9.55 630 9.55 663 9.55 695 9. 55 728 9.58 606 9. 58 644 9. 58 681 9. 58 719 9. 58 757 0.41 394 0.41 356 0. 41 319 0. 41 281 0.41 213 9. 96 991 9. 96 986 9. 96 981 9. 96 976 9.96 971 55 54 53 52 51 35 40 36 32 28 24 24 40 44 48 52 56 10 11 12 13 14 9. 55 761 9. 55 793 9. 55 826 9.55 858 9. 55 891 32 33 32 33 32 33 32 33 32 32 33 32 32 33 32 32 32 32 32 33 32 32 32 32 32 31 32 32 32 32 32 31 32 32 32 31 32 31 32 32 31 32 31 31 32 31 32 31 31 32 9. 58 794 9. 58 832 9.58 869 9.58 907 9.58 944 0. 41 206 0.41 168 0.41 131 0.41 093 0.41 056 9.96 966 9. 96 962 9. 96 957 9.96 952 9. 96 947 50 49 48 47 46 35 20 16 12 8 4 25 4 8 12 16 15 16 17 18 19 9.55 923 9.65 956 9.55 988 9. 56 021 9.56053 9.58 981 9. 59 019 9.59 066 9. 59 094 9.59 131 0.41 019 0. 40 981 0.40 944 0.40 906 0.40 869 9. 96 942 9. 96 937 9. 96 932 9. 96 927 9.% 922 45 44 43 42 41 35 56 52 48 44 25 20 24 28 32 36 20 21 22 23 24 9.56 085 9.56 118 9.56 150 9. 56 182 9. 56 215 9. 59 168 9.59205 9. 59 243 9.59 280 9. 59 317 0. 40 832 0. 40 795 0.40 757 0.40 720 0.40 683 9. 96 917 9. 96 912 9.% 907 9.% 903 9. 96 898 40 39 38 37 36 34 40 36 32 28 24 25 40 44 48 52 56 25 26 27 28 29 9. 56 247 9. 56 279 9. 56 311 9.56 343 9. 56 375 9.59 354 9.59 391 9.59 429 9. 59 466 y.5y ."><:; 0. 40 646 0.40609 0. 40 571 0.40534 0. 40 497 9.96 893 9.% 888 9. 96 883 9. 96 878 9.96 873 35 34 33 32 31 34 20 16 12 8 4 26 4 8 12 16 30 31 32 33 34 9.56 408 9.56 440 9.56 472 9.56 504 9.56 536 9.59 540 9. 59 577 9. 59 614 9. 59 651 y. 59 osx 0. 40 460 0. 40 423 0.40 386 0.40 349 0.40 312 9.96 868 9.96 863 9.96 858 9.% 853 9. 96 848 30 29 28 27 26 34 56 52 48 44 26 20 24 28 32 36 35 36 37 38 39 9.56 568 9.56 599 9. 56 631 9.56 663 9.56 695 9.59 725 9. 59 762 9,59 799 9.59 835 9. 59 872 0. 40 275 0. 40 238 0.40 201 0. 40 165 0. 40 128 9.96 843 9. 96 838 9. 96 833 9. 96 828 9. 96 823 25 24 23 22 21 33 40 36 32 28 24 26 40 44 48 52 56 40 41 42 43 44 9.56 727 9.56 759 9. 56 790 9. 56 822 9.56 854 9.59 909 9. 59 946 9. 59 983 9. 60 019 9.60 056 0.40 091 0. 40 051 0. 40 017 0. 39 981 0. 39 944 9. % 818 9. 96 813 9. 96 808 9.96 803 9.96 798 20 19 18 17 16 33 20 16 12 8 4 27 4 8 12 16 45 46 47 48 49 9.56 886 9.56 917 9.56 949 9.56 980 9. 57 012 9.60 093 9.60 130 9.60 166 9. 60 203 9. 60 240 0. 39 907 0. 39 870 0. 39 834 0. 39 797 0. 39 760 9. 96 793 9.96 788 9. 96 783 9. 96 778 9. 96 772 15 14 13 12 11 33 56 52 48 44 27 20 24 28 32 36 50 51 52 53 54 9.57 044 9. 57 075 9.57 107 9.57 138 9. 57 169 9. 60 276 9. 60 313 9.60 349 9.60 386 9. 60 422 0.39 724 0. 39 687 0. 39 65-1 0. 39 614 0. 39 578 9. 96 767 9. 96 762 9. 96 757 9.96 752 9.96 747 10 9 8 7 6 32 40 36 32 28 24 27 40 44 48 52 56 55 56 57 58 59 9. 57 201 9. 57 232 9.57 264 9.57 295 9. 57 326 9. 60 459 9. 60 495 9. 60 532 9.60 568 9.60 605 0. 39 541 0.39 505 0. 39 468 0. 39 432 0.39395 9.96 742 9. 96 737 9. 96 732 9. 96 727 9. 96 722 5 5 5 5 5 5 4 3 2 1 32 20 16 12 8 4 28 60 9.57 358 9.60 641 0. 39 359 9.96 717 32 I* Los. d. L. Cotg. c. d. L. Tang. L. Sin. d. ' m. s. 68 170 GEOGEAPHIC TABLES AND FORMULAS. TARLE 22. Five-place logarithms of circular functions, etc. Continued. l h 22 m. s. ' L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. d. 28 4 8 12 16 ] 2 3 4 9. 57 358 9. 57 389 9. 57 420 9. 57 451 9. 57 482 31 31 31 31 32 9. 60 641 9. 60 677 9. 60 714 9. 60 750 9. 60 786 36 37 36 36 37 0.39 359 0. 39 323 0. 39 286 0.39 250 0. 39 214 9. 96 717 9. 96 711 9. 96 706 9. 96 701 9. 96 696 6 5 5 5 5 60 59 58 57 56 32 56 52 48 44 28 20 24 28 32 36 5 6 7 8 9 9. 57 514 9.57 545 9. 57 576 9.57 607 9. 57 638 31 31 31 31 31 9. 60 823 9. 60 859 9. 60 895 9. 60 931 9. 60 967 36 36 36 36 37 0. 39 177 0. 39 141 0. 39 105 0. 39 069 0. 39 033 9. 96 691 9. 96 686 9. 96 681 9. 96 676 9. 96 670 5 5 5 6 5 55 54 53 52 51 31 40 36 32 28 24 28 40 44 48 52 56 10 11 12 13 14 9.57 669 9.57 700 9.57 731 9. 57 762 9. 57 793 31 31 31 31 31 9.61 004 9. 61 040 9. 61 076 9.61 112 9.61 148 36 36 36 86 36 0. 38 996 0. 38 960 0.38 924 0. 38 888 0. 38 852 9. 96 665 9. 96 660 9. 96 655 9. 96 650 9.96 645 5 5 5 5 5 50 49 48 47 46 31 20 16 12 8 4 29 4 8 12 16 15 16 17 18 19 9. 57 824 9.57 855 9.57 885 9. 57 916 9. 57 947 31 30 31 31 31 9.61 184 9.61 220 9. 61 256 9.61 292 9.61 328 36 36 36 36 36 0. 38 816 0.38 780 0. 38 744 0. 38 708 0. 38 672 9.96 640 9. 96 634 9. 96 629 9. 96 624 9. 96 619 6 5 5 5 5 45 44 43 42 41 31 56 52 48 44 29 20 24 28 32 36 20 21 22 23 24 9. 57 978 9.58 008 9. 58 039 9. 58 070 9.58 101 30 31 31 31 30 9.61 364 9.61 400 9. HI 436 9.61 472 9. 61 508 36 36 36 36 36 0.38 636 0. 38 600 0. 38 564 0. 38 528 0. 38 492 9. 96 614 9. 96 608 9. 96 603 9. 96 598 9. 96 593 6 5 5 5 5 40 39 38 37 36 30 40 36 32 28 24 29 40 44 48 52 56 25 26 27 28 29 9. 58 131 9. 58 162 9. 58 192 9.58 223 9. 58 253 31 30 31 30 31 9,61 544 9.61 579 9. 61 615 9.61 651 9.61 687 35 36 36 36 35 0. 38 456 0. 38 421 0. 38 385 0. 38 349 0. 38 313 9. 96 588 9. 96 582 9. 96 577 9.96 572 9. 96 567 6 5 5 5 5 35 34 33 32 31 30 20 16 12 8 4 30 4 8 12 16 30 31 32 33 34 9.58 284 9.58 314 9. 58 345 9. 58 375 9. 58 406 30 31 30 31 30 9.61 722 9.61 758 9.61 794 9.61 830 9. 61 865 36 36 .36 35 36 0. 38 278 0. 38 242 0. 38 206 0. 38 170 0.38 135 9. 96 562 9.96 556 9.96 551 9. 96 546 9.96 541 6 5 5 5 6 30 29 28 27 26 30 56 52 48 44 30 20 24 28 32 36 35 36 37 38 39 9.58 436 9. 58 467 9. 58 497 9. 58 527 9.58 557 31 30 30 30 31 9.61 901 9.61 936 9.61 972 9. 62 008 9. 62 043 35 36 36 35 36 0. 38 099 0. 38 064 0. 38 028 0.37 992 0. 37 957 9. 96 535 9. 96 530 9. 96 525 9. 96 520 9.96 514 5 5 5 6 5 25 24 23 22 21 29 40 36 32 28 24 30 40 44 48 52 56 40 41 42 43 44 9. 58 588 9. 58 618 9. 58 648 9. 58 678 9. 58 709 30 30 30 31 30 9. 62 079 9. 62 114 9.62 150 9.62 185 9. 62 221 35 36 35 36 35 0.37 921 0. 37 886 0. 37 850 0. 37 815 0. 37 779 9. 96 509 9. 96 504 9. 96 498 9. 96 493 9. 96 488 5 6 5 5 5 20 19 18 17 16 29 20 16 12 8 4 31 4 8 12 16 45 46 47 48 49 9. 58 739 9. 58 769 9. 58 799 9. 58 829 9. 58 859 30 30 30 30 30 9, 62 256 9. 62 292 9. 62 327 9. 62 362 9. 62 398 36 35 25 36 35 0.37 744 0. 37 708 0. 37 673 0.37 638 0.37 602 9. 96 483 9. 96 477 9. 96 472 9. 96 467 9.96 461 6 5 5 6 5 15 14 13 12 11 29 56 52 48 44 31 20 24 28 32 36 50 51 52 53 54 9. 58 889 9.58 919 9.58 949 9. 58 979 9. 59 009 30 30 30 30 30 9. 62 433 9. 62 468 9.62 504 9. 62 539 9. 62 574 35 36 35 35 35 0. 37 567 0. 37 532 0.37 49n 0. 37 461 0. 37 426 9. 96 456 9. 96 451 9. 96 445 9. 96 440 9. 96 4&5 5 6 5 5 6 10 9 8 6 28 40 36 32 28 24 31 40 44 48 52 56 55 56 57 58 59 9. 59 039 9. 59 069 9. 59 098 9. 59 128 9.59 158 30 29 30 30 30 9. 62 609 9. 62 645 9. 62 680 9. 62 715 9. 62 750 36 ' 35 35 35 35 0. 37 391 0.37 355 0.37 320 0. 37 285 0. 37 250 9. 96 429 9. 96 424 9. 96 419 9. 96 413 9. 96 408 5 5 6 5 5 5 4 3 2 1 28 20 16 12 8 4 32 60 9. 59 188 9. 62 785 0. 37 215 9. 96 403 28 L. Cos. d. L. Cotg. c. d. L. Tang. L. Sin. d. i m. s. 67 GEOQKAPHIC TABLES AND FORMULAS. 171 TABLE 22. Five-place logarithms of circular functions, etc. Continued. l h * 23 m. s. ' L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. d. 32 4 8 12 16 1 2 3 4 9.59 188 9. 59 218 9. 59 247 9. 59 277 9. 59 307 30 29 30 30 29 9. 62 785 9. 62 820 9. 62 855 9. 62 890 9.62 926 35 35 35 36 35 0.37215 0.37 180 0.37 145 0. 37 110 0. 37 074 9. 96 403 9. 96 397 9. 96 392 9. 96 387 9.96 381 6 5 5 6 <> 60 59 58 57 56 28 56 52 48 44 32 20 24 28 32 36 5 6 7 8 9 9. 59 336 9.59 366 9. 59 396 9.59 425 9. 59 455 30 30 29 30 29 9. 62 961 9.62 996 9. 63 031 9.63 066 9.63 101 35 35 35 35 34 0. 37 039 0. 37 004 0. 36 969 0. 36 934 0. 36 899 9. 96 376 9. 96 370 9.96 365 9.96 360 9.96 354 6 5 5 6 5 55 54 53 52 51 27 40 36 32 28 24 32 40 44 48 52 56 10 11 12 13 14 9.59 484 9. 59 514 9. 59 543 9. 59 573 9.59 602 30 29 30 29 30 9. 63 135 9.63 170 9.63 205 9. 63 240 9. 63 275 35 35 35 35 35 0.36 865 0. 36 830 0.36 795 0.36 760 0. 36 725 9. 96 349 9.96 343 9.96 338 9. 96 333 9. 96 327 6 5 5 6 5 50 49 48 47 46 27 20 16 12 8 4 33 4 8 12 16 15 16 17 18 19 9. 59 632 9. 59 661 9. 69 690 9. 59 720 9.59 749 29 29 30 29 29 9. 63 310 9.63 345 9. 63 379 9.63414 9.63 449 35 34 35 35 35 0. 36 690 0. 36 655 0. 36 621 0.36 586 0. 36 551 9.96 322 9. 96 316 9. 96 311 9. 96 305 9.96 300 6 5 6 5 6 45 44 43 42 41 27 56 52 48 44 33 20 24 28 32 36 20 21 22 23 24 9.59 778 9. 59 808 9.59837 9. 59 866 9. 59 895 30 29 29 29 29 9.63 484 9. 63 519 9.63 553 9.63 588 9.63 623 35 34 35 35 34 0. 36 516 0. 36 481 0. 36 447 0. 36 412 0. 36 377 9.96 294 9. 96 289 9.96 284 9. 96 278 9.96273 5 5 6 5 6 40 39 38 37 36 26 40 36 32 28 24 33 40 44 48 52 56 jr. 26 27 28 29 9.59 924 9. 59 954 9.59 983 9. 60 012 9.60 041 30 29 29 29 29 9.63 657 9.63 692 9.63 726 9. 63 761 9.63 796 35 34 35 35 34 0.36 343 0.36 308 0. 36 274 0. 36 239 0. 36 204 9. 96 267 9. 96 262 9. 96 256 9. 96 251 9. 96 245 5 6 5 6 5 35 34 33 32 31 26 20 16 12 8 4 34 4 8 12 16 30 31 32 33 34 9. 60 070 9.60 099 9.60 128 9. 60 157 9.60 186 29 29 29 29 29 9.63 830 9.63 865 9.63 899 9.63 934 9.63968 35 34 35 34 35 0.36 170 0.36 135 0.36 101 0.36 066 0. 36 032 9.96 240 9.96 234 9. 96 229 9. 96 223 9. % 218 6 5 6 5 6 30 29 28 27 26 26 56 52 48 44 34 20 24 28 32 36 35 36 37 38 39 9. 60 215 9. 60 244 9.60 273 9.60 302 9.60 331 29 29 29 29 28 y. M OOH 9. 64 037 9.64 072 9.64 106 9.64 140 34 35 34 34 35 0.35 997 0.35 963 0.35 928 0. 35 894 0. 35 860 9. 96 212 9. 96 207 9. 96 201 9. 96 196 9.96 190 5 6 5 6 5 25 24 23 22 21 25 40 36 32 28 24 34 40 44 48 52 56 40 41 42 43 44 9.60359 9.60 388 9. 60 417 9. 60 446 9. 60 474 29 29 29 28 29 9.64 175 9.64 209 9. 64 243 9. 64 278 9. 64 312 34 34 35 34 34 0.35825 0. 35 791 0. 35 757 0. 35 722 0.35 688 9. 96 185 9.96 179 9.96 174 9. 96 168 9. 96 162 6 5 6 6 5 20 19 18 17 16 25 20 16 12 8 4 35 4 8 12 16 45 46 47 48 49 9.60 503 9. 60 532 9.60 561 9. 60 589 9. 60 618 29 29 28 29 28 9.64 346 9.64 381 9. 64 415 9. 64 449 9.64 483 35 34 34 34 34 0.35 654 0. 35 619 0.35 585 0.35 551 0. 35 517 9.96 157 9. 96 151 9.96 146 9. 96 140 9. 96 135 6 5 6 5 6 15 14 13 12 11 25 56 52 48 44 35 20 24 28 32 36 50 51 52 53 54 9. 60 646 9. 60 675 9. 60 704 9. 60 732 9. 60 761 29 29 28 29 28 9. 64 517 9. 64 552 9.64 586 9.64 620 9.64 654 35 34 34 34 34 0.35 483 0. 35 448 0.35414 0.35 380 0.35 346 9. 96 129 9.96 123 9. 96 118 9.96 112 9.96 107 6 5 6 5 6 10 9 8 7 6 24 40 36 32 28 24 35 40 44 48 62 56 55 56 57 58 59 9. 60 789 9.60 818 9.60 846 9.60 875 9.60 903 29 28 29 28 28 9.64 688 9.64 722 9.64 756 9.64 790 9.64 824 34 34 34 34 34 0. 35 212 0.35 278 0.35 244 0.35 210 0. 35 176 9. 96 101 9. 96 095 9. 96 090 9. 96 084 9.96 079 6 5 6 5 6 5 4 3 2 1 24 20 16 12 8 4 36 60 9. 60 931 9.64 858 0.35 142 9.96 073 24 L. Cos. d. L. Cotg. c. d. L. Tang. L. Sin. d. / m. s. I 172 GEOGRAPHIC TABLES AND FORMULAS. TABLE 22. Five-place logarithms of circular functions, etc. Continued. l h 24 m. s. ' L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. d. 36 4 8 12 16 1 2 3 4 9. 60 931 9. 60 960 9.60 988 9.61 016 9.61 045 29 28 28 29 9. 64 858 9.64 892 9.64 926 9. 64 960 9.64994 34 34 34 34 0. 35 142 0. 35 108 0. 35 074 0.35 040 0.35 006 9. 96 073 9. 96 067 9. 96 062 9. 96 056 9. 96 050 6 5 6 6 60 69 58 57 56 24 56 52 48 44 36 20 24 28 32 36 5 6 7 8 9 9. 61 073 9.61 101 9.61 129 9. 61 158 9. 61 186 28 28 29 28 9.65 028 9. 65 062 9. 65 096 9. 65 130 9.65 164 34 34 34 34 0.34 972 0. 34 938 '0. 34 904 0. 34 870 0. 34 836 9. 96 045 9.96 039 9. 96 034 9. 96 028 9.96 022 6 5 6 6 55 54 53 52 51 23 iO 36 32 28 24 36 40 44 48 52 56 10 11 12 13 14 9. 61 214 9.61 242 9.61 270 9. 61 298 9.61 326 28 28 28 28 9. 65 197 9.65 231 9. 65 265 9. 65 299 9.65 333 34 34 34 34 0. 34 803 0. 34 769 0.34 735 0. 34 701 0.34 667 9. 96 017 9. 96 Oil 9. 96 005 9.96 000 9. 95 994 6 6 5 6 50 49 48 47 46 23 20 16 12 8 4 37 4 8 12 16 15 16 17 18 19 9.61 354 9. 61 382 9. 61 411 9. 61 438 9. 61 466 28 29 27 28 9. 65 366 9. 5 400 9. 65 434 9. 65 467 9. 65 501 34 34 33 34 0.34634 0.34 600 0.34 566 0. 34 533 0. 34 499 9. 95 988 9. 95 982 9, 95 977 9.95 971 9. 95 965 6 5 6 6 45 44 43 42 41 23 56 52 48 44 37 20 24 28 32 36 20 21 22 23 24 9. 61 494 9.61 522 9.61 550 9.61 578 9. 61 606 28 28 28 28 9. 65 535 9. 65 568 9. 65 602 9. 65 636 9. 65 669 33 34 34 33 0. 34 465 0. 34 432 0. 34 398 0. 34 364 0. 34 331 9.95 960 9. 95 954 9. 95 948 9. 95 942 9. 95 937 6 6 6 5 40 39 38 37 36 22 40 36 32 28 24 37 40 44 48 52 56 25 26 27 28 29 9. 61 634 9. 61 662 9.61 689 9. 61 717 9.61 745 , 28 27 28 28 9. 65 703 9.65 736 9. 65 770 9. 65 803 9. 65 837 33 34 33 34 0. 34 297 0. 34 264 0. 34 230 0. 34 197 0. 34 163 9. 95 931 9.95 925 9. 95 920 9. 95 914 9.95 908 6 5 6 6 35 34 33 32 31 22 20 16 12 8 4 38 4 8 12 16 30 31 32 34 9. 61 773 9. 61 800 9.61 828 9.61 856 9.61 883 27 28 28 27 9. 65 870 9.65 904 9. 65 937 9.65 971 9.66 004 34 33 34 33 04 0. 34 130 0. 34 096 0. 34 063 0. 34 029 0.33 996 9.95 902 9. 95 897 9. 95 891 9.95 885 9. 95 879 5 6 6 6 30 29 28 27 26 2-2 56 52 48 44 38 20 24 28 32 36 35 36 37 38 39 9.61 911 9.61 939 9.61 966 9.61 994 9. 62 021 28 27 28 27 9. 66 038 9. 66 071 9.66 104 9. 66 138 9.66 171 33 33 34 33 .0.33 962 0. 33 929 0. 33 896 0. 33 862 0.33 829 9. 95 873 9. 95 868 9. 95 862 9.95 856 9.95 850 5 6 6 6 25 24 23 22 21 21 40 36 32 28 24 38 40 44 48 52 56 40 41 42 43 44 9. 62 049 9. 62 076 9. 62 104 9. 62 131 9.62 159 27 28 27 28 9. 66 204 9. 66 238 9.66 271 9.66 304 9. 66 337 34 33 33 33 0. 33 796 0. 33 762 0.33 729 0. 33 696 0.33 663 9.95 844 9. 95 839 9. 95 833 9. 95 827 9. 95 821 5 6 6 6 20 19 18 17 16 21 20 16 12 8 4 39 4 8 12 16 45 46 47 48 49 9.62 186 9. 62 214 9. 62 241 9. 62 268 9. 62 296 28 27 27 28 9. 66 371 9. 66 404 9. 66 437 9. 66 470 9.66 503 33 33 33 33 04 0. 33 629 0. 33 596 0. 33 563 0. 33 530 0. 33 497 9. 95 815 9. 95 810 9. 95 804 9. 95 798 9.95 792 5 6 6 6 15 14 13 12 11 21 56 52 48 44 39 20 24 28 32 36 50 51 52 53 54 9. 62 323 9.62 350 9. 62 377 9. 62 405 9. 62 432 27 27 28 27 9. 66 537 9.66 570 9. 66 603 9.66 636 9.66 669 33 33 33 33 0.33 463 0.33 430 0. 33 397 0.33 364 0.33 331 9. 95 786 9. 95 780 9.95 775 9.95 769 9. 95 763 6 5 6 6 10 9 8 7 6 20 40 36 32 28 24 39 40 44 48 52 56 55 56 57 58 59 9. 62 459 9. 62 486 9. 62 513 9.62 541 9.62 568 27 27 28 27 9.66 702 9. 66 735 9.66 768 9.66 801 9.66 834 33 33 33 33 0. 33 298 0. 33 265 0. 33 232 0.33 199 0.33 166 9.95 757 9. 95 751 9. 95 745 9.95 739 9.95 733 6 6 6 6 5 4 3 2 1 20 20 16 12 8 4 40 60 9. 62 595 9. 66 867 0. 33 133 9. 95 728 20 L. Cos. d. L. Cotg. c. d. L. Tang. L. Sin. d. ' m. s. 65 ( GEOGRAPHIC TABLES AND FORMULAS. 173 TABLE 22. Five-place logarithms of circular functions, etc. Continued. l h 25 m. s. > L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. d. 40 4 8 12 16 1 2 3 4 9. 62 595 9. 62 622 9. 62 649 9.62 676 9. 62 703 27 27 27 27 9.66 867 9.66 900 9. 66 9a3 9. 66 966 9.66 999 33 33 33 33 0.33 133 0.33 100 0. 33 067 0. 33 034 0. 33 001 9. 95 728 9. 95 722 9. 95 716 9. 95 -710 9. 95 704 6 6 6 6 60 59 58 57 56 20 56 52 48 44 40 20 24 28 32 36 5 6 8 9 9. 62 730 9.62 757 9. 62 784 9. 62 811 9.62 838 27 27 27 27 9. 67 032 9.67 065 9.67 098 9.67 131 9.67 163 33 33 33 32 0. 32 968 0. 32 935 0. 32 902 0. 32 869 0. 32 837 9.95698 9.95 692 9. 95 686 9. 95 680 9. 95 674 6 6 6 6 55 54 53 52 51 19 40 36 32 28 24 40 40 44 48 52 56 10 11 12 13 14 9. 62 865 9. 62 892 9. 62 918 9.62 945 9. 62 972 27 26 27 27 9.67 196 9. 67 229 9. 67 262 9. 67 295 9. 67 327 33 33 33 32 0.32 804 0. 32 771 0. 32 738 0. 32 705 0. 32 673 9.95 668 9. 95 663 9. 95 657 9.95651 9. 95 645 5 6 6 6 50 49 48 47 46 19 20 16 12 8 4 41 4 8 12 16 15 16 17 18 19 9.62 999 9.63 026 9.63 052 9.63 079 9.63 106 27 26 27 27 9. 67 360 9. 67 393 9. 67 426 9. 67 458 9.67 491 33 33 32 33 0. 32 640 0.32 607 0. 32 574 0. 32 5-12 0.32509 9. 95 639 9. 95 633 9. 95 627 9. 95 621 9.95615 6 6 6 6 45 44 43 42 41 19 56 52 48 44 41 20 24 28 32 36 20 21 22 23 24 9. 63 133 9. 63 159 9.63 186 9.63213 9. 63 239 26 27 27 26 9. 67 524 9.67 556 9. 67 589 9. 67 622 9.67 654 32 33 33 32 0. 32 476 0.32 444 0. 32 411 0. 32 378 0. 32 346 9.95609 9. 95 603 9. 95 597 9. 95 591 9.95 585 6 6 6 6 40 39 38 37 36 18 40 36 32 28 24 41 40 44 48 52 56 25 26 27 28 29 9.63 266 9. 63 292 9. 63 319 9.63 345 9. 63 372 26 27 26 27 9. 67 687 9. 67 719 9.67 752 9.67 785 9.67 817 32 33 33 32 0.32 313 0. 32 281 0. 32 248 0. 32 215 0. 32 183 9. 95 579 9. 95 673 9. 95 567 9. 95 5-51 9.95 555 6 6 6 6 35 34 33 32 31 18 20 16 12 8 4 42 4 8 12 16 30 31 32 33 34 9. 63 398 9.63 425 9. 63 451 9. 63 478 9.63 504 27 26 27 26 9.67 850 9. 67 882 9. 67 915 9. 67 947 9. 67 980 32 33 32 33 0.32 150 0.32 118 0.32 085 0.32053 0. 32 020 9. 95 549 9. 95 543 9. 95 537 9. 95 531 9.95 525 6 6 6 6 30 29 28 27 26 18 56 52 48 44 42 20 24 28 32 36 36 36 37 38 39 9.63531 9. 63 557 9.63 583 9. 63 610 9.63 636 26 26 27 26 9.68012 9.68 044 9. 68 077 9.68 109 9. 68 142 32 33 32 33 0.31 988 0.31 956 0.31 923 0.31 891 0.31 858 9. 95 519 9.95 513 9. 95 507 9.95500 9. 95 494 6 6 ' 7 6 25 24 23 22 21 17 40 36 32 28 24 42 40 44 48 52 56 40 41 42 43 44 9.63 662 9.63 689 9. 63 715 9. 63 741 9. 63 767 27 26 26 26 9. 68 174 9. 68 206 9. 68 239 9. 68 271 9.68 303 32 33 32 32 0.31 826 0.31 794 0.31 761 0. 31 729 0. 31 697 9. 95 488 9. 95 482 9. 95 476 9. 95 470 9.95464 6 6 6 6 20 19 18 17 16 17 20 16 12 8 4 43 4 8 12 16 45 46 47 48 49 9.63 794 9. 63 820 9.63 846 9. 63 872 9.63 898 26 26 26 26 9. fi 336 9.68 368 9. 68 400 9. 68 432 9.68 465 33 32 32 32 33 0. 31 664 0.31 632 0.31 600 0. 31 568 0. 31 535 9. 95 458 9. 95 452 9. 95 446 9. 95 440 9. 95 434 6 6 6 6 15 14 13 12 11 17 56 52 48 44 43 20 24 28 32 36 50 51 52 53 54 9.63 924 9. 63 950 9. 63 976 9.64 002 9.64 028 26 26 26 26 9.68 497 9. 68 529 9. 68 561 9.68 593 9. 68 626 32 32 32 33 0.31 503 0.31 471 0. 31 439 0.31 407 0.31 374 9. 95 427 9. 95 421 9. 95 415 9. 95 409 9. 95 403 6 6 6 6 10 9 8 7 6 16 40 36 32 28 24 43 40 44 48 52 56 55 56 57 58 59 9.64 054 9.64 080 9.64 106 9.64 132 9.64 158 26 26 26 26 9.68 658 9.68 690 9.68 722 9.68 754 9. 68 786 32 32 32 32 0.31 342 0.31 310 0.31 278 0.31 246 0. 31 214 9. 95 397 9. 95 391 9. 95 384 9. 95 378 9. 95 372 6 7 6 6 5 4 3 2 1 16 20 16 12 8 4 44 60 9.64 184 9. 68 818 0.31 182 9.95 366 16 L. Cos. d. L. Cotg. C.d. L. Tang. L. Sin. d. / m. s. 64 C 174 GEOGRAPHIC TABLES AND FORMULAS. TABLE 22. Five-place logarithms of circular functions, etc. Continued. l h 26 m. s. ' L. Sin. d. L. Tang. c.d. L. Cotg. L. Cos. d. 44 4 8 12 16 1 2 3 4 9. 64 184 9.64210 9. 64 236 9. 64 262 9. 64 288 26 26 26 26 25 9. 68 818 9.68850 9. 68 882 9. 68 914 9. 68 946 32 32 32 32 32 0.31 182 0.31 150 0.31 118 0. 31 086 0. 31 054 9. 95 366 9. 95 360 9. 95 354 9. 95 348 9. 95 341 6 6 6 7 ft 60 59 58 57 56 16 56 52 48 44 44 20 24 28 32 36 5 6 7 8 9 9.64 313 9.64 339 9. 64 365 9. 64 391 9. 64 417 26 26 26 26 25 9. 68 978 9. 69 010 9. 69 042 9. 69 074 9.69 106 32 32 32 32 32 0.31 022 0.30 990 0. 30 958 0. 30 926 0. 30 894 9. 95 335 9. 95 329 9. 95 323 9. 95 317 9. 95 310 6 6 6 7 fi 55 54 53 52 51 15 40 36 32 28 24 44 40 44 48 52 56 10 11 12 13 14 9. 64 442 9. 64 468 9. 64 494 9. 64 519 9.64 545 26 26 25 26 26 9. 69 138 9. 69 170 9. 69 202 9. 69 234 9. 69 266 32 32 32 32 32 0. 30 862 0. 30 830 0. 30 798 0. 30 766 0. 30 734 9.95 304 9. 95 298 9. 95 292 9.95286 9. 95 279 6 6 6 fi 50 49 48 47 46 15 20 16 12 8 4 45 4 8 12 16 15 16 17 18 19 9. 64 571 9.64 596 9.64 622 9. 64 647 9. 64 673 25 26 25 26 25 9. 69 298 9. 69 329 9. 69 361 9. 69 393 9. 69 425 31 32 32 32 32 0. 30 702 0. 30 671 0. 30 639 0. 30 607 0. 30 575 9. 95 273 9. 95 267 9. 95 261 9. 95 254 9. 95 248 6 6 6 6 45 44 43 42 41 15 56 52 48 44 45 20 24 28 32 36 20 21 22 23 24 9. 64 698 9. 64 724 9. 64 749 9. 64 775 9.64 800 26 25 26 25 26 9. 69 457 9. 69 488 9. 69 520 9. 69 552 9.69 584 31 32 32 32 31 0. 30 543 0. 30 512 0.30 480 0. 30 448 0.30 116 9. 95 242 9. 95 236 9. 95 229 9. 95 223 9. 95 217 6 6 6 6 40 39 38 37 36 14 40 36 32 28' 24 45 40 44 48 52 56 25 26 27 28 29 9. 64 826 9.64 851 9. 64 877 9.64 902 9.64927 25 26 25 25 26 9. 69 615 9. 69 647 9. 69 679 9. 69 710 9. 69 742 32 32 31 32 32 0.30 385 0. 30 353 0. 30 321 0. 30 290 0.30258 9. 95 211 9. 96 204 9. 95 198 9. 95 192 9.95 185 7 6 6 7 6 35 34 33 32 31 14 20 16 12 8 4 46 4 8 12 16 30 31 32 33 34 9. 64 953 9. 64 978 9. 65 003 9. 65 029 9.65 054 25 25 26 25 25 9.69774 9. 69 805 9. 69 837 9. 69 868 9.69 900 31 32 31 32 32 0.30 226 0. 30 195 0. 30 163 0. 30 132 0.30 100 9. 95 179 9. 95 173 9. 95 167 9. 95 160 9.95 154 6 6 7 6 6 30 29 28 27 26 14 56 52 48 44 46 20 24 28 32 36 35 36 37 38 39 9. 65 079 9.65 104 9.65130 9.65 155 9.65 180 25 26 25 25 25 9. 69 932 9. 69 963 9. 69 995 9. 70 026 9. 70 058 31 32 31 32 31 0.30 068 0. 30 037 0.30 005 0. 29 974 0. 29 942 9. 95 148 9. 95 141 9.95 135 9.95 129 9. 95 122 7 6 6 7 6 25 24 23 22 21 13 40 36 32 28 24 46 40 44 48 52 56 40 41 42 43 44 9.65 205 9.65 230 9.65 255 9. 65 281 9. 65 306 25 25 26 25 26 9. 70 089 9. 70 121 9. 70 152 9. 70 184 9. 70 215 32 31 32 31 32 0.29 911 0. 29 879 0. 29 848 0.29816 0.29 785 9. 95 116 9.95 110 9. 95 103 9. 95 097 9.95 090 6 7 6 7 6 20 19 18 17 16 13 20 16 12 8 4 47 4 8 12 16 45 46 47 48 49 9.65 331 9.65356 9. 65 381 9. 65 406 9. 65 431 25 25 25 25 25 9. 70 247 9. 70 278 9. 70 309 9. 70 341 9. 70 372 31 31 32 31 32 0.29 753 0. 29 722 0. 29 691 0.29 659 0.29 628 9. 95 084 9. 95 078 9. 95 071 9.95 065 9. 95 059 6 7 6 6 7 15 14 13 12 11 13 56 52 48 44 47 20 24 28 32 36 50 51 52 53 54 9.65 456 9. 65 481 9.65 506 9. 65 531 9.65 556 25 25 25 25 24 9. 70 404 9. 70 435 9. 70 466 9. 70 498 9. 70 529 31 31 32 31 31 0.29 596 0.29 565 0. 29 534 0.29 502 0.29471 9. 95 062 9. 95 046 9. 95 039 9. 95 033 9. 95 027 6 7 6 6 7 10 9 8 7 6 12 40 36 32 28 24 47 40 44 56 55 56 57 58 59 9. 65 58Q 9.65 605 9.65 630 9.65 655 9.65 680 25 25 25 25 25 9. 70 560 9. 70 592 9. 70 623 9.70 654 9.70 685 32 31 31 31 32 0. 29 440 0.29 408 0. 29 377 0. 29 346 0.29 315 9. 95 020 9. 95 014 9. 95 007 9. 95 001 9. 94 995 6 7 6 6 7 5 4 3 2 1 12 20 16 12 8 4 48 60 9. 65 705 9. 70 717 0. 29 283 9.94 988 12 L.Cos. d. L. Cotg. c.d. L. Tang. L. Sin. d. ' m. s. 63 GEOGRAPHIC' TABLES AND FORMULAS. 175 TABLE 22. Five-place logarithms of circular functions, etc. Continued. l h 27 m. i L. Sin. d. L. Tang. c.d. L. Cotg. L. Cos. d. 48 4 8 12 16 1 2 3 4 9.65 705 y. CM 7-_> 9.65 754 9. 65 779 9. 65 804 24 25 25 25 9. 70 717 9. 70 748 9. 70 779 9. 70 810 9. 70 841 31 31 31 31 0.29 283 0. 29 252 0. 29 221 0. 29 190 0.29 159 9. 94 988 9. 94 982 9. 94 975 9. 94 969 9. 94 962 6 7 6 60 59 58 57 50 12 56 52 48 44 48 20 24 28 32 36 5 6 7 8 9 9. 65 828 9.65 853 9. 65 878 9.65 902 9.65 927 25 25 24 25 9. 70 873 9.70 904 9. 70 935 9. 70 966 9. 70 997 31 31 31 31 0.29 127 0. 29 096 0. 29 065 0. 29 034 0. 29 003 9. 94 956 9. 94 949 9.94 943 9. 94 936 9. 94 930 7 6 6 7 55 54 53 52 51 11 40 36 32 28 24 48 40 44 48 V2 56 10 11 12 13 14 9.65 952 9. 65 976 9. 66 001 9.66 025 9.66 050 24 25 24 25 9. 71 028 9.71 059 9.71 090 9. 71 121 9. 71 153 31 31 31 32 0. 28 972 0. 28 941 0. 28 910 0. 28 879 0. 28 847 9. 94 923 9. 94 917 9.94 911 9. 94 904 9. 94 898 6 6 7 6 7 50 49 48 47 46 11 20 16 12 8 4 49 4 8 12 16 15 16 17 18 19 9. 66 075 9. 66 099 9. 66 124 9. 66 148 9. 66 173 24 25 24 25 9.71 184 9. 71 215 9. 71 246 9.71 277 9.71 308 31 31 31 31 0.28 816 0. 28 785 0. 28 754 0. 28 723 0. 28 692 9. 94 891 9. 94 885 9. 94 878 9. 94 871 9. 94 865 6 7 7 6 45 44 43 42 41 11 56 52 48 44 49 20 24 28 32 36 20 21 22 23 24 9. 66 197 9.66 221 9. 66 246 9. 66 270 9.66 295 24 25 24 25 9. 71 339 9.71 370 '.'.71 mi 9. 71 431 9.71 462 31 31 30 31 0.2S tilil 0. 28 630 0.28 599 0. 28 569 0. 28 538 9.94 858 9.94 852 9. 94 845 9.94839 9. 94 832 6 7 6 7 40 39 38 37 36 10 40 36 32 28 24 49 40 44 48 52 56 25 26 27 28 29 9. 66 319 9.66 343 9. 66 368 9. 66 392 9.66 416 24 25 24 24 9. 71 493 9. 71 524 9.71 555 9. 71 586 9.71 617 31 31 31 31 0. 28 507 0. 28 476 0.28 445 0. 28 414 0.28 383 9. 94 826 9. 94 819 9. 94 813 9. 94 806 9.94 799 7 6 7 7 35 34 33 32 31 10 20 16 12 8 4 50 4 8 12 16 30 31 82 33 34 <>. 66 441 9. 66 465 9. 66 489 9. 66 513 9. 66 537 24 24 24 24 OK 9. 71 648 9. 71 679 9.71 709 9. 71 740 9.71 771 31 30 31 31 0. 28 352 0. 28 321 0. 28 291 0.28 260 0.28 229 9. 94 793 9.94 786 9. 94 780 9. 94 773 9. 94 767 7 6 7 6 30 29 28 27 26 10 56 52 48 44 50 20 24 28 32 36 35 36 37 38 39 9.66 562 9.66 586 9. 66 610 9.66 634 9.66 658 24 24 24 24 9.71 802 9. 71 833 9. 71 863 9.71 894 9. 71 925 31 30 31 31 0.28 198 0.28 167 0. 28 137 0.28 106 0.28075 9. 94 760 9. 94 753 9. 94 747 9.94 740 9. 94 734 7 6 7 6 25 24 23 22 21 9 40 36 32 28 24 50 40 44 48 52 56 40 41 42 43 44 9. 66 682 9.66 706 9. 66 731 9. 66 755 9. 66 779 24 25 24 24 9. 71 955 9.71 986 9. 72 017 9. 72 048 9. 72 078 31 31 31 30 0.28045 0. 28 014 0. 27 983 0.27 952 0.27 922 9. 94 727 9. 94 720 9. 94 714 9. 94 707 9. 94 700 6 7 7 20 19 18 17 16 9 20 16 12 8 4 51 4 8 12 16 45 46 47 48 49 9.66803 9. 66 827 9. 66 851 9. 66 875 9. 66 899 24 24 24 24 9.72 109 9. 72 140 9. 72 170 9.' 72 201 9. 72 231 31 30 31 30 0. 27 891 0. 27 860 0. 27 830 0. 27 799 0. 27 769 9.94 694 9. 94 687 9.94 680 9. 94 674 9. 94 667 7 7 6 7 15 14 13 12 11 9 56 52 48 44 51 20 24 28 32 36 50 51 52 53 54 9.66 922 9. 66 946 9. 66 970 9.66 994 9. 67 018 24 24 24 24 9. 72 262 9. 72 293 9. 72 323 9. 72 354 9.72 384 31 30 31 30 0.27 738 0.27 707 0. 27 677 0. 27 646 0. 27 C16 9. 94 660 9. 94 654 9. 94 647 9. 94 640 9. 94 634 6 7 7 6 10 9 8 7 6 8 40 36 32 28 24 51 40 44 48 52 56 55 56 57 58 59 ( .).f)7 012 9.67 066 9.67 090 9. 67 113 9. 67 137 24 24 23 24 9. 72 415 9.72 445 9. 72 476 9. 72 506 9. 72 537 30 31 30 31 0. 27 585 0. 27 f>. r >5 0. 27 524 5. 27 494 0. 27 463 9. 94 627 9.94 620 9. 94 614 9. 94 607 9.94600 7 6 7 7 5 4 3 2 1 8 20 16 12 8 1 52 60 9. 67 161 9. 72 567 0. 27 433 9. 94 593 8 .0 L. Cos. d. L. Cotg. c.d. L. Tang. L. Sin. d. / m. s. 62 176 GEOGRAPHIC TABLES AND FORMULAS. TABLE 22. Five-place logarithms of circular functions, etc. Continued. l h 28 m. s. / L. Sin. d. L. Tang. c.d. L. Cotg. L. Cos. ' d. 52 4 8 12 16 1 2 3 4 9. 67 161 9. 67 185 9. 67 208 9. 67 232 9. 67 256 24 23 24 24 24 9. 72 567 9. 72 598 9. 72 628 9. 72 659 9. 72 689 31 30 31 30 31 0. 27 433 0.27 402 0.27 372 0. 27 341 0.27 311 9. 94 593 9. 94 587 9. 94 580 9.94573 9. 94 567 6 7 7 6 7 60 59 58 57 56 8 56 52 48 44 52 20 24 28 32 36 5 6 7 8 9 9. 67 280 9. 67 303 9. 67 327 9. 67 350 9. 67 374 23 24 23 24 24 9. 72 720 9. 72 750 9. 72 780 9. 72 811 9. 72 841 30 30 31 30 31 0. 27 280 0.27 250 0.27 220 0. 27 189 0.27 159 9. 94 560 9. 94 553 9. 94 646 9. 94 540 9.94 533 7 7 6 7 7 55 54 53 52 51 7 40 36 32 28 24 52 40 44 48 52 66 10 11 12 13 14 9. 67 398 9. 67 421 9.67 445 9. 67 468 9. 67 492 23 24 23 24 23 9. 72 872 9. 72 902 9. 72 932 9. 72 963 9. 72 993 30 30 31 30 30 0.27 128 0. 27 098 0. 27 068 0. 27 037 0. 27 007 9. 94 526 9.94 519 9. 94 513 9.94 506 9. 94 499 7 6 7 7 7 50 49 48 47 46 7 20 16 12 8 4 53 4 8 12 16 15 16 17 18 19 9. 67 515 9. 67 539 9. 67 662 9. 67 586 9. 67 609 24 23 24 23 24 9.73 023 9.73 054 9. 73 084 9. 73 114 9. 73 144 31 30 30 30 31 0.26 977 0. 26 946 0. 26 916 0.26 886 0. 26 856 9.94 492 9.94485 9. 94 479 9. 94 472 9. 94 495 7 6 7 7 45 44 43 42 41 7 56 52 48 44 53 20 24 28 32 36 20 21 22 23 24 9.67 633 9. 67 656 9. 67 680 9. 67 703 9. 67 726 23 24 23 23 24 9. 73 175 9. 73 20 9. 73 235 9. 73 265 9.73 295 30 30 30 30 31 0.26 825 0. 26 795 0. 26 765 0. 26 735 0. 26 705 9. 94 458 9, 94 451 9.94 445 9. 94 438 9. 94 431 7 6 7 7 7 40 39 38 37 36 6 40 36 32 28 24 53 40 44 48 52 66 25 26 27 28 29 9.67 750 9. 67 773 9.67 796 9. 67 820 9.67 843 23 23 24 23 23 9. 73 326 9. 73 356 9. 73 386 9. 73 416 9. 73 446 30 30 30 30 30 0. 26 674 0. 26 644 0. 26 614 0.26 584 0.26 554 9. 94 424 9.94 417 9. 94 410 9. 94 404 9. 94 397 7 7 6 7 7 35 34 33 32 31 6 20 16 12 8 4 54 4 8 12 16 30 31 32 33 34 9. 67 866 9. 67 890 9. 67 913 9. 67 936 9. 67 959 24 23 23 23 23 9. 73 476 9. 73 507 9. 73 537 9. 73 567 9. 73 597 31 30 30 30 30 0. 26 524 0. 26 493 0. 26 463 0. 26 433 0. 26 403 9. 94 390 9. 94 383 9.94 376 9. 94 369 9. 94 362 7 7 7 7 7 30 29 28 27 26 6 56 52 48 44 64 20 24 28 32 36 35 36 37 38 39 9. 67 982 9.68 006 9. 68 029 9. 68 052 9. 68 075 24 23 23 23 23 9. 73 627 9. 73 657 9. 73 687 9. 73 717 9. 73 747 30 30 30 30 30 0.26 373 0. 26 343 0.26 313 0.26 283 0. 26 253 9.94 355 9.94 349 9: 94 342 9. 94 335 9. 94 328 6 7 7 7 7 25 24 23 22 21 5 40 36 32 28 24 54 40 44 48 52 56 40 41 42 43 44 9. 68 098 9. 68 121 9. 68 144 9. 68 167 9.68190 23 23 23 23 23 9. 73 777 9. 73 807 9. 73 837 9. 73 867 9. 73 897 30 30 30 30 30 0.26 223 0. 26 193 0.26 163 0. 26 133 0.26 103 9.94 321 9.94 314 9. 94 307 9.94 300 9. 94 293 7 7 7 7 7 20 19 18 17 16 5 20 16 12 8 4 55 4 8 12 16 45 46 47 48 49 9. 68 213 9. 68 237 9. 68 260 9. 68 283 9. 68 305 24 23 23 22 23 9. 73 927 9. 73 957 9. 73 987 9. 74 017 9. 74 047 30 30 30 30 30 0. 26 073 0. 26 043 0. 26 013 ' 0.25 983 0.25 953 9. 94 286 9. 94 279 9. 94 273 9. 94 266 9. 94 259 7 6 7 7 7 15 14 13 12 11 5 56 52 48 44 55 20 24 28 32 36 50 51 52 53 54 9. 68 328 9. 68 351 9. 68 374 9. 68 397 9. 68 420 23 23 23 23 23 9. 74 077 9. 74 107 9. 74 137 9. 74 166 9. 74 196 30 30 29 30 30 0. 25 923 0. 25 893 0. 25 863 0. 25 834 0. 25 804 9. 94 252 9. 94 245 9. 94 238 9.94 231 9.94 224 7 7 7 7 7 10 9 8 7 6 4 40 36 32 28 24 55 40 44 48 52 56 55 56 57 58 59 9. 68 443 9.68466 9. 68 489 9. 68 512 9. 68 634 23 23 23 22 23 9. 74 226 9. 74 256 9. 74 286 9. 74 316 9. 74 345 30 30 30 29 30 0.25 774 0. 25 744 0. 25 714 0. 25 684 0.25 655 9.94 217 9. 94 210 9. 94 203 9.94 196 9. 94 189 7 7 7 7 7 5 4 3 2 1 4 20 16 12 8 4 66 60 9. 68 657 9. 74 375 0.25626 9. 94 182 4 L. Cos. d. L. Cotg. c.d. L. Tang. L. Sin. d. ' m. s. 61 GEOGRAPHIC TABLES AND FORMULAS. 177 TABLE 22. Five-place logarithms of circular functions, etc. Continued. l h 29 m. s. ' L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. d. 56 4 8 12 16 1 2 4 9.68 557 9. 68 580 9.68 603 9. 68 625 9. 68 648 23 23 22 23 23 9. 74 375 9. 74 405 9. 74 435 9. 74 465 9. 74 494 30 30 30 29 30 0. 25 625 0. 25 595 0. 25 565 0. 25 535 0.25 506 9. 94 182 9. 94 175 9. 94 168 9. 94 161 9. 94 154 7 7 7 7 7 60 59 58 57 56 4 56 52 48 44 56 20 24 28 32 36 5 6 7 8 9 9. 68 671 9. 68 694 9. 68 716 9. 68 73o 9. 68 76 2 23 22 23 23 22 9. 74 524 9.74 554 9.74 583 9. 74 613 9. 74 643 30 29 30 30 30 0. 25 476 0. 25 446 0. 25 417 0. 25 387 0. 25 357 9. 94 147 9. 94 140 9.94 133 9. 94 126 9. 94 119 7 7 7 7 7 55 54 53 52 51 3 40 36 32 28 24 56 40 44 48 52 56 10 11 12 13 14 9. 68 784 9. 68 807 9. 68 829 9.68 852 9. 68 875 23 22 23 23 22 9. 74 673 9. 74 702 9. 74 732 9. 74 762 9. 74 791 29 30 30 29 30 0. 25 327 0. 25 298 0. 25 268 0.25 238 0. 25 209 9. 94 112 9. 94 105 9. 94 098 9. 94 090 9. 94 083 7 7 8 7 50 49 48 47 - 46 3 20 16 12 8 4 57 4 8 12 16 15 16 17 18 19 9. 68 897 9. 68 920 9. 68 942 9. 68 965 9.68 987 23 22 23 22 23 9. 74 821 9. 74 851 9.74 880 9. 74 910 9. 74 939 30 29 30 29 30 0. 25 179 0. 25 149 0.25 120 0. 25 090 0. 25 061 9. 94 076 9. 94 069 9. 94 062 9. 94 055 9. 94 048 7 7 7 7 7 45 44 43 42 41 3 56 52 48 44 57 20 24 28 32 36 20 21 22 23 24 9. 69 010 9. 69 032 9. 69 055 9. 69 077 9. 69 100 22 23 22 23 22 9. 74 969 9. 74 998 9.75 028 9. 75 058 9. 75 087 29 30 30 29 30 0. 25 031 0. 25 002 0. 24 972 0. 24 942 0. 24 913 9. 94 041 9.94034 9. 94 027 9. 94 020 9. 94 012 7 7 7 8 7 40 39 38 37 36 2 40 36 32 28 24 57 40 44 48 52 56 25 26 27 28 29 9. 69 122 9. 69 144 9. 69 167 9. 69 189 9. 69 212 22 23 22 23 22 9.75 117 9. 75 146 9. 75 176 9. 75 205 9. 75 235 29 30 29 30 29 0. 24 883 0. 24 854 0. 24 824 0. 24 795 0. 24 765 9. 94 005 9. 93 998 9. 93 991 9. 93 984 9. 93 977 7 7 7 7 7 35 34 33 32 31 2 20 16 12 8 4 58 4 8 12 16 30 31 32 33 34 9.69 234 9. 69 2.56 9. 69 279 9. 69 301 9. 69 323 22 23 22 22 22 9. 75 264 9.75 294 9.75 323 9. 75 353 9. 75 382 30 29 30 29 29 0.24736 0. 24 706 0. 24 677 0.24 647 0. 24 618 9. 93 970 9. 93 96? 9. 93 955 9. 93 948 9. 93 941 7 8 7 7 7 30 29 28 27 26 2 56 52 48 44 58 20 24 28 32 36 35 36 37 38 39 9. 69 345 9. 69 368 9. 69 390 9. 69 412 9. 69 434 23 22 22 22 22 9. 75 411 9. 75 441 9. 75 470 9. 75 500 9. 75 529 30 29 30 29 29 0. 24 589 0.24 559 0. 24 530 0. 24 500 0.24 471 9. 93 934 9. 93 927 9. 93 920 9. 93 912 9. 93 905 7 7 8 7 7 25 24 23 22 21 1 40 36 32 28 24 58 40 44 48 52 56 40 41 42 43 44 9.69 456 9. 69 479 9. 69 501 9. 69 523 9. 69 545 23 22 22 22 22 9. 75 558 9.75 588 9. 75 617 9. 75 647 9. 75 676 30 29 30 29 29 0. 24 442 0. 24 412 0. 24 383 0. 24 353 0.24 324 9. 93 898 9. 93 891 9. 93 884 9. 93 876 9. 93 869 7 7 8 7 7 20 19 18 17 16 1 20 16 12 8 4 59 4 8 12 16 45 46 47 48 49 9. 69 567 9. 69 589 9. 69 611 9. 69 633 9. 69 655 22 22 22 22 22 9. 75 705 9. 75 735 9. 75 764 9. 75 793 9. 75 822 30 29 29 29 30 0. 24 29 0.24 265 0. 24 236 0. 24 207 0. 24 178 9. 93 862 9. 93 855 9. 93 847 9. 93 840 9. 93 833 7 8 7 7 7 15 14 13 12 11 1 56 52 48 44 59 20 24 28 32 36 50 51 52 53 54 9. 69 67.7 9. 69 699 9. 69 721 9. 69 743 9. 69 765 22 22 22 22 22 9. 75 852 9. 75 881 9. 75 910 9. 75 939 9. 75 969 29 29 29 30 29 0. 24 148 0.24 119 0. 24 090 0. 24 061 0. 24 031 9. 93 826 9. 93 819 9. 93 811 9. 93 804 9. 93 797 7 8 7 7 8 10 9 8 7 6 40 36 32 28 24 59 40 44 48 52 56 55 56 57 58 59 9. 69 787 9.69 809 9. 69 831 9. 69 853 9. 69 875 22 22 22 22 22 9. 75 998 9. 76 027 9. 76 056 9. 76 086 9. 76 115 29 29 30 29 29 0. 24 002 0. 23 973 0. 23 944 0.23 914 0. 23 885 9. 93 789 9. 93 782 9. 93 775 9. 93 768 9. 93 760 7 7 7 8 7 5 4 3 2 1 20 16 12 8 4 60 60 9. 69 897 9. 76 144 0.23 856 9. 93 753 L.Cos. d. L. Cotg. c.d. L. Tang. L. Sin. d. / m. s. 60 4606108 12 178 GEOGRAPHIC TABLES AND FORMULAS. TABLE 22. Five-place logarithms of circular functions, etc. Continued. 2 h 30 m. s. t L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. d. 4 8 12 16 1 2 3 4 9. 69 897 9.69 919 9. 69 941 9. 69 963 9. 69 984 22 22 22 21 22 9. 76 144 9. 76 173 9. 76 202 9. 76 231 9. 76 261 29 29 29 30 29 0. 23 856 0. 23 827 0. 23 798 0. 23 769 0.23 739 9. 93 753 9. 93 746 9. 93 738 9. 93 731 9. 93 724 7 8 7 7 7 60 59 58 57 56 60 56 52 48 44 20 24 28 32 36 5 7 8 9 9. 70 006 9. 70 028 9. 70 050 9. 70 072 9. 70 093 22 22 22 21 22 9.76 290 9. 76 319 9. 76 348 9. 76 377 9. 76 406 29 29 29 29 29 0. 23 710 0. 23 681 0.23 652 0. 23 623 0.23 594 9. 93 717 9. 93 709 9. 93 702 9. 93 695 9. 93 687 8 7 7 8 7 55 54 53 52 51 59 40 36 32 28 24 40 44 48 52 56 10 11 12 13 14 9. 70 115 9. 70 137 9. 70 159 9. 70 180 9. 70 202 ' 22 22 21 22 22 9. 76 435 9. 76 464 9. 76 493 9. 76 522 9. 76 551 29 29 29 29 29 0. 23 565 0. 23 636 0.23 507 0.23 478 0. 23 449 9. 93 680 9.93 673 9. 93 665 9. 93 658 9. 93 650 7 8 7 8 7 50 49 48 47 46 59 20 16 12 8 4 1 4 8 12 16 15 16 17 18 19 9. 70 224 9. 70 245 9. 70 267 9. 70 288 9. 70 310 21 22 21 22 22 9.76 580 9. 76 609 9. 76 639 9. 76 668 9. 76 697 29 30 29 29 28 0. 23 420 0. 23 391 0. 23 361 0.23 332 0.23 303 9. 93 643 9. 93 636 9. 93 628 9. 93 621 9. 93 614 7 8 7 7 8 45 44 43 42 41 59 56 52 48 44 1 20 24 28 32 36 20 21 22 23 24 9.70 332 9. 70 353 9. 70 375 9. 70 396 9. 70 418 21 22 21 22 21 9. 76 725 9. 76 754 9. 76 783 9. 76 812 9. 76 841 29 29 29 29 29 0. 23 275 0. 23 246 0. 23 217 0. 23 188 0. 23 159 9.93 606 9. 93 599 9. 93 591 9. 93 684 9. 93 577 7 8 7 7 8 40 39 38 37 36 58 40 36 32 28 24 1 40 44 48 52 56 25 26 27 28 29 9. 70 439 9. 70 461 9. 70 482 9. 70 504 9. 70 525 22 21 22 21 22 9. 76 870 9. 76 899 9. 76 928 9. 76 957 9.76 986 29 29 29 29 29 0.23 130 0. 23 101 0. 23 072 0. 23 043 0. 23 014 9. 93 569 9. 93 562 9. 93 554 9. 93 547 9. 93 539 7 8 7 8 35 34 33 32 31 58 20 16 12 8 4 2 4 8 12 16 30 31 32 33 34 9. 70 547 9. 70 568 9. 70 590 9.70 611 9. 70 633 21 22 21 22 21 9. 77 015 9. 77 044 9. 77 073 9.77 101 9. 77 130 29 29 28 29 29 0. 22 985 0. 22 956 0. 22 927 0. 22 899 0. 22 870 9. 93 532 9. 93 525 9. 93 517 9. 93 510 9. 93 502 7 8 8 7 30 29 28 27 '16 58 56 52 48 44 2 20 24 28 32 36 35 36 37 38 39 9. 70 654 9. 70 675 9. 70 697 9. 70 718 9. 70 739 21 22 21 21 22 9. 77 159 9. 77 188 9. 77 217 9. 77 246 9. 77 274 29 29 29 28 29 0. 22 841 0. 22 812 0.22 783 0. 22 754 0.22 726 9. 93 495 9. 93 487 9. 93 480 9. 93 472 9. 93 465 8 ' 7 8 7 8 25 24 23 22 21 57 40 36 32 28 24 2 40 44 48 52 56 40 41 42 43 44 9. 70 761 9. 70 782 9. 70 803 9. 70 824 9. 70 846 21 21 21 22 21 9. 77 303 9. 77 332 9. 77 361 9. 7-7 390 9. 77 418 29 29 29 28 29 0. 22 697 0. 22 668 0.22 639 0. 22 610 0. 22 582 9. 93 457 9. 93 450 9. 93 442 9. 93 435 9. 93 427 7 8 7 8 7 20 19 18 17 16 57 20 16 12 8 4 3 4 8 12 16 45 46 47 48 49 9. 70 867 9. 70 888 9. 70 909 9. 70 931 9. 70 952 21 21 22 21 21 9. 77 447 9. 77 476 9. 77 505 9. 77 533 9. 77 562 29 29 28 29 29 0. 22 553 0. 22 524 0. 22 495 0. 22 467 0.22 438 9. 93 420 9. 93 412 9. 93 405 9. 93 397 9. 93 390 8 7 8 7 8 15 14 13 12 11 57 56 52 48 44 3 20 24 28 32 36 50 51 52 53 54 9. 70 973 9. 70 994 9. 71 015 9. 71 036 9. 71 058 21 21 21 22 21 9. 77 591 9. 77 619 9.77 648 9.77 677 9. 77 706 28 29 29 29 28 0. 22 409 0. 22 381 0. 22 352 0. 22 323 0. 22 294 9. 93 382 9. 93 375 9. 93 367 9. 93 360 9.93 352 7 8 7 8 8 10 9 8 7 6 56 40 36 32 28 24 3 40 44 48 52 56 55 56 57 58 59 9. 71 079 9.71 100 9.71 121 9.71 142 9.71 163 21 21 21 21 21 9. 77 734 9. 77 763 9.77 791 9. 77 820 9. 77 849 29 28 29 29 28 0-22 266 0. 22 237 0. 22 209 0. 22 180 0. 22 151 9. 93 344 9. 93 337 9. 93 329 9. 93 322 9. 93 314 7 8 7 8 5 4 3 2 1 56 20 16 12 8 4 4 60 9.71 184 9. 77 877 0.22 123 9. 93 307 56 L. Cos. d. L. Cotg. c. d. L. Tang. L. Sin d. / m. s. 59 GEOGRAPHIC TABLES AND FORMULAS. 179 TABLE 22. Five-place logarithms of circular functions, etc. Continued. 2 h 31 m. s. ' L. Sin. d. L. Tang. c.d. L. Cotg. L. Cos. d. 4 4 8 12 16 1 2 3 4 9. 71 184 9.71 205 9.71 226 9. 71 247 9. 71 268 21 21 21 21 21 9. 77 877 9. 77 906 9. 77 935 9. 77 963 9.77 992 29 29 28 29 28 0.22 123 0. 22 094 0. 22 065 0.22 037 0. 22 008 9. 93 307 9. 93 299 9. 93 291 9. 93 284 9. 93 276 8 8 7 8 7 60 59 58 57 56 56 56 52 48 44 4 20 24 28 32 36 5 6 7 8 9 9.71 289 9.71 310 9.71 331 9.71 352 9. 71 373 21 21 21 21 20 9. 78 020 9. 78 049 9. 78 077 9.78 106 9. 78 1&5 29 28 29 29 28 0.21 980 0.21 951 0.21 923 0.21 894 0.21 865 9. 93 269 9. 93 261 9. 93 253 9. 93 246 9. 93 238 8 8 7 8 8 55 54 53 52 51 55 40 36 32 28 24 4 40 44 48 52 56 10 11 12 13 14 9.71 393 9.71 414 9. 71 435 9. 71 456 9.71 477 21 21 21 21 21 9.78 163 9. 78 192 9. 78 220 9. 78 249 9. 78 277 29 28 29 28 29 0.21 837 0.21 808 0.21 780 0.21 751 0.21 723 9. 93 230 9. 93 223 9.93 215 9. 93 207 9.93 200 7 8 8 7 8 50 49 48 47 46 55 20 16 12 8 4 5 4 8 12 16 15 16 17 18 19 9.71 498 9. 71 519 9. 71 539 9.71 560 9,71 581 21 20 . 21 21 21 9.78 306 9. 78 334 9.78 363 9. 78 391 9. 78 419 28 29 28 28 29 0.21 694 0. 21 666 0.21 637 0.21 609 0. 21 581 9.93 192 9. 93 184 9. 93 177 9. 93 169 9. 93 161 8 7 8 8 7 45 44 43 42 41 55 56 52 48 44 5 20 24 28 32 36 20 21 22 23 24 9.71 602 9.71 622 9.71 643 9. 71 664 9.71 685 20 21 21 21 20 9. 78 448 9. 78 476 9.78 505 9.78 533 9. 78 562 28 29 28 29 28 0.21 552 0, 21 524 0.21 495 0.21 467 0. 21 438 9. 93 154 9. 93 146 9. 93 138 9. 93 131 9.93 123 8 8 7 8 8 40 39 38 37 36 54 40 36 32 28 24 5 40 44 48 52 56 25 26 27 28 29 9.71 705 9.71 726 9.71 747 9. 71 767 9.71 788 21 21 20 21 21 9. 78 690 9. 78 618 9. 78 647 9. 78 6.75 9. 78 704 28 29 28 29 28 0. 21 410 0. 21 382 0.21 353 0.21 325 0.21296 9. 93 115 9. 93 108 9. 93 100 9. 93 092 9. 93 084 7 8 8 8 7 35 34 33 32 31 54 20 16 12 8 4 6 4 b 12 16 30 31 32 33 34 9. 71 809 9. 71 829 9.71 850 9. 71 870 9.71 891 20 21 20 21 20 9. 78 732 9. 78 760 9. 78 789 9. 78 817 9. 78 845 28 29 28 28 29 0.21 268 0.21 240 0.21 211 0.21 183 0.21 155 9. 93 077 9. 93 069 9. 93 061 9. 93 053 9. 93 046 8 8 8 7 8 80 29 28 27 26 54 56 52 48 44 6 20 24 28 32 36 35 36 37 38 39 9. 71 911 9.71 932 9.71 952 9. 71 973 9.71 994 21 20 21 21 20 9. 78 874 9.78 902 9. 78 930 9. 78 959 9. 78 987 28 28 29 28 28 0.21 126 0. 21 098 0.21 070 0. 21 041 0. 21 013 9. 93 038 9. 93 030 9. 93 022 9. 93 014 9.93 007 8 8 8 7 8 25 24 23 22 21 53 40 36 32 28 24 6 40 44 48 52 56 40 41 42 43 44 9. 72 014 9. 72 034 9. 72 055 9. 72 075 9.72 0% 20 21 20 21 20 9. 79 015 9. 79 043 9. 79 072 9. 79 100 9.79 128 28 29 28 28 28 0.20985 0. 20 957 0. 20 928 0. 20 900 0. 20 872 9.92 999 9. 92 991 9. 92 983 9. 92 976 9.92 968 8 8 7 8 8 20 19 18 17 16 ;:; -ju 16 ' 8 4 7 4 8 12 16 45 46 47 48 49 9. 72 116 9.72 137 9.72 157 9. 72 177 9.72 198 21 20 20 21 20 9. 79 156 9. 79 185 9. 79 213 9. 79 241 9. 79 269 29 28 28 28 28 0. 20 844 0. 20 815 0. 20 787 0. 20 759 0. 20 731 9. 92 960 9. 92 952 9. 92 944 9.92 936 9.92 929 8 8 8 7 8 15 14 13 12 11 53 56 52 48 44 7 20 24 28 32 36 50 51 62 53 54 9. 72 218 9. 72 238 9. 72 259 9. 72 279 9. 72 299 20 21 20 20 21 9. 79 297 9. 79 326 9.79 354 9. 79 382 9. 79 410 29 28 28 28 28 0. 20 703 0. 20 674 0. 20 646 0.20 618 0.20 590 9.92 921 9. 92 913 9.92 905 9. 92 897 9.92 889 8 8 8 8 8 10 9 8 7 6 52 40 36 32 28 24 7 40 44 48 52 56 55 56 57 58 59 9. 72 320 9. 72 340 9.72 360 9. 72 381 9. 72 401 20- 20 21 20 20 9. 79 438 9. 79 466 9. 79 495 9. 79 523 9. 79 551 28 29 28 28 28 0. 20 562 0. 20 534 0. 20 505 0. 20 477 0. 20 449 9. 92 881 9. 92 874 9. 92 866 9. 92 858 9. 92 850 7 8 8 8 8 5 4 3 2 1 52 20 16 12 8 4 8 60 9. 72 421 9. 79 579 0. 20 421 9.92 842 52 L. Cos. d. L. Cotg. c. d. L. Tang. L. Sin. d. ' m. s. 58 C 180 GEOGRAPHIC TABLES AND FORMULAS. TABLE 22. Five-place logarithms of circular functions, etc. Continued. 2 h 32 m. s. / L. Sin. d. L. Tang. c.d. L. Cotg. L. Cos. d. 8 4 8 12 16 1 2 3 4 9. 72 421 9. 72 441 9. 72 461 9. 72 482 9.72 502 20 20 21 20 20 9. 79 579 9. 79 607 9. 79 6&5 9. 79 663 9. 79 691 28 28 28 28 28 0. 20 421 0. 20 393 0. 20 365 0. 20 337 0. 20 309 9. 92 842 9. 92 834 9. 92 826 9. 92 818 9. 92 810 8 8 8 8 7 60 59 58 57 56 52 56 52 48 44 8 20 24 28 32 36 5 6 7 8 9 9. 72 522 9. 72 542 9.72 562 9. 72 582 9.72 602 20 20 20 20 20 9. 79 719 9. 79 747 9. 79 776 9. 79 804 9. 79 832 28 29 28 28 28 0. 20 281 0.20 253 0. 20 224 0.20 196 0.20 168 9. 92 803 9. 92 795 9. 92 787 9. 92 779 9. 92 771 8 8 8 8 8 55 54 53 52 51 51 40 36 32 28 24 8 40 44 48 52 56 10 11 12 13 14 9. 72 622 9. 72 643 9.72 663 9. 72 683 9. 72 703 21 20 20 20 20 9. 79 860 9. 79 888 9. 79 916 9. 79 944 9. 79 972 28 28 28 28 28 0. 20 140 0. 20 112 0. 20 084 0. 20 056 0. 20 028 9.92 763 9. 92 755 9. 92 747 9. 92 739 9. 92 731 8 8 8 8 8 50 49 48 47 46 51 20 16 12 8 4 9 4 8 12 16 15 16 17 18 19 9. 72 723 9. 72 743 9. 72 763 9. 72 783 9. 72 803 20 20 20 20 9Q 9.80 000 9. 80 028 9. 80 056 9.80084 9. 80 112 26 28 28 . 28 28 0.20 000 0. 19 972 0. 19 944 0. 19 916 0. 19 888 9. 92 723 9.92 715 9.92 707 9. 92 699 9. 92 691 8 8 8 8 8 45 44 43 42 41 51 56 52 48 44 9 20 24 28 32 36 20 21 22 23 24 9. 72 823 9. 72 843 9. 72 863 9. 72 883 9. 72 902 20 20 20 19 20 9. 80 140 9.80 168 9.80 195 9. 80 223 9. 80 251 28 27 28 28 28 0. 19 860 0. 19 832 0. 19 805 0. 19 777 0. 19 749 9. 92 683 9.92 675 9. 92 667 9. 92 659 9. 92 651 8 8 8 8 8 40 39 38 37" 36 50 40 36 32 28 24 9 40 44 48 52 56 25 26 27 28 29 9. 72 922 9.72 942 9. 72 962 9. 72 982 9. 73 002 20 20 20 20 20 9. 80 279 9. 80 307 9. 80 335 9. 80 363 9. 80 391 28 28 28 28 28 0. 19 721 0. 19 693 0. 19 665 0. 19 637 0. 19 609 9.92 643 9. 92 635 9. 92 627 9. 92 619 9. 92 611 8 8 8 8 8 35 34 33 32 31 50 20 16 12 8 4 10 4 8 12 16 30 31 32 33 34 9. 73 022 9.73 041 9. 73 061 9. 73 081 9. 73 101 19 20 20 20 20 9. 80 419 9. 80 447 9.80 474 9.80 502 9.80530 28 27 28 28 28 0. 19 581 0. 19 553 0. 19 426 0. 19 498 0. 19 470 9. 92 603 9. 92 595 9. 92 587 9. 92 579 9. 92 571 8 8 8 8 8 30 29 28 27 26 50 56 52 48 44 10 20 24 28 32 36 35 36 37 38 - 39 9. 73 121 9. 73 140 9. 73 160 9. 73 180 9. 73 200 19 20 20 20 19 9.80 558 9.80 586 9. 80 614 9. 80 642 9. 80 669 28 28 28 27 28 0. 19 442 0. 19 414 0. 19 386 0. 19 358 0. 19 331 9. 92 563 9. 92 555 9. 92 546 9. 92 538 9. 92 530 8 9 8 8 8 25 24 23 22 21 49 40 36 32 28 24 10 40 44 48 52 56 40 41 43 44 9. 73 219 9. 73 239 9. 73 259 9. 73 278 9.73 298 20 20 19 20 20 9. 80 697 9.80 725 9. 80 753 9. 80 781 9.80808 28 28 28 27 28 0. 19 303 0. 19 275 0. 19 247 0. 19 219 0. 19 192 9. 92 522 9. 92 514 9. 92 506 9. 92 498 9.92 490 8 8 8 8 s 20 19 18 17 16 49 20 16 12 8 4 11 4 8 12 16 45 46 47 48 49 9. 73 318 9. 73 337 9.73 357 9. 73 377 9. 73 396 19 20 20 19 20 9. 80 836 9. 80 864 9. 80 892 9. 80 919 9.80 947 28 28 27 28 28 0. 19 164 0. 19 136 0. 19 108 0. 19 081 0. 19 053 9. 92 482 9. 92 473 9. 92 465 9. 92 457 9.92 449 9 8 8 8 8 15 14 13 12 11 49 56 52 48 44 11 20 24 28 32 36 50 51 52 53 54 9. 73 416 9. 73 435 9. 73 455 9. 73 474 9. 73 494 19 20 19 20 19 9. 80 975 9.81 003 9. 81 030 9.81 058 9. 81 086 28 27 28 28 27 0.19 025 0. 18 997 0. 18 970 0. 18 942 0. 18 914 9. 92 441 9. 92 433 9.92 425 9. 92 416 9. 92 408 8 8 9 8 g 10 9 8 7 6 48 40 36 32 28 24 11 40 44 48 52 56 55 56 57 58 59 9. 73 513 9. 73 533 9. 73 552 9. 73 572 9. 73 591 20 19 20 19 20 9.81 113 9.81 141 9. 81 169 9.81 196 9.81 224 28 28 27 28 28 0. 18 887 0. 18 859 0. 18 831 0. 18 804 0. 18 776 9. 92 400 9. 92 392 9.92 384 9. 92 376 9. 92 367 8 8 8 9 8 5 4 3 2 1 48 20 16 12 8 4 12 60 9. 73 611 9. 81 252 0. 18 748 9. 92 359 48 L. Cos. d. L. Cotg. c.d. L. Tang. L. Sin. d. i m. s. 57 GEOGRAPHIC TABLES AND FORMULAS. 181 TABLE 22. Five-place logarithms of circular functions, etc. Continued. 2 h 33 m. s. ' L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. d. 12 4 8 12 16 1 2 3 4 9. 73 611 9. 73 630 9.73650 9. 73 669 9. 73 689 19 20 19 20 1Q 9.81 252 9.81 279 9.81 307 9.81 335 9.81 362 27 28 28 27 00 0. 18 748 0. 18 721 0. 18 693 0. 18 665 0. 18 638 ' 9. 92 359 9. 92 351 9. 92 343 9. 92 335 9. 92 326 8 8 8 9 60 59 58 57 56 48 56 52 48 44 12 20 24 28 32 36 5 6 7 8 9 9. 73 708 9. 73 727 9. 73 747 9. 73 766 9. 73 785 19 20 19 19 9.81 390 9.81 418 9.81 445 9.81 473 9.81 500 28 27 28 27 0. 18 610 0. 18 582 0.18 555 0. 18 527 0. 18 500 9. 92 318 9. 92 310 9. 92 302 9. 92 293 9. 92 285 8 8 9 8 55 54 53 52 51 47 40 36 32 28 24 12 40 44 48 52 56 10 11 12 13 14 9.73 805 9. 73 824 9. 73 843 9.73 863 9. 73 882 19 19 20 19 9.81 528 9.81 556 9.81 583 9. 81 611 9.81 638 28 27 28 27 0. 18 472 0. 18 444 0. 18 417 0. 18 389 0. 18 362 9. 92 277 9. 92 269 9. 92 260 9. 92 252 9. 60 59 58 57 56 12 56 52 48 44 48 20 24 28 32 36 5 6 7 8 9 9. 82 621 9. 82 635 9. 82 649 9. 82 663 9. 82 677 14 14 14 14 14 9. 95 571 9. 95 596 9. 95 622 9. 95 647 9. 95 672 25 26 25 25 26 0. 04 429 0. 04 404 0. 04 378 0. 04 353 0. 04 328 9.87 050 9. 87 039 9. 87 028 9.87 016 9. 87 005 11 11 12 11 12 55 54 53 52 51 11 40 36 32 28 24 48 40 44 48 52 56 10 11 12 13 14 9. 82 691 9. 82 705 9.82 719 9. 82 733 9. 82 747 14 14 14 14 14 9. 95 698 9. 95 723 9. 95 748 9. 95 774 9. 95 799 25 25 26 25 26 0. 04 302 0. 04 277 0. 04 252 0. 04 226 0. 04 201 9. 86 993 9. 86 982 9. 86 970 9. 86 959 9. 86 947 11 12 11 12 11 50 49 48 47 46 11 20 16 12 8 4 49 4 8 12 16 15 16 17 18 19 9. 82 761 9.82 775 9. 82 788 9. 82 802 9. 82 816 14 13 14 14 14 9. 95 825 9. 95 .850 9. 95 875 9. 95 901 9. 95 926 25 25 26 25 26 0.04 175 0. 04 150 0.04 125 0. 04 099 0. 04 074 9. 86 936 9. 86 924 9. 86 913 9. 86 902 9. 86 890 12 11 11 12 11 45 44 43 42 41 11 56 52 48 44 49 20 24 28 32 36 20 21 22 23 24 9. 82 830. 9. 82 844 9. 82 858 9.82 872 8.82.885 14 14 14 13 14 9. 95 952 9. 95 977 9. 96 002 9. 96 028 9. 96 053 25 25 26 25 25 0.04 048 0. 04 023 0.03 998 0. 03 672 0. 03 947 9. 86 879 9. 86 867 9. 86 855 9. 86 844 9. 86 832 12 12 11 12 11 40 39 38 37 36 10 40 36 32 28 24 49 40 44 48 52 56 25 26 27 28 29 9. 82 899 9. 82 913 9. 82 927 9. 82 941 9. 82 955 14 14 14 14 13 9. 96 078 9. 96 104 9.96 129 9.96 155 9. 96 180 26 25 26 25 25 0. 03 922 0. 03 896 0. 03 871 0. 03 845 0. 03 820 9. 86 821 9. 86 809 9. 86 798 9. 86 786 9.86 775 12 11 12 11 12 35 34 33 32 31 10 20 16 12 8 4 50 4 8 12 16 30 31 32 33 34 9. 82 968 9. 82 982 9. 82 996 9. 83 010 9. 83 023 14 14 14 13 14 9. 96 205 9. 96 231 9.96 256 9. 96 281 9. 96 307 26 25 25 26 25 0. 03 795 0.03 769 0. 03 744 0. 03 719 0. 03 693 9. 86 763 9. 86 752 9.86 740 9. 86 728 9.86 717 11 12 12 11 V? 30 29 28 27 26 10 56 52 48 44 50 20 24 28 32 36 35 36 37 38 39 9. 83 037 9.63 051 9.83 065 9. 83 078 9. 83 092 14 14 13 14 14 9. 96 332 9.96 357 9. 96 383 9. 96 408 9. 96 433 25 26 25 25 26 0. 03 668 0. 03 643 0. 03 617 0. 03 592 0.03 567 9. 86 705 9.86 694 9. 86 682 9. 86 670 9. 86 659 11 12 12 11 25 24 23 22 21 9 40 36 32 28 24 50 40 44 48 52 56 40 41 42 43 44 9.83 106 9. 83 120 9.83 133 9. 83 147 9.83 161 14 13 14 14 13 9. 96 459 9. 96 484 9.96 510 9. 96 535 9.96 560 25 26 25 25 26 0. 03 541 0.03 516 0. 03 490 0. 03 465 0. 03 440 9. 86 647 9. 86 635 9. 86 624 9. 86 612 9. 86 600 12 11 12 12 11 20 19 18 17 16 9 20 16 12 8 4 51 4 8 12 16 45 46 47 48 49 9.83 174 9.83 188 9.83 202 9. 83 215 9. 83 229 14 14 13 14 13 9. 96 586 9.96 611 9 96 636 9. 96 662 9. 96 687 25 25 26 25 25 0. 03 414 0.03 389 0. 03 3(54 0.03 338 0. 03 313 9. 86 589 9. 86 577 9. 86 565 9. 86 554 9. 86 542 12 12 11 12 12 15 14 13 12 11 9 56 52 48 44 51 20 24 28 32 36 50 51 52 53 54 9. 83 242 9. 83 256 9. 83 270 9. 83 283 9. 83 297 14 14 13 14 13 9. 96 712 9. 96 738 9. 96 763 9. 96 788 9. 96 814 26 25 25 26 25 0. 03 288 0. 03 262 0. 03 237 0. 03 212 0.03 186 9. 86 530 9. 86 518 9. 86 507 9. 86 495 9. 86 483 12 11 12 12 11 10 9 8 7 6 8 40 36 32 28 2* 51 40 44 48 52 56 55 56 57 58 59 9.83 310 9. 83 324 9 83 338 9. 83 351 9, 83 365 14 14 13 14 13 9. 96 839 9. 96 864 9. 96 890 9.96 915 9. 96 940 25 26 25 25 26 03 161 03 136 0.03 110 0. 03 085 0. 03 060 9. 86 472 9.86 460 9.86 448 9. 86 436 9. 86 425 12 12 12 11 12 5 4 3 2 1 8 20 16 12 8 4 52 60 9. 83 378 9.96 966 0. 03 034 9.86 413 8 L. Cos. d. L.Cotg. c. d. L. Tang. L. Sin. d. ' m. s. 47' GEOGRAPHIC TABLES AND FORMULAS. 191 TABLE 22. Five-place logarithms of circular functions, etc. Continued. 2 h 43 m. 8. ' L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. d. 52 4 8 12 16 1 2 3 4 9.83 378 9.83 392 9.83 405 9. 83 419 9. 83 432 14 13 14 13 14 9.96 966 9.96 991 9. 97 016 9. 97 042 9.97 067. 25 25 26 25 25 0. 03 034 0. 03 009 0. 02 984 0. 02 958 0.02 933 9. 86 413 9.86401 9. 86 389 9. 86 377 9. 86 366 12 12 12 11 T> GO 59 58 57 56 8 56 52 48 44 52 20 24 28 32 36 5 6 7 8 9 9.83 446 9. 83 459 9. 83 473 9.83 486 9.83 500 13 14 13 14 13 9. 97 092 9. 97 118 9. 97 143 9.97 168 9.97 193 26 25 25 25 26 0. 02 908 0. 02 882 0. 02 857 0. 02 832 0. 02 807 9. 86 354 9. 86 342 9. 86 330 9. 86 318 9. 86 306 12 12 12 12 11 55 54 53 52 51 7 40 36 32 28 24 52 40 44 48 52 56 10 11 12 13 14 9.83 513 9.83 527 9. 83 540 9.83 554 9.83 567 14 13 14 13 14 9. 97 219 9. 97 244 9.97 269 9. 97 295 9. 97 320 25 25 26 25 25 0.02 781 0.02 756 0.02 731 0.02 705 0. 02 680 9. 86 295 9. 86 283 9. 86 271 9. 86 259 9. 86 247 12 12 12 12 1? 50 49 48 47 46 7 20 16 12 8 4 53 4 8 12 16 15 16 17 18 19 9.83 581 9.83 594 9. 83 608 9. 83 621 9. 83 634 13 14 13 13 14 9. 97 345 9. 97 371 9.97 396 9.97 421 9. 97 447 26 25 25 26 25 0.02 655 0. 02 629 0. 02 604 0.02 579 0. 02 553 9.86 235 9. 86 223 9.86 211 9.86 200 9.86 188 12 12 11 12 12 45 44 43 42 41 7 56 52 48 44 53 20 24 28 32 36 20 21 22 23 24 9.83 648 9. 83 661 9. 83 674 9.83 688 9. 83 701 13 13 14 13 14 9.97 472 9. 97 497 9.97 523 '.). 97 5 18 9.97 573 25 26 25 25' 25 0. 02 528 0.02 503 0.02 477 0. 02 452 0.02 427 9.86 176 9. 86 164 9.86 152 9. 86 140 9. 86 128 12 12 12 12 V? 40 39 38 37 36 6 40 36 32 28 24 53 40 44 48 52 56 25 26 27 28 29 9.83 715 9. 83 728 9.83 741 9.83 755 9. 83 768 13 13 14 13 13 9. 97 598 9.97 624 9. 97 649 9.97 674 9.97 700 26 25 25 26 25 0. 02 402 0.02 376 0. 02 351 0. 02 326 0.02 300 9. 86 116 9. 86 104 9. 86 092 9.86 080 9. 86 068 12 12 12 12 12 35 34 33 32 31 6 20 16 12 8 4 54 4 8 12 16 30 31 32 33 34 9.83 781 9.83 795 9.83 808 9.83 821 9.83 834 14 13 13 13 14 9. 97 725 9.97 750 9.97 776 9.97 801 9. 97 826 25 26 25 25 25 0. 02 275 0.02 250 0.02 224 0.02 199 0.02 174 9. 86 056 9.86 044 9. 86 032 9. 86 020 9.86 008 12 12 12 12 12 30 29 28 27 26 6 56 52 48 44 54 20 24 28 32 36 35 36 37 38 39 9. 83 848 9.83 861 9.83 874' 9. 83 887 9.83901 13 13 13 14 13 9. 97 851 9. 97 877 9. 97 902 9. 97 927 9.97 953 26 25 25 26 25 0.02 149 0.02 123 0.02 098 0. 02 073 0. 02 047 9. 86 996 9. 85 984 9.85 972 9. 85 960 9. 85 948 12 12 12 12 19, 25 24 23 22 21 5 40 36 32 28 24 54 40 44 48 52 56 40 41 42 43 44 9.83 914 9. 83 927 9. 83 940 9. 83 954 9. 83 967 13 13 14 13 13 9.97 978 9.98 003 9.98 029 9. 98 054 9. 98 079 25 26 25 25 25 0. 02 022 0.01 997 0.01 971 0.01 946 0.01 921 9. 85 936 9. 85 924 9. 85 912 9. 85 900 9. 85 888 12 12 12 12 12 20 19 18 17 16 5 20 16 12 8 4 55 4 8 12 16 45 46 47 48 49 9.83 980 9.83 993 9.84 006 9. 84 020 9. 84 033 13 13 14 13 13 9.98 104 9. 98 130 9. 98 155 9. 98 180 9. 98 206 26 25 25 26 25 0. 01 896 0.01 870 0.01 845 0. 01 820 0.01 794 9. 85 876 9. 85 864 9. 85 851 9. 85 839 9.85827 12 13 12 12 12 15 14 13 12 11 5 56 52 48 44 55 20 24 28 32 36 50 51 52 53 54 9. 84 046 9. 84 059 9. 84 072 9.84 085 9.84 098 13 13 13 13 14 9. 98 231 9. 98 256 9. 98 281 9. 98 307 9. 98 332 25 25 26 25 25 0. 01 769 0.01 744 0.01 719 0.01 693 0.01 668 9.85815 9. 85 803 9. 85 791 9. 85 779 9. 85 766 12 12 12 13 12 10 9 8 7 6 4 40 36 32 28 24 55 40 44 48 52 56 55 56 57 58 59 9.84 112 9.84 125 9.84 138 9. 84 151 9. 84 164 13 13 13 13 13 9. 98 357 9. 98 383 9. 98 408 9. 98 433 9. 98 458 26 25 25 25 26 0. 01 643 0.01 617 0. 01 592 0. 01 567 0.01 542 9. 85 754 9. 85 742 9. 85 730 9.85 718 9. 85 706 12 12 12 12 13 5 4 3 2 1 4 20 16 12 8 4 56 00 .9.84 177 9. 98 484 0. 01 516 9. 85 693 4 L. Cos. d. L. Cotg. c. d. L. Tang. L. Sin. d. / m. s. 192 GEOGKAPHIC TABLES AND FORMULAS. TABLE 22. Five-pl&ce logarithms of circular functions, etc. Continued. 2 h 44 m. s. ' L. Sin. d. L. Tang. c. d. L. Cotg. L. Cos. d. 56 4 8 12 16 1 2 3 4 9. 84 177 9. 84 190 9. 84 203 9. 84 216 9. 84 229 13 13 13 13 13 9. 98 484 9. 98 509 9. 98 534 9. 98 560 9.98 585 25 25 26 25 25 0.01 516 0.01 491 0.01 466 0.01 440 0.01 415 9. 85 693 9. 85 681 9. 85 669 9. 85 657 9. 85 645 12 12 12 12 13 60 59 58 57 56 4 "56 52 48 44 56 20 24 28 32 36 5 6 7 8 9 9. 84 242 9. 84 255 9. 84 269 9. 84 282 9. 84 295 13 14 13 13 13 9.98 610 9. 98 635 9. 98 661 9. 98 686 9. 98 711 25 26 25 25 26 0.01 390 0.01 365 0.01 339 0.01 314 0.01 289 9. 85 632 9. 85 620 9. 85 608 9. 85 596 9. 85 583 12 12 12 13 12 55 54 53 52 51 3 40 36 32 28 24 56 40 44 48 52 56 10 11 12 13 14 9. 84 308 9. 84 321 9.84 334 9. 84 347 9.84360 13 13 13 13 13 9. 98 737 9. 98 762 9.98 787 9. 98 812 9.98 838 25 25 25 26 25 0. 01 263 0. 01 238 0. 01 213 0.01 188 0.01 162 9. 85 571 9. 85 559 9. 85 547 9. 85 534 9. 85 522 12 12 13 12 12 50 49 48 47 46 3 20 16 12 8 4 57 4 8 12 16 15 J6 17 18 19 9. 84 373 9.84 385 9. 84 398 9. 84 411 9. 84 424 12 13 13 13 13 9. 98 863 9. 98 888 9.98 913 9. 98 939 9. 98 964 25 25 26 25 25 0.01 137 0.01 112 0. 01 087 0.01 061 0. 01 036 9. 85 510 9. 85 497 9.85 485 9. 85 473 9.85460 13 12 12 13 12 45 44 43 42 41 3 56 52 48 44 57 20 24 28 32 36 20 21 22 23 24 9. 84 437 9. 84 450 9. 84 463 9. 84 476 9. 84 499 13 13 13 13 13 9. 98 989 9. 99 015 9. 99 040 9.99 065 9. 99 090 26 25 25 25 26 0.01 Oil 0.00 985 0. 00 960 0.00 935 0.00 910 9. 85 448 9. 85 436 9. 85 423 9. 85 411 9. 85 399 12 13 12 12 13 40 39 38 37 36 2 40 36 32 28 24 57 40 44 48 52 56 25 26 27 28 29 9. 84 502 9. 84 515 9. 84 528 9. 84 540 9. 84 553 13 13 12 13 13 9.99 116 9. 99 141 9. 99 166 9.99 191 9. 99 217 25 25 25 26 25 0. 00 884 0.00859 0. 00 834 0. 00 809 0. 00 783 9. 85 386 9. 85 374 9. 85 361 9. 85 349 9. 85 337 12 13 12 12 13 35 34 33 32 31 2 20 16 12 8 4 58 4 8 12 16 30 31 32 33 34 9.84 566 9. 84 579 9. 84 592 9. 84 605 9.84 618 13 13 13 13 12 9. 99 242 9. 99 267 9. 99 293 9. 99 318 9. 99 343 25 26 25 25 25 0.00 758 0.00 733 0. 00 707 0.00 682 0. 00 657 9. 85 324 9. 85 312 9.85 299 9. 85 287 9. 85 274 12 13 12 13 12 30 29 28 27 26 2 56 52 48 44 58 20 24 28 32 36 35 36 37 38 39 9. 84 630 9. 84 643 9.84 656 9. 84 669 9. 84 682 13 13 13 13 12 9. 99 368 9. 99 394 9. 99 419 9. 99 444 9. 99 469 26 25 25 25 26 0. 00 632 0. 00 606 0. 00 581 0. 00 556 0. 00 531 9. 85 262 9.85 250 9. 85 237 9. 85 225 9. 85 212 12 13 12 13 12 25 24 23 22 21 1 40 36 32 28 24 58 40 44 48 52 56 40 41 42 43 44 9. 84 694 9. 84 707 9.84 720 9.84 733 9.84 745 13 13 13 12 13 9.99 495 9. 99 520 9. 99 545 9. 99 570 9. 99 596 25 25 25 26 25 0. 00 505 0.00 480 0. 00 455 0. 00 430 0.00 404 9. 85 200 9. 85 187 9.85 175 9. 85 162 9. 85 150 13 12 13 12 13 20 19 18 17 16 1 20 16 12 8 4 59 4 8 12 16 45 46 47 48 49 9.84 758 9. 84 771 9.84 784 9. 84 796 9. 84 809 13 13 12 13 13 9. 99 621 9. 99 646 9. 99 672 9. 99 697 9. 99 722 25 26 25 25 25 0.00 379 0.00 354 0. 00 328 0. 00 303 0. 00 278 9. 85 137 9.85 125 9.85 112 9. 85 100 9.85 087 12 13 12 13 13 15 14 13 12 11 1 56 52 48 44 59 20 24 28 32 36 50 51 52 53 54 9. 84 822 9. 84 835 9. 84 847 9.84 860 9. 84 873 13 12 13 13 12 9.99 747 9. 99 773 9. 99 798 9.99 823 9. 99 848 26 .25 25 25 26 0. 00 253 0. 00 227 0.00202 0.00 177 0.00 152 9. 85 074 9. 85 062 9. 85 049 9. 85 037 9. 85 024 12 13 12 13 12 10 9 8 6 40 36 32 28 24 59 40 44 48 52 56 55 56 57 58 59 9. 84 885 9. 84 898 9. 84 911 9. 84 923 9. 84 936 13 13 12 13 13 9. 99 874 9. 99 899 9.99 924 9. 99 949 9. 99 975 25 25 25 26 25 0. 00 126 0. 00 101 0. 00 076 0. 00 051 0.00 025 9. 85 012 9. 84 999 9. 84 986 9. 84 974 9. 84 961 13 13 12 13 12 5 4 3 2 1 20 16 12 8 4 60 60 9. 84 949 0.00 000 0.00 000 9. 84 949 L. Cos. d. L. Cotg. c. d. L. Tang. L. Sin. d. ' m. s. 45 C GEOGRAPHIC TABLES AND FORMULAS. 193 TABLE 23. GEODETIC POSITION COMPUTATIONS. TABLE OF LOGARITHMS OF FACTORS A, B, C, D, E, F^ BASED UPON THE CLARKE SPHE- ROID OF 1866 AND THE METRIC SYSTEM, BETWEEN LATITUDES AND 72. [Extracted from reports of the U. S. Coast and Geodetic Survey.] CONSTANTS. A = ~ (1 g 2 sin 2 \ " df>n ( 10 000001 log D 2. 3674 " [I+II] 2 6.0568 log (III) 8.4242 log E 6. 0124 14 s 2 sinV 8.8371 " (I) 3.0279 log (VI) 2. 776614 da - 597 77 .876 -9 7 57 77 .876 Azimuth check. log (IV) 7. 8774 (I) 1066.286+ \ (II) 1.242+ i (III) .026+ [I+H] 1067.528 (IV) .008- log " 3.028 f m-TTl 2 6.056 3792 Check: 7584 Snher. anffle GEOGRAPHIC TABLES AND FORMULAS. 195 Azimuth a: Chusca Spherical angle: Azimuth a x : Chusca da +180 Azimuth (a) : Zuni Latitude. o / // 0: 35 53 06.746 Chusca. d(p 45 40.818 Geo. Pos. No / // Nell. 339 21 40.150 25 11 38. 601 Zuni. 4 33 18.751 179 57 25. 650 Chusca. 184 30 44.401 Longitude. / // A: 108 50 14.518 .4. dh +4 25.768 (f> / 35 07 25.928 Zuni. Geo. Pos. No Computation for latitude: log s 4. 9280539 " B 8.5111594 " cosa x 9.9986260 A/ 108 54 40.286 . 6. Computation for longitude: log s 4. 9280539 " sina' 8.8999280 " A' 8.5092394 " sec < x 0.0872944 log (I) 3.4378393 log (V) 2. 4245028 dl +265 /x .768 Computation of azimuth: log (V) 2. 424503 " B in(^) 9.764002 " '68 85 4 40 83 590 72 87 05 37 76 637 76 89 6 35 70 684 80 91 7 33 63 732 84 93 8 30 56 779 88 95 9 28 49 826 92 97 10 8. 509 6126 8.512 3342 0. 86873 2. 1196 5.7099 11 24 35 921 2. 1200 5. 7101 12 21 28 0. 86968 04 03 13 19 22 0. 87015 08 04 14 17 15 062 12 06 15 14 08 109 16 08 16 12 3301 156 20 10 . 17 10 3294 202 24 12 18 08 87 249 28 14 19 05 80 2% 32 16 20 8. 509 6103 8.512 3273 0.87343 2. 1236 5.7118 7.705 21 6101 66 389 40 20 2iJ 6098 59 436 44 22 23 96 52 483 47 24 24 94 45 529 51 25 25 91 39 576 55 27 26 89 32 622 59 29 27 87 25 669 63 31 28 84 18 715 67 33 29 82 11 761 71 35 30 8. 509 6080 8.512 3204 0. 87808 2. 1275 5. 7137 31 77 3197 854 79 39 32 75 9D 900 83 41 33 73 83 947 87 43 34 70 76 0. 87993 90 45 35 68 69 0.88039 94 47 36 66 62 085 2. 1298 49 37 63 55 131 2. 1302 51 38 61 48 177 06 52 39 59 41 223 10 54 40 8.509 6056 8.512 3133 0. 88269 2.1314 5. 7156 7.712 41 54 26 315 17 58 42 52 19 360 21 60 43 49 12 406 25 62 44 47 3105 452 29 64 45 45 3028 498 33 66 46 42 91 543 37 68 47 40 84 589 40 70 48 37 77 63J 44 72 49 35 70 680 " 48 74 50 8. 509 6033 8.512 3063 0. 88726 2.1352 5. 7176 51 30 56 771 56 78 5> 28 48 816 59 80 53 26 41 862 63 82 54 23 34 907 67 84 55 21 27 952 71 86 56 18 20 ' 0.88998 74 88 57 16 13 0. 89043 78 90 58 14 3006 088 82 92 59 11 2998 133 86 94 60 8. 509 6009 8. 512 2991 0. 89178 2. 1390 5.7196 7.719 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 17. 218 Lat. log A diff.l"=-0.04 logB diff.l"=-0.12 logC diff.l"=-0.73 logD diff.l"=+0.06 logE diff.l"=+0.03 logF o / 17 00 8.509 6009 8.512 2991 0.89178 2.1390 5. 7196 77719 1 06 84 223 93 97 2 04 77 268 2. 1397 99 3 6002 70 313 2. 1401 5.7201 4 5999 62 358 04 03 05 97 55 403 08 05 6 94 48 448 12 07 7 92 41 493 16 09 8 90 34 538 19 11 9 87 26 583 23 13 10 8.509 5985 8. 512 2919 0.89627 2. 1427 5. 7215 11 82 12 672 30 17 12 , 80 2905 717 34 19 13 78 2897 761 38 21 14 75 90 806 42 23 15 73 83 850 45 25 16 70 76 895 49 27 17 68 68 939 53 29 18 65 61 0.89984 56 81 19 63 54 0.90028 60 33 20 8. 509 5961 8.512 2846 0.90072 2.1464 5. 7235 7.726 21 58 39 117 67 37 22 56 32 161 71 39 23 53 24 205 75 41 24 . 51 17 249 78 43 25 48 10 294 82 45 26 46 2802 338 85 47 27 44 2795 382 89 49 28 41 88 426 93 51 29 39 80 470 2. 14% 53 30 8. 509 5936 8.512 2773 0. 90514 2.1500 5. 7255 31 34 66 558 04 57 32 31 58 602 07 59 33 29 51 646 11 61 34 26 44 689 14 64 35 24 36 733 18 66 36 21 29 777 22 68 37 19 21 821 25 70 38 16 14 864 29 72 39 14 2707 908 32 74 40 8. 509 5912 8. 512 2699 0.90952 2. 1536 5. 7276 7.732 41 09 92 0.90995 39 78 42 07 84 0. 91039 43 80 43 04 77 082 47 82 44 5902 69 126 50 84 45 5899 62 169 54 86 46 97 55 212 57 88 47 94 47 256 61 90 48 92 40 299 64 92 49 89 32 342 68 94 50 8.509 5887 8.512 2625 0.91386 2. 1571 5.7296 51 84 17 429 75 5. 7298 52 82 10 472 78 5.7300 53 79 2602 515 82 02 54 77 2595 558 85 04 55 74 87 601 89 06 56 72 80 644 92 08 57 69 72 687 96 11 58 67 65 730 2. 1599 13 59 64 57 773 2. 1603 15' 60 8.509 6862 8.512 2550 0. 91816 2.1606 5. 7317 7.738 214 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. sLATITUDE 18. Lat. log A diff. 1"= -0.04 logB diff.l"=-0.13 logC diff.l"=+0.70 logD diff. 1"=+0.06 logE diff. 1"=+0.03 logF diff. 10'= +3.0 o i 18 00 8. 509' 5862 8. 512 2550 0. 91816 2.1606 5. 7317 7.738 1 59 42 859 10 19 2 57 35 902 13 21 3 54 27 945 17 23 4 52 19 0. 91987 20 25 05 49 12 0. 92030 24 27 6 46 8. 512 2504 073 27 29 7 44 8. 512 2497 115 * 31 31 8 41 89 158 34 33 9 39 81 201 38 35 10 8.509 5836 8.512 2474 0. 92243 2. 1641 5. 7337 11 34 66 286 44 39 12 31 59 328 48 41 13 29 51 371 51 44 ' 14 26 43 413 ' 55 46 15 24 36 456 58 48 16 21 28 498 62 50 17 19 20 540 65 52 18 16 13 582 68 54 19 13 8. 512 2405 625 72 56 20 8.509 5811 8. 512 2397 0. 92667 2. 1675 5. 7358 7.744 21 08 90 709 79 60 22 06 82 751 82 62 23 03 74 793 85 64 24 8. 509 5801 67 836 89 67 25 8. 509 5798 59 878 92 69 26 96 51 920 95 71 27 i 93 44 0. 92962 2. 1699 73 28 90 36 0. 93004 2. 1702 75 29 88 28 046 06 77 30 8. 509 5785 8. 512 2320 0. 93088 2. 1709 5. 7379 31 83 13 129 12 81 32 80 8. 512 2305 171 16 83 33 78 8.512 2297 213 19 85 34 75 90 255 22 88 35 72 82 296 26 90 36 70 74 338 29 92 37 67 66 380 32 94 38 65 58 421 36 96 39 62 51 463 39 5. 7398 40 8.509 5759 8. 512 2243 0. 93505 2. 1742 5.7400 7.750' 41 57 35 546 46 02 42 54 27 588 49 05 43 52 19 629 52 07 44 49 12 671 56 09 45 46 8. 512 2204 712 59 11 46 44 8. 512 2196 753 62 13 47 41 88 795 65 15 48 39 80 836 69 17 49 36 72 877 72 19 50 " 8. 509 5733 8.512 2165 0. 93919 2. 1775 5.7422 51 31 57 0. 93960 79 24 52 28 49 0.94001 82 26 53 25 41 042 85 28 54 23 33 083 88 30 55 20 25 125 92 32 56 18 17 166 95 34 57 15 10 207 2. 1798 37 58 12 8. 512 2102 248 2. 1801 39 59 10 8. 512 2094 289 05 41 60 8. 509 5707 8. 512 2086 . 0.94330 2. 1808 5.7443 7.756 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE. 19. 215 Lat. log A diff. 1"=- 0.04 logB logC logD diff.l"=-0.13 diff.l" = +0.67 diff. 1"== +0.05 logE diff. 1" = +0.04 logF diff. 10' = +2.7 o / 19 00 8.509 5707 8. 512 2086 0. 94330 2.1808 5. 7443 7.756 1 04 78 370 11 . 45 2 8.509 5702 70 411 14 47 3 8.509 5699 62 452 18 49 4 96 54 493 21 52 05 94 46 534 24 54 6 91 38 575 27 56 7' 89 30 615 30 58 8 86 22 656 34 60 9 83 14 697 37 62 10 8.509 5681 8.5122006 0. 94737 2.1840 5.7464 11 78 8.512 1999 778 43 67 12 75 91 819 46 69 13 73 83 859 50 71 14 70 75 900 53 73 15 67 67 940 56 75 16 65 59 0. 94981 59 78 17 62 51 0.95021 62 80 18 59 43 061 66 82 19 ! 57 35 102 69 84 20 8. 509 5654 8. 512 1927 0.95142 2. 1872 5.7486 7.761 21 52 19 182 75 88 22 49 11 223 78 91 23 46 8.512 1903 263 81 93 24 43 8. 512 1895 303 34 95 25 41 87 344 88 97 26 38 79 384 91 5. 7499 27 35 71 424 94 5.7501 28 33 63 464 2. 1897 04 29 i 30 55 504 2.1900 06 30 8. 509 5627 8.512 1847 0.95544 2.1903 5.7508 31 25 38 584 07 10 32 22 30 624 10 12 33 19 22 664 13 15 34 16 14 704 16 17 35 14 8. 512 1806 744 19 19 36 11 8.512 1798 784 22 21 37 08 90 824 25 23 38 06 82 863 28 26 39 03 74 903 31 28 40 8.509 5600 8. 512 1766 0. 95943 2. 1934 5.7530 7.767 41 8. 509 5598 57 0. 95983 38 32 42 95 49 0.96022 41 34 43 92 41 062 44 37 44 89 33 102 47 39 45 87 25 142 50 41 46 84 17 181 53 43 47 81 08 221 46 48 78 8.512 1700 260 59 48 49 76 8.512 1692 300 62 50 50 8.509 5573 8.512 1684 0.96339 2.1965 5. 7552 51 70 75 379 68 54 52 68 67 418 71 57 53 65 59 457 74 59 54 62. 51 497 77 61 55 59 43 536 80 63 56 67 34 575 83 65 57 54 26 615 M 68 58 51 18 654 89 70 59 48 10 693 92 72 60 y.509 5546 8.512 1602 0. 96733 2.1996 5. 7574 7. 772 216 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 20. Lat. log A diff.l"= -0.05 logB diff.l"=-0.14 logC diff.l"=+0.64 logD diff.l" = +0.05 logE diff.l"=+0.04 logF diff.lO'=+2.5 O 1 20 00 8. 509 5546 8.512 1602 0. 96733 2.1996 5. 7574 7.772 1 43 . 8. 512 1593 772 2.1999 77 - 2 40 85 811 2.2002 79 3 37 77 850 05 81 4 35 68 889 08 83 05 32 60 928 11 86 6 29 52 0. 96967 14 88 . 7 26 44 0.97006 17 90 ' 8 24 35 045 20 92 9 21 27 084 23 94 10 8. 509 5518 8.512 1519 0. 97123 2. 2026 5. 7597 11 15 10' 162 28 5. 7599 12 12 8.512 1502 201 31 5. 7601 13 10 8. 512 1494 240 34 03 14 07 &5 279 37 06 15 04 77 318 40 08 16 8. 509 5501 69 356 43 10 17 8.509 5499 60 395 46 12 18 96 5? 434 49 15 19 93 44 472 52 17 20 i 8. 509 5490 8.512 1435 0. 97511 2.2055 5. 7619 7.777 21 87 27 550 58 21 22 85 18 588 61 24 23 82 10 627 64 26 24 79 8.512 1402 666 67 28 25 76 8. 512 1393 704 70 30 26 73 85 743 73 33 27 71 76 781 76 35 28 68 68 819 79 37 29 65 60 858 81 40 30 8.5095462 8.512 1351 0. 97896 2. 2084 5. 7642 31 59 43 935 87 44 32 57 34 0. 97973 90 46 33 54 26 0. 98011 93 49 34 51 17 050 96 51 35 48 09 088 2.2099 53 36 45 8.512 1301 126 2. 2102 55 37 42 8.512 1292 164 05 58 88 40 84 203 08 60 39 37 75 241 10 62 40 8. 509 5434 8.512 1267 0. 98279 2.2113 5. 7664 7.782 41 31 58 317 16 67 42 28 50 355 19 69 43 25 41 393 22 71 4-4 23 33 431 25 74 45 20 24 469 28 76 46 17 16 507 31 78 47 14 8.512 1207 545 33 81 48 11 8.512 1199 583 36 83 49 08 90 621 39 85 50 8.509 5406 8.512 1182 0. 98659 2. 2142 5.7688 51 03 73 697 45 90 52 8. 509 5400 64 735 48 92 53 8. 509 5397 56 773 50 91 54 94 47 811 53 97 55 91 39 * 848 56 5. 7699 56 88 30 886 59 5. 7701 57 86 21 924 62 04 58 83 13 962 65 06 59 80 8.512 1104 0. 98999 67 08 60 8.509 6377 8.512 1096 0. 99037 2. 2170 5.7711 7.787 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 21. 217 log A *** diff. 1"= -0.05 logB diff. 1"= -0.15 logC diff.l"= +0.062 diff logD .1"=+0.04 logE diff. 1"= +0.04 logF diff. 10' =+2.2 o / 21 00 8. 509 5377 8.512 1096 0.99037 2. 2170 5. 7711 7.787 1 74 87 075 73 13 2 71 79 112 76 15 3 68 70 150 79 18 4 66 62 187 81 20 05 63 53 225 84 22 6 60 45 262 87 24 7 57 36 300 90 27 8 54 27 337 93 29 9 51 19 375 95 31 10 8.509 5348 8.512 1010 0.99412 2. 2198 5. 7734 11 46 8.512 1002 450 2. 2201 36 12 43 8.512 0993 487 04 38 13 40 84 524 07 41 14 37 76 562 09 43 15 34 67 599 12 45 16 31 58 636 15 48 17 28 ' 50 673 18 50 18 25 41 711 20 52 19 22 32 748 23 55 20 8. 509 5320 8.512 0924 0.99785 2.2226 5.7757 7.791 21 17 15 822 29 59 - 22 14 8. 512 0906 859 31 62 23 11 8. 512 0897 8% 34 64 24 08 89 ' 933 37 66 25 05 80 0.99971 40 69 . 26 8.509 5302 71 1.00008 42 71 27 8. 509 5299 62 045 45 73 28 96 54 082 48 76 29 93 45 119 50 78 30 8.509 5290 8.512 0836 1.00156 2.2253 5.7780 31 88 27 192 56 83 32 85 19 229 59 85 33 82 10 266 61 87 34 79 8. 512 0801 303 64 90 35 76 8.5120792 340 67 92 36 73 84 377 69 94 37 70 75 413 72 97 38 67 66 450 75 5. 7799 39 64 57 487 78 5.7802 40 8.5095261 8.5120748 1.00524 2.2280 5.7804 7. 796 41 58 39 560 83 06 42 55 31 597 86 09 43 52 22 634 88 11 44 49 13 670 91 13 45 46 8.5120704 707 94 16 46 44 8. 512 0695 743 96 18 47 41 86 780 2. 2299 20 48 38 78 816 2. 2301 23 49 35 69 853 04 25 50 8.509 5232 8.512 0660 1.00890 2.2307 5. 7828 51 29 51 926 09 30 52 26 42 962 12 32 53 23 33 1.00999 15 35 54 20 24 1.01035 17 37 55 17 15 072 20 40 56 14 8.512 0606 108 23 42 57 11 8. 512 0598 144 25 44 . 58 08 89 181 28 47 59 05 80 217 31 49 60 8.509 5202 8. 512 0571 1. 01253 2.2333 5.7851 7.800 218 GEOGRAPHIC TABLES AND FOEMTJLAS. TABLE 23. Geodetic position computations Continued. LATITUDE 22. Lat. log A diff.l"=-0.05 logB diff.l"=-0.15 logC diff.l"=+0.59 logD diff.l"=+0.04 logE diff.l"=+0.04 logF diff.lO'=+2.0 / 22 00 8. 509 5202 8. 512 0571 1. 01253 2. 2333 5. 7851 7.800 1 8. 509 5199 62 289 36 54 2 96 53 326 38 56 3 93 44 362 41 59 4 90 35 398 44 61 05 87 26 434 46 63 6 84 17 470 49 66 7 81 8. 512 0508 506 51 68 8 78 8. 512 0499 542 54 71 9 75 90 578 57 73 10. 8. 509 5172 8. 512 0481 1. 01615 2.2359 5. 7875 11 69 72 651 62 78 12 66 63 687 64 80 13 63 54 723 67 83 14 60 45 759 70 85 15 57 36 794 72' 87 16 54 27 830 75 . 90 17 51 18 866 77 92 18 48 09 902 80 95 19 45 8.512 0400 938 83 97 20 8. 509 5142 8. 512 0391 1. 01974 2. 2385 5. 7899 7.804 21 39 82 1.02010 88 5. 7902 22 36 73 045 90 04 23 33 64 081 . 93 07 24: 30 55 117 95 09 25 27 46 153 2. 2398 11 26 24 37 188 2.2400 14 27 21 .. 28 224 03 16 28 18 19 260 06 19 29 15 10 295 08 21 30 8. 509 5112 8. 512 0301 1. 02331 2.2411 5.7924 31 09 8. 512 0292 367 13 26 32 06 83 402 16 28 33 03 73 438 18 31 34 8. 509 5100 64 473 2] 33 35 8. 509 5097 55 509 23 36 36 94 46 544 26 38 37 91 37 580 28 41 38 88 28 615 31 43 39 85 19 651 33 45 40 j 8. 509 5082 8. 512 0210 1.02686 2.2436 5. 7948 7.808 41 79 8. 512 0200 721 38 50 42 76 8.512 0191 757 41 53 43 72 82 792 43 55 44 69 73 828 46 58 45 66 64 863 48 60 46 63 55 898 51 62 47 60 46 933 53 65 48 57 36 . 1 -02969 56 67 49 54 27 1 -03004 58 70 50 8.509 5051' 8. 512 0118 1. 03039 2. 2461 5. 7972 51 48 09 074 63 75 52 45 8. 512 0100 109 66 77 53 . 42 8. 512 0090 145 68 80 54 39 81 180 70 82 55 36 72 215 73 84 56 33 63 250 75 87 57 30 54 285 78 89 58 27 44 320 80 92 59 23 35 365 83 94 60 8.509 5020 8. 512 0026 1.03390 2. 2485 5.7997 7.812 GEOGRAPHIC TABLES AND FORMULAS. 219 TABLE 23. Geodetic position computations Continued. LATITUDE 23. Lat. log A diff. 1"= 0.05 logB diff. 1"= -0.16 logC diff. 1"= +0.57 logD diff. 1"=+ 0.04 logE diff. 1"= +0.04 logF diff. 10' = +1.8 i o r 23 00 8. 509 5020 8. 512 0026 1.03390 2. 2485 5. 7997 7. 812 1 17 17 425 88 5. 7999 2 14 8.5120008 460 90 5. 8002 3 11 8.511 9998 495 93 04 4 08 89 530 95 07 05 05 80 565 2. 2497 09 6 8.509 5002 71 600 2.2500 12 7 8. 509 4999 61 634 02 14 % 52 669 05 16 93 43 704 07 19 10 8. 509 4990 8.511 9934 1. 03739 2. 2510 5. 8021 11 87 24 774 12 24 12 83 15 809 14 26 13 80 8. 511 9906 843 17 29 * 14 77 8.511 9896 878 19 31 lo 74 87 913 22 34 16 71 78 947 24 36 17 68 68 1.03982 26 39 18 65 59 1.04017 29 41 19 62 50 052 31 44 20 8. 509 4959 8. 511 9840 1.04086 2.2534 5.8046 7.816 21 55 31 121 36 49 22 52 22 155 38 51 23 49 12 190 41 54 24 46 8.511 9803 224 43 56 25 43 8.511 9794 259 45 59 26 40 84 293 48 61 27 37 75 328 50 64 28 34 66 362 53 66 29 31 56 397 55 69 30 8. 509 4927 8.511 9747 1.04431 2.2557 5.8071 31 24 37 466 60 74 32 21 28 500 62 76 33 18 19 534 64 79 34 15 09 569 67 81 35 12 8.511 9700 603 69 84 36 09 8.511 9690 637 71 86 37 : 05 81 672 74 89 38 8. 509 4902 71 706 76 91 39 8. 509 4899 62 740 78 93 40 8. 509 4896 8,511 9653 1.04775 2.2581 5.8096 7. 819 41 ! 93 43 809 83 5. 8099 42 90 34 843 85 5. 8101 43 87 24 877 88 04 44 83 15 911 90 06 45 80 8.511 9605 945 92 09 46 77 8.511 9596 1.04980 95 11 47 74 86 1.05014 97 14 48 71 77 048 2. 2599 16 49 . 68 67 082 2. 2601 19 50 8.509 4865 8.511 9558 1. 05116 2.2604 5. 8121 51 61 48 150 06 24 52 58 39 184 09 26 53 55 29 218 11 29 54 52 20 252 13 31 55 49 10 286 16 34 56 45 8.511 9501 320 18 36 57 42 8.511 9491 354 , 20 39 58 '39 82 388 23 41 59 36 72 422 25 44 60 8.509 4833 8.511 9463 1.05456 2. 2627 5.8146 7.823 220 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 24. Lat. log A cliff. 1"= -0.06 logB cliff. 1"= -0.16 logC cliff. 1"= +0.56 logD diff.l"=+0.04 log E log F cliff. 1"== +0.04 cliff. 10'= +1.6 o r 24 00 8. 509 4833 8.511 9463 1.05456 2. 2627 5. 8146 7. 823 1 30 53 490 29 49 2 26 44 523 31 51 3 23 34 557 34 54 4 20 24 591 36 57 05 17 15 625 08 59 6 14 8.511 9405 658 41 62 7 10 s.511 9396 692 43 C4 8 07 86 726 45 67 9 04 77 760 47 69 10 | 8.509 4801 8.511 9367 1.05794 2.2650 5. 8172 11 8. 509 4798 58 827 52 74 13 94 48 861 54 77 13 91 - 38 894 56 79 14 88 29 928 59 82 15 85 19 . 962 61 86 16 82 09 1.05995 63 87 17 78 8.511 9300 1.06029 65 90 18 75 8.511 9290 062 68 92 19 72 81 096 70 95 20 8. .509 4769 s. oil 9271 1.06130 2. 2672 5.8197 7.826 21 66 61 163 74 5.8200 22 62 52 197 77 02 28 / 59 42 230 79 05 24 56 32 263 81 07 25 53 23 297 83 10 26 50 13 330 85 13 >- 46 8.511 9203 364 88 15 28 43 8.511 9194 397 90 18 29 40 84 431 92 20 30 8.509 4737 S.all 9174 1.06464 2. 2694 5.8223 31 33 65 497 96 25 32 30 55 530 2. 2699 28 33 27 45 .564 2. 2701 31 34 24 35 597 03 33 35 20 26 630 05 36 36 17 16 664 07 38 37 14 8.511 9106 697 10 41 38 11 8.511 9096 730 12 43 on 07 87 763 14 46 40 8. 509 4704 8.511 9077 1.06797 2.2716 5. 8249 7. 829 41 8. 509 4701 67 830 18 51 42 8. 509 4698 58 863 20 54 43 94 48 896 23 56 44 91 38 929 25 59 45 S8 28 962 27 61 46 85 18 1. 06995 29 64 47 81 8.511 9009 1. 07028 31 67 48 78 8. 511 8999 061 33 69 49 75 89 095 36 72 60 8.509 4672 8.511 8979 1.07128 2. 2738 5. 8274 51 68 70 161 40 77 52 65 60 194 42 80 53 62 50 226 44 82 54 59 40 259 46 85 55 .55 30 292 49 87 56 52 21 325 51 90 57 49 11 358 53 92 58 45 8.511 8901 391 55 95 59 42 8. 511 8891 424 57 5. 8298 60 8. 509 4639 8. 511 8881 1.07457 2.2759 5.8300 7.832 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computation* Continued. LATITUDE 25. 221 T at 1& A Lat - diff.l"=-0'06 logB diff.l"=-0-16 logC diff.l"=-r0'54 d logD iff. 1"= +0-0 logE 3 difM"=+0-04 logF diff.!0' = +l-5 o / 25 00 8. 509 4639 8.511 8881 1. 07457 2. 2759 5.8300 7.832 1 36 71 490 61 03 2 32 62 523 63 05 3 29 52 555 66 08 4 26 42 588 68 11 05 23 32 621 70 13 6 19 22 654 72 16 7 16 12 687 74 18 8 13 8.511 8802 719 76 21 9 09 8.511 8793 752 78 24 10 8.5094606 8.511 8783 1.07785 2. 2780 5. 8326 11 03 73 817 82 29 12 8. 509 4600 63 850 85 32 13 8. 509 45% 53 883 87 34 14 93 43 915 89 37 15 90 33 948 91 39 16 86 23 1.07981 93 42 17 83 13 1.0S013 95 45 18 80 8.511 8704 046 97 47 19 76 8.511 8694 078 2. 2799 50 20 ! 8. 509 4573 8.511 8684 1.08111 2.2801 5. 8352 7.835 21 70 74 143 03 55 22 66 64 176 05 59 23 63 51 208 07 60 24 60 44 241 10 63 25 56 34 273 12 66 26 53 24 306 14 68 27 50 14 338 16 71 28 8.511 8604 370 18 73 29 43 8.511 8594 403 20 76 30 8. 509 4540 8.511 8584 1.08435 2. 2822 5. 8379 31 ' 37 74 468 24 81 32 ! 33 64 500 26 84 33 30 54 532 28 87 34 26 44 565 30 89 35 23 34 597 32 . 92 36 20 24 629 34 94 37 17 14 662 36 5. 8397 38 13 8.511 8504 694 38 5.8400 39 10 8. 511 8494 726 40 02 40 8. 509 4507 8.511 8484 1.08758 2.2842 5.8405 7.838 41 03 74 791 44 08 42 8. 509 4500 64 823 46 10 43 8.509 44% 54 855 48 13 44 93 44 887 50 16 45 90 34 919 52 18 46 86 24 951 54 21 47 83 14 1.08984 56 24 48 80 8.511 8404 1.09016 58 26 49 76 8. 511 8393 048 60 29 50 8. 509 4473 8.511 8383 1.09080 2. 2862 5. 8431 51 70 73 112 64 34 52 66 63 141 66 37 53 63 53 176 68 39 54 60 43 208 70 42 55 56 33 240 72 45 56 53 23 272 74 47 57 50 13 304 76 50 58 46 8.511 8303 336 78 53 59 43 8. 511 8293 -368 80 55 60 8.509 4439 8.511 8283 1.09400 2.2882 . 5.8458 7.841 222 GEOGRAPHIC TABLES ADD FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 26. Lat. log A diff.l"=-0-06 logB diff.l"=-0-17 c logC Liff.l"=+0 logD 52 diff.l"=-fO-03 log E log F diff.l"=+0-04 diff.lO' = +l-3 o / 26 00 8. 509 4439 8.511 8283 1.09400 2.2882 5.8458 7.841 1 36 72 432 84 61 2 33 62 464 86 63 3 29 52 496 88 66 4 26 42 527 90 69 05 22 32 ' 559 92 71 6 19 22 591 94 74 7 16 12 623 96 77 8 12 8. 511 8201 655 2. 2898 79 9 09 8.511 8191 687 2.2900 82 10 8.509 4406 8.511 8181 1. 09718 2. 2902 5.8485 11 8. 509 4402 71 750 04 88 12 8. 509 4399 61 782 06 90 13 95 51 814 08 93 14 92 40 845 10 96 15 88 30 877 12 5. 8498 16 85 20 909 14 5.8501 17 82 10 940 16 04 18 78 8. 511 8100 1.09972 18 06 19 75 8.511 8089 1.10004 20 09 20 8. 509 4372 8. 511 8079 1. 10036 2.2922 5.8512 7.844 21 68 69 067 23 14 22 65 59 099 25 17 23 61 48 130 27 20 24 58 38 162 29 22 25 54 28 194 31 25 26 51 18 225 33 28 27 48 8. 511 8008 257 35 30 28 44 8. 511 7997 288 37 33 29 41 87 320 39 36 30 8. 509 4337 8.511 7977 1.10351 2.2941 5.8539 . 31 34 67 383 43 41 32 31 56 414 45 44 33 27 46 446 47 47 34 24 36 477 48 49 35 20 25 509 50 52 36 17 15 540 52 55 37 13 8.511 7905 571 54 57 38 10 8.511 7895 603 56 60 39 07 84 634 58 63 40 8. 509 4303 8.511 7874 1.10666 2.2960 5.8566 7.846 41 8. 509 4300 .64 697 62 68 42 ' 8. 509 4296 53 728 63 71 43 93 43 760 65 74 44 89 33 791 67 76 45 86 22 822 69 79 46 83 12 854 71 82 47 79 8.511 7802 885 73 85 48 76 8.511 7791 916 75 87 49 72 81 947 77 90 , 50 8. 509 4269 8.511 7771 1. 10979 2.2978 5.8593 51 65 60 1. 11010 80 95 52 62 50 041 82 5.8598 53 58 40 072 84 5. 8601 54 55 29 103 86 04 55 52 19 134 88- 06 56 48 8.511 7709 166 89 09 57 45 8.511 7698 197 91 12 58 41 88 228 93 14 * 59 38 77 259 95 17 60 8.509 4234 8.511 7667 1.11290 2. 2997 5. 8620 7.849 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 27. 223 Tit log A Lat - diff.l"=-0.06 logB diff.l"=-0.18 logC diff.l"=+0.51 logD' diff.l"=+0.03 logE diff.l"=+0.05 logF diff.lO' = +l.l o / 27 00 8.509 4234 8.511 7667 1.11290 A 2997 5.8620 7.849 1 31 57 321 2.2999 23 2 27 46 352 2. 3001 25 3 24 36 383 03 28 4 J 20 25 414 04 31 06 17 15 445 06 34 6 13 8.511 7605 476 08 36 7 10 8.511 7594 507 10 39 8 06 84 538 12 42 9 03 73 569 14 44 10 8. 509 4200 8.511 7563 1.11600 2.3015 5. 8647 11 8.5094196 53 631 17 50 12 93 42 662 19 53 13 89 32 693 21 56 14 86 21 724 23 58 15 82 11 755 24 61 16 79 8.511 7500 786 26 64 17 75 8.511 7490 817 28 66 18 72 79 848 30 69 19 68 69 878 32 72 20 8. 509 4165 5.511 7458 1. 11909 2.3033 5.8675 7.851 21 61 48 940 35 77 22 58 37 1. 11971 37 80 23 54 27 1.12002 39 83 24 51 16 032 41 86 25 47 8.511 7406 063 42 88 26 44 8.511 7395 094 44 91 27 40 85 126 46 94 28 37 74 156 48 97 29 33 64 186 50 5.8699 30 31 8. 509 4130 8.511 7353 43 1.12217 248 2. 3051 53 5. 8702 05 32 23 32 278 55 08 33 19 22 309 57 10 34 16 11 340 58 13 35' 12 8.511 7301 370 60 16 36 08 8.511 7290 401 62 19 37 05 80 432 64 22 38 8.509 4101 69 462 65 24 39 8. 509 4098 58 493 67 27 40 8.509 4094 8.511 7248 1.12623 2.3069 5.8730 7.853 41 91 37 554 70 33 42 87 27 584 72 35 43 84 16 615 74 38 44 80 8.511 7206 646 76 41 45 77 8.511 7195 676 78 44 46 73 84 707 79 46 47 70 74 737 81 49 48 66 63 768 83 52 49 63 53 798 85 55 50 8. 509 4059 8.511 7142 1.12829 2.3086 5. 8757 51 56 31 859 88 60 52 52 21 889 90 63 53 49 10 920 91 66 54 45 8. 511 7100 950 93 69 55 41 8.511 7089 1.12981 95 72 56 38 78 1. 13011 97 74 57 34 68 041 2.3099 77 58 31 57 072 2.3100 80 59 27 46 102 02 83 60 8.509 4024 8.611 7036 1.13132 2. 3104 5.8785 7.855 224 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 28. Lat. log A diff.l"=-0.06 logB 3iff.l"=-0.1 logC diff.l"=+0.50 logD diff.l"=+0.03 logE diff.l"=+0.05 logF diff.lO"=+1.0 o / 28 00 8.509 4024 8.511 703(> 1. 13132 2.3104 5.8785 7.855 1 20 25 163 05 88 2 17 14 193 07 91 3 13 8.511 7004 223 09 94 4 10 8. 511 6993 254 10 97 05 06 82 284 12 5.8799 6 8. 509 4002 72 314 14 5.8802 7 8. 509 3999 61 345 16 05 8 95 50 375 17 08 9 92 40 405 19 11 10 8. 509 3988 8.511 6929 1.13435 2. 3121 5.8813 11 85 18 465 22 16 12 81 8.511 6908 496 24 19 13 78 8. 511 6897 526 26 22 14 74 86 556 27 25 15 70 75 586 29 27 16 67 65 616 31 30 17 63 54 646 32 33 18 60 43 677 34 36 19 56 33 707 36 39 20 8. 509 3952 8.511 6822 1. 13737 2.3137 5.8841 7.857 21 49 11 767 39 44 22 45 8. 511 6800 797 41 47 23 42 8.511 6790 827 42 50 24 38 79 857 44 53 25 35 68 887 46 55 26 31 57 917 47 58 27 27 47 947 49 61 28 24 36 1.13977 51 64 29 20 25 1. 14007 52 67 30 8. 509 3917 8. 511 6714 1.14037 2.3154 5. 8870 31 13 8.511 6704 067 56 72 32 09 8.511 6693 097 57 75 33 06 82 127 59 78 34 8. 509 3902 71 157 61 81 35 8. 509 3899 61 187 62 84 36 95 50 217 64 87 37 92 39 247 65 89 38 88 28 277 67 92 39 84 17 307 69 95 40 8. 509 3881 8.511 6607 1. 14337 2. 3170 5.8898 7.859 41 77 8. 511 6596 366 72 5.8901 42 73 85 396 74 04 43 70 74 426 75 06 44 66 63 456 77 09 45 63 52 486 78 12 46 59 42 516 80 15 47 55 31 545 82 18 48 52 20 575 83 21 49 48 8.511 6509 605 85 23 50 8. 509 3845 8.511 6498 1.14635 2.3187 5.8926 51 41 87 664 88 29 52 37 76 694 90 32 53 34 66 724 91 35 54 30 55 754 93 38 55 26 44 783 95 40 56 23 33 813 96 43 57 19 22 843 98 46 58 16 11 872 2.3199 49 59 12 8.511 6400 902 2. 3201 52 60 8.509 3808 8.511 6389 1.14932 2.3203 5.8956 7.861 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 29. 225 Lat. leg A diff.l"=-0.06 logB diff.l"=-0.18 logC diff.l"=+0.49 logD diff.l"=+0.03 log E log F diff.l"=+0.05 diff.lO'=+O.S o / 29 00 8.509 3808 8.511 6389 1. 14932 2. 3203 5. 8955 7. 861 1 05 78 961 04 58 2 8.509 3801 68 1. 14991 06 60 3 8. 509 3797 57 1.15021 07 63 4 94 46 050 09 66 05 90 35 080 10 69 6 86 24 109 12 72 7 83 13 139 14 75 8 79 8.511 6302 168 15 78 9 76 8.511 6291 198 17 80 10 8. 509 3772 8.511 6280 1.15228 2. 3218 5. 8983 11 68 69 257 20 86 12 65 58 287 21 89 13 61 47 316 23 92 14 57 36 346 25 95 15 54 26 375 26 5.8998 16 50 15 405 28 5.9000 17 46 8.511 6204 434 29 03 18 43 8.511 6193 464 31 06 19 39 82 493 32 09 20 8.509 3735 8.511 6171 1.15522 2. 3234 5. 9012 7. 863 21 32 60 552 35 15 22 28 49 581 37 18 23 24 38 611 38 21 24 21 27 640 40 23 25 17 16 670 42 26 26 13 8.511 6105 699 43 29 27 10 8.511 6094 728 45 32 28 06 83 758 46 35 29 8. 509 3702 72 787 48 38 30 8. 509 3699 8.511 6061 1. 15816 2.3249 5.9041 31 95 50 846 51 43 32 91 39 875 52 46 33 88 28 904 54 49 34 84 17 934 55 52 35 80 K.511 6006 963 57 55 36 77 8.511 5995 1.15992 58 58 37 73 84 1.16021 60 61 38 69 73 051 61 64 39 66 61 080 63 67 40 8. 509 3662 S.511 5950 1.16109 2. 3264 5. 9069 7. 8C.4 41 58 39 138 66 72 42 55 28 167 67 75 43 51 17 197 69 78 44 47 8.511 5906 226 70 81 45 44 8.511 5895 255 7'2 84 46 40 84 284 73 87 47 36 73 313 75 90 48 33 62 343 76 93 49 29 51 372 78 % 50 8. 509 3625 S.511 5840 1.16401 2. 3279 5. 9098 51 21 29 430 81 5. 9101 52 18 18 459 82 04 53 14 8.511 5806 488 84 07 54 19 8.511 5795 517 85 10 55 07 84 546 87 13 56 8. 509 3603 73 575 88 16 57 8. 509 3599 62 604 90 19 58 % 51 633 91 22 59 92 40 663 93 25 60 8.5093588 8.511 5729 1.16692 2. 3294 5. 9127 7. 866 1 4606108 15 226 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 30. Lat. log A diff. 1"= -0.06 log diff. 1"= B = -0.19 logC diff. 1"= +0.48 logD diff. 1"= +0.02 logE diff. 1"= +0.05 logF diff. 10'= +0.7 o / 30 00 8.509 3588 8. 511 5729 1.16692 2. 3294 5. 9127 7.866 1 84 18 721 96 30 2 81 8.511 5706 750 97 33 3 77 8.511 5695 778 2. 3298 36 4 73 84 807 2.3300 39 05 69 73 836 01 42 6 66 62 865 03 45 7 62 51 894 04 48 8 58 40 923 06 51 9 55 28 952 07 54 10' 8. 509 3551 8.511 5617 1. 16981 2.3309 5. 9157 11 47 8.511 5606 1. 17010 10 59 12 43 8.511 5595 ' 039 12 62 13 40 84 068 13 65 14 36 73 097 14 68 15 32 61 126 16 71 10 29 50 155 17 74 17 25 39 184 18 77 18 21 28 212 20 80 19 17 17 241 22 83 20 8. 509 3514 8.511 5505 1.17270 2. 3323 5. 9186 7.867. 21 10 8.511 5494 299 24 89 22 06 83 328 26 92 23 8. 509 3502 72 357 27 95 24 8.509 3499 61 385 29 5. 9198 25 95 49 414 30 5.9200 26 91 38 443 32 03 27 88 27 472 33 06 28 84 16 500 34 09 29 80 8.511 5404 529 36 12 30 8. 509 3476 8.511 5393 1.17558 2.3337 5. 9215 31 72 82 587 39 18 32 69 71 615 40 21 33 65 59 644 41 24 34 61 48 673 43 27 35 57 37 701 44 30 36 54 26 730 46 33 37 50 14 759 47 36 38 46 8.511 5303 788 48 39 39 42 8.511 5292 816 50 42 40 8. 509 3439 8.511 5281 1.17845 2.3351 5. 9245 7.869 41 35 69 874 53 48 42 31 58 902 54 Kl 43 27 47 931 55 53 44 24 35 959 57 56 45 20 24 1. 17988 58 59 46 16 13 1.18017 59 62 47 12 8.511 5202 045 61 65 48 09 8.511 5190 074 62 68 49 05 79 102 64 71 50 8. 509 3401 8.511 5168 1.18131 2.3365 5. 9274 51 8. 509 3397 56 160 66 77 52 94 45 188 68 80 53 90 34 217 69 83 54 86 22 245 70 86 55 82 11 274 72 89 56 78 8.511 5100 302 73 92 57 75 8.511 5088 331 74 95 .58 71 77 359 76 5. 9298 59 67 66 388 77 5. 9301 60 8.509 3363 s. f>i 1 5054 1.18416 2.3379 5. 9304 7.870 GEOGKAPHIC TABLES AND FOKMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 31. 227 Lt. log A diff.l"=-0.06 logB diff.l"=-0.19 logC diff.l"=+0.47 logD diff.l"=+0.02 logE diff.l"=+0.05 logF diff. 10'= +0.5 O 1 31 00 8.509 3363 8. 511 CJ54 1.18416 2. 3379 ft. 9304 7.870 1 60 43 445 80 07 2 56 32 473 81 10 3 52 20 501 83 13 4 48 8.511 5009 530 84 16 05 44 8.511 4998 558 85 19 6 41 86 587 87 22 7 37 75 615 88 25 8 33 64 643 89 28 9 29 52 672 91 31 10 S. 509 3325 S.511 4941 1.18700 2. 3392 ft. 9334 11 22 29 729 93 37 12 18 18 757 95 39 13 14 8.511 4907 785 96 42 14 10 8. 511 4895 813 97 45 15 06 84 842 2. 3399 48 16 8.509 3303 72 870 2.3400 51 17 8.5093299 61 898 01 54 18 95 50 927 03 57 19 91 38 955 04 60 20 8. 509 3287 8.511 4827 1.18983 2. 3405 5.9363 7.871 21 84 15 1. 19012 06 66 22 80 8.511 4804 040 08 69 23 76 8. 511 4793 068 09 72 24 72 81 096 10 75 25 68 70 125 12 78 26 65 58 153 13 81 27 61 47 181 14 84 28 57 35 209 16 87 29 53 24 238 17 90 30 8. 509 3249 8.511 4713 1.19266 2. 3418 5. 9393 31 46 8.511 4701 294 20 96 32 42 8. 511 4690 322 21 5. 9399 33 38 78 351 22 5.9402 34 34 67 379 23 05 35 30 55 407 25 08 36 26 44 435 26 11 37 23 32 463 27 14 38 19 . 21 491 29 17 39 15 8.511 4609 520 30 20 40 8. 509 3211 8.511 4598 1 . 19548 2.3431 ft. 9423 7. 872 41 07 86 576 32 26 42 03 75 604 34 29 43 8.509 3200 63 632 35 32 44 8. 509 3196 52 660 36. 35 45 92 40 688 37 38 46 88 29 716 39 41 47 84 17- 744 40 44 48 81 8.511 4506 772 41 47 49 77 8.511 4494 800 43 50 50 8. 509 3173 8.511 4483 1.19828 2.3444 5.9453 51 69 71 856 45 56 52 65 60 884 46 59 H 61 48 912 48 62 54 57 37 940 49 65 55 54 25 968 50 68 56 50 14 1.19996 51 72 57 46 8.511 4402 1.20024 53 75 58 42 8.511 4391 052 54 78 59 38 79 080 55 81 60 8. 509 3134 8.511 4368 1. 20108 2.3456 ft. 9484 7.873 228 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 32. Lat. log A diff. 1"= -0.06 log diff. l"= B = 0.19 log C diff. 1"= +0.46 logD diff. 1"= +0.02 log E log F diff. 1"-= +0.05 diff. 10' = +0.3 o / 32 00 8.509 3134 8. 511 4368 1.20108 2. 3456 5. 9484 7. 873 1 31 56 136 57 87 2 27 44 164 59 90 3 23 33 192 60 93 4 19 21 220 61 96 05 15 8.511 4310 248 62 5. 9499 6 11 8.511 4298 276 64 5.9502 7 07 87 304 65 05 8 04 75 332 66 08 9 8.509 3100 63 360 67 11 10 8. 509 3096 S. 51 1 4252 1.20387 2. 3469 5. 9514 11 92 40 415 70 17 12 88 29 443 71 20 13 84 17 471 72 23 14 80 8.511 4205 499 73 26 15 76 8.511 4194 527 75 29 16 73 82 555 76 32 17 69 71 582 77 35 18 65 59 610 78 38 19 61 47 638 79 41 20 logF diff.lO'=+0.2 o / 33 00 8.509 2901 8.511 3669 1. 21772 2. 3527 5. 9667 7.875 1 8. 509 2897 57 799 29 70 2 94 45 827 30 73 3 90 33 854 31 76 4 86 22 882 32 79 05 82 8.511 3610 909 33 82 6 78 8.511 3598 937 34 85 1 74 86 964 35 88 8 70 75 1.21992 36 92 9 66 63 1.22019 38 95 10 8.509 2862 8.511 3551 1.22047 2. :39 5. 9698 11 58 39 074 40 5. 9701 12 54 28 101 41 04 13 51 16 129 42 07 14 47 8.511 3504 156 43 10 15 43 8.511 3492 184 44 13 16 39 80 211 45 16 17 35 69 238 46 19 18 31 57 266 48 22 19 27 45 293 49 26 20 8.509 2823 8.511 3433 1.22321 2.3550 r>. 9729 7. 876 21 19 21 348 51 32 22 15 8.511 3410 375 52 35 23 11 8.511 3398 403 53 38 24 07 86 430 54 41 25 8. 509 2803 74 457 55 44 26 8. 509 2799 62 485 56 47 27 95 51 512 57 50 28 91 39 539 58 53 29 88 27 567 60 57 30 s. T>09 2784 8. 511 3315 1.22594 2. 3561 5. 9760 31 80 8.511 3303 621 62 63 32 76 8.511 3291 648 63 66 33 72 80 676 64 69 34 68 68 703 fc 65 72 35 64 56 730 66 75 36 60 44 757 67 78 37 56 32 785 68 81 38 52 20 812 69 85 39 48 8.511 3209 839 70 88 40 8.509 2744 8.511 3197 1.22866 2.3571 5. 9791 7.876 41 40 85 893 72 94 42 36 73 921 73 5. 9797 43 32 61 948 75 5. 9800 44 28 49 1 -22975 76 03 77 06 45 24 37 1.23002 46 20 25 029 78 10 47 16 13 057 79 13 48 12 8.511 3102 084 80 16 49 08 8.511 3090 111 81 19 50 8. 509 2704 8.511 3078 1.23138 2. 3582 5. 9822 51 8. 509 2701 66 165 83 25 52 8. 509 2697 54 192 H4 28 53 93 42 220 85 31 54 89 30 247 86 35 55 85 18 274 87 38 56 81 8.511 3006 301 88 41 57 77 8.511 2995 328 89 44 58 73 83 355 90 47 59 69 71 382 91 50 CO 8.509 2665 8.511 2959 1.23409 2. 3592 5. 9853 7.877 230 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 34. Lat. log A logB ' diff. 1"=-0.20 logC diff. 1"= +0.45 logD diff. l"= +0.02 logE diff. 1"= +0.05 logF diff. 10'= +0.0 o / 34 00 8. 509 2665 8.511 2959 1.23409 2. 3592 5. 9853 7.877 1 61 47 437 93 ' 57 2 57 35 464 94 60 3 53 23 491 95 63 4 49 8.511 2911 518 96 66 05 45 8.511 2899 545 97 69 6 41 87 572 98 72 7 37 75 599 2.3599 75 8 33 63 626 2.3600 79 9 29 51 653 01 82 10 8. 509 2625 8.511 '.840 1.23680 2. 3602 5. 9885 11 21 28 707 03 88 12 17 16 734 04 91 13 13 8.511 804 761 05 94 14 09 8.511 1792 788 06 5. 9897 15 05 80 815 07 5.9901 16 8. 509 2601 68 842 08 04 17 8. 509 2597 56 869 09 07 18 93 44 896 10 10 19 89 32 923 11 13 20 8. 509 2585 8.511 1720 1. 23950 2. 3612 5. 9916 7.877 21 81 8.511 2708 1.23977 13 19 22 77 8. 511 -2C96 1.24004 14 23 23 73 84 031 15 26 24 6J 72 058 16 29 25 65 60 085 17 32 26 61 48 112 18 35 27 57 36 139 19 38 28 53 24 165 20 42 29 49 12 192 21 45 30 8. .509 2545 8.511 2600 1.2 219 1. 3. 22 5. 9948 31 41 8.511 2588 246 23 51 32 37 76 27.S 24 54 33 33 64 3JO 25 57 34 29 52 327 26 61 35 25 40 354 27 64 36 21 28 381 28 67 37 17 16 408 29 70 38 13 8. 511 2504 431 30 73 39 09 8. 511 2492 461 31 76 40 8. 509 2505 8.511 2480 1.24488 2. 3632 r>. 9980 7. 877 41 8. 509 2501 68 515 33 83 42 8. 509 2497 56 542 34 86 43 93 44 569 35 89 44 89 32 595 . 36 92 45 85 20 622 37 96 46 81 8.511 2408 649 38 5.9999 47 77 8. 511 2396 676 39 6.0002 . 48 73 84 703 40 05 49 69 72 729 08 41 50 8. 509 2465 8.611 2360 1.24756 2.3642 6.0011 51 61 48 783 43 15 52 57 35 810 43 18 53 53 23 837 44 21 54 49 8.511 2311 863 45 24 -55 45 8.611 2299 890 46 27 56 41 87 917 47 31 57 37 V5 944 48 34 68 33 63 970 49 37 59 29 51 1.24997 50 40 60 8.509 2425 8.511 2239 1.26024 2.3651 6.0043 7.877 GEOGRAPHIC TABLES AND FOEMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 35. 231 Lat. log A d iff. 1"= -0.07 log diff. 1"= B = -0.20 logC diff. 1"= +0.44 logD diff. 1"= +0.01 logE diff.l"=+0.05 logF diff. 10'= +0.0 o / 35 00 8. 509 2425 8.511 2239 1.25024 2. 3651 6.0043 7.877 1 21 27 050 52 47 2 17 15 077 53 50 3 13 8.511 2203 101 54 53 4 09 8.511 2191 131 55 56 06 05 78 157 56 59 6 8. 509 2401 66 184 56 63 7 8. 509 23% 54 211 57 66 8 92 42 237 58 69 9 88 30 264 59 72 10 8.509 2384 8.511 2118 1.25291 2.3660 6. 0075 11 80 8.511 2106 317 61 79 12 76 8.511 2094 344 62 82 13 72 82 371 63 85 14 68 70 397 64 88 15 64 57 424 65 91 16 60 45 451 66 95 17 56 33 477 66 6.0098 18 52 21 504 67 6. 0101 19 48 8.511 2009 531 68 04 20 8.509 2344 8.511 1997 1.25557 2.3669 6. 0107 7.877 21 40 85 584 70 11 22 36 72 610 71 14 23 32 60 637 72 17 24 28 48 664 73 20 25 24 36 690 74 23 26 20 24 717 75 27 27 16 12 743 75 30 28 12 8.511 1900 770 76 33 29 08 8.511 1887 796 71 36 30 8.509 2304 8.511 1875 1.25823 2. 3678 (1. 0140 31 8.509 2300 6:5 850 79 43 32 8. 509 2296 51 876 80 46 33 92 39 903 81 49 34 87 27 929 82 52 35 98 15 956 82 56 36 79 8.511 1802 1.25982 83 59 37 75 8.511 1790 1.26009 84 62 38 71 78 035 85 65 39 67 K 062 86 69 40 8.509 2263 8. 51 1 1754 1 . 26088 2. 3B87 6.0172 7.877 41 59 41 115 88 75 42 55 29 141 MS 78 43 51 17 168 W 81 44 47 8. 511 170f> 194 90 85 45 43 8.511 1693 221 91 88 46 39 80 247 9-2 91 47 35 68 274 93 94 48 31 56 300 94 6. 0198 49 27 44 327 94 6. 0201 50 8. 509 2222 8.511 1632 1.26353 2. 3159ft 6. 0204 51 18 20 380 96 07 52 14 8.511 1607 406 97 11 53 10 8.511 159o 432 98 14 54 06 83 459 99 17 55 8. 509 220-2 71 485 2. 3699 20 56 fc. 509 '2198 58 512 2 3700 24 57 91 46 538 01 27 58 90 34 565 0-2 30 59 86 22 591 03 33 60 8. 509 2182 8.511 1510 1.26617 2.3701 0. 0237 7.877 232 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 36. Lat. log A diff.l"=-0.07 logB diff. 1"= -0.20 logC diff. 1"= +0.44 logD diff. 1"= +0.01 log E log F diff.l"=+0.05 diff.lO'=-0.2 o / 36 00 8. 509 2182 8.511 1510 1.26617 2.3704 6. 0237 7. 877 1 78 8.511 1497 644 04 40 2 74 85 670 05 43 3 70 73 697 06 46 4 65 61 723 07 50 05 61 48 749 08 53 6 57 36 776 09 56 7 53 24 802 09 59 8 49 8.511 1412 828 10 63 9 45 8.511 1399 855 11 66 10 8. 509 2141 8.511 1387 1 . 26881 2. 3712 6. 0269 11 37 75 908 13 12 33 63 934 13 76 13 29 50 960 14 79 14 25 38 1. 26987 15 82 15 21 26 1.27013 16 85 16 16 14 039 17 89 17 12 8. 511 1301 066 17 92 18 08 8.511 1289 092 18 95 19 04 77 118 19 6.0299 20 8. 509 2100 8.511 1265 1.27145 2. 3720 6. 0302 7. 877 21 8. 509 2096 52 171 21 05 22 92 40 197 21 08 23 88 28 223 22 12 24 84 15 250 23 15 25 80 8.511 1203 276 24 18 26 75 8.511 1191 302 25 21 27 71 79 329 25 25 28 67 66 355 26 28 29 63 54 381 27 31 30 8. 509 2059 8.511 1142 1.27407 2. 3728 6. 0334 31 55 29 434 29 38 32 51 17 460 29 41 33 47 8.511 1105 486 30 44 34 43 8.511 1092 512 31 48 35 39 80 539 32 51 36 35 68 565 32 54 37 30 56 591 33 57 38 26 43 617 34 61 39 22 31 644 35 64 40 8. 509 2018 8.511 1019 1.27670 2. 3735 6. 0367 7. 877 41 14 8.511 1006 696 36 71 42 10 8.511 0994 722 37 74 43 06 82 748 38 77 44 8.509 2002 69 775 39 80 45 8.509 1998 57 SOI 39 84 46 93 45 827 40 87 47 89 32 853 41 90 48 85 20 879 42 94 49 81 N.511 0908 905 42 6. 0397 50 8.509 1977 -s.511 0895 1 . 27932 2.3743 6. 0400 51 73 83 958 44 03 52 69 71 1.27984 45 07 53 65 58 1.2X010 45 10 54 61 46 036 46 13 55 56 34 062 47 17 56 52 21 088 48 20 57 48 S.511 0809 114 48 23 58 -II . 0768 7.873 41 16 14 810 16 72 42 12 8. 510 9501 83G 17 75 43 08 8. 510 9488 862 18 78 44 04 76 887 18 82 45 8.509 1500 63 913 19 85 46 8.509 1495 51 939 19 89 47 91 38 965 20 92 48 87 26 1.30990 20 95 49 83 13 1.31010 21 G. 0799 50 8. 509 1479 8. 510 9401 1.31042 2. 3822 6. 0802 51 75 8. 510 9388 067 22 06 52 70 76 093 23 09 53 66 63 119 23 13 54 62 50 144 24 16 55 58 38 170 24 19 56 53 25 196 25 23 57 49 13 221 25 26 58 45 8.510 9300 2-17 26 30 59 41 8.510 9287 . 273 27 33 60 8.509 1437 8.510 9275 I.3TO9 2. 3S27 c.. os3<; 7.872 GEOGRAPHIC CABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 39. 285 Lat. log A diff. 1"= -0.07 logB diff. 1"= -0.21 logC diff. 1"= +0.43 diff logD 1"=+0.01 logE diff. 1"= +0.06 logF diff.lO' = ~0.5 o / . 39 00 8.509 1437 8.510 9275 1.31299 2.3827 6.0836 7. 872 1 33 62 324 28 40 2 28 50 350 28 43 3 24 37 375 29 47 4 20 25 401 29 50 05 16 8.5109212 427 30 53 6 12 8. 510 9199 452 30 57 7 07 87 478 31 60 8 8.509 1403 74 504 31 64 9 8. 509 1399 62 529 32 67 10 8.509 1395 8.510 9149 1.31555 2. 3832 (5.0871 11 91 36 581 33 74 12 86 24 606 33 77 13 82 8.510 9111 632 34 81 14 78 8. 510 9098 658 35 84 15 74 86 683 35 88 16 70 73 709 36 91 17 65 61 734 36 95 18 61 48 760 37 6.0898 19 57 36 786 37 6.0902 20 8.509 1353 8. 510 9023 1.31811 2.3838 6.0905 7.871 21 49 8.5109010 837 38 ' 08 22 44 8. 510 8998 862 39 12 23 40 85 888 39 15 24 36 73 913 40 19 25 32 60 939 40 22 26 28 47 965 41 26 27 23 35 1.31990 41 29 28 19 22 1.32016 42 32 29 15 8.510 8909 041 42 36 30 8.509 1311 8.510 8897 1.32067 2.3843 6.0939 31 07 84 092 43 43 32 8.509 1302 72 118 44 46 33 8.509 1298 59 144 44 50 34 94 46 169 45 53 35 90 34 195 45 57 36 86 21 220 46 60 37 81 8. 510 8808 246 46 63 38 77 8. 510 8796 271 47 67 39 73 83 297 47 70 40 8. 509 1269 8.510 8771 1.32323 2.3848 (>. 0974 7.870 41 64 58 348 48 77 42 60 45 374 49 81 43 56 33 399 49 84 44 52 20 425 50 88 45 48 8. 510 8707 450 50 91 46 43 8. 510 8695 476 51 95 47 39 82 501 51 6.0998 48 35 69 527 52 6.1002 49 31 57 552 52 05 50 8. 509 1227 8. 510 8644 1.32578 2.3852 6. 1008 51 22 31 603 53 12 52 18 19 629 53 15 53 14 8. 510 8606 654 54 19 54 10 8. 5H) 8593 680 54 22 55 06 81 705 55 26 56 8.509 1201 68 731 55 29 67 8.509 1197 55 756 56 33 58 93 43 782 56 36 59 89 30 807 57 40 60 8.509 1184 8.610 8517 1.32833 2.3857 6.1043 7.869 236 GEOGRAPHIC TABLES AND FOEMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 40. Lat. log A diff. 1"= -0.07 logB diff.l"=-0.21 logC diff. 1"=+0.42 logD diff. 1"=+0.01 logE diff. 1"= +0.06 logF diff. 10'= 0.7 o / 40 00 8.509 1184 8. 510 8517 1.32833 2.3857 6. 1043 7.869 1 80 8. 510 8505 858 58 47 2 76 8. 510 8492 884 58 50 3 72 79 909 58 54 4 67 67 935 59 57 05 63 54 960 59 61 6 59 41 1. 32986 60 64 7 55 29 1.33011 60 67 8 50 16 037 60 71 9 46 8.510 8403 062 61 74 10 8. 509 1142 8. 510 8391 1.33088 2. 3861 6.1078 11 38 78 113 62 81 12 34 65 139 62 85 13 29 53 164 63 88 14 25 40 189 63 92 15 21 27 215 64 95 16 17 15 240 64 6.1099 17 12 8. 510 8302 266 65 6.1102 18 08 8. 510 8289 291 65 06 19 04 77 317 65 09 20 8.509 1100 8.510 8264 1.33342 2. 3866 (',.1113 7.867 21 8.509 1096 51 368 66 16 22 91 38 393 67 20 23 87 26 418 67 23 24 83 13 444 68 27 25 79 8. 510 8200 469 68 30 26 74 8. 510 8188 495 68 34 27 70 75 520 69 37 28 66 62 546 69 41 29 62 50 571 70 44 30 8.509 1057 8. 510 8137 1.33596 2. 3870 6.1148 31 53 24 622 70 51 32 49 8.510 8111 647 71 55 33 45 8. 510 8099 673 71 58 34 41 86 698 72 62 35 36 73 723 72 65 36 32 61 749 72 69 37 28 48 774 73 72 38 24 35 800 73 76 39 19 23 825 74 79 40 8.509 1015 8. 510 8010 1.33850 2. 3874 6.1183 7.866 41 11 8. 510 7997 876 74 86 42 07 84 901 75 90 43 8. 509 1002 72 926 75 93 44 8. 509 0998 59 952 76 6.1197 45 94 46 1.33977 76 6. 1200 46 90 33 1.34003 76 04 47 85 21 028 77 07/ 48 81 8.510 7908 053 77 11 -19 77 8. 510 7895 079 77 15 50 8. 509 0973 8.510 7883 1.34104 2.3878 6.1218 51 68 70 129 78 22 52 64 57 155 79 25 53 60 44 180 79 29 54 56 82 206 79 32 55 52 19 231 80 36 56 47 8. 510 7806 256 80 39 57 43 8. 510 7793 282 80 43 58 39 81 307 81 46 59 34 68 332 81 50 60 8.509 0930 8.510 7755 1.34358 2. 3882 6. 1253 7.864 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 41. 237 Lat. log A diff.l"=-0.07 log B log C diff.l"=-0.21 diff.l"= + 0.4'2 log D log E log F diff.l"=+0.01 diff.l" = +0.06 diff.lO' = -0.8 o / 41 00 8.509 0930 8. 510 7755 1.34358 2/3882 6. 1253 7. 864 1 26 42 383 82 57 2 22 30 408 82 60 3 18 17 434 83 64 4 13 8. 510 7704 459 83 67 05 09 8.510 7691 484 83 71 6 05 79 510 84 75 7 8.509 0900 66 535 84 78 8 8.509 089(5 53 560 84 82 9 92 40 586 85 85 10 8.509 0888 S.510 7628 1.84011 2. 3885 6. 1289 11 83 15 636 85 92 V2 79 8. 510 7602 662 86 96 13 75 8.510 7590 687 86 6. 1299 14 71 712 87 6.1303 15 67 64 738 87 06 16 62 51 763 87 10 17 58 39 788 88 14 18 54 26 814 88 17 19 49 13 839 88 21 20 8. 509 0845 8.510 7500 1.34864 2.3889 6.1324 7.863 21 41 8. 510 7488 890 89 28 22 37 75 915 89 31 23 32 62 940 90 35 24 28 49 965 90 38 25 24 36 1.34991 30 42 26 20 24 1.35016 91 46 27 15 8.510 7411 041 91 49 28 11 8. 510 7398 066 91 53 29 07 85 092 91 56 30 8. 509 0803 S. 510 7373 1.35117 2.3892 ti.1360 31 8. 509 0798 60 142 92 63 32 94 47 168 92 67 33 90 34 193 93 70 34 86 22 218 93 74 35 81 8. 510 7309 243 93 78 36 77 8. 510 7296 269 94 81 37 73 83 294 94 85 38 69 70 319 94 88 39 64 58 345 95 92 40 j 8. 509 0760 X.510 7245 1.35370 2. 3895 6.1395 7.861 41 1 56 32 395 95 6.1399 42 52 19 420 96 6. 1403 43 47 8.510 7207 446 96 06 44 43 8. 510 7194 471 % 10 45 39 81 496 97 13 46 35 68 522 97 17 47 30 55 547 97 20 48 26 43 572 97 24 49 22 30 597 98 28 50 S.509 071* 8.510 7117 1.35623 2. 3898 6. 1431 51 13 8. 510 7104 648 98 35 63 09 8. 510 7091 673 98 38 53 05 79 698 99 42 54 8.509 0700 66 723 99 46 55 8. 509 0696 53 749 2.3899 49 ' 56 92 40 774 2.3900 53 57 88 27 799 00 56 58 83 15 824 00 60 M 79 8. 510 7002 850 00 63 60 8.509 0676 8. 510 6989 1.35875 2.3901 6.1467 7.860 238 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 42. Lat. log A diff.l"-~0.07 logB diff.l"=-0.21 d logC iff. 1"= +0.4 logD 2 diff.l"=+0.00 logE diff.l"=+0.06 logF diff.lO'=-0.9 o / 42 00 8. 509 0675 8. 510 6989% 1.35875 2. 3901 <;.Ht>7 7.860 1 71 76 900 01 71 2 66 64 925 01 74 3 62 51 951 01 78 4 58 38 1.35976 02 81 05 54 26 1.36001 02 85 6 49 12 026 02 89 j 45 8. 510 6900 052 03 92 8 41 8. 510 6887 077 03 96 9 36 74- 102 03 6.1499 10 8.5090632 8. 510 6861 1.36127 2.3903 6. 1503 11 28 48 152 04 07 12 24 36 178 04 10 13 19 23 203 04 14 14 15 8. 510 6810 228 04 17 15 11 8. 510 6797 253 05 21 16 07 84 278 05 25 17 8. 509 0602 72 304 05 28 18 8. 509 0598 59 329 05 32 19 94 46 354 06 35 20 8. 509 0590 8. 510 6733 1.36379 2.3906 ti. 1539 7.858 21 86 20 404 06- 43 22 81 8. 510 6707 430 06 46 23 77 8. 610 6695 455 07 50 24 72 82 480 07 54 25 68 69 505 07 57 "26 64 56 530 07 61 27 60 43 556 08 64 28 55 31 581 08 68 29 51 18 606 08 72 30 8. 509 0547 8. 510 6605 1.36631 2. 3908 (>. 1575 31 43 8. 510 6592 656 08 79 32 38 79 682 09 83 33 34 66 707 09 86 34 30 54 732 09 90 35 25 41 757 09 93 36 21 28 782 10 6. 1597 37 17 15 808 10 (i. 1601 38 13 8. 510 6502 833 10 04 39 08 8.510 6490 858 10 08 40 8.5090504 8. 510 6477 1.36883 2.3910 (i. 1612 7.856 41 8. 509 0500 64 908 11 15 42 8. 509 0496 51 934 11 19 43 91 38 959 11 22 44 87 25 1.36984 11 26 45 83 13 1.37009 12 30 46 . 78 8. 510 6400 034 12 33 47 74 8. 510 6387 059 12 37 48 70 74 085 12 41 49 66 61 110 12 44 50 8.509 0461 8. 510 6348 1.37135 2.3913 6.1648 51 57 36 160 13 52 52 53 23 185 13 55 53 48 8. 510 6310 210 13 69 54 44 8. 510 6297 235 13 63 55 40 84 261 14 66 66 36 71 286 14 70 57 31 59 311 14 73 68 27 46 336 14 77 59 23 33 361 14 si 60 8. 509 0419 8.510 6220 1.37386 2. 3914 6.1684 7.854 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 43. 239 Lat. log A diff.l"=-0.07 logB diff.l"=-0.21 logC cliff. 1"= +0.42 logD cliff. 1"= +0.00 log E log F cliff. 1"= +0.06 diff.lO'=-1.0 o / 43 CO 8. 509 0419 8.510 6220 1.37386 2. 3914 0.1684 7.854 1 14 8. 510 6207 412 15 88 2 10 8.510 6195 437 15 92 3 06 82 462 15 95 4 8.509 0401 69 487 15 6.1699 05 8. 509 0397 56 512 15 6. 1703 6 93 43 537 16 06 7 89 30 563 16 10 8 84 17 588 16 14 9 80 8.510 6105 613 16 17 10 8.509 0376 8. 510 6092 1.37638 1. 3916 ti. 1721 11 71 79 663 16 25 12 67 66 688 17 28 13 63 53 713 17 32 14 59 40 739 17 36 15 54 28 764 17 39 16 50 15 789 17 43 17 46 8. 510 6002 814 17 47 18 41 8. 510 5989 839 18- 50 19 37 76 864 18 > 54 20 8.509 0333 8.510 5963 1.37889 _>. 3918 6.1758 7.852 21 29 50 915 18 61 22 24 38 940 18 65 23 20 25 965 18 69 24 16 8. 510 5912 1.37990 18 72 25 12 8.510 5899 1. 38015 19 76 26 07 86 040 19 80 27 8.509 0303 73 065 19 83 28 8.5D9 0299 60 091 19 87 29 94 48 116 19 91 30 8.509 0290 8.510 5835 1.38141 '2. 3919 6.1795 31 86 22 166 20 6. 1798 32 82 8. 510 5809 191 20 6.1802 33 77 8.510 57% 216 20 06 34 73 83 241 20 09 35 69 71 266 20 13 36 64 58 292 20 17 37 60 45 i)17 20 20 38 56 32 342 20 24 39 52 19 367 21 28 40 8. 509 0247 8. 510 5706 1.38392 2. 3921 C..1831 7.850 41 43 8. 510 5693 417 21 35 42 39 81 442 21 39 43 34 68 467 21 42 44 30 55 492 21 46 45 26 42 518 21 50 46 22 29 543 21 53 47 17 16 568 22 57 48 13 8. 510 5603 593 22 61 49 09 8. 510 5591 618 22 65 50 8. 509 0204 8. 510 6578 1.38643 2. 3922 H. 1868 51 8.509 0200 65 668 22 72 52 8. 509 0196 52 693 22 76 53 92 39 719 22 79 54 87 26 744 22 83 55 83 13 769 22 87 56 79 8. 510 5501 794 23 91 57 74 8. 510 5488 819 23 94 58 70 75 844 23 f>. 1898 f>9 66 62 869 23 6.1902 60 8. 509 0162 8. 510 5449 1.38894 2. 3928 6.1905 7 ; 848 240 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 44. Lat. log A diff. 1"--0.07 logB cliff. 1"=-0.21 logC diff. 1" = +0.42 logD diff. 1"= +0.00 log E log F diff. 1"= + 0.06 diff. 10' =1.2 o / 44 00 8.509 0162 8.510 5449 1.38894 2. 3923 6. 1905 7. 848 1 57 36 919 23 09 2 53 23 945 23 13 3 49 8.510 5411 970 23 17 4 44 8. 510 5398 1.38995 23 20 05 40 85 1.39020 23 24 6 36 72 045 24 28 7 31 59 070 24 31 8 27 46 095 24 35 9 23 33 120 24 39 10 8.509 0119 8. 510 5320 1.39145 2. 3924 6.1943 11 14 8. 510 5307 171 24 46 12 10 8. 510 5295 196 24 50 13 06 82 221 24 54 14 8.509 0102 69 246 24 58 15 8. 509 0097 56 271 24 61 16 93 43 296 24 , 65 17 89 30 321 24 69 18 84 18 346 24 72 19 80 8. 510 5205 371 25 76 20 8. 509 0076 8., 510 5192 1 . 39396 2. 3925 6. 1980 7. 845 21 72 79 422 25 84 22 67 66 447 25 87 23 63 53 472 25 91 24 59 40 497 25 95 25 54 28 522 25 6. 1999 26 50 15 547 25 6.2002 27 46 8. 510 5102 572 25 06 28 42 8. 510 5089 597 25 10 - ^9 37 76 623 25 14 30 8. 509 0033 8. 510 5063 1.39648 2. 3925 6.2017 31 29 50 673 25 21 32 24 37 698 25 25 33 20 25 723 25 29 34 16 8. 510 5012 748 25 32 35 11 8.510 4999 773 25 36 36 07 86 798 26 40 37 8.509 0003 73 823 26 44 38 8. 508 9999 60 848 26 47 39 94 47 873 26 51 40 8.508 9990 8.510 4935 1.39898 2.8326 6. 2055 7. 843 41 86 22 924 26 59 42 81 8.510 4909 949 26 62 43 77 8. 510 4896 974 26 66 44 73 83 1 . 39999 26 70 45 69 70 1.40024 26 74 46 64 57 049 26 77 47 60 44 074 26 81 48 56 32 099 26 85 49 51 19 124 26 89 .50 8.508 WIT 8.510 4806 1.40149 2. 3926 6. 2092 51 43 8. 510 4793 174 26 6.2096 52 39 80 200 26 6. 2100 53 34 67 225 26 04 54 30 54 250 26 08 55 26 41 275 26 11 56 21 29 300 26 15 57 17 16 S25 26 19 58 13 8. 510 4703 350 26 23 59 09 8. 510 4690 375 26 27 60. 8.508 9904 8. 510 4677 1.40400 2. 3926 6. 2130 7. 840 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 45. 241 Lat. log A diff. 1" = - 0.07 logB diff. 1"= -0.21 logC diff. 1"=+0.42 logD diff. 1"= 0.00 diff. logE 1"=+0.06 logF diff.lO' = -1.3 o / 45 00 8.508 9904 8.510 4677 1.40400 2.3926 6.2130 7.840 1 8.508 9900 64 425 26 34 2 8.508 9896 61 450 26 38 3 91 39 475 26 42 4 87 26 501 26 46 05 83 13 526 26 49 6 78 8.510 4600 551 26 53 7 74 8. 510 4587 576 26 57 8 70 74 601 26 61 9 66 61 626 26 64 10 8. 508 9861 8.510 4548 1.40651 2. 3926 6.2168 11 57 36 676 26 72 12 53 23 . ' 701 26 76 13 48 8. 510 4510 727 26 80 14 44 8.510 4497 752 26 83 15 40 8* 777 26 87 16 36 71 802 26 91 17 31 59 827 26 95 18 27 46 852 26 6.2199 19 23 33 877 26 6. 2202 20 8.508 9818 8.5104420 1.40902 2. 3926 6.2206 7.838 21 14 8. 510 4407 927 26 10 22 10 8. 510 4394 952 26 14 23 06 81 1.40978 26 18 24 8. 508 9801 68 1.41003 26 21 25 8. 508 9797 56 028 26 25 26 93 43 053 26 29 27 88 3f 078 26 33 28 84 IV 103 26 37 29 80 8.510 4304 128 26 40 30 8.508 9776 8. 510 4291 1.41153 2. 3926 6.2244 31 71 78 178 26 48 32 67 65 203 26 52 33 63 52 229 26 56 34 58 40 254 26 60 35 54 27 279 26 63 36 50 14 30-1 25 67 37 46 8. 510 4201 329 25 71 38 41 8.510 4188 354 25 75 39 37 75 379 25 79 40 8. 508 9733 8.510 4162 1.41404 2. 3925 0. 2283 7.835 41 28 49 429 25 86 42 24 37 454 25 90 43 20 24 479 25 94 44 16 8.510 4111 505 25 6. 2298 45 11 8. 510 4098 530 25 6. 2302 46 07 85 555 25 06 47 8. -508 9703 72 580 25 09 48 8. 508 9698 60 005 25 13 49 94 17 630 25 17 50 8.508 9689 8. 510 4034 1. '11 055 2. 3925 6. 2321 51 85 21 68J 25 25 52 81 8.510 4008 705 25 29 53 77 8. 510 3995 731 25 32 54 72 82 756 24 36 56 68 69 781 24 40 56 64 57 800 24 44 57 60 44 831 24 48 58 55 31 856 24 52 59 51 18 881 24 55 60 8. 508 9647 8. 510 3905 1.41906 2. 3924 6.2359 7.832 4(KH)1 08- -16 242 GEOGEAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 46. Lat. log A diff.l"=-0.07 logB diff. 1"= -0.21 logC diff. 1"= +0.42 logD diff. V'= -0.00 log E log F diff. 1"= +0.06 diff. 10'= -1.1 o / 46 00 8. 5C8 9647 8. 510 3905 1.41906 2. 3924 6. 2359 7. 832 1 43 8.510 3892 931 24 63 2 38 79 957 24 67 3 34 67 1. 41982 24 71 4 30 54 1.42007 24 75 05 25 41 032 24 79 6 21 28 057 23 82 7 17 15 082 23 86 8 13 8. 510 3802 107 23 90 9 08 8. 510 3789 132 23 94 10 8. 508 9604 8. 510 3776 1.42157 2. 3923 6. 2398 11 8. 508 9600 64 183 23 6.2402 12 8. 508 9595 51 208 23 06 13 91 38 233 23 09 14 87 25 258 23 13 15 83 8. 510 3712 283 23 17 16 78 8. 510 3699 308 23 21 17 74 86 333 22 25 18 70 74 358 22 29 19 65 61 384 22 33 20 8. 508 9561 8. 510 13648 1.42409 2.3922 6. 2436 7. 830 21 57 35 434 22 40 22 53 22 459 22 44 23 48 8. 510 3609 484 22 48 24 44 8. 510 3596 509 22 52 25 40 84 534 22 56 26 35 71 559 21 60 27 31 58 584 21 64 28 27 45 610 21 67 29 23 32 635 21 71 30 8.508 9518 8.510 3519 1. 42660 2. 3921 6. 2475 31 14 8. 510 3506 685 21 79 32 10 8. 510 3494 710 21 83 33 05 81 735 21 87 34 8. 508 9501 68 760 20 91 35 8. 508 9497 55 786 20 95 36 93 42 811 20 6. 2499 37 88 29 836 20 6. 2502 38 84 17 861 20 06 39 80 8. 510 3404 886 20 10 40 8. 508 9475 8. 510 3391 1.42911 2. 3920 6.2514 7.827 41 71 78 936- 19 18 42 67 65 961 19 22 43 63 52 1. 42987 19 26 44 58 39 1.43012 19 30 45 54 27 037 19 34 46 50 14 062 19 38 47 45 8. 510 3301 087 19 41 48 41 8. 510 3288 112 18 45 49 37 75 137 18 49 50 8. 508 9433 8. 510 3262 1.43163 2. 3918 6. 2553 51 28 49 188 18 57 52 24 37 213 18 61 53 20 24 238 18 65 54 16 8.510 3211 263 18 69 55 11 8. 510 3198 288 17 73 56 07 85 314 17 77 57 8. 508 9403 72 339 17 81 58 8. 508 9398 60 364 17 84 59 94 47 389 17 88 60 8. 508 9390 8. 510 3134 1.43414 2. 3917 6, 2592 7. 824 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 47. 243 Lat. log A diff. 1"= -0.07 logB diff. 1"= -0.21 logC d iff. 1"= +0.42 logD diff. 1"= -0.00 log E log F diff. 1"= +0.07 diff. 10' = -1.6 o / 47 00 8.508 9390 8. 510 3134 1. 43414 2. 3917 6. 2592 7.824 1 86 21 439 16 6. 25% 2 81 8. 510 3108 465 16 6.2600 3 77 8.510 3095 490 16 04 4 73 82 515 16 08 05 68 70 540 16 12 6 64 57 565 16 16 7 60 44 590 15 20 8 56 31 615 15 24 9 51 18 641 15 28 10 8. 508 9347 8. 510 3005 1.43666 2. 3915 6. 2632 11 43 8. 510 2993 691 15 35 12 38 80 716 14 39 13 34 67 741 14 43 14 30 54 766 14 47 15 26 41 792 14 51 16 21 28 817 14 55 17 17 16 842 13 59 18 13 8. 510 2903 867 13 63 19 09 8.510 2890 892 13 67 20 8.5089304 8.510 2877 1.43917 2.3913 G. 2671 7. 821 21 8. 508 9300 64 943 13 75 22 8.508 9296 51 968 12 79 23 91 39 1.43993 12 83 24 87 26 1.44018 12 87 25 83 13 043 12 91 26 79 8. 510 2800 069 12 95 27 74 8. 510 2787 094 11 6. 2699 28 70 74 119 11 6. 2702 29 66 62 144 11 06 30 8. 508 9261 8.510 2749 1.44169 2.3911 6. 2710 31 57 36 195 11 14 32 53 23 220 10 18 - 33 49 8.510 2710 245 10 22 34 44 8. 510 2698 270 10 26 35 40 85 295 10 30 36 36 72 321 10 34 37 32 59 346 09 38 38 27 46 371 09 42 39 23 33 396 09 46 40 8. 508 9219 8. 510 2621 1.44421 2.3909 6.2750 7.817 41 14 8.510 2608 447 08 54 42 10 8.5102595 472 08 58 43 06 82 497 08 62 44 8. 508 9202 69 522 08 66 45 8. 508 9197 57 547 07 70 46 93 44 673 07 74 47 89 31 598 07 78 48 84 18 623 07 82 49 80 8.510 2505 648 07 86 50 8.508 9176 8. 510 2493 1.44673 2.3906 6.2790 51 72 80 699 06 94 52 67 67 724 06 6. 2798 53 63 54 749 06 6.2802 54 59 41 774 05 06 55 55 28 800 05 10 56 50 16 825 05 14 57 46 8.510 2403 850 05 18 58 42 8.510 2390 875 04 22 59 38 77 900 04 26 60 8. 508 9133 8. 510 2364 1 . 44926 2. 3904 6.2830 7.814 244 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 48. Lat. log A diff.l"=-0.07 logB diff.l"=-0.21 logC logD 2 diff.l"; 0.00 logE diff.l"=+0.07 diff. logF 10' 1.7 o / 48 00 8.5089133 8.510 2364 1.44926 2.3904 6.2830 7.814 1 29 52 951 04 34 2 25 39 1.44976 03 38 3 20 26 1.45001 03 42 4 16 13 027 03 46 05 12 8. 510 2300 052 02 50 6 08 8. 510 2288 077 02 54 7 8. 508 9103 75 102 02 58 8 8. 508 9099 62 128 02 62 9 95 49 153 01 66 10 8. 508 9091 8.510 2236 1.45178 2.3901 6.2870 11 86 24 203 01 74 12 82 8. 510 2211 229 01 78 13 78 8. 510 2198 254 00 82 14 74 85 279 00 86 15 69 72 304 2.3900 90 16 65 60 330 2.3899 94 17 61 47 355 99 6.2898 18 57 34 380 99 6.2902 19 52 21 406 99 06 20 8.508 9048 8. 510 2108 1.45431 2. 3898 6.2910 7.811 21 44 8. 510 2096 456 98 14 22 39 83 481 98 18 23 35 70 507 97 22 24 31 57 532 97 26 25 27 45 557 97 30 26 22 32 582 97 34 27 18 19 608 96 38 28 14 8. 510 2006 633 96 42 29 10 8.510 1993 658 96 46 30 8. 508 9005 S.510 1981 1.45683 2. 3895 6.2950 31 8. 508 9001 68 709 95 54 32 8.508 8997 55 734 95 58 33 93 42 759 95 62 34 88 30 785 94 66 35 84 17 810 94 70 36 80 8.510 1901 835 94 74 37 76 8.510 1891 861 93 78 38 71 78 886 93 82 39 67 66 911 93 86 40 8. 508 8963 8.510 1853 1.45937 2. 3892 6.2990 7.807 41 59 40 982 92 94 42 54 27 1.45987 92 6. 2998 43 50 15 1.46012 91 6.3002 44 46 8.510 1802 038 91 06 45 41 8.510 1789 063 91 10 46 37 76 088 90 15 47 33 64 . 114 90 19 48 29 51 189 90 23 49 24 38 164 89 27 50 8.508 8920 8.510 172"! 1.46190 2.3889 6.3031 51 16 13 215 89 35 52 12 8.510 1700 240 88 39 53 08 8.510 1687 266 88 43 54 8. 508 8903 74 291 88 47 55 8. 508 8899 62 316 87 51 56 95 49 342 87 55 57 90 36 367 87 59 58 86 23 392 86 63 59 82 8.510 1610 418 86 67 60 8.508 8878 8,510 1598 1 . 46443 2.3886 6.3071 7.804 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 49. 245 Lat. log A diff. 1"= -0.07 logB diff . 1"= -0.21 logC diff. 1" =+0.42 logD diff. 1"= -0.01 log E log F d iff. 1"=+ 0.07 diff. 10'= -1.9 o / 49 00 8. 508 8878 8.510 1598 1.46443 2.3886 6. 3071 7. 804 1 73 85 468 85 75 2 69 72 494 85 79 3 65 59 519 85 84 4 61 47 544 84 88 05 57 34 570 84 92 6 52 21 595 84 6.30% 7 48 8.510 1508 621 83 6. 3100 8 44 8.510 14% 646 83 04 9 39 83 671 83 08 10 8.508 8835 8.510 1470 1.466% 2. 3882 6.3112 11 31 58 722 82 16 12 27 45 747 81 20 13 23 32 773 81 24 14 18 19 798 81 28 15 14 8.510 1407 824 80 32 16 10 8. 510 1394 849 80 37 17 06 81 - 874 80 41 18 8.508 8801 68 899 79 45 19 8. 508 8797 56 925 79 49 20 8. 508 8793 8.510 1343 1.46950 2. 3878 6.3153 7.800 21 89 30 1.46976 78 57 22 84 17 1.47001 78 61 23 80 8.510 1305 026 77 65 24 76 8. 510 1292 052 77 69 25 72 79 077 77 73 26 67 67 103 76 78 27 63 54 128 76 82 28 59 41 153 75 86 29 55 28 179 75 90 30 8. 508 8750 8.510 1216 1.47204 2.3875 6.3194 31 46 8.510 1'203 230 74 6.3198 32 42 8.510 1190 255 74 (I. *202 33 38 78 281 73 06 34 33 65 306 73 10 35 29 52 331 73 15 36 25 39 357 72 19 37 21 27 382 72 23 38 16 14 408 71 27 39 12 8.510 1101 433 71 31 40 8. 508 8708 8.510 1088 1.47459 2. 3871 6. 3235 7. 796 41 04 76 484 70 39 42 8. 508 8700 63 509 70 43 43 8.508 8695 50 535 69 47 44 91 38 560 69 52 45 87 25 586 69 56 46 83 12 611 68 60 47 78 8.510 1000 637 68 64 48 74 8. 510 0987 662 67 68 49 70 74 688 67 72 50 8.508 8666 8.510 0962 1.47713 2.3866 6. 3276 51 61 49 738 66 81 52 57 36 764 66 85 53 53 23 789 65 89 54 49 8.510 0911 815 65 93 55 45 8.510 0898 840 64 6. 3297 56 40 85 866 64 6.3301 57 36 73 891 63 05 58 32 60 917 63 09 59 28 48 942 63 14 CO 8. 508 8623 8. 510 0835 1.47968 2.3862 6.3318 7.792 246 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 50. Lat. log A diff. l"= -0.07 logB diff. 1"= -0.21 logC diff. 1"- +0.43 logD diff 1"= -0.01 diff. logE 1"-+0.07 diff. logF 10' = -2.0 o / 50 00 8. 508 8623 8. 510 0835 1. 47968 2.3862 6. 3318 7. 792 1 19 22 1.47993 62 22 2 15 8. 510 0809 1. 48019 61 26 3 11 8. 510 0797 044 61 30 4 06 84 070 60 34 05 8. 508 8602 71 095 60 39 6 8. 508 8598 59 121 60 43 7 94 46 146 59 47 8 90 33 172 59 51 9 85 21 197 58 55 10 8. 508 8581 8. 510 0708 1.48223 2. 3858 6. 3359 11 77 8. 510 0695 248 57 63 12 73 83 274 57 68 13 68 70 299 56 72 14 64 57 325 56 76 15 60 45 350 55 80 16 56 32 376 55 84 17 52 19 401 65 88 18 47 8. 510 0607 427 54 93 19 43 8. 510 0594 452 54 6. 3397 20 8. 508 8539 8. 510 0581 1.48478 2.3863 6. 3401 7.788 21 35 69 504 53 06 22 30 66 529 52 09 23 26 43 555 52 14 24 22 31 680 51 18 25 18 18 606 51 22 26 14 8. 510 0505 631 60 26 27 09 8. 510 0493 657 50 30 28 05 80 682 49 34 29 8.508 8601 67 708 49 39 30 8. 508 8497 8. 510 0455 1 48734 2.3848 6. 3443 31 93 42 759 48 47 32 88 29 786 47 51 33 84 17 810 47 55 34 80 8. 510 0404 836 46 60 35 76 8. 510 0392 861 46 64 36 71 79 887 45 68 37 38 67 63 R 913 938 45 44 72 76 39 59 41 964 44 81 40 8. 508 8455 8 510 0328 1.48989 2. 3843 6. 3485 7.784 41 50 16 1 49015 43 89 42 46 8 510 0303 041 42 93 43 42 8.510 0291 066 42 6 3497 44 38 78 092 41 6.3502 45 34 65 117 41 06 46 29 53 143 40 10 47 25 40 169 40 14 48 21 27 194 39 18 49 17 15 2-20 39 23 50 8.508 8413 8.510 0202 1 . 49246 2. 383S 6. 3527 51 08 8.510 0190 271 38 31 52 04 77 297 37 35 53 8. 508 8400 64 322 37 40 54 8. 508 8396 52 348 36 , 44 55 92 39 374 36 48 56 87 27 399 35 52 57 83 14 425 35 56 58 79 8.510 0101 451 34 61 59 75 8.510 0089 476 34 65 60 8.508 8371 8.510 0076 1.49502 2.3833 6.3569 7.780 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 51. 247 Lat. log A diff.l"=-0.07 logB diff.l"=-0.21 logC diff.l"=+0.43 logD diff.l"=-0.01 Jog E log F diff. 1" = +0.07 diff.lO'=~2.2 O ' 51 00 8.508 8371 8.510 0076 1.49502 2.3833 6. 3569 7. 780 1 66 64 528 33 73 2 62 51 553 32 78 3 58 38 579 32 82 4 54 26 605 31 86 05 50 13 630 31 90 6 45 8.510 0001 656 30 95 7 41 8. 509 9988 682 29 6.3599 8 37 75 707 29 6. 3603 9 33 63 733 28 07 10 8. 508 8329 8. 509 9950 J . 49759 2.3828 6. 3612 11 24 38 785 27 16 12 20 25 810 27 20 13 16 13 836 26 24 14 VI 8. 509 9900 862 26 28 15 | 08 8. 509 9887 887 25 33 16 8. 508 8303 75 913 25 37 17 8.508 8299 62 939 24 41 18 95 50 965 23 45 19 91 37 1.49990 2& 50 20 8. 508 8287 8.509 9825 1.50016 2.3822 6. 3654 7. 776 21 82 8. 509 9812 042 22 58 2-2 78 8. 509 9799 067 21 63 23 74 87 093 21 67 24 70 74 119 20 71 25 66 62 145 20 75 26 62 49 170 19 80 27 67 37 1% 18 84 28 53 24 222 18 88 29 49 8.509 9711 248 17 92 30 8. 508 8245 8. 509 9699 1.50273 2.3817 6. 3697 31 41 86 299 16 6. 3701 32 36 74 325 16 05 33 32 61 351 15 10 34 28 49 376 14 14 35 24 36 402 14 18 36 20 24 428 13 22 37 16 8.509 9611 454 13 27 38 11 8.509 9599 480 12 81 39 07 86 505 11 35 40 8. 508 8203 8. 509 9574 , 1.50531 2.3811 6. 3740 7. 772 41 8.508 8199 61 557 10 44 42 95 48 583 10 48 43 90 36 609 09 52 44 86 23 634 08 57 45 82 8. 509 9511 660 08 61 46 78 8.509 9498 686 07 65 47 74 86 712 07 70 48 70 73 738 06 74 49 65 61 764 05 78 50 8. 508 8161 8. 509 9448 1.50789 2.3805 6. 3782 51 57 36 815 04 87 52 53 23 841 04 91 53 49 8. 509 9411 867 03 6. 3795 54 45 8. 509 9398 893 02 6.3800 55 40 86 919 02 04 56 36 73 944 01 08 57 32 61 970 01 13 58 28 48 1.50996 2.3800 17 59 24 36 1.51022 2. 3799 21 60 8. 508 8120 8. 509 9323 1.51048 2. 3799 6. 3826 7. 767 248 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 52. Lat. log A diff.l"--0.07 logB diff.l"=-0.21 logC diff.l"=+0.43 logD diff.l"=-0.01 d log E log F iff. l" = -f 0.07 diff.10'^-2.3 r> / 52 00 8. 508 8120 8. 509 9323 1.51048 2. 3799 6. 3826 7. 767 1 15 8.509 9311 074 98 30 2 11 8. 509 9298 100 97 34 3 07 86 126 97 39 4 8. 508 8103 73 151 96 43 05 8. 508 8099 61 177 96 47 6 95 48 203 95 52 7 90 36 229 94 56 8 86 23 255 94 60 9 82 8.509 9211 281 93 65 10 8. 508 8078 8.509 9198 1.51307 2. 3792 6.3869 11 74 86 333 92 73 12 70 73 359 91 78 13 65 61 385 91 82 14 61 48 411 90 86 15 57 36 436 89 91 16 53 23 462 88 95 17 49 8.509 9111 488 88 6.3899 18 45 8.509 9099 514 87 6.3904 19 41 86 640 87 08 20 8. 508 8036 8. 509 9074 1.51566 2.3786 6. 3912 7. 763 21 32 61 592 85 17 22 28 49 618 85 21 23 24 36 644 84 25 24 20 24 670 83 30 25 16 8.509 9011 696 83 34 26 11 8. 509 8999 722 82 38 27 07 86 748 81 43 28 8. 508 8003 74 774 81 47 29 8. 508 7999 62 800 80 51 30 8.508 7995 8. 509 8949 1. 51826 2. 3779 6.3956 31 91 37 852 79 60 32 87 24 878 78 66 33 82 8.509 8912 904 78 69 34 78 8.509 8899 930 77 73 35 74 87 956 76 78 36 70 74 1.51982 75 82 37 66 62 1.52008 75 86 38 62 50 034 74- 91 39 58 37 060 73 6. 3995 40 8. 508 7953 8.509 8825 1.52086 2.3773 6.4000 7.758 41 49 12 112 72 04 42 45 8.509 8800 138 . 71 08 43 41 8. 509 8788 164 71 13 44 37 75 190 70 17 45 33 63 216 69 21 46 29 50 242 68 26 47 24 38 268 68 30 48 20 25 294 67 35 49 16 13 320 66 39 50 8.508 7912 8. 509 8701 1.52347 2.3766 7.4043 51 08 8. 509 8688 373 65 48 52 04 76 399 64 52 53 8.508 7900 63 425 64 67 54 8.508 7895 51 451 63 61 55 91 39 477 62 65 56 87 26 5C3 61 70 57 83 14 529 61 74 58 79 8.509 8602 555 60 79 59 75 8.509 8589 581 59 83 60 8.508 7871 8.509 8577 1.52608 2. 3759 6. 4088 7. 753 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 53. 249 Lat. log A diff.l"=-0.07 logB diff.l"=-0.21 logC diff.l"= +0.44 logD diff.l"=-0.01 logE diff.l" -+0.07 diff.lO'=-2.5 o / 53 00 8.508 7871 8. 509 8577 1.52608 2. 3759 6.4088 7. 753 1 67 64 634 58 92 2 62 52 660 57 6.4096 3 58 40 686 56 6. 4101 4 54 27 712 56 05 05 50 15 738 55 10 6 46 8.509 8502 764 54 14 7 42 8. 509 8490 790 53 18 8 38 78 817 53 28 9 34 65 843 52 27 10 8. 508 7829 8. 509 8453 1.52869 2.3751 6.4132 11 25 41 895 51 36 12 21 28 921 50 41 13 17 16 947 49 45 14 13 8.509 8404 1.52974 48 49 15 09 8. 509 8391 1.53000 48 54 16 " 05 79 026 47 58 17 8. 508 7801 67 052 46 63 18 8. 508 7797 54 078 45 67 19 92 42 105 45 72 20 8. 508 7788 8.509 8329 1.53131 2. 3744 6. 4176 7.748 21 84 17 157 43 80 22 80 8.5098305 183 42 85 23 76 8. 509 8292 209 42 89 24 72 80 236 41 94 25 68 68 262 40 6. 4198 26 64 55 288 39 6.4203 27 60 43 314 39 07 28 55 31 341 38 12 29 51 18 367 37 16 30 8.508 7747 8.509 8206 1.53393 2.3736 6. 4221 31 43 8. 509 8194 419 36 25 32 39 82 446 35 29 33 35 69 472 34 34 34 31 57 498 33 38 35 27 46 524 33 43 36 23 32 551 32 47 37 18 20 577 31 52 38 14 8.509 8108 603 30 56 39 10 8.509 8095 630 29 61 40 8.508 7706 8.5098083 1.53656 2.3729 6.4265 7.743 41 8.508 7702 71 682 28 70 42 8. 508 7698 58 709 27 74 43 94 46 735 26 79 44 90 34 761 26 83 45 86 22 788 25 88 46 82 8.509 8009 814 24 92 47 77 8.509 7997 840 23 6.4297 48 73 85 867 22 6.4301 49 69 72 893 22 06 50 8.508 7665 8.509 7960 1.53919 2. 3721 6. 4310 51 61 48 946 20 15 52 57 36 972 19 19 53 53 23 1.53998 18 24 54 49 8.509 7911 1.54025 18 28 55 45 8. 509 7899 051 17 33 56 41 87 077 16 37 57 37 74 104 15 42 58 32 62 130 14 46 59 28 60 157 14 51 60 8.508 7624 8.509 7838 1.54183 2. 3713 6.4355 7.738 250 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 54. Lat. log A diff. 1"=-0.07 logB diff.l"=-0.20 logC diff. 1"= +0.44 logD diff. 1"= -0.01 logE diff. 1"=+0.08 diff logF 10'= -2.6 o / 64 00 8.508 7624 8.509 7838 1.54183 2.3713 6. 4355 7.738 1 20 25 209 12 60 2 16 13 236 11 64 3 12 8. 509 7801 262 10 69 4 08 8.509 7789 288 09 73 05 04 76 315 09 78 6 8. 508 7600 64 341 08 82 7 8. 508 7596 52 368 07 87 8 92 40 394 06 91 9 88 27 421 05 6. 4396 10 8. 508 7584 8.509 7715 1. 54447 2. 3705 6.4400 11 79 8. 509 7703 474 04 05 12 75 8. 509 7691 500 03 09 13 71 78 527 02 14 14 67 66 553 01 18 15 63 54 580 00 23 16 59 42 606 2.3700 28 17 55 30 633 2. 3699 32 18 51 17 659 98 37 19 47 8.509 7605 686 97 41 20 8. 508 7543 8. 509 7593 1.54712 2. 3696 6. 4446 7.733 21 39 81 739 95 . 50 22 35 69 765 94 55 23 31 56 792 94 59 24 27 44 818 93 64 25 22 32 845 92 68 26 18 20 871 91 73 27 14 8. 509 7508 898 90 78 28 10 8. 509 7495 924 89 82 29 06 83 951 88 87 30 8.508 7502 8. 509 7471 1.54977 2. 3688 6. 4491 31 8. 508 7498 59 1.55004 87 6. 4496 32 94 47 031 86 6.4500 33 90 34 057 85 05 34 86 22 084 84 09 35 82 8.509 7410 110 83 14 36 78 8. 509 7398 137 82 19 37 74 86 163 82 23 38 70 74 190 81 28 39 66 61 217 80 32 40 8.508 7462 8.509 7349 1.55243 2. 3679 6. 4537 7.728 41 58 37 270 78 41 42 53 25 297 77 46 43 49 13 323 76 51 44 45 8.509 7301 350 75 55 45 41 8.509 7289 376 74 60 46 37 76 403 74 64 47 33 64 430 73 69 48 29 52 456 72 74 49 25 40 483 71 78 50 8. 508 7421 8.509 7228 1.55510 2.3670 6.4583 51 17 16 536 69 87 52 13 8.509 7204 563 68 92 53 09 8.509 7191 590 67 6. 4597 54 05 79 616 66 6. 4601 55 8. 508 7401 67 643 66 06 56 8. 508 7397 55 670 65 10 57 93 43 696 64 15 58 89 31 723 63 20 59 85 19 750 62 24 60 8. 508 7381 8.509 7107 1. 55777 2.3661 6.4629 7.723 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 65. 251 Lat. log: A diff. 1"= -0.07 logB diff.l"=-0.20 logC diff. 1" +0. logD 5 diff. 1"=-0.02 log E log F diff.l"-+O.CX diff.iy=-2.8 o / 55 00 8. 508 7381 8. 509 7107 1.55777 2.3661 6.4629 7.723 1 77 8. 509 7095 803 60 33 2 73 82 830 59 38 3 69 70 857 58 43 4 65 58 884 57 47 05 61 46 910 56 52 6 56 34 937 56 57 7 52 22 964 55 61 8 48 8. 509 7010 1. 55991 54 6 9 44 8.509 6998 1.56017 53 70 10 8. 508 7340 8.509 6986 1.56044 2.3652 6. 4675 11 36 74 071 51 80 12 32 62 098 50 84 13 28 49 125 49 89 14 24 37 151 48 94 15 20 25 178 47 6. 4698 16 16 13 205 46 6. 4703 17 12 8.5096901 232 45 08 18 08 8.509 6889 259 44 12 19 04 77 286 43 IV 20 8.508 7300 8. 509 6865 1.56312 2. 3642 6. 4721 7. 717 21 8.508 7296 53 339 42 26 22 92 41 366 41 31 23 88 29 393 40 35 24 84 17 420 39 40 25 80 8.509 6805 447 38 45 26 76 8. 509 6793 474 37 49 27 72 81 500 36 54 28 68 69 527 35 59 29 64 57 554 34 63 30 8.508 7260 8. 509 6745 1.56581 2. 3633 6.4768 31 56 33 608 32 73 32 52 21 635 31 77 33 48 8. 509 6709 662 30 82 34 44 8.509 6696 689 29 87 35 40 84 716 28 91 36 36 72 743 27 6.4796 37 32 60 770 26 6.4801 38 28 48 797 25 05 39 24 36 823 24 10 40 8. 508 7220 8.509 6624 I.. r 6850 2.3623 6. 4815 7. 711 41 16 12 877 22 20 42 12 8.509 6600 904 21 24 43 08 8.509 6588 931 20 29 44 04 76 958 19 34 45 8. 508 7200 64 1.56985 18 38 46 8. 508 7196 52 1.57012 17 43 47 92 40 039 16 48 48 88 28 066 15 52 49 84 16 093 14 57 50 8. 508 7180 8.509 6505 1.57120 2. 613 6.4862 51 76 8. 509 6493 147 12 66 52 72 81 174 11 71 53 68 69 201 10 76 54 64 57 229 09 81 55 60 45 256 08 85 56 56 33 283 07 90 67 52 21 310 06 6. 4895 58 48 8.509 6409 337 06 0.4900 59 44 8.509 6397 364 04 04 60 8.508 7140 8. 509 6385 1.57391 2. 3603 6. 4909 7. 706 252 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 56. Lat. log A diff.l"=-0.07 logB diff.l" = -0.20 logC diff.l"=+0.45 logD diff.l" = -0.02 logE diff.l" = +0.0 logF 8 diff.lO' = -3.0 o / 56 00 S. 508 7140 8. 509 6385 1. 57391 2.3603 6.4909 7.706 1 36 73 418 02 14 2 32 61 445 01 18 3 - 28 49 472 2.3600 23 4 24 37 499 2.3599 28 05 20 25 526 98 33 6 16 13 554 97 37 7 12 8. 509 6301 581 96 42 8 08 8. 509 6289 608 95 47 9 04 77 635 94 52 10 8. 508 7100 8. 509 (J26C 1.57662 2.3593 6.4956 11 8. 508 7096 54 689 92 61 12 92 42 717 91 66 13 88 30 744 90 71 14 84 18 771 89 75 15 80 8. 509 6206 798 88 80 16 76 8. 509 6194 825 -87 85 17 72 82 852 86 90 18 69 70 880 85 94 19 65 58 907 84 0. 4999 20 8. 508 7061 8.509 (147 1. 57934 2.3583 C>. .5004 7.700 21 57 35 961 82 09 22 53 23 1. 57989 81 13 23 49 8.509 6111 1.58016 80 18 24 45 8.509 6099 043 78 23 26 41 87 070 77 28 26 37 75 098 76 32 27 33 63 125 75 37 28 29 51 152 74 42 29 25 40 179 73 47 30 8. 508 7021 8. 509 6028 1.58207 2.3572 6.5052 31 17 16 234 71 56 32 13 8.509 6004 261 70 61 33 09 8.509 5992 289 69 66 34 05 80 316 68 71 35 8.508 7001 68 343 67 75 36 8. 508 6997 57 371 66 80 37 93 45 398 65 85 38 89 33 425 64 90 39 86 21 453 62 95 40 8. 508 6982 8.509 5909 1.58480 2.3561 6.5099 7.694 41 78 8. 509 5897 507 60 6.5104 42 74 86 535 59 09 43 70 74 562 58 14 44 66 62 589 57 19 45 62 50 617 56 24 46 58 38 644 55 28 47 54 27 672 54 33 48 50 15 699 53 38 49 46 8 509 5803 726 52 43 50 8. 508 6942 8.509 5791 1.58754 2.3550 6.5148 51 38 79 781 49 52 52 34 67 809 48 57 . 53 30 56 836 47 62 54 26 44 864 46 67 55 23 32 891 45 72 56 19 20 919 44 77 57 15 8. 509 5709 946 43 81 58 11 8. 509 5697 1.58974 42 86 59 07 85 1.59001 41 91 60 8.508 6903 8.509 5673 1.59028 2. 3539 6.5196 7.688 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 57. 253 Lat. log A diff.l"=-0.06 logB diff.l"=-0.19 logC diff.l"=+0.46 logD diff.l"=-0.02 logE diff.l"=+0.08 logF diff.lO'=-3.2 o / 57 00 8.508 6903 8. 509 5673 1.59028 2.3539 6.51% 7.688 1 8.508 6899 61 056 38 6. 5201 2 95 50 083 37 06 3 91 38 111 36 10 4 87 26 139 35 15 ' 05 83 14 166 34 20 6 79 8.509 5603 194 33 25 7 75 8. 509 5591 221 32 30 8 72 79 249 30 35 9 68 67 276 29 40 10 8.508 6864 8.509 5556 1.59304 2.3528 6. 5244 11 60 44 331 27 49 12 56 32 359 26 54 13 52 20 387 25 59 14 48 8.509 5509 414 24 64 15 44 8.509 5497 442 22 69 16 40 85 469 21 74 17 36 73 497 20 79 18 32 62 525 19 83 19 28 50 552 18 88 - 20 C.508 6825 8.509 5438 1.59580 2. 3517 6.5293 7.682 21 21 27 608 16 6. 5298 22 17 15 635 14 6. 5303 23 13 8. 509 5403 663 13 08 24 09 8.509 5392 691 12 13 25 05 80 718 11 18 26 8. 508 6801 68 746 10 22 27 8.508 6797 56 774 09 27 28 93 45 801 07 32 29 90 33 829 06 37 30 8. 508 6786 8. 509 5321 1.59857 2. 3505 f>. 5342 31 82 8.509 5310 885 04 47 32 78 8. 509 5298 912 03 52 33 74 86 940 02 57 44 70 75 968 2.3500 62 35 66 63 1.599% 2.3499 67 36 62 51 1.60023 98 72 37 58 40 051 97 76 38 54 28 079 % 81 39 51 16 107 95 86 10 8. 508 6747 8. 509 5205 1.60134 2. 3493 6. 5391 7.675 41 43 8.509 5193 162 92 6. 5396 42 39 81 190 91 6.5401 43 35 70 218 90 06 44 31 58 246 89 11 45 27 46 274 87 16 46 23 35 301 86 21 47 20 23 329 85 26 48 16 12 357 84 31 49 12 8. 509 5100 385 83 36 50 8. 508 6708 8. 509 5088 1.60413 2. 3481 6. 5441 51 04 77 441 80 46 52 8. 508 6700 65 469 79 50 53 8.508 6696 54 4% 78 55 54 92 42 524 76 60 55 89 30 552 75 65 56 85 19 580 74 70 57 81 8.509 5007 608 73 75 58 77 8.509 49% 636 72 80 M 73 84 664 70 85 60 8.5086669 8.509 4972 1.60692 2. 3469 6.5490 7. 669 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 58. Lat. log A diff.l"=-0.06 logB diff.l"=-0.19 logC diff.l"=+0.47 logD diff.l"=-0.02 log E log F diff. 1"= +0.08 diff. 10'=-3.3 o / 58 00 8. 508 6669 8. 509 4972 1. 60692 2.3469 6. 5490 ' 7. 669 1 65 61 720 68 6.5495 2 62 49 748 67 6.5500 3 58 38 776 66 05 4 54 26 804 64 10 05 50 14 832 63 15 6 46 8. 509 4903 860 62 20 7 42 8. 509 4891 888 61 25 8 38 80 916 59 30 9 35 68 944 58 35 10 8. 508 6631 8. 509 4857 1.60972 2.3457 6.5540 11 27 45 1.61000 56 45 12 23 33 028 54 50 13 19 22 056 53 55 14 15 8. 509 4810 084 52 60 15 11 8. 509 4799 112 51 65 16 08 87 140 49 70 17 04 76 168 48 75 18 8. 508 6600 64 197 47 80 19 . 8. 508 6596 53 225 46 85 20 8.508 6592 8. 509 4741 1.61253 2.3444 6.5590 7.362 21 88 30 281 43 6.5595 22 85 18 309 42 6.5600 23 81 8. 509 4707 337 41- 05 24 77 8. 509 4695 365 39 10 25 73 84 393 38 15 26 69 72 422 37 20 27 65 61 450 35 25 28 62 49 478 34 30 29 58 38 506 33 35 30 8.508 6554 8. 509 4626 1.61534 2. 3432 6.5640 31 50 15 563 30 45 32 46 8. 509 4603 591 29 50 33 42 8.509 4592 619 28 55 34 39 80 647 26 60 35 35 69 675 25 65 36 31 57 704 24 70 37 27 46 732 23 75 38 23 35 760 21 80 39 20 23 789 20 86 40 8. 508 6516 8.509 4512 1.61817 2. 3419 6.5691 7.656 41 12 8.509 4500 845 17 6.5696 42 08 8. 509 4489 873 16 6. 5701 43 04 77 902 15 06 44 8.508 6500 66 930 14 11 45 8. 508 6497 54 958 12 16 46 93 43 1 . 61987 11 21 47 89 32 1.62015 10 26 48 85 20 043 08 31 49 81 8. 509 4409 072 07 36 50 8. 508 6478 8.509 4397 1.62100 2.3406 6. 5741 51 74 86 129 04 46 52 70 74 157 03 51 53 66 63 185 02 56 54 62 52 214 2.3400 62 55 59 40 242 2. 3399 67 56 55 29 271 98 72 57 51 17 299 96 77 58 47 8. 509 4306 327 95 82 59 43 8. 509 4295 356 94 87 60 8.508 6440 8. 509 4283 1.62384 2.3392 6. 5792 7. 649 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computation!) Continued. LATITUDE 59. 255 Lat. log A diff.l"=-0.06 logB diff.l"=.-0.19 logC diff.l"=+0.48 logD diff.l"=-0.02 logE diff.l"= +0.09 losrF diff.lO' = -3.5 o / 59 00 8. 508 6440 8.509 4283 1.62384 2.3392 6. 5792 7.649 1 36 72 413 91 6. 5^97 2 32 61 441 90 6.5802 3 28 49 470 88 07 4 24 38 498 87 13 5 21 26 527 86 18 6 17 15 555 84 23 7 13 8. 509 4204 584 83 28 8 09 8. 509 4192 612 82 33 9 05 81 641 80 38 10 8. 508 6402 8.509 4170 1.62669 2. 3379 6. 5843 11 8. 508 6398 58 698 78 48 12 94 47 727 76 54 13 90 36 755 75 59 14 87 24 784 74 64 15 83 13 812 72 69 16 79 8. 509 4102 841 71 . 74 17 75 8.509 4090 870 69 79 18 71 79 898 68 84 19 68 68 927 67 89 20 8. 508 6364 8.509 4056 1.62955 2. 3365 6. 5895 7.642 21 60 45 1.62984 64 6.5900 22 56 34 1.63013 63 05 23 53 22 041 61 10 24 49 11 070 60 15 25 45 8.509 4000 099 58 20 26 41 8. 509 3989 127 57 26 27 38 77 156 56 31 28 34 66 185 54 36 29 30 55 214 53 41 30 8. 508 6326 8. 509 3943 1.63242 2.3351 6. 5946 31 23 32 271 50 51 32 19 21 300 49 57 33 15 8.509 3910 329 47 62 34 11 8. 509 3898 357 46 67 35 08 87 386 44 72 36 04 76 415 43 77 37 8. 508 6300 65 444 42 82 38 8. 508 62% 53 473 40 88 39 93 42 501 39 .93 40 8. 508 6289 8. 509 3831 1.63530 2.3337 6.5998 7.635 41 85 20 559 36 6.6003 42 81 8.509 3808 588 35 08 43 78 8.509 3797 617 33 14 44 74 86 646 32 19 45 70 75 674 30 24 46 66 63 703 29 29 47 63 52 732 28 34 48 59 41 761 26 40 49 55 30 790 25 45 50 8. 508 6251 8.509 3719 1.03819 2. 3323 6.6050 51 48 8. 509 3708 848 22 55 52 44 8. 509 3696 877 20 61 53 40 85 906 19 66 54 36 74 935 17 71 55 33 63 964 16 76 56 29 52 1.63993 15 81 57 25 40 1.64022 13 87 58 22 29 051 12 92 59 18 18 080 10 G. 6097 60 8. 508 6214 8. 50V 4607 1.64109 2.3309 6. 6102 7.627 256 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. -Geodetic position computations Continued. LATITUDE 60. Lat, log A diff. 1"=-0.06 logE diff. 1"=-0. logC iC diff. 1"=+0.49 logD diff. 1"=-0.0 log E log F 3 diff. 1"= +0.09 diff.lO'= -3.7 O 1 CO 00 8. 508 6214 8. 509 3607 1.64109 2.3309 6. 6102 7. 627 1 10 8.509 3596 138 07 08 2 07 85 167 06 13 3 8.508 6203 73 196 04 18 x 4 8. 508 6199 62 225 03 23 05 96 51 254 02 29 6 92 40 283 2.3300 34 7 88 29 312 2.3299 39 8 84 18 "841 97 44 9 81 8.509 3507 370 96 50 10 8. 508 6177 8.509 3495 1. 64400 2. 3294 6.6155 11 73 84 429 93 60 12 70 73 458 91 66 13 66 62 487 90 71 14 62 51 516 88 76 15 58 40 545 87 81 16 55 29 574 85 87 17 51 18 604 84 92 18 47 8. 509 3407 633 82 6. 6197 13 44 8. 509 3395 662 81 6. 6203 20 8. 508 6140 8.509 3384 1.64691 2. 3279 6.6208 7.620 21 36 73 720 78 13 22 33 62 750 76 18 23 29 51 779 75 24 24 25 40 808 73 29 25 21 29 838 72 34 26 18 18 867 70 40 27 14 8. 509 3307 896 69 45 28 10 8. 509 32% 925 67 50 29 07 85 955 66 56 30 8. 508 6103 8.509 3274 1.64984 2. 3264 6. 6261 31 8. 508 6099 63 1.65013 63 66 32 % 52 043 61 72 33 92 40 072 60 77 34 88 29 101 58 82 35 85 18 131 57 87 36 81 8. 509 3207 160 55 93 37 77 8. 509 3196 190 54 6. 6298 38 74 85 219 52 6. 6304 39 70 74 248 51 09 40 8.508 6066 8. 509 3163 1.65278 2.3249 6.6314 7.613 41 63 52 307 48 20 42 59 41 337 46 25 43 55 30 366 45 30 44 52 19 3% 43 36 45 48 8. 509 3108 425 41 41 46 44 8.509 3097 455 40 46 47 41 86 484 38 52 48 37 75 514 37 57 49 33 64 543 35 62 50 8. 508 6030 8.509 3053 1.65573 2. 3234 6.6368 51 26 42 602 32 73 52 22 31 632 31 79 53 19 20 661 29 84 54 15 8.509 3010 691 28 89 55 11 8.509 2999 721 26 6.6395 56 08 88 750 24 6.6400 57 04 77 780 23 05 58 8. 508 6000 66 809 21 11 59 8. 508 5997 . 55 839 20 16 60 8. 508 5993 8.509 2944 1.65869 2. 3218 C. 6422 . 7. 605 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued, LATITUDE 61. 257 Lat. log A diff.l"=-0.06 logB diff.l"=-0.18 logC diff.l"=+0.50 logD diff.l"=-0.03 logE diff.l"=+0.09 logF diff.lO'=-4.0 o / 61 00 8. 508 5993 8.509 2944 1.65869 2.3218 6.6422 7.605 1 89 33 898 17 27 2 86 22 928 15 32 3 82 11 958 13 38 4 79 5.509 2900 1. 65987 12 43 05 75 8.509 2889 1.66017 10 48 6 71 78 047 09 54 7 68 67 076 07 59 8 64 56 106 06 65 9 60 46 136 04 70 10 8. 508 5957 8. 509 2835 1.66166 2.3202 6. 6476 11 53 24 195 2. 3201 81 12 49 13 225 2. 3199 87 13 46 8. 509 2802 255 98 92 14 42 8. 509 2791 285 % 6. 6497 15 39 80 315 94 6. 6503 16 35 69 344 93 08 17 31 58 374 91 14 18 28 48 404 90 19 19 24 37 434 88 25 20 8. 508 5920 8.509 2726 1.66464 . 2. 3186 6. 6530 7.597 21 17 15 494 85 36 22 13 8.509 2704 524 83 41 23 10 8. 509 2693 553 81 46 24 06 83 583 80 52 25 8.508 5902 72 613 78 57 26 8.508 5899 61 643 77 63 27 95 50 673 75 68 28 92 39 703 73 74 29 88 28 733 72 79 30 8.508 5884 8. 509 2618 1.66763 2. 3170 6. 6585 31 81 8. 509 2607 793 68 90 32 77 8. 509 2696 823 67 6. 6596 33 74 85 853 65 6. 6601 34 70 74 883 64 07 35 66 64 913 S2 12 36 63 53 943 60 18 37 59 42 1.66973 58 23 38 56 31 1.67003 57 29 39 52 20 033 55 34 40 8.508 5848 8. 509 2510 1.67063 2. 3154 6. 6640 7.589 41 45 8. 509 2499 094 52 45 42 41 88 124 50 51 43 38 77 154 49 |6 44 34 67 184 47 62 45 30 56 214 45 67 46 27 45 244 44 73 47 23 34 274 42 78 48 20 24 305 40 84 49 16 1 335 39 89 50 8. 508 5813 8. 509 2402 1. 67365 2. 3137 6. 6695 51 09 8. 509 2391 395 35 6.6700 52 05 81 425 34 06 53 8.508 5802 70 456 32 12 54 8. 508 5798 59 486 30 17 55 95 49 516 29 23 56 91 38 547 27 28 57 88 27 577 25 34 '58 84 16 607 23 39 59 80 8. 509 2306 637 22 45 60 8.508 5777 8.5092295 1.07668 2. 3120 6.6750 7. 581 4606108 17 258 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 62. Lat. log A diff.l"=-0.06 logB diff. 1"= -0.18 logC d iff. 1"= +0.51 logD diff.l"=-0.03 logE diff. 1"= +0.09 logF diff. 10' = -4.2 o / ' 62 00 8. 508 5777 8. 509 2295 1. 67668 2. 3120 6.6750 7.581 1 73 84 698 18 56 2 70 74 728 17 61 3 66 63 759 15 67 4 63 52 789 13 73 05 59 42 820 12 78 6 55 31 850 10 84 7 52 20 880 08 89 8 48 8. 509 2210 911 06 6. 6795 9 45 8.509 2199 941 05 6.6801 10 8. 508 5741 8. 509 2188 1.67972 2.3103 6.6806 11 38 78 1.68002 01 12 12 34 67 033 2.3100 17 13 30 56 063 2.3098 23 14 27 46 094 96 29 15 24 35 124 94 34 16 20 25 155 93 40 17 16 14 185 91 45 18 13 8.509 2103 216 89 51 19 09 8. 509 2093 246 87 57 20 8.508 5706 8. 509 2082 1.68277 2. 3086 6. 662 7.573 21 8. 508 5702 71 307 84 68 22 8. 508 5699 61 338 82 73 23 95 50 369 80 79 24 92 40 399 79 85 25 88 29 430 77 90 26 85 19 461 75 6.6896 27 81 8. 509 2008 491 74 6.6902 28 78 8. 509 1997 522 72 07 29 74 87 553 - 70 13 30 8. 508 5671 8.509 1976 1,68583 2.3068 6. 6919 31 67 66 614 66 24 32 64 55 645 65 30 33 60 45 675 63 36 34 56 34 706 61 41 35 53 23 737 59 47 36 49 13 768 58 53 37 46 8.509 1902 799 56 58 38 42 8.509 1892 829 54 64 39 39 81 860 52 70 40 8. 508 5635 8.509 1871 1.68891 2.3050 6. 6975 7.564 41 32 60 922 49 81 42 28 50 953 47 87 43 25 39 1.68984 45 92 44 21 29 1. 69014 43 6. 6998 45 18 18 045 42 6.7004 46 14 8.509 1808 076 40 09 47 11 8. 509 1797 107 38 15 48 07 87 138 36 21 49 04 76 169 34 26 50 8. 508 5600 8.509 1766 1.69200 2. 3033 6. 7032 51 8. 508 5597 55 231 31 38 52 93 45 262 29 44 53 90 34 293 27 49 54 86 24 324 25 55 55 83 14 355 23 61 56 80 8.509 1703 386 22 67 57 76 8.509 1693 417 -20 72 58 73 82 448 18 78 59 69 72 479 16 84 60 8. 508 5566 8.509 1661 1.69510 2.3014 6. 7089 7.556 GEOGRAPHIC TABLES AND FORMULAS. TAHLE 23. Geodetic position computations Continued. LATITUDE 63. 259 Lat. log A diff.l"=-0.06 logB diff.l"=-0.17 logC diff.l"=+0.52 logD diff.l"=-0.03 logE diff.l"=+0.10 d logF iff. 10' = -4.5 o / 63 00 8.508 ;Vx;r> 8. 509 1661 1.69510 2. 3014 6. 7089 7.556 1 62 51 541 13 6. 7095 2 59 40 572 11 6. 7101 3 55 30 603 09 07 4 52 20 635 07 12 05 48 8. 509 1609 666 05 18 6 45 8. 509 1599 697 03 24 7 41 88 728 02 30 8 38 78 759 2.3000 35 9 34 68- 791 2. 2998 41 10 8.508 5531 8.509 1557 1.69822 2. 2996 6. 7147 11 27 47 853 94 53 12 24 36 884 92 59 13 20 26 915 90 64 14 17 16 947 89 70 15 14 8.509 1505 1.69978 87 76 16 10 8.509 1495 1.70009 85 82 17 07 85 041 83 88 18 03 74 072 81 93 19 8.508 5500 64 103 79 6.7199 20 8. 508 5496 8. 509 1454 1.70135 2.2977 6. 7205 7.547 21 93 43 166 75 11 22 89 33 197 74 17 23 86 23 229 72 22 24 83 12 260 70 28 25 79 8.509 1402 292 68 34 26 76 8.509 1392 323 66 40 27 72 81 355 64 46 28 69 71 386 62 51 29 65 61 417 60 57 30 8. 508 5462 8. 509 1350 1.70449 2.2958 6. 7263 31 5* 40 480 57 69 32 55 30 512 55 75 33 52 19 544 53 81 34 48 8.509 1309 575 51 86 35 45 *. 509 1299 607 49 92 36 41 89 638 47 6. 7298 37 38 78 670 45 6. 7304 38 34 68 701 43 10 39 31 58 733 41 16 40 8.508 5428 8. 509 1248 1.70765 2. 2939 6. 7322 7. 538 41 24 37 796 37 28 42 21 27 828 36 33 43 17 17 860 .34 39 44 14 8.509 1207 891 32 45 45 11 8.509 1196 923 30 51 46 07 86 955 28 57 47 04 76 1.70986 26 63 48 8. 508 5400 66 1.71018 24 69 49 8. 508 5397 55 050 22 75 50 8. 508 5394 8.509 1145 1. 71082 2. 2920 6.7381 51 90 35 114 18 86 52 87 25 145 16 92 53 83 15 177 14 6. 7398 54. 80 8.509 1104 209 12 6.7404 55 77 8. ,509 1094 241 10 10 56 73 84 273 08 16 57 70 74 305 06 - 22 58 66 64 337 04 28 59 n 54 368 02 34 60 8. 508 5360 8.509 1043 1.71400 2.2901 6. 7440 7.529 260 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 64. Lat. log A diff. 1"=-0.06 logB diff. l"= -0.17 log C diff. 1"= +0.54 logD diff. 1"= -0.03 diff. log E 1"=+0.10 diff. log F 10' = -4.7 / 64 00 8. 508 5360 8.509 1043 1.71400 2. 2901 6. 7440 7. 529 1 56 33 432 2. 2899 46 2 53 23 464 - 97 52 '3 49 13 496 95 58 4 46 8.509 1003 528 93 63 05 43 8. 509 0993 560 91 69 6 39 82 592 89 75 7 36 72 624 87 81 8 33 62 656 85 87 9 29 52 688 83 93 10 8. 508 5326 8.509 0942 1.71720 2. 2881 6. 7499 11 22 32 752 79 6. 7505 12 19 22 785 77 11 13 16 12 817 75 17 14 12 8.509 0902 849 73 23 15 09 8. 509 0891 881 71 29 16 06 81 913 69 35 17 8.508 5302 71 945 67 41 18 8. 508 5299 61 1.71977 65 47 19 96 51 1. 72010 63 53 20 8. 508 5292 8. 509 0841 1. 72042 '2. 2861 6. 7559 7. 520 21 89 31 074 59 65 22 85 21 106 57 71 28 82 11 139 55 77 24 79 8.509 0801 171 53 83 25 75 8. 509 0791 203 51 89 26 72 81 235 49 6. 7595 27 69 71 268 47 6. 7601 28 65 61 300 45 07 29 62 51 332 42 13 30 8. 508 5259 8. 509 0741 1. 72365 2. 2840 6. 7619 31 55 31 397 38 25 32 52 21 430 36 31 33 49 11 462 34 37 34 45 8.509 0701 495 32 43 35 42 8. 509 0691 527 30 49 36 39 81 559 28 56 37 35 71 592 26 62 38 32 61 624 24 68 39 29 51 657 22 74 40 8. 508 5225 8.509 0641 1.72689 2. 2820 6. 7680 7.511 41 22 31 722 18 86 42 19 21 755 16 92 43 15 11 787 14 6. 7698 44 12 8.509 0601 820 12 6. 7704 45 09 8.509 0591 852 10 10 46 05 81 885 07 16 47 8. 508 5202 71 918 05 22 48 8. 508 5199 61. 950 03 28 49 95 51 1.72983 2.2801 35 50 8.508 5192 8. 509 0541 1.73016 2. 2799 6. 7741 51 89 31 048 97 47 52 86 21 081 95 53 53 82 11 114 93 59 54 79 8. 509 0501 146 91 65 55 76 8. 509 0491 179 89 71 56 72 82 212 87 77 57 . 69 72 245 84 84 58 66 62 278 82 90 59 62 52 310 80 6.7796 60 8.5085159 8.509 0442 1.73343 2. 2778 6. 7802 7.501 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 65. 261 Lat. log A logB diff.l"=-0.16 logC diff.l"=+0.56 logD diff.l" 0.04 logE diff.l"=+0.10 logP diff.lO' = -5.0 o / 65 00 8. 508 5159 8.509 0442 1.73343 12. 277S 6. 7802 7.501 1 56 32 376 76 08 2 52 22 409 74 14 3 49 12 442 72 20 4 46 8.509 0402 475 70 27 05 43 8. 509 0393 508 68 33 6 39 83 541 65 39 7 36 73 574 63 45 8 33 63 607 61 51 9 30 53 640 59 57 10 8. 508 5126 8.5090344 1. 73673 2. 2757 6.7864 11 23 34 706 55 70 12 20 24 739 53 76 13 17 14 772 50 82 14 13 8.509 0304 805 48 88 15 10 8. 509 0295 838 46 6. 7895 16 07 85 871 44 6.7901 17 03 75 - 904 42 07 18 8. 508 5100 65 937 40 13 19 8. 508 5097 55 1. 73970 38 19 20 8.508 5094 8.509 0245 1.74004 2. 2735 6.7926 7.491 21 90 36 037 33 32 22 87 26 070 31 38 23 84 16 103 29 44 24 81 8.5090206 136 27 51 25 77 8. 509 0197 170 24 57 26 74 87 203 22 63 27 71 77 236 20 69 28 68 67 270 . 18 76 29 64 57 303 16 82 30 8.508 5061 8.5090148 1. 74336 2. 2714 6. 7988 31 58 38 370 11 6.7994 32 54 28 403 09 6.8001 33 51 18 436 07 07 34 48 8.509 0109 470 or> 13 35 45 8.5090099 503 03 19 36 41 89 537 2.2700 26 37 38 80 570 2. 2698 32 38 35 70 604 96 38 39 32 60 637 94 44 40 8.508 5029 8. 509 0051 1.74670 2.2692 6. 8051 7.481 41 25 41 704 89 57 42 22 31 738 87 63 43 19 22 771 85 70 44 16 12 805 83 76 45 13 8.509 0002 838 80 82 46 09 '8. 508 9993 872 78 89 47 06 83 906 76 6.8095 48 03 73 939 74 6.8101 49 8.5085000 64 1.74973 72 07 50 8.508 49% 8. 508 9954 1.75007 2. 2669 6. 8114 51 93 44 040 67 20 52 90 35 074 65 27 63 87 , 25 108 63 33 54 84 15 142 60 39 55 80 8.508 9906 175 68 46 56 77 8. 508 98% 209 56 52 57 74 87 243 53 58 58 71 77 277 51 65 59 t;s 67 311 49 71 60 8.508 4964 8.5089858 1.75344 2.2647 6. 8177 7.471 262 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 66. Lat. log A diff.l"=-0.05 logB diff.l"=-0.16 logC diff.l"=+0.57 logD diff.l"=-0.04 log E log F diff.l"=+0.11 diff. 10'=-5.3 o / 66 00 8. 508 4964 8. 508 9858 1.75344 2. 2647 6.8177 7.471 61 48 378 44 84 2 58 39 412 42 90 3 55 29 446 40 6. 8196 4 52 20 480 38 6. 8203 05 48 10 514 35 09 6 45 8. 508 9801 548 33 16 7 42 8. 508 9791 582 31 22 8 39 82 616 28 28 9 36 72 650 26 35 10 8.508 4933 8. 508 9762 1.75684 2. 2624 6. 8241 11 29 53 718 22 48 12 26 43 752 19 54 13 23 34 786 17 61 14 20 24 820 15 67 15 17 14 854 12 73 16 13 8.5089705 889 10 80 17 10 8. 508 9696 923 08 86 18 07 86 957 05 93 19 04 77 1. 75991 03 6.8299 20 8. 508 4901 8.508 9667 1.76025 2. 2601 6. 8306 7. 461 21 8. 508 4898 58 060 2. 2598 12 22 95 48 094 96 19 23 91 39 128 94 25 24 88 29 163 91 31 25 85 20 197 89 38 26 82 11 231 87 44 27 79 8. 508 9601 266 84 51 28 76 8. 508 9592 300 82 57 29 73 82 334 80 64 30 8. 508 4869 8. 508 9573 1.76369 2.2578 6.8370 31 66 63 403 75 77 32 63 54 438 73 83 33 60 44 472 70 90 34 57 35 507 68 6.8396 35 54 25 541 66 6.8403 36 50 16 576 63 09 37 47 8. 508 9507 610 61 16 38 44 8. 508 9497 645 59 22 39 41 88 679 56 29 40 8. 508 4838 8. 508 9478 1. 76714 2.2554 6. 8436 7. 450 41 35 69 749 51 42 42 32 60 783 49 49 43 29 51 818 47 55 44 26 41 853 44 62 45 22 32 887 42 68 46 19 23 922 39 75 47 16 13 957 37 81 48 13 8.508 9404 1. 76991 35 88 49 10 8. 508 9395 1. 77026 32 6. 8495 50 8. 508 4807 8.508 9385 1. 77061 2. 2530 6.8501 51 04 76 096 27 08 52 8.508 4801 66 131 25 14 53 8. 508 4797 57 166 28 21 54 94 48 200 ' 20 27 55 91 38 235 18 34 56 88 29 270 15 41 57 85 20 305 13 47 58 82 10 340 11 54 59 79 8. 508 9301 375 08 60 60 8.5084776 8.608 9292 1. 77410 2.2506 6.8667 7.440 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position compulations Continued. LATITUDE 67. 263 Lat. log A diff.l"=-0.05 logB diff.l"=-0.15 logC diff.l"=+OT59 logD diff.l"=-0.04 logE diff.l"=+0.11 logF diff.lO'=-5.6 / 67 00 8.508 4776 8. 508 9292 1. 77410 2.2506 6.8567 7.440 1 73 83 445 03 74 2 70 73 480 2.2501 80 3 66 64 515 2. 2498 87 4 63 55 550 96 6.8594 05 60 46 585 93 6.8600 6 57 36 620 91 07 7 54 27 656 89 14 8 51 18 691 86 20 9 48 8.508 9208 726 84 27 10 8.5084745 8.508 9199 1.77761 2.2481 6.8634 11 42 90 796 79 40 12 39 81 831 76 47 13 36 72 867 74 54 14 33 62 902 71 60 15 30 53 937 69 67 16 26 44 1.77973 66 74 17 23 35 1.78008 64 80 18 20 26 043 61 87 19 17 16 079 59 6.8694 20 8. 508 4714 8.508 9107 1.78114 2.2456 6.8700 7.429 21 11 8.508 9098 149 64 07 22 08 89 185 51 U 23 05 80 220 49 20 24 8. 508 4702 71 256 46 27 25 8. 508 4699 62 291 44 34 26 96 52 327 41 41 27 93 43 362 39 47 28 90 34 398 36 54 29 87 25 433 34 61 30 8.508 4684 8. 508 9016 1.78469 2.2431 6.8768 31 81 8.508 9007 505 29 74 32 78 8. 608 8998 540 26 81 33 75 88 576 24 88 34 72 79 612 21 6.8795 35 68 70 647 19 6.8802 36 65 61 683 16 08 37 62 52 719 14 15 38 59 43 756 11 22 39 56 34 790 09 29 * 40 8.5084653 8.508 8925 1.78826 2.?406 6.8835 7.418 41 50 16 862 J3 42 42 47 8. 508 8907 898 2.2401 49 43 44 8. 508 8898 934 2. 2398 56 44 41 89 1. 78970 96 63 45 38 80 1.79006 93 70 46 35 71 042 91 76 47 32 62 078 88 83 48 29 53 114 86 90 49 26 44 150 ' 83 6. 8897 50 8.508 4623 8.508 8834 1.79186 2.2380 6.8904 51 20 25 222 78 10 52 17 16 258 75 17 53 14 8.508 8807 294 73 24 54 11 8. 508 8798 330 70 31 55 08 89 366 67 38 56 05 80 402 65 45 57 8.508 4602 71 438 62 52 58 8.508 4599 62 474 60 59 59 96 54 511 57 65 60 8.508 4593 8. 508 8746 1.79547 2.2354 6. 8972 7.406 264 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 68. Lat. log A diff.l"=-0.05 logB diff.l" = -0.15 logC diff.l"=+0.62 logD difi.l"=-0.4 log E log F diff.l"=+0.12 diff.lO'=.--5.9 1 68 00 8. 508 4593 8. 508 8745 1. 79547 2.2354 6. 8972 7. 406 1 90 36 583 52 79 2 87 27 620 49 86 3 84 18 656 47 6. 8993 4 81 09 692 44 6.9000 05 78 8.508 8700 728 41 07 6 76 8. 508 8691 765 39 14 7 73 82 801 36 21 8 70 73 838 33 28 9 67 64 874 31 35 10 8. 508 4564 8. 508 8656 1. 79911 2.2328 6.9042 11 61 47 947 26 48 12 58 38 1. 79984 23 55 13 55 29 1.80020 20 62 14 52 20 057 18 69 15 49 11 093 15 76 16 46 8. 508 8602 130 12 83 17 43 8. 508 8593 166 10 90 18 40 84 203 07 6.9097 19 37 75 240 04 6. 9104 20 8. 508 4534 8.508 8566 1.80276 2.2302 6. 9111 7. 395 21 31 58 313 2.2299 18 22 28 49 350 96 25 23 25 40 387 94 32 24 22 31 423 91 39 25 19 22 460 88 46 26 16 13 497 86 53 27 13 8.508 8505 534 83 60 28 10 8.508 8496 571 80 67 29 07 87 608 77 74 30 8. 508 4504 8. 508 8478 1.80645 2.2275 6. 9181 31 8. 508 4501 69 682 72 88 32 8. 508 4499 60 719 69 6. 9195 33 96 52 756 67 6.9203 34 93 43 793 64 10 35 90 34 830 61 17 36 87 25 867 58 24 37 84 17 904 56 31 38 81 8.508 8408 941 53 38 39 78 8. 508 8399 1. 80978 50 45 7.383 40 8. 508 4475 8. 508 8390 1.81015 2.2248 6.9252 41 72 82 052 45 59 42 70 73 089 42 66 43 67 64 127 39 73 44 64 56 164 36 80 45 61 47 201 34 88 46 58 38 239 31 6. 9295 47 55 30 276 28 6.9302 48 52 21 313 26 09 49 49 12 350 23 16 50 8. 508 4446 8. 508 8303 1.81388 2.2220 6.9323 51 43 8. 508 8295 425 17 30 52 40 86 463 14 37 53 38 77 500 12 45 54 35 68 538 09 52 55 32 60 575 06 69 56 29 51 613 03 66 57 26 43 650 2.2201 73 58 23 34 688 2. 2198 80 59 20 25 726 95 88 60 8. 508 4417 8. 508 8217 1.81763 2. 2192 6.9395 7.371 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 69. 265 Lat. log A diff. 1"=-0.05 log B diff. 1"=-0.14 logC diff. 1"= +0.64 log D diff. 1"= -0.05 logE diff. 1"= +0.12 log F diff. 10' =-6.2 / 69 00 8. 508 4417 8. 508 8217 1.81763 2.2192 6. 9395 7.371 .1 14 08 801 89 6.9402 2 12 8.508 8200 838 87 09 3 09 8. 508 8191 876 84 16 4 06 82 914 81 . 24 05 03 74 952 78 31 6 8. 508 4400 65 1.81989 75 38 7 8. 508 4397 57 1.82027 72 45 8 94 48 065 70 52 9 92 39 103 67 60 10 8.508 4389 8. 508 8131 1. 82141 2.2164 6. 9467 11 86 22 179 61 74 12 83 14 217 58 82 13 80 8. 508 8105 255 55 89 14 77 8.508 8096 293 53 6.9496 15 74 88 330 50 6.9503 16 71 79 369 47 11 17 69 71 407 44 18 18 66 62 445 41 25 19 63 54 483 38 32 20 8.508 436J3 8.508 8045 1.82521 2. 2136 6.9540 7.358 21 57 37 559 33 47 22 55 28 597 3D 54 23 52 20 636 27 62 24 49 11 674 24 69 25 46 8.5088003 712 21 76 26 43 8.508 7994 750 18 84 ' 27 40 86 789 15 91 28 37 77 827 12 6. 9598 29 35 69 865 10 6.9606 30 8.5084332 8.508 7960 1.82904 2. 2107 6. 9613 31 29 52 942 04 20 32 26 43 1.82981 2. 2101 28 33 23 35 1.83019 2. 2098 35 34 21 26 058 95 42 35 18 18 096 92 50 36 15 09 135 89 57 37 12 8.508 7901 173 86 65 38 09 8. 508 7893 212 83 72 39 06 84 250 80 79 40 8. 508 4304 X. 508 7876 1.83289 2.2078 6.9687 7.346 41 8. 508 4301 67 328 75 6. 9694 42 8.508 4298 59 366 72 6.9702 43 95 51 405 69 09 44 93 42 444 66 16 45 90 34 483 63 24 46 f 87 26 521 60 31 47 84 17 560 57 39 48 81 09 599 54 46 49 79 8. 508 7801 638 51 54 50 8.508 4276 8.508 7792 1.83677 2.2048 6.9761 51 73 84 716 45 69 52 70 75 755 42 76 53 67 67 794 39 84 54 65 59 833 36 91 55 62 50 872 33 6. 9799 56 59 - 42 911 30 6. 9806 57 M 34 950 27 14 58 54 25 1. 83989 24 21 59 51 17 1.84028 21 29 00 8. 508 4248 8.508 7709 1.84068 2.2018 6.9836 7.333 266 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 70. Lat. log A diff. 1"= -0.04 logB diff. 1"=-0.14 logC diff. 1"= +0.67 logD diff. 1"= -0.05 logE diff. 1"= +0.13 logF diff.lO'=-6.7 o / 70 00 8. 508 4248 8. 508 7709 1.84068 2. 2018 6. 9836 7.333 1 45 8.508 7701 107 15 44 2 43 8.508 7692 146 12 51 3 40 84 185 09 59 4 37 76 225 06 66 05 34 68 264 03 74 6 32 59 303 2.2000- 81 7 29 51 343 2. 1997 89 8 26 43 382 94 6. 9896 9 23 35 421 91 6.9904 10 8. 508 4221 8.508 7626 1. 84461 2.1988 6. 9912 11 18 18 500 85 19 12 15 10 540 82 27 13 12 8.508 7602 579 79 34 14 10 8. 508 7594 619 76 42 15 07 86 658 73 50 16 04 78 698 70 57 17 8. 508 4201 69 738 66 65 18 8. 508 4199 61 778 63 73 19 96 52 817 60 80 20 8. 508 4193 8. 508 7544 1.84857 . 2. 1957 6.9988 7.320 21 90 36 897 54 6. 9995 22 88 ' 28 937 51 7.0003 23 85 20 1.84976 48 11 24 82 12 1.85016 45 18 25 80 8. 508 7504 056 42 26 26 77 8.508 7495 096 39 34 27 74 87 136 36 41 28 71 79 176 33 49 29 69 71 216 29 57 30 8. 508 4166 8.508 7462 1.85256 2. 1926 7.0064 31 63 54 296 23 72 32 60 46 336 20 80 33 58 38 376 17 88 34 , 55 80 416 14 7.0095 35 52 22 456 11 7. 0103 36 50 14 497 08 11 37 47 8.508 7406 537 04 19 38 44 8. 508 7398 577 2.1901 26 39 42 90 618 2. 1898 . 34 40 8. 508 4139 8. 508 7382 1.85658 2. 1895 7. 0142 7.307 41 36 74 698 92 50 42 34 66 739 89 57 43 31 58 779 85 65 44 28 50 819 82 73 45 26 42 860 79 81 46 23 34 900 76 88 47 20 26 941 73 7. 0196 48 18 18 1. 85981 70 7.0204 49 15 10 1.86022 66 12 50 8.508 4112 8. 508 7302 1.86063 2.1863 7.0220 51 10 8. 508 7294 103 60 27 52 07 8& 144 57 35 53 04 77 185 54 43 . 54 8.508 4101 69 225 50 51 55 8. 508 4099 61 266 47 59 56 96 53 307 44 67 57 93 45 348 41 75 58 91 38 389 38 82 59 88 30 430 34 90 60 8.508 4086 8. 508 7222 1. 86470 . 2. 1831 7.0298 7.293 GEOGRAPHIC TABLES AND FORMULAS. TABLE 23. Geodetic position computations Continued. LATITUDE 71. 267 Lat. log A diff.l" = -0.04 logB diff.l"=-0.13 logC diff.l"=+0.70 logD diff.l"=-0.05 logE diff.l"=+0.13 logF diff.lO"=-7.2 O 1. 71 00 8.5084086 8. 508 7222 1.86470 2.1831 7. 0298 7.293 1 83 14 511 28 7.0306 2 80 8.508 7206 552 25 14 3 78 8. 508 7198 593 21 22 4 75 90 634 18 30 05 72 82 675 15 38 6 70 74 717 12 46 7 67 66 758 08 54 8 64 58 799 05 62 * 9 62 50 840 2.1802 70 10 8. 508 4059 8. 508 7142 1.86881 2. 1799 7. 0378 11 57 34 923 95 85 12 54 27 1. 86964 92 7. 0393 13 51 19 1.87005 89 7.0401 14 49 11 046 86 09 15 46 8. 508 7103 088 82 17 16 43 8. 508 7095 129 79 25 17 41 87 171 76 33 18 38 79 212 72 41 19 36 72 254 69 49 20 8. 508 4033 8.508 7064 1.87295 2. 1766 7.0457 7.279 21 30 56 337 62 65 22 28 48 378 59 73 23 25 40 420 56 82 24 23 S3 462 52 90 25 20 25 503 49 7. 0498 26 17 17 545 46 7.0506 27 ' 15 09 587 42 14 28 12 8.508 7002 629 39 22 29 10 8.508 6994 671 36 30 30 8.508 4007 8.508 6986 1. 87712 2. 1732 7.0538 31 05 78 754 29 46 32 8.508 4002 71 796 26 54 33 8. 508 3999 63 838 22 62 34 97 55 880 19 70 35 94 47 922 16 79 36 92 40 1.87964 12 87 37 89 32 1.88006 09 7. 0595 38 86 24 049 06 7. 0603 39 84 16 091 2. 1702 11 40 8.508 3981 8.508 6908 1.88133 2.1699 7.0619 7.265 41 79 8. 508 6901 175 95 27 42 76 8. 508 6893 217 92 36 43 74 85 260 89 44 44 71 78 302 ' 85 52 45 68 70 344 82 60 46 66 62 387 78 68 47 63 55 429 75 77 48 61 47 472 72 85 49 58 40 514 68 7.0693 50 8.508 3956 8. 508 6832 1.88557 2. 1665 7. 0701 51 53 24 599 61 09 52 51 17 642 58 18 53 48 09 685 54 26 54 46 8.508 6802 727 51 34 55 43 8.508 6794 770 48 42 56 41 86 813 44 61 57 88 79 855 41 59 58 36 71 898 37 67 59 33 64 941 34 75 60 8. 508 3930 8. 508 6756 1.88984 2. 1630 7.0784 7.250 268 GEOGRAPHIC TABLES AND FORMULAS, Table of values of log sec % {Aq>). A

1,563 21.3 265 28.6 474 54 175.2 350.3 525 701 876 1, 051 1,226 ,401 1,576 21.4 267 28.8 480 55 176.7 353.4 530 707 883 1,060 1,237 ,414 1,590 21.5 270 29.0 487 56 178.2 356.5 535 713 891 1,069 1,248 ,426 1,604 21.6 272 29.2 494 57 179.8 359.5 539 719 899 1,079 1,258 ,438 1,618 21.7 275 29.4 501 58 181.3 362.6 544 725 907 1,088 1,269 ,450 1,632 21.8 277 29.6 507 59 182. 8 365.7 549 731 914 1,097 1,280 ,465 1,643 21.9 280 29.8 514 60 184.4 368.8 553 738 922 1,106 1,291 1,475 1,659 22.0 282 30.0 521 j a For all distances under 1.6 miles the correction may be taken as +5 feet. Height of instrument is assumed 4.5 feet. GEOGRAPHIC TABLES AND FORMULAS. 277 TABLE 27. For obtaining differences of altitude for any minute, etc. Continued. 1 2 3 * 5 6 7 8 9 Corrections for curva- ture, refraction, and height of instruments 184.4 368.8 553 738 922 1,106 1,291 1,475 ,659 1 185.9 371.8 558 744 930 1,116 1,301 1,487 ,673 Miles. Feet. M-tte*. Feet. 2 187.5 374.9 562 750 937 1,125 1,312 1,500 ,687 1.6 6 10.2 64 3 189.0 378 567 756 945 ,134 1,323 1,512 ,701 2.1 7 10.3 65 4 190.5 381.1 572 762 953 ,143 1,334 1,524 ,715 2.5 8 10.4 67 5 192.1 384.1 576 768 960 ,152 1,344 1,537 ,729 2.8 9 10.5 68 6 193.6 387.2 581 774 968 ,162 1,355 1,549 ,742 3.1 10 10.6 69 7 195.1 390.3 585 781 976 ,171 1,366 1,561 ,756 3.4 11 10.7 70 8 196.7 393.4 590 787 983 ,180 1,377 1,573 ,770 3.6 12 10.8 71 9 198.2 396.4 595 793 991 ,189 1,388 1,586 ,784 3.8 13 10.9 73 10 199.8 399.5 599 799 999 ,199 1,398 1,598 1,798 4.1 14 ii.o 74 11 201.3 402.6 604 805 1,006 ,208 1,409 1,610 1,812 4.3 15 11.1 75 12 202.8 405.7 609 811 1,014 ,217 1,420 1,623 1,826 4.5 16 11.2 77 13 204.4 408.8 613 818 1,022 ,226 1,431 1,635 1,839 4.7 17 11.3 78 14 205.9 411.8 618 824 1,030 ,235 1,441 1,647 1,853 4.,H 18 11.4 79 15 207.5 414.9 622 830 1,037 ,245 1,452 1,660 1,867 5.0 19 11. 5 80 16 209.0 418.0 627 836 1,045 ,254 1,463 1,672 1,881 5.2 20 11.6 82 17 210. 5 421.1 632 842 1,053 ,263 1,474 1,684 1,895 5.4 21 11.7 83 18 212.1 424.1 636 848 1,060 ,272 1,484 1,697 1,909 5.5 22 11.8 84 19 213.6 427.2 641 854 1,068 ,282 1, 495 1,709 1,932 5.7 23 11.9 86 20 215.1 430.3 645 861 1,076 ,291 1,506 1,721 1,936 5.8 24 12.0 87 21 216.7 650 867 1,083 ,300 1,517 1,733 1,950 6.0 25 12.1 89 22 218. 2 436.4 655 873 1,091 ,309 1,528 1,746 1,964 6.1 26 12.2 90 23 219.8 439.5 659 879 1,099 ,319 1,538 1,758 1,978 6.3 27 12.3 91 24 221.3 442.6 664 885 1,106 ,328 1,549 1,770 1, 992 6.4 28 12.4 93 25 222.8 ! 445.7 669 891 1,114 ,337 1,560 1,783 2,006 6.5 29 12.5 94 26 224.4 448.7 673 897 1,122 ,346 1,571 , 795 2, 019 8,7 30 12.6 96 27 225.9 451.8 678 904 1,130 , 355 1,581 ,807 2, 033 6.8 31 12.7 97 28 227.5 454.9 682 910 1, 137 ,365 1,592 ,820 2,047 6.9 32 12.8 99 29 229.0 458.0 687 916 1,145 ,374 1,603 ,832 2,061 7.0 33 12.9 100 30 230.5 461.1 692 922 1,153 ,383 1,614 ,844 2, 075 7.2 34 13.0 102 31 232.1 464.1 696 928 1,160 ,392 1,624 ,857 2,089 7.3 35 13.1 103 32 233.6 467.2 701 934 1,168 ,402 1,635 ,869 2, 102 7.4 90 13.2 105 33 235.1 470.3 705 941 1,176 ,411 1,646 ,881 2, 116 7.5 37 13.3 10(1 34 236.7 473.4 711 947 1,183 ,420 1,1 '.57 ,893 2,130 7.6 38 13.4 108 35 238.2 476.4 715 953 1,191 ,429 1,668 ,906 2, 144 7.8 39 13.5 109 36 239.8 479.5 719 959 1,199 ,439 1,678 ,918 2,158 7.9 40 13.6 111 37 241.3 482.6 724 965 1,207 , 448 1,689 ,930 2,172 8.0 41 13.7 112 38 242. 8 485.7 729 971 1,214 ,457 1,700 ,943 2,186 8.1 42 13.8 114 39 244.4 488.8 733 978 1, 222 ,466 1,711 ,955 2,199 8.2 43 13.9 115 40 245. 9 491.8 738 984 1 , 230 ,476 1,721 ,967 2,213 8.3 44 14.0 117 41 '_' 1 7 5 494.9 742 990 1,237 ,485 1,732 ,980 2,227 8.4 46 14.1 119 42 249.0 497.0 747 996 1,245 ,494 1.743 ,992 2, 241 8.5 46 14.2 120 48 250.5 501.1 752 1,002 1,253 .5(i:; ].75l 2,004 2,255 8.6 47 14.3 122 44 252. 1 504.2 756 ,008 1,260 ,612 1,765 2,017 2, 269 8.7 48 14.4 124 45 253. 6 507. 2 761 ,014 1,268 , 522 1,775 2,029 2,283 8.8 49 11.5 125 4fi 255. 2 510. 3 765 ,021 1 , 276 ,531 1,786 2,041 2,296 8.9 50 14.6 127 47 256.7 513. 4 770 ,027 1,283 ,540 1,797 2,054 2,310 9.0 51 11.7 129 48 258.2 516.5 775 ,033 1,291 ,549 1,808 2,066 2, 324 9.1 52 14.8 130 49 259. 8 519.5 779 ,039 1,299 ,559 1,818 2,078 2,338 9.2 53 14.9 132 50 261.3 522.6 784 ,045 1,307 ,568 1,829 2,091 2,352 9.3 54 15.0 134 51 262.9 525. 7 789 ,051 1,314 ,577 1,840 2,103 2,366 9.4 55 15.1 135 52 264.4 528. 8 793 ,058 1,322 ,586 1,851 2, 115 2,380 9.5 56 15.2 137 53 265.9 531.9 798 ,064 1,330 ,596 1,862 2, 127 2,393 9.6 58 15.3 139 54 267. 5 534. 9 802 ,070 1,337 ,605 1,872 2, 140 2, 407 9.7 59 15.4 141 55 269.0 538.0 807 ,076 1,345 ,614 1,883 2,152 2,421 9.8 60 15.5 142 56 270. 6 541.1 812 ,082 1,353 (i'*:'i 1,894 2,164 2,435 9.9 61 15.6 144 57 272. 1 544.2 816 ,088 1,360 ,633 1,905 2,177 2,449 10.0 52 15.7 146 58 273.6 547. 3 821 ,095 1,368 ,642 1,915 2,189 2, 463 10.1 63 15.8 148 275.2 550.3 826 ,101 1,376 , (151 1,926 2, 201 2,477 15.9 1.50 16,0 151 60 276.7 553.4 830 1,107 1,384 1,660 1,937 2,214 2,490 For all distances under 1.6 miles the correction may be taken as +5 feet. Height of instrument is assumed 4.5 feet. 278 GEOGRAPHIC TABLES AND FORMULAS. TABLE 27. For obtaining differences of altitude for any minute, etc. Continued. 3 1 2 3 4 5 6 7 8 9 Corrections for curva- ture, refraction, and height of instrument.** 276.7 553.4 830 1,107 1,384 1,660 1,937 2, 214 2,490 Miles. Feet. 1 278. 3 556.5 835 1,113 1,391 1,670 1,948 2,226 2, 504 10.1 63 2 279. 8 559.6 839 1,119 1, 399 1,679 1,959 2, 238 2,518 10.2 64 3 281.3 562.7 844 1, 125 1,407 1,688 1,969 2, 251 1,532 10.3 65 4 282.9 565.7 849 1,131 1,414 ,697 1,980 2,263 2,546 10.4 67 5 284.4 568.8 853 1,138 1,422 ,706 1,991 2,275 2,560 10.5 68 6 286.0 571.9 858 1,144 1,430 ,716 2,002 2, 288 2,574 10.6 69 7 237.5 575.0 862 1,150 1,437 ,725 2,012 2,300 2,587 10.7 70 8 289.0 578.1 867 1,156 1,445 ,734 2,023 2, 312 2,601 10.8 71 9 290.6 581.2 872 1, 162 1,453 ,743 2,034 2, 325 2,615 10.9 73 10 292.1, 584.2 876 1,168 1,461 1,753 2,045 2,337 2, 629 11.0 75 11 293.7 587 3 881 1,175 1,468 ,762 2, 056 2,349 2,643 11.2 77 12 295.2 590.4 886 1,181 1,576 ,771 2, 066 2,362 2,657 11.4 79 13 296.7 593.5 890 1,187 1,484 ,780 2,077 2,373 2,671 11.6 82 14 298.3 596.6 895 1,193 1,491 ,790 2,088 2,386 2,685 11.8 84 15 299.8 599.6 899 1,199 1,499 ,799 2,099 2,399 2,698 12.0 87 16 301.4 602.7 904 1,205 1,507 ,808 2,110 2,411 2, 712 12.2 90 17 302.9 605.8 909 1,212 1,515 ,817 2,120 2, 423 2,726 12.4 93 18 304.4 608.9 913 1, 218 1,522 ,827 2,131 2,436 2,740 12.6 96 19 306.0 612.0 918 1,224 1,530 ,836 2,142 2, 448 2,754 12.8 99 20 307.5 615.0 923 1,230 1,538 ,845 2,153 2,460 2,768 13.0 102 21 309.1 618.1 927 1,236 1,545 ,854 2,163 2, 473 2, 782 13.2 105 22 310.6 621.2 932 1,242 1,553 ,864 2,174 2,485 2,795 13.4 108 23 312.1 624. 3 936 1,249 1, 561 ,873 2,185 2,497 2,809 13.6 111 24 313.7 627.4 941 1,255 1,568 ,882 2,196 2,510 2,823 13.8 114 25 315. 2 930.5 946 1, 261 1,576 ,891 2,207 2, 522 2,837 14.0 117 26 316.8 633.5 950 1,267 1,584 ,901 2, 217 2,534 2,851 14.2 120 27 318.3 636.6 955 1,273 1,592 ,910 2, 228 2,547 2,865 14.4 124 28 319.9 639.7 960 1,279 1,599 ,919 2,240 2,559 2,879 14.6 127 29 321. 4 642.7 964 1,286 1,607 ,928 2,250 2,571 2,893 14.8 130 30 322.9 645.9 969 1,292 1,615 ,938 2,261 2,584 2,906 15.0 132 31 324. 5 649.0 973 1,298 1,622 ,947 2, 271 2,596 2,920 15.2 137 32 326.0 652. 978 1,304 1,630 ,956 2, 282 2, 608 2,934 15.4 141 33 327.6 655.1 983 1,310 1 , 63* ,965 2, 293 2,621 2,948 15.6 144 34 329.1 658. 2 987 1,316 1,646 ,975 2, 304 2,633 2, 962 15. 8 148 35 330.6 661.3 992 1,323 1,653 ,984 2, 315 2,645 2,976 16.0 151 36 332. 2 664.4 997 1,329 1,661 1,993 2, 325 2,658 2,990 16.2 153 37 333.7 667.5 1,001 1,335 1,669 2, 002 2,336 2,670 3,004 16.4 ; 159 38 335.3 670. 5 1,006 1,341 1,676 2,012 2,347 2,682 3,017 16.6 163 39 336.8 673.6 1,010 1,347 1 , 684 2, 021 2,358 2,695 3,031 16.8 167 40 338.4 676.7 1,015 1, 353 1,692 2,030 2,369 2,707 3,045 17.0 170 41 339.9 679.8 1,020 1,360 1,700 2, 039 2,379 2,719 3,059 17.2 174 42 341.4 682. 9 1,024 1,366 1,707 2,049 2,390 2, 732 3,073 17.4 178 43 343.0 686.0 1,029 1,372 1,715 2, 058 2, 401 2,744 3,087 17.6 182 44 344.5 689.1 1,034 1,378 1,723 2, 067 2,412 2,756 3,101 17.8 186 45 346.1 692.1 1,038 1,384 1,730 2, 076 2,422 2, 769 3,115 18.0 190 46 347.6 695.2 1,043 1,390 1,738 2, 086 2, 433 2,781 3, 129 18.2 195 47 349.2 698.3 1,047 1,397 1,746 2,095 2,444 2,793 3,142 18.4 199 48 350.7 701.4 ,052 1,403 1,753 2,104 2, 455 2,806 3,156 18.6 203 49 352. 2 704.5 ,057 1,409 1,761 2,113 2,466 2,818 3,170 18.8 207 50 353.8 707.6 ,061 1,415 1,769 2,123 2,476 2,830 3,184 19.0 212 51 355.3 710.7 ,066 1,421 1,777 2, 132 2,487 2,843 3,198 19.2 216 52 356.9 713.7 ,071 1,427 1,784 2, 141 2,498 2,855 3, 212 19.4 221 53 358.4 716.8 ,075 1,434 1,792 2,150 2,509 2, 867 3,226 19.6 225 54 360.0 719.9 1,080 1,440 1,800 2,160 2, 520 2,880 3,240 19.8 230 55 361.5 723. 1, 085 1,446 1,807 2,169 2,530 2, 892 3, 253 20.0 234 56 363.0 726. 1 1,089 1,452 1,815 2,178 2, 541 2,904 3,267 21.0 258 57 364.6 729.2 1,094 1,458 1,823 2, 188 2, 552 2, 917 3,281 22.0 282 58 366.1 732.3 1,098 1,465 1,831 2,197 2,563 2,929 3,295 23.0 308 59 367.7 735.3 1,103 1,471 1,838 2, 206 2,574 2,941 3,309 24.0 335 60 369.2 738.4 1,108 1,477 1,846 2,215 2,584 2,954 3,323 25.0 363 a For all distances under 1.6 miles the correction may be taken as +5 feet. Height of instrument is assumed 4.5 feet. GEOGEAPHIC TABLES AND FORMULAS. 279 TABLE 27. For obtaining differences of altitude for any minute, etc. Continued. Corrections for curva- ture, refraction, and height of instrument." 369.2 738 1,108 1,477 1,846 2,215 2,584 2,954 3,323 1 370.8 742 1,112 1,483 1,854 2,225 2,595 2,966 3,337 Miles. Feet. Miles Feet. 2 372.3 745 1,117 1,489 1,862 2,234 2,606 2,978 3,351 1.6 6 10.2 64 3 373.8 748 1,122 1,495 1,869 2,243 2,617 2,991 3, 365 2.1 7 10.3 65 4 375.4 751 1,126 1,502 1,877 2, 252 2,628 3,003 3,378 2.5 8 10.4 67 5 376.9 754 1,131 1,508 1,885 2,262 2,639 3,015 3,392 2.8 9 10.5 68 6 378.5 757 1,135 1,514 1,892 2,271 2,649 3, 028 3,406 3.1 10 10.6 69 7 380.0 760 1,140 1,520 1,900 2,280 2,660 3,040 3,420 3.4 11 10.7 70 8 381.6 763 1,145 1,526 1,908 2,289 2,671 3,053 3,434 3.6 12 10.8 71 9 383.1 766 1,149 1,532 1,916 2,299 2,682 3,065 3,448 3.8 13 10.9 73 10 384.7 769 1,154 1,539 1,923 2,308 2, 693 3,077 3,462 4.1 14 11.0 74 11 386.2 772 1,159 1,545 1,931 2,317 2,703 3,090 3,476 4.3 15 11.1 75 12 387.7 775 1,163 1,551 1,939 2,326 2,714 3,102 3,490 4.5 16 11.2 77 13 389.3 779 1,168 1,557 1,946 2,336 2,725 3,114 3,504 4.7 17 11.3 78 14 390.8 782 1,172 1,563 1,954 2,345 2,736 3,127 3,517 4.8 18 11.4 79 15 392.4 785 1,177 1,569 1,962 2,354 2,747 3,139 3,531 5.0 19 11.5 80 16 393.9 788 1,182 1,576 1,970 2,363 2,757 3,151 3,545 5.2 20 11.6 82 17 395.5 791 1,186 1,582 1,977 2,373 2,768 3,164 3, 559 5.4 21 11.7 83 18 397.0 794 1,191 1,588 1,985 2,382 2,779 3,176 3,573 5.5 22 11.8 84 19 398.6 797 1,196 1,594 1,993 2,391 2,790 3,188 3,587 5.7 23 11.9 86 20 400.1 800 1,200 1,600 2,000 2,401 2,801 3,201 3,601 5.8 24 12.0 87 21 401.6 S03 1,205 1,607 2,008 2, 410 2,811 3,213 3,615 6.0 25 12.1 89 22 403.2 806 1,210 1,613 2,016 2,419 2,822 3,225 3,629 6.1 26 12.2 90 23 404. 7 809 1,214 1,619 2,024 2, 428 2, 833 3,238 3,643 6.3 27 12.3 91 24 406. 3 813 1,219 1,625 2,031 2,438 2,844 3,250 3,656 6.4 28 12.4 93 J.~> 407. 8 816 1,223 1,631 2,039 2,447 2,855 3,263 3, 670 6.5 29 12.5 94 20 409.4 819 1,228 1,637 2,047 2,456 2,866 3,275 3,684 6.7 30 12.6 96 27 410.9 822 1,233 : 1,644 2,055 2,465 2,876 3,287 3,698 6.8 31 12.7 97 28 412.5 825 1,237 1,650 2,062 2,475 2,887 3,300 3,712 6.9 32 12.8 99 29 414.0 828 1,242 1,656 2,070 2,484 2,898 3,312 3,726 7.0 33 12.9 100 30 415.5 831 1,247 1,662 2,078 2,493 2,909 3,324 3,740 7.2 34 13.0 102 31 417.1 834 1,251 1,668 2,085 2,503 2,920 3,337 3,754 7.3 35 13.1 103 32 418. 6 837 1,256 \ 1,675 2,093 2,512 2,930 3,349 3,768 7.4 36 13.2 105 33 420. 2 840 1,261 1,681 2,101 2,521 2,941 3,361 3,782 7.5 37 13.3 106 : 421.7 843 1,265 1,687 2,109 2, 530 2, 952 3,374 3,796 7.6 38 13.4 108 35 423. 3 847 1,270 1,693 2,116 2,540 2,963 3,386 3,809 7.8 39 13.5 109 36 424. 8 850 1,274 1,699 2,124 2,549 2,974 3,399 3,823 7.9 40 13.6 111 ::7 426.4 853 1,279 1,705 2,132 2,558 2,985 3,411 3,837 8.0 41 13.7 112 38 427. 9 856 1,284 1,712 2,140 2,567 2,995 3, 423 3,851 8.1 42 13.8 114 39 429.5 859 1,288 1,718 2,147 2,577 3,006 3,436 3,865 8.2 43 13.9 115 40 431.0 862 1,293 1,724 2,155 2.586 3,017 3,448 3,879 8.3 44 14.0 117 t: 432.5 865 1,298 1,730 2,163 2,595 3,028 3,460 3.S93 8.4 45 14.1 119 4'2 434. 1 ' 868 1,302 1,736 2, 170 2, 605 3,039 3,473 3,907 8.5 46 14.2 120 43 435. 6 871 1,307 1,743 2,178 2, 614 3,049 3, 485 3,921 8.6 47 14.3 122 44 437. 2 874 1,312 1,749 2,186 2,623 3,060 3,498 3, 935 8.7 48 14.4 124 45 438. 7 877 1,316 1,755 2,194 2,632 3,071 3,510 3,949 8.8 49 14.5 125 46 440. 3 881 1,321 1,761 2,201 2,642 3,082 3,522 3,963 8.9 50 14.6 127 47 441.8 884 1,325 1,767 2,209 2,651 3,093 3,535 3,976 9.0 51 14.7 129 48 443. 4 887 1,330 1,773 2,217 2,660 3,104 3,547 3,990 9.1 52 14.8 130 491 444.9 890 1,335 1,780 2,225 2,669 3,113 3,558 4,003 9.2 53 14.9 132 50 446.5 893 1,339 1,786 2,232 2,679 3,125 3,572 4,018 9.3 54 15.0 134 51 448.0 896 1,344 1,792 2, 240 2,688 3,136 3,584 4,032 9.4 55 15.1 135 52 449. 6 899 1,349 1,798 2,248 2,697 3,147 3,596 4,046 9.5 56 15.2 137 68 451.1 902 1,353 1,804 2,256 2,707 3,158 3,609 4,060 9.6 58 15.3 139 54 452. 7 905 1,358 1,811 2, 263 2,716 3,169 3,621 4,074 9.7 59 15.4 141 55 454.2 908 1,363 1,817 2,271 2, 725 3,179 3,634 4,088 9.8 60 15.5 142 56 455.8 912 1,367 1,823 2,279 2,735 3,190 3,646 4,102 9.9 61 15.6 144 57 457. 3 915 1,372 1,829 2,286 2,744 3,201 3,658 4,116 10.0 62 15.7 146 58 i 458.8 918 1,377 1/835 2,294 2,753 3,212 3,671 4,130 10.1 63 15.8 148 69 460.4 921 1,381 1,842 2, 302 2,762 3,223 3,683 4,144 15.9 150 16.0 151 60 461.9 924 1,386 1,848 2,310 2,772 3,234 3,6% 4,157 a For all distances under 1.6 miles the correction may be taken as + 6 feet. Height of instrument is assumed 4.5 feet. 280 GEOGRAPHIC TABLES AND FORMULAS. TABLE 27. For obtaining differences of altitude for any minute, etc. Continued. 5 1 2 3 4 5 6 7 8 9 Corrections for curva- ture, refraction, and height of instrument.a 461.9 924 1,386 1,848 2,310 2,772 3,234 3,696 4,157 1 463.5 927 1,390 1,854 2,317 2,781 3,244 3, 708 4,171 Miles. Feet. Miles: Feet. 2 465.0 930 1,395 1,860 2,325 2,790 3,255 3,720 4,185 1.6 6 10.2 64 3 466.6 933 1,400 1,866 2,333 2,800 3,266 3,733 4,199 2.1 7 10.3 65 4 468.1 936 1,405 1,873 2,341 2,809 3,277 3,745 4,213 2.5 8 10.4 67 5 469.7 939 1,409 1,879 2,348 2,818 3,288 3,757 4,227 2.8 9 10.5 68 6 471.2 942 1,414 1,885 2,356 2,827 3,299 3,770 4,241 3.1 10 10.6 69 7 472.8 946 1,419 1,891 2,364 2,837 3,309 3, 782 4,255 3.4 11 10.7 70 8 474.3 949 1,423 1,897 2,372 2, 846 3,320 3, 795 4,269 3.6 12 10.8 71 9 475.9 952 1,428 1,904 2,379 2,855 3,331 3,807 4,283 3.8 13 10.9 73 10 477.4 955 1,432 1,910 2,387 2,865 3,342 3, 819 4,297 4.1 14 11.0 74 11 479.0 958 1,437 1,916 2,395 2,874 3,353 3,832 4,311 4.3 15 11.1 75 12 480.5 961 1,442 1,922 2,403 2,883 3, 364 3,844 4,325 4.5 16 11.2 77 13 482.1 964 1,447 1,928 2,410 2,892 3,375 3,857 4,339 4.7 17 11.3 78 -14 483.6 967 1,451 1,935 2,418 2, 902 3,385 3,869 4,353 4.8 18 11.4 79 15 485.2 970 1,456 1,941 2,426 2,911 3,396 3,881 4,367 5.0 19 11.5 80 16 486.7 973 1,461 1,947 2,434 2, 920 3,407 3,894 4,381 5.2 20 11.6 82 17 488.3 976 1,465 1,953 2,441 2,930 3,418 3,906 4,394 5.4 21 11.7 83 18 489.8 980 1,470 1,959 2,449 2,939 3, 429 3,919 4,408 5.5 22 11.8 84 19 491.3 983 1,475 1,966 2,457 2,948 3,440 3,931 4,422 5.7 23 11.9 86 20 492.9 986 1,479 1,972 2,465 2,958 3,450 3,943 ,436 5.8 24 12.0 87 21 494.5 989 1,483 1,978 2, 472 2,967 3,461 3, 956 ,450 6.0 25 12.1 89 22 496.0 992 1,488 1,984 2, 480 2,976 3, 472 3,968 ,464 6.1 26 12.2 90 23 497.6 995 1,493 1,990 2,488 2,985 3,483 3,981 ,478 6.3 27 12.3 91 24 499.1 998 1,498 1,996 2,496 2,995 3, 494 3,993 ,492 6.4 28 12.4 93 25 500. 7 ,001 1,502 2,003 2,503 3,004 3, 505 4,005 ,506 6.5 29 12.5 94 26 502.2 ,004 1,507 2,009 2, 511 3,013 3,515 4,018 ,520 6.7 30 12.6 96 27 503.8 ,007 1,512 2,015 2,519 3,023 3, 526 4,030 4,534 6.8 31 12.7 97 28 505.3 ,010 1,516 2,021 2,527 3, 032 3,537 4,042 4,548 6.9 32 12.8 99 29 506.9 ,014 1,521 2,027 2,534 3,041 3,548 4,055 4,562 7.0 33 12.9 100 30 508.4 ,017 1,525 2,034 2,542 3,050 3,559 4,067 4,576 7.2 34 13.0 102 31 510.0 ,020 1,530 2,040 2, 550 3,060 3,570 4,080 4,590 7.3 35 13.1 103 32 511.5 ,023 1,535 2,046 2,558 3,069 3,581 4, 092 4,604 7.4 36 13.2 105 33 513.0 ,026 1,539 2,052 2,565 3,078 3,591 4,105 4,618 7.5 37 13.3 106 34 514.6 ,029 1,544 2, 058 2,573 3,088 3,602 4,117 4, 632 7.6 38 13.4 108 35 516.2 ,032 1,549 2,065 2,581 3,097 3,613 4,129 4,645 7.8 39 13.5 109 36 517.7 ,035 1,553 2,071 2, 589 3,106 3, 624 4,142 4,659 7.9 40 13.6 111 37 519.3 ,039 1,558 2,077 2,596 3,116 3,635 4,154 4,673 8.0 41 13.7 112 38 520.8 ,042 1,563 2,083 2,604 3,125 3,646 4,167 4,687 8.1 42 13.8 114 39 522. 4 ,045 1,568 2,089 2,612 3,134 3,657 4,179 4,701 8.2 43 13.9 115. 40 523.9 ,048 1,572 2,095 2,620 3,144 3,667 4,191 4,715 8.3 44 14.0 117 41 525.5 ,051 1,576 2, 102 2, 627 3,153 3,678 4, 204 4,729 8.4 45 14.1 i*e 42 527.0 ,054 1,581 2,108 2,635 3, 162 3,689 4, 216 4, 743 8.5 46 '14.2 120 43 528.6 ,057 1,586 2,114 2,643 3,172 3,700 4,229 4,757 8.6 47 14.3 122 44 530.1 ,060 1,591 2,121 2,651 3,181 3,711 4,241 4,771 8.7 48 14.4 124 45 531.7 ,063 1,595 2,127 2,658 3,190 3, 722 4,253 4,785 8.8 49 14.5 125 46 533.2 ,066 1,600 2,133 2,666 3,199 3,733 4, 266 4,799 8.9 50 14.6 127 47 534.8 ,070 1,605 2,139 2,674 3,209 3,743 4,278 4,813 9.0 51 14.7 129 48 536.3 ,073 1,609 2,145 2, 682 3,218 3,754 4,291 4,827 9.1 52 14.8 130 49 537.9 ,076 1,614 2,154 2,689 3,227 3,765 4,303 4,841 9.2 53 14.9 132 50 539.4 ,079 1,618 2,158 2,697 3,237 3,776 4,315 4,855 9.3 54 15.0 134 51 541.0 ,082 1,623 2, 166 2,705 3,246 3,787 4, 32S 4,869 9.4 55 15.1 135 52 542.5 ,085 1,628 2,170 2,713 3,255 3,798 4,340 4,883 9.5 56 15.2 137 53 544. 1 ,088 1,632 2,176 2,721 3,265 3,809 4,353 4,897 9.6 58 15.3 139 54 545.6 ,091 1,637 2,183 2,728 3,274 3,819 4,365 4,911 9.7 59 15.4 141 55 547.2 ,094 1,642 2,189 2,736 3,283 3,830 4,378 4,925 9.8 60 15.5 142 56 548.7 ,097 1,646 2,195 2,743 3,292 3,841 4,390 4,939 9.9 61 15.6 144 57 550.3 1,101 1,651 2,201 2,752 3, 302 3,852 4, 402 4,953 10.0 62 15.7 146 58 551.8 1,104 1,656 2,207 2,759 3,311 3,863 4, 415 4,967 10.1 63 15.8 148 59 553.4 1,107 1,661 2,214 2, 76.7 3,320 3,874 4,427 4,981 15.9 150 16.0 151 60 555. 1,110 1,665 2,220 2,775 3,330 3,885 4,440 4,995 a For all distances under 1.6 miles the correction may be taken as + 5 feet. Height of instrument is assumed 4.5 feet. GEOGRAPHIC TABLES AND FORMULAS. 281 TABLE 27. For obtaining differences of altitude for any minute, etc. Continued. 6 1 2 3 4 5 6 1 8 9 Corrections for curva- ture, refraction and height of instrument.** 555.0 1,110 1,665 2,220 2,775 3,330 3,885 4,440 4,995 1 556.5 1,113 1,670 2,226 2,783 3,339 3,896 4,452 5 009 Miles Feet. Miles. Feet. 2 558.1 1,116 1,674 2, 232 2,790 3,348 3,906 4,464 5,023 1.6 6 10.2 64 3 559.6 1,119 1,679 2,238 2, 798 3,358 3,917 4,477 5,037 2.1 7 10.3 65 4 561.2 1,122 1,684 2, 245 2,806 3,367 3, 928 4, 489 5,050 2.5 8 10.4 67 5 562.7 1,125 1,688 2,251 2,814 3,376 3,939 4, 502 5,064 2.8 9 10.5 68 6 564.3 1,129 1,693 2, 257 2,821 3,386 3,950 4,514 5,078 3.1 10 10.6 69 7 565.8 1,132 1,697 2, 263 2,829 3,395 3,961 4,527 5, 092 3.4 11 10.7 70 8 567.4 1,135 1,702 2, 270 2, 837 3,404 3, 972 4,539 5,106 3.6 12 10.8 71 9 568.9 1,138 1,707 2, 276 2,845 3,414 3, 983 4,551 5,120 3.8 13 10.9 73 10 570.5 1,141 1,711 2, 282 2,852 3,423 3,993 4,564 5, 134 4.1 14 11.0 74 11 572.0 1,144 1,716 2,288 2,860 3, 432 4,004 4,576 5,148 4.3 15 11.1 75 12 573.6 1,147 1,721 2,294 2,868 3,442 4,015 4,589 5,162 4.5 16 11. 2 77 13 575.2 1,150 1,725 2,301 2,876 3,451 4,026 4,601 5,176 4.7 17 11.3 78 14 576.7 1,153 1,730 2,307 2,884 3,460 4,037 4,614 5,190 4.8 18 11.4 79 15 578.3 1,157 1,7135 2,313 2, 891 3,470 4,048 4,626 5,204 5.0 19 11.5 80 16 579.8 1,160 1,739 2,319 2,899 3,479 4,059 4,639 5,218 5.2 20 11.6 82 17 581.4 1,163 1,744 2,325 2,907 3,488 4,070 4,651 5,232 5.4 21 11.7 83 18 582.9 1,166 1,749 2,332 2,915 3,498 4,080 4,663 5,246 5.5 22 11.8 84 19 584.5 1,169 1,753 2,338 2,922 3,507 4, 091 4,676 5,260 5.7 23 11.9 86 ! 20 586.0 1,172 1,758 2,344 2,930 3,516 4,102 4,688 5,274 5.8 24 12.0 87 21 587.6 1,175 1,763 2,350 2,938 3,526 4,113 4,701 5,288 6.0 25 12.1 89 22 589.1 1,178 1,767 2,357 2,946 3, 535 4,124 4,713 5,302 6.1 26 12.2 90 23 590.7 1,181 1,772 2,363 2, 953 3,544 4,135 4,726 5, 316 6.3 27 12.3 91 J! 592.2 1,185 1,777 2,369 2,961 3,554 4,146 4,738 5,330 6.4 28 12.4 93 25 593.8 1,188 1,781 2,375 2,969 3,563 4,157 4,750 5,344 6.5 29 12.5 94 26 595.4 1,191 1,786 2,381 2,977 3,572 4,168 4,763 5,358 6.7 30. 12.6 96 27 596.9 1,194 1,791 2,388 2,985 3,581 4,178 4,775 5, 372 6.8 31 12.7 97 28 598. 5 1,197 1,795 2,394 2,992 3,591 4,189 4,788 5,386 6.9 32 12.8 99 29 600.0 1,200 1,800 2,400 3,000 3,600 4,200 4,800 5,400 7.0 33 12.9 100 30 601.6 1,203 1,805 2,406 3,008 3,609 4,211 4,813 5, 414 7.2 34 13.0 102 31 603.1 1,206 1,809 2,413 3,016 3,619 4,222 4,825 5,428 7.3 35 13.1 103 32 604.7 1,209 1,814 2,419 3,023 3, 628 4,233 4,838 5, 442 7.4 36 13.2 105 33 606.3 1,213 1,819 2, 425 3,031 3,637 4,244 4,850 5, 456 7.5 37 13.3 106 34 607.8 1,216 1,823 2,431 3,039 3,647 1,255 4,862 5,470 7.6 38 13.4 108 35 609.4 1,219 1,828 2,437 3,047 3,656 4, 266 4,875 5,484 7.8 39 13.5 109 36 ! 610.9 1,222 1,833 2,444 3, 055 3,666 4,276 4,887 5,498 7.9 40 13.6 111 37 612. 5 1,225 1,837 2,450 3,062 3,675 4,287 4,900 5,512 8.0 41 13.7 112 38 614. 1,228 J.8-I2 2,456 3,070 3,684 4,298 4,912 5,526 8.1 42 13.8 114 39 615. 5 1,231 1,847 2,462 3,078 3,694 4,309 4,925 5,540 8.2 43 13.9 115 40 617.2 1,234 1,851 2,469 3,086 3,703 4,320 4,937 5,554 8.3 44 14.0 117 41 618.7 1,237 1,856 2,475 3,094 3,712 4, 331 4,950 5,568 8.4 46 14.1 119 42 620.3 1,241 1,861 2,481 3,101 3,722 4,342 4, 962 5,582 8.5 46 14.2 120 43 621.8 1,244 1,865 2,487 3,109 3,731 4,353 4,975 5,596 8.6 47 14.3 122 44 623.4 1,247 1,870 2,494 3,117 3,740 4,364 4,987 5, 610 8.7 48 14.4 124 45 624.9 1,250 1,875 2,500 3, 125 3,750 4,374 4,999 5, 624 8.8 49 14.5 125 46 626.5 1,253 1,879 2,506 3,132 3,759 4, 385 5, 012 5,638 8.9 50 14.6 127 47 628.0 1,256 1,884 2, 512 3,140 3,768 4,396 5, 024 5,653 9.0 51 14.7 129 48 629.6 1,259 1,889 2,518 3,148 3,778 4,407 5,037 5,667 9.1 52 14.8 130 49 631.2 1,262 1,894 2, 525 3,156 3,787 4,418 5,049 5,681 9.2 53 14.9 132 50 632.7 1,265 1,898 2, 531 3,164 3,796 4,429 5,062 5,695 9.3 54 15.0 134 51 634.3 1 1,269 1,903 2, 537 3,171 3,806 4,440 5,074 5,709 9.4 55 15. 1 135 52 635.8 1,272 1,908 2,543 3,179 3,815 4,451 5,087 5,723 9.5 56 15.2 137 53 637.4 1,275 1,912 2,550 3,187 3,824 4,462 5,099 5,737 9.6 58 15.3 139 54 638.9 1,278 1,917 2, 556 3, 195 3,834 4,473 5,112 5,751 9.7 59 15.4 141 55 640.5 1,281 1,922 2,562 3,203 3,843 4,484 5,124 5.765 9.8 60 15.5 142 M 642.1 1,284 1,926 2,568 3,210 3,852 4,494 5, 136 5,779 9.9 61 15.6 144 57 643.6 1,287 1,931 2, 575 3,218 3,862 4,505 5,149 5,793 10.0 62 15.7 146 58 645. 2 1,290 1,936 2,581 3,226 3,871 4,516 5,161 5, 807 10.1 63 15.8 148 59 646.7 1,293 1,940 2,587 3,234 3,880 4, 527 5,174 5,821 15.9 150 16.0 151 60 648.3 1,297 1, 945 2, 59o 3,242 3,890 4,538 5,186 5,835 a For all distances under 1.6 miles the correction may be taken as + 5 feet. Height of instrument is assumed 4.6 feet. 282 GEOGRAPHIC TABLES AND FORMULAS. TABLE 27. For obtaining differences of altitude for any minute, etc. Continued. 7 1 2 3 4 6 7 8 9 Corrections for curva- ture, refraction and height of instrument.a 648.3 1,297 1,945 2, 593 3,242 3,890 4,538 5,186 5,835 1 649.9 1,300 1,950 2,599 3,249 3,899 4,549 5,199 5,849 Miles. Feet. Miles. Feet. 2 651.4 ,303 1,954 2,606 3,257 3,909 4,560 5,211 5, 863 1.6 6 10.2 64 3 653.0 ,306 1,959 2, 612 3,265 3,918 4,571 5, 224 5, 877 2.1 7 10.3 65 4 654.5 ,309 1,964 2,618 3,273 3, 927 4,582 5,236 5,891 2.5 8 10.4 67 5 656.1 ,312 1,968 2,624 3,281 3,937 4,593 5, 249 5,905 2.8 9 10.5 68 6 657.7 ,315 1,973 2,631 3,288 3,946 4,604 5, 261 5,919 3.1 10 10.6 69 7 659. 2 ,318 1,978 2,637 3,296 3, 955 4,615 5,274 5, 933 3.4 11 10.7 70 8 660.8 1,322 1,982 2, 643 3,304 3,965 4,626 5,286 5, 947 3.6 12 10.8 71 9 662.4 1,325 1,987 2,649 3,312 3,974 4,636 5, 299 5,961 3.8 13 10.9 73 10 663.9 1,328 1,992 2,656 3,320 3,983 4,647 5,311 5,975 4.1 14 11.0 74 11 665.5 1,331 1,996 2,662 3, 327 3,993 4,658 5, 324 5, 989 4.3 15 11.1 75 12 667.0 1.334 2,001 2,668 3,335 4,002 4,669 5,336 6,003 4.5 16 11.2 77 13 668.6 1,337 2,006 2, 674 3, 343 4,012 4,680 5,349 6,017 4.7 17 11.3 78 14 670.2 1,340 2, 010 2,681 3,351 4,021 4,691 5,361 6,031 4.8 18 11.4 79 15 671.7 1,343 2,015 2,687 3, 359 4,030 4, 702 5,374 6,045 5.0 19 11.5 80 16 673.3 1,347 2,020 2,693 3,366 4,040 4,713 5,386 6,060 5.2 20 11.6 82 17 674.8 1,350 2,025 2,699 3,374 4,049 4,724 5,399 6,074 ' 5.4 21 11.7 83 18 676.4 J,353 2,029 2,706 3,382 4,058 4,735 5,411 6,088 5.5 22 11.8 84 19 678.0 1,356 2,034 2,712 3,390 4,068 4,746 5,424 6,102 5.7 23 11.9 86 20 679.5 1,359 2,039 2,718 3,398 ,077 4,757 5,436 6,116 5.8 24 12.0 87 21 681.1 1,362 2,043 2,724 3, 405 ,087 4,768 5, 449 6,130 6.0 25 12.1 89 22 682.6 1,365 2,048 2,731 3,413 ,096 4,779 5,461 6,144 6.1 26 12.2 90 23 684.2 1, 368 2,053 2, 737 3,421 ,105 4,789 5,474 6,158 6.3 27 12.3 91 24 685.8 1,372 2, 057 2,743 3, 429 ,115 4,800 5,486 6,172 6.4 28 12.4 93 25 687.3 1,375 2,062 2, 749 3,437 ,124 4,811 5,499 6,186 6.5 29 12.5 94 26 688.9 1,378 2, 067 2,756 3,444 4,133 4,822 5,511 6, 200 6.7 30 12.6 96 27 690.5 1,381 2, 071 2, 762 3,452 4,143 4,833 5, 524 6,214 6.8 31 12.7 97 28 692.0 1,384 2,076 2,768 3,460 4,152 4,844 5,536 6,228 6.9 32 12.8 99 29 693. 6 1,387 2,081 2,774 3,468 4,161 4,855 5,549 6,242 7.0 33 12.9 100 30 695.1 1,390 2, 085 2,781 3,476 4,171 4,866 5,561 6, 256 7.2 34 13.0 102 31 696.7 1,393 2,090 2,787 3,483 4,180 4,877 5, 574 6, 270 7.3 35 13.1 103 32 698.3 ,396 2, 095 2,793 3,491 4,190 4,888 5, 586 6, 284 7.4 36 13.2 105 33 699.8 ,400 2,099 2,799 3, 499 4,199 4,899 5, 599 6,298 7.5 37 13.3 106 34 701.4 ,403 2, 104 2,806 3,507 4,208 4,910 5, 611 6, 312 7.6 38 13.4 108 35 702.9 ,406 2, 109 2,812 3,515 4, 218 4,921 5,624 6, 327 7.8 39 13.5 109 36 704.5 ,409 2,114 2,818 3,523 4, 227 4,932 5,636 6,341 7.9 40 13.6 111 37 706.1 ,412 2,118 2,824 3,530 4,236 4,943 5,649 6, 355 8.0 41 13.7 112 38 707.6 ,415 2, 123 2,831 3,538 4,246 4,953 5,661 6,369 8.1 42 13.8 114 39 709.2 ,418 2,128 2,837 3,546 4,255 4,964 5,674 6,383 8.2 43 13.9 115 40 710.8 ,422 2, 132 2,843 3,554 4,265 4,975 5,686 6,397 8.3 44 14.0 117 41 712.3 ,425 2,137 2,849 3,562 4, 274 4,986 5,699 6,411 8.4 45 14.1 119 42 713.9 ,428 2,142 2,856 3,569 4, 283 4,997 5,711 6,425 8.5 46 14.2 120 43 715. 5 ,431 2,146 2,862 3, 577 4, 293 5, 008 5, 724 6,439 8.6 47 14.3 122 44 717.0 ,434 2, 151 2,868 3, 585 4,302 5,019 5,736 6,453 8.7 48 14.4 124 45 718.6 ,437 2,156 2, 874 3,593 4,312 5,030 5,749 6,467 8.8 49 14.5 125 46 720. 2 ,440 2,160 2,881 3,601 4,321 5,041 5, 761 6,481 8.9 50 14.6 127 47 721.7 ,443 2, 165 2,887 3,609 4,330 5, 052 5, 774 6, 495 9.0 51 14.7 129 48 723.3 ,447 2, 170 2,893 3,616 4,340 5,063 5, 786 6, 510 9.1 52 14.8 130 49 724.8 , 450 2, 175 2,899 3,624 4,349 5, 074 5,799 6,524 9.2 53 14.9 132 50 726.4 , 453 2, 179 2,906 3, 632 4,358 5,085 5,811 6,538 9.3 54 15.0 134 51 728.0 , 456 2, 184 2,912 3,640 4,368 5, 096 5,824 6, 552 9.4 55 15.1 135 52 729.5 , 459 2, 189 2, 918 3,648 4,377 5,107 5,836 6, 566 9.5 56 15.2 137 53 731.1 , 462 2, 193 2,924 3,656 4,387 5,118 5,849 6,580 9.6 58 15.3 139 54 732.7 , 465 2, 198 2,931 3,663 4,396 5, 129 5,861 6,594 9.7 59 15.4 141 55 734.2 , 468 2, 203 2,037 3,671 4, 405 5, 140 5,874 6,608 9.8 60 15.5 142 56 735.8 ,472 2,207 2,943 3,679 4,415 5,151 5,886 6,622 9.9 61 15.6 144 57 737.4 ,475 2,212 2,949 3,687 4,424 5,162 5,899 6,636 10.0 62 15.7 146 58 738.9 ,478 2,217 2,956 3,695 4,434 5,172 5,911 6,650 10.1 63 15.8 148 59 740.5 ,481 2,221 2,962 3,702 4,443 5,183 5,924 6,664 15.9 J50 16.0 151 60 742.1 1,484 2,226 2,968 ,3, 710 4,452 5, 194 5,936 6,678 a For all distances under 1.6 miles the correction may be taken as + 5 feet. Height of instrument is assumed 4.5 feet. GEOGRAPHIC TABLES AND FORMULAS. 283 TABLE 27. For obtaining differences of altitude for any minute, etc. Continued. 8 1 2 3 4 5 6 7 8 9 Corrections for curva- ture, refraction, and height of instruments 742. 1 1,484 2,226 2,968 3,710 4,452 5,194 5,936 6,678 1 743.6 1,487 2, 231 2, 974 3, 718 4,462 5,205 5,949 6,693 Miles. Feet. Miles. Feet. 2 745. 2 1,490 '2, 236 2,981 3, 726 4,471 5,216 5,962 6,707 1.6 6 10.2 64 3 746.8 1,494 2, 240 2, 987 3.734 4,481 5,227 5, 974 6,721 2.1 7 10.3 65 4 748. 3 1,497 2, 245 2, 993 3,742 4,490 5,238 5,987 6,735 2.5 8 10.4 67 5 749. 9 1,500 2,250 3,000 3,749 4,499 5,249 5,999. 6,749 2.8 9 10.5 68 6 751. 5 1,503 2,254 3,006 3,757 4,509 5,260 6,012 6,763 3.1 10 10,6 69 7 753.0 1,506 2,259 3, 012 3,765 4,518 5,271 6, 024 6,777 3.4 11 10.7 70 8 754.6 1,509 2, 264 3,018 3,773 4,528 5, 282 6,037 6,791 3.6 12 10.8 71 9 756. 2 1,512 2,269 3,025 3,781 4,537 5,293 6,049 6;806 3.8 13 10.9 73 10 757.7 1,515 2,273 3,031 3,789 4,546 5,304 6,062 6,820 4.1 14 11.0 74 11 759. 3 1,519 2,278 3,037 3,797 4,556 5,315 6,074 6,834 4.3 15 11.1 75 12 760. 9 1,522 2,283 3,043 3,804 4,565 5,326 6,087 6,848 4.5 16 11.2 77 13 762.4 1,525 2,287 3,050 3,812 4,575 5,337 6,100 6,862 4.7 17 11.3 78 14 764. 1,528 2, 292 3,056 3,820 4,584 5,348 6, 112 6,876 4.8 18 11.4 79 15 765. 6 1,531 2, 297 3, 062 3,828 4,593 5,359 6, 125 6,890 5.0 19 11.5 80 16 767. 1 1,534 2,301 3,069 3,836 4,603 5,370 6,137 6,904 5.2 20 11.6 82 17 768. 7 1,537 2,306 3,075 3, 844 4, 612 5,381 6,150 6,918 5.4 21 11.7 83 18 770.3 1,541 2,311 3,081 3,851 4, 622 5,392 6,162 6,933 5.5 22 11.8 . 84 19 771.8 1,544 2,316 3,087 3,859 4, 631 5,403 6,175 6,947 5.7 23 11.9 86 20 773.4 1,547 2, 320 3,094 3,867 4,640 5,414 6,187 6,961 5.8 24 12.0 87 21 775.0 1,560 2,325 3,100 3, 875 4,650 5,425 6,200 6,975 6.0 25 12.1 89 22 776. 6 1,563 2,330 3,106 3,883 4,659 5,436 6, 212 6,989 6.1 26 12.2 90 23 778. 1 1,556 2, 334 3, 112 3,891 4,669 5,447 6,225 7,003 6.3 27 12.3 91 24 779. 7 1,559 2,339 3,119 3,898 4,678 5,458 6, 237 7,017 6.4 28 12.4 93 25 781. 3 1,562 2,344 3,125 3,906 4,688 5,469 6, 250 7,031 6.5 29 12.5 94 26 782.8 1,566 2,348 3,131 3,914 4,697 5,480 6,263 7,045 6.7 30 12.6 96 27 784. 4 1,569 2,353 3,138 3, 922 4,706 5,491 6, 275 7,060 6.8 31 12.7 97 28 786.0 1,572 2, 358 3, 144 3,930 4,716 5,502 6,288 7,074 6.9 32 12.8 99 29 787.5 1,575 2,363 3,150 3,938 4, 725 5,513 6,800 7,088 7.0 33 12.9 100 30 789.1 1,578 2,367 3,156 3,945 4,735 5,524 6,313 7, 102 7.2 34 13.0 102 Ml 790.7 1,581 2, 372 3, 163 3,953 4,744 5,535 6,325 7,116 7.3 35 13.1 103 32 792.2 1,584 2,377 ! 3,169 3,961 4,753 5,546 6,338 7,130 7.4 36 13.2 105 33 798. 8 1, 588 2,381 3,175 3,969 4,763 5,557 6, 351 7,144 7.5 37 13.3 106 34 795.4 1, r>'.l 2, 386 3, 182 3,977 4,772 5,568 6,363 7,159 7.6 38 13.4 108 35 796.9 1,594 2,391 i 3,188 3,985 4,782 5,579 6,376 7,173 7.8 39 13.5 109 36 798.5 1,597 2,396 ' 3,194 3,993 4,791 5,590 6,388 7,187 7.9 40 18.6 111 37 800.1 1,600 2,400 i 3,200 4, 001 4, 801 5,601 6,401 7,201 8.0 41 13.7 112 38 801.7 1,603 2,405 3, 207 4,008 4,810 5,612 6,414 7,215 8.1 42 13.8 114 39 803. 2 1,607 2,410 3,213 4,016 4,820 5,623 6,426 7,229 8.2 43 13.9 115 4u 804.8 1,610 2,414 3,219 4,024 4,829 5,634 6, 439 7,243 8.3 44 14.0 117 41 806.4 1,613 2,419 3,226 4, 032 4,838 5, 645 6,451 7,258 8.4 45 14.1 119 42 808.0 1,616 2,424 3, 232 4,040 4,848 5,656 6,464 7, 272 8.5 46 14.2 120 43 809.5 1,619 2,429 3,238 4,048 4,857 5,667 6,476 7,286 8.6 47 14.3 .122 44 811.1 1,622 2,433 3,244 4,056 4,867 5,678 6,489 7,300 8.7 48 14.4 124 45 812.7 1,625 2, 438 3,251 4,063 4,876 5,689 6,501 7,314 8.8 49 14.5 125 46 814.2 1,628 2,443 3,257 4,071 4,886 5,700 6,514 7,328 8.9 50 14.6 127 47 815.8 1, 632. 2,447 3,263 4,079 4,895 5,711 6, 527 7, 342 9.0 51 14.7 129 48 817.4 1,635 2,452 3,270 4,087 4,904 5,722 6,539 7,357 9.1 52 14.8 130 49 819.0 1,638 2,457 3,276 4,095 4,914 5,733 6,552 7,371 9.2 53 14.9 132 50 820.5 1,641 2,462 3,282 4,103 4,923 5,744 6,564 7,385 9.3 54 15.0 134 51 822.1 1,644 2,466 3,288 4,111 4,933 5,755 6,577 7,399 9.4 55 15.1 135 52 823.7 1,647 2,471 3,295 4,118 4, 942 5,766 6,590 7, 413 9.5 56 15.2 137 53 825.3 1,651 2, 476 3,301 4,126 4,952 5,777 6,602 7,427 9.6 58 15.3 139 54 826.8 1,654 2, 481 3,307 4,134 4,961 5,788 6,615 7,442 9.7 59 15.4 141 55 828.4 1,657 2,485 3,314 4,142 4,970 5,799 6,627 7,456 9.8 60 15.5 142 66 830.0 1,660 2,490 3,320 4,150 4,980 5, 810 6,640 7,470 9.9 81 15.6 144 57 831.5 1,663 2,495 3,326 4,158 4,989 5,821 6,652 7,484 10.0 62 15.7 146 58 833.1 1,666 2, 499 3,332 4,166 4,999 5,832 6, 665 7,498 10.1 63 15.8 148 59 834.7 1,669 2,504 3,339 4,173 5,008 5,843 6,678 7,512 15.9 150 16.0 151 60 836.3 1,673 2,509 3,345 4,181 6,018 5,854 6,690 7,526 For all distances under 1.6 miles the correction may be taken as + 5 feet. Height of instrument is assumed 4.5 feet. ' 284 GEOGRAPHIC TABLES AND FORMULAS. TABLE 27. 'For obtaining differences of altitude for any minute, etc. Continued. 9 1 2 3 4 5 6 7 8 9 Corrections for curva- ture, refraction, and height of instruments , 836.3 1,673 2,509 3,345 4,181 5,018 5,854 6,690 7,526 1 837.8 1,676 2,514 3,351 4,189 5,027 5, 865 6,703 7,541 Miles. Feet. Miles. Feet. 2 839.4 1,679 2, 518 3,358 4,197 5,037 5,876 6,715 7,555 1.6 6 10.2 64 3 841.0 1, 682 2,523 3,364 4, 205 5,046 5,887 6, 728 7,569 2.1 7 10.3 65 4 842.6 1,685 2,528 3,370 4,213 5,055 5,898 6,741 7,583 2.5 8 10.4 67 5 844.2 1,688 2,532 3,377 4. 221 5, 065 5,909 6,753 7, 597 2.8 9 10.5 68 6 845.7 1,691 2,537 3, 383 4,229 5,074 5,920 6,766 7,612 3.1 10 10.6 69 7 847.3 1,695 2,542 3,389 4,237 5,084 5,931 6,778 7,626 3.4 11 10.7 70 8 848.9 1,698 2,547 3,396 4,244 5,093 5, 942 6,791 7,640 3.6 12 10.8 71 9 850.5 1,701 2,551 3, 402 4,252 5,103 5,953 6,804 7,654 3.8 13 10.9 73 10 852.0 1,704 2,556 3,408 4,260 5,112 5,964 6,816 7,668 4.1 14 11.0 74 11 853.6 1,707 2,561 3,414 4,268 5,122 5,975 6,829 7,683 4.3 15 11.1 75 12 855.2 1,710 2,566 3,421 4,276 5. 131 5,986 6,842 7,697 4.5 16 11.2 77 x3 856.8 1,714 2,570 3,427 4,284 5! 141 5,997 6,854 7,711 4.7 17 11.3 78 14 858.3 1.717 2,575 3,433 4,292 1 5,150 6,008 6,867 7,725 4.8 18 11.4 79 15 859.9 1,720 2,580 3,440 4.300 | 5,160 6, 020 6,879 7,739 5.0 19 11.5 80 16 861.5 1, 723 2,585 3,446 4,308 j 5,169 6,031 6,892 7,754 5.2 20 11.6 82 17 863.1 1,726 2,589 3,452 4,315 ! 5,179 6,042 6,905 7,768 5.4 21 11.7 83 18 864.7 1,729 2,594 3,459 4,323 5.188 6,053 6,917 7,782 5.5 22 1J.8 84 19 866.2 1,732 2, 599 3,465j 4,331 5,197 6,064 6,930 7,796 5.7 23 11.9 86 20 867.8 1,736 2,603 3,471 j 4,339 5, 207 6,075 6,943 7,810 5.8 24 12.0 87 21 869.4 1,739 2, 608 3,478 4,347 5,216 6,086 6, 955 7, 825 6.0 25 12.1 89 22 871.0 1,742 2,613 3,484 4,355 5,226 6,097 6,968 7,839 6.1 26 12.2 90 23 872.5 1,745 2,618 3,490 4,363 5,235 6,108 6, 980 7, 853 6.3 27 12.3 91 24 874.1 1,748 2, 622 3,496 4,371 5,245 6,119 6,993 7,867 6.4 28 12.4 93 25 875.7 1,751 2, 627 3,503 4,379 5,254 6,130 7,006 7,881 6.5 29 12.5 94 26 877.3 1,755 2, 632 3,509 4,386 5,264 6,141 7,018 7,896 6.7 30 12.6 96 27 878.8 1,758 2, 637 3,515 4,394 5,273 6, 152 7,031 7,910 6.8 31 12.7 97 28 880.4 1,761 2,641 3,522 4,402 5,283 6,163 7,043 7,924 6.9 32 12.8 99 29 882.0 1,764 2,646 3,528 4,410 5, 292 6,174 7,056 7,938 7.0 33 12.9 100 30 883.6 1,767 2,651 "3,534 4,418 5,302 6,185 7,068 7, 952 7.2 34 13.0 102 31 885.2 1,770 2, 656 3,541 4,426 5,311 6,196 7.081 7,967 7.3 35 13.1 103 32 886.7 1,774 2,660 3,547 4,434 5,320 6,207 7,094 7,981 7.4 36 13.2 105 33 888.3 1,777 2,665 3,553 4,442 5,330 6,218 7,107 7,995 7.5 37 13.3 106 34 889.9 1,780 2,670 3,560 4,450 5,339 6,229 7,119 8,009 7.6 3S 13.4 108 35 891.5 1,783 2,674 3,566 4,457 5,349 6.240 7,132 8,023 7.8 39 13.5 109 36 893.1 1,786 2,679 3,572 4,465 5, 358 6, 252 7,145 8,038 7.9 40 13.6 111 37 894.6 1,789 2,684 3,579 4,473 5,368 6,263 7,157 8,052 8.0 41 13.7 112 38 896.2 1,792 2,689 3,585 4,481 5,377 6, 274 7,170 8,066 8.1 42 13.8 114 39 897.8 1,796 2,693 3,591 4,489 5,387 6,285 7,183 8,080 8.2 43 13.9 115 40 899.4 1,799 2,698 3,598 4,497 5,396 6,296 7,195 8,095 8.3 44 14.0 117 41 901.0 1,802 2, 703 3, 604 4,505 5,406 6,307 7,208 8,109 8.4 45 14.1 119 42 902.5 1,805 2, 708 3,610 4,513 5,415 6,318 7,220 8,123 8.5 46 14.2 120 43 904.1 1,808 2,712 3,617 4, 521 5,425 6, 329 7,233 8,137 8.6 47 14.3 122 44 905.7 1,811 2,717 3,623 4,529 5,434 6,340 7, 246 8,151 8.7 48 14.4 124 45 907.3 1,814 2, 722 3,629 4,537 5,444 6,351 7,258 8,166 8.8 49 14.5 125 46 908.9 1,818 2,727 3,636 4,544 5,453 6,362 7,271 8,180 8.9 50 14.6 127 47 910.5 1,821 2,731 3, 642 4,552 5,463 6,373 7,284 8, 194 9.0 51 14.7 129 48 912.0 1,824 2,736 3,648 4,560 5,472 6,384 7,296 8,208 9.1 52 14.8 130 49 913.6 1,827 2, 741 3,654 4,568 5,482 6,395 7,309 8,223 9.2 53 14.9 132 50 915.2 1,830 2,746 3,661 4,576 5,491 6,406 7,322 8,237 9.3 54 15.0 134 51 916.8 1,833 2,750 3,667 4,584 5,501 6,417 7,334 8,251 9.4 55 15.1 135 52 918.4 1,837 2,755 3,673 4, 592 5, 510 6,429 7,347 8,265 9.5 56 15.2 137 53 919.9 1,840 2, 760 3,680 4,600 5,520 6,440 7,360 8,279 9.6 58 15.3 139 54 921.5 1,843 2, 765 3,686 4,608 5, 529 6,451 7, 372 8,294 9.7 59 15 4 141 55 923.1 1,846 2,769 3,692 4,616 5,539 6, 462 7,385 8,308 9.8 60 15.5 142 56 924.7 1,849 2,774 3,699 4,623 5,548 6,473 7,397 8, 322 9.9 61 15.6 144 57 926.3 1,852 2,779 3,705 4,631 5,558 6,484 7,410 8,336 10.0 62 15.7 146 58 927.8 1,855 2,784 3,711 4,639 5,567 6,495 7,423 8,351 10.1 63 15.8 148 59 929.4 1,859 2,788 3,718 4,647 5,577 6,506 7,435 8,365 15.9 150 16.0 151 60 931.0 1,862 2, 793 3, 724 4,655 5,586 6,517 7,448 8,379 For all distances under 1.6 miles the correction may be taken as + 5 feet. Height of instrument is assumed 4.5 feet. GEOGRAPHIC TABLES AND FORMULAS. 285 TABLE 27. For obtaining differences of altitude for any minute, etc. Continued. 10 1 2 3 4 5 6 7 8 9 Corrections for curva- ture, refraction and height of instruments 931.0 ,862 2,793 3,724 4,655 5,586 6,517 7,448 8,379 1 932.6 ,865 2,798 3,730 4,663 5,596 6,528 7,461 8,393 Miles. Feet. Miles. Feet. 2 934.2 ,868 2,803 3,737 4,671 5,605 6,539 7,473 8,408 1.6 6 10.2 64 3 935.8 ,872 2,807 3,743 4,679 5,615 6,550 7,486 8,422 2.1 7 10.3 65 4 937.4 ,875 2,812 3,749 4,687 5,624 6,561 7,499 8,436 2.5 8 10.4 67 5 938.9 ,878 2,817 3,756 4,695 5,634 6,573 7,512 8,450 2.8 9 10.5 68 6 940.5 ,881 2,822 3, 762 4,703 5,643 6,584 7, 524 8,465 3.1 10 10.6 69 7 942.1 ,884 2,826 3,768 4,711 5,653 6,595 7,537 8,479 3.4 11 10.7 70 8 943.7 ,887 2,831 3,775 4,718 5,662 6,606 7, 550 8,493 3.6 12 10.8 71 g 945.3 ,891 2,836 3,781 4,726 5,672 6,617 7,562 8,508 3.8 13 10.9 73 10 946.9 ,894 2,841 3,787 4,734 5,681 6,628 7, 575 8,522 4.1 14 11.0 74 11 948.5 ,897 2,845 3,794 4,742 5,691 6,639 7,588 8,536 4.3 15 11.1 75 12 950.0 ,900 2,850 3,800 4,750 5,700 6,650 7,600 8,550 4.5 16 11.2 77 13 951.6 ,903 2,855 3,807 4,758 5,710 6,661 7,613 8,565 4.7 17 11.3 78 14 953.2 ,906 2,860 3,813 4,766 5,719 6,672 7,626 8,579 4.8 18 11.4 79 15 954.8 ,910 2,864 3,819 4,774 5,729 6,684 7,638 8,593 5.0 19 11.5 80 16 956.4 ,913 2,869 3. 826 4,782 5,738 6,695 7,651 8,607 5.2 20 11.6 82 17 958.0 ,916 2,874 3; 832 4,790 5,748 6,706 7,664 8,622 5.4 21 11.7 83 IN 959.6 ,919 2,879 3,838 4,798 5,757 6,217 7,676 8,636 5.5 22 11.8 84 I'.i 961.1 ,922 2, 883 3, 845 4,806 5,767 6,728 7,689 8,650 6.7 23 11.9 86 20 962.7 .926 2,888 ' 3,851 4,814 5,776 6,739 7,702 8,665 5.8 24 12.0 87 21 964.3 1 ^929 2,893 3,857 4, 822 5,786 6,750 7,715 8,679 6.0 25 12.1 89 22 965.9 ,932 2,898 3,864 4,830 5,795 6,751 7,727 8,693 6.1 26 12.2 90 23 967.5 ,935 2,902 3,870 4,837 5,805 6,772 7,740 8,707 6.3 27 12.3 91 24 969.1 ,938 2,907 3,876 4,845 5,814 6,784 7,753 8,722 6.4 28 12.4 93 25 970.7 ,941 2,912 3,883 4,853 5,824 6,795 7,765 8,736 6.5 29 12.5 94 26 972.2 ,944 2,917 3,889 4,861 5,833 6,806 7,778 8,750 6.7 30 12.6 96 27 '.'7:;. s ,948 2,921 3,895 4,869 5,843 6,817 7,791 8,764 6.8 31 12.7 97 2* 975.4 ,951 2,926 3,902 4 877 5,853 6,828 7,803 8,779 6.9 32 12.8 99 29 977.0 ,954 2,931 3,908 4,885 5,862 6,839 7,816 8,793 7.0 33 12.9 100 30 978.6 ,957 2,936 3,914 4,893 5,872 6,850 7,829 8,807 7.2 34 13.0 102 31 980.2 ,960 2,941 3,921 4,901 5,881 6,861 7,841 8,822 7.3 35 13.1 103 32 981.8 ,964 2,945 3,927 4,909 5,891 6,872 7,854 8,836 7.4 36 13.2 105 33 983.4 ,967 2.950 3,933 4,917 5,900 6,884 7,867 8,850 7.5 37 13.3 106 34 985.0 , 970 2, 955 3,940 4,925 5,910 6,895 7,880 8,865 7.6 38 13.4 108 35 986.5 ,973 2,960 3,946 4,933 5,919 6,906 7,892 8,879 7.8 39 13.5 109 M 988.1 ,976 2,964 3,953 4,941 5,929 6,917 7,905 8,893 7.9 40 13.6 111 37 989.7 ,980 2,969 3,959 4,949 5,938 6,928 7,918 8,908 8.0 41 13.7 112 38 991.3 ,983 2,974 3,965 4,957 5,948 6,939 7,931 8,922 8.1 42 13.8 114 39 992.9 ,986 2,979 3,972 4,965 5,957 6,950 7,943 8,936 8.2 43 13.9 115 40 994.5 ,989 2,984 3,978 4,973 5,967 6,962 7,956 8,951 8.3 44 14.0 117 41 996.1 ,992 2,988 3,984 4,980 5,977 6,973 7,969 8,965 8.4 45 14.1 119 42 997.7 1,995 2,993 3,991 4,988 5,986 6,984 7,981 8,979 8.5 46 14.2 120 43 999.3 1,999 2,998 3,997 4,996 5,996 6,995 7,994 8,993 8.6 47 14.4 122 44 1,000.9 2,002 3,003 4,003 5,004 6,005 7,006 8,007 9,008 8.7 48 14.3 124 45 1,002.5 2, 005 3,007 4,010 5,012 6, 015 7, 017 8, 020 9,022 8.8 49 14.5 125 46 1,004.0 2,008 3,012 4,016 5, 020 6,021 7,028 8,032 9,036 8.9 50 14.6 127 47 1,005.6 2,011 3,017 4,023 5,028 6,034 7,039 8,045 9,051 9.0 51 14.7 129 48 1,007.2 2,014 3,022 4,029 5,036 6,043 7,051 8,058 9,065 9.1 52 14.8 130 49 1,008.8 2,018 3,026 4,035 5,044 6,053 7,062 8,071 9,079 9.2 53 14.9 132 50 1,010.4 2,021 3,031 4,042 5,052 6,062 7,073 8,083 9,094 9.3 54 15.0 134 51 1,012.0 2,024 3,036 4,048 5,060 6,072 7,084 8,096 9,108 9.4 55 15.1 135 52 1,013.6 2,027 3,041 4,054 5,068 6,082 7,095 1 8,109 9,122 9.5 56 15.2 137 58 1,015.2 2,030 3,046 4,061 5,076 6,091 7,106 | 8,121 9,137 9.6 58 16.3 139 54 1,016.8 2, 034 3, 050 4,067 5.084 6,101 7,117 8,134 9,151 9.7 59 15.4 141 55 1,018.4 2,037 3,055 4,073 5,092 6,110 7, 129 8, 147 9,165 9.8 60 15.5 142 61 1,020.0 2,040 j 3,060 4,080 5,100 6,120 7,140 8,160 9,180 9.9 61 15.6 144 57 1, 021. 5 2,043 ! 3,065 4,086 5,108 6,129 7,151 8,172 9,194 10.0 62 15.7 146 58 1,023.1 2, 046 3, 069 4,093 5,116 6,139 7,162 8,185 9,208 10.1 63 15.8 148 59 1,024.7 2,049 3,074 4,099 5,124 6,148 7,173 8,198 9,223 15.9 150 16.0 151 60 1,026.3 2,053 3,079 4,105 5,132 6,158 7,184 8,211 9,237 1 a For all distances under 1.6 miles the correction may be taken as + 5 feet. Height of instrument is assumed 4.5 feet. 286 GEOGRAPHIC TABLES AND FORMULAS. TABLE 27. For obtaining differences of altitude for any minute, etc. Continued. 11 1 2 3 4 5 6 7 8 9 Corrections for curva- ture, refraction, and height of instrument, a 1, 026. 3 2,053 3,079 4,105 5,132 6,158 7,184 8,211 9,237 1 1,027.9 2,056 3,084 4,112 5,140 6,168 7,195 8,223 9,251 Miles. Feet. Miles. Feet. 2 1,029.5! 2,059 3,089 4,118 5,148 6,177 7,207 8,236 9,266 1.6 6 10.2 64 3 1,031.1| 2,062 3,093 4,124 5,156 6,187 7,218 8,249 9,280 2.1 7 10.3 65 4 1, 032. 7 2,065 3,098 4,131 5,164 6,196 7,229 8,262 9,294 2.5 8 10.4 67 5 1, 034. 3 2,069 3,103 4,137 5,172 6,206 7,240 8, 275 9,309 2.8 9 10.5 68 6 1,036 2,072 3,108 4,144 5,180 6,215 7,251 8,287 9,323 3.1 10 10.6 69 7 1,038 2,075 3,113 4,150 5,188 6,225 7,263 8,300 9,338 3.4 11 10.7 70. 8 1,039 2,078 3,117 4,156 5,196 6,235 7,274 8,313 9,352 3.6 12 10.8 71 9 1,041 2,081 3,122 4,163 5,204 6,244 7,285 8,326 9,366' 3.8 13 10.9 73 10 1,042 2,085 3,127 4,169 5,212 6,254 7,296 8,338 9,381 4.1 14 11.0 74 11 1,044 2,088 3,132 4,176 5,219 6,263 7,307 8,351 9,395 4.3 15 11.1 75 12 1,045 2,091 3,136 4,182 5, 227 6,273 7,318 8,364 9,409 4.5 16 11.2 77 13 1,047 2,094 3,141 4,188 5,235 6,283 7; 330 8,377 9,424 4.7 17 11.3 78 14 1,049 2, 097 3,146 4,195 5,243 6,292 7,341 8,390 9,438 4.8 18 11.4 79 15 1,050 2,101 3,151 4,201 5,251 6,302 7,352 8,402 9,453 5.0 19 11.5 80 16 1,052 2,104 3,156 4,208 5,259 6,311 7,363 8,415 9,467 5.2 20 11.6 82 17 1,053 2,107 3,160 4,214 5, 267 6,321 7,374 8,428 8,481 5.4 21 11.7 83 18 1,055 2,110 3,165 4,220 5,275 6,330 7,386 8,441 9, 496 5. 5 22 11.8 84 19 1,057 2,113 3,170 4,227 5,283 6,340 7,397 8,453 9,510 i 5.7 23 11.9 86 20 1,058 2,117 3,176 ,233 5,291 6,350 7,408 8,466 9,524 5.8 24 12.0 87 21 1,060 2,120 3,180 ,239 5,299 6,359 7,419 8,479 9,539 6.0 25 12.1 89 22 1,061 2,123 3,184 4,246 5,307 6,369 7,430 8,492 9,553 6.1 26 12.2 90 23 1,063 2,126 3,189 ,252 5,315 6,378 7,441 8,504 9,568 6.3 27 12.3 91 24 1,065 2,129 3,194 ,259 5,323 6,388 7,453 8,517 9,582 6.4 28 12.4 93 25 1,066 2,133 3,199 4,265 5,331 6,398 7,464 8,530 9,596 6.5 29 12.5 94 26 1,068 2,136 3,204 4,271 5,339 6,407 7,475 8,543 9,611 6.7 30 12.6 96 27 1,069 2,139 3,208 4,278 5,347 6,417 7,486 8,556 9, 625 6.8 31 12.7 97 28 1,071 2,142 3,213 5, 355 6,426 7,497 8,568 9,639 6.9 32 12.8 99 29 1,073 2,145 3,218 4^291 5,363 6,436 7,509 8,581 9,654 7.0 33 12.9 100 30 1,074 2,148 3,223 4,297 5,371 6,445 7,520 8,594 9,668 7.2 34 13.0 102 31 1,076 2,152 3,227 4,303 5,379 6,455 7,531 8,607 9,682 7.3 35 13.1 103 32 1,077 2,156 3,232 4,310 5,387 6,465 7,542 8,619 9,697 7.4 36 13.2 105 33 1,079 2,158 3,237 4,316 5,395 6,474 7,553 8,632 9,711 7.5 37 13.3 106 34 1,081 2,161 3, 242 4,323 5, 403 6,484 7,564 8,645 9,726 7.6 38 13.4 108 35 1,082 2,164 3,247 4,329 5,411 6,493 7,576 8,658 9,740 7.8 39 13.5 109 36 1,084 2,168 3,252 4,335 5,419 6,503 7.587 8,671 9,755 7.9 40 13.6 111 37 1,085 2,171 3,256 4,342 5,427 6,513 7,598 8,683 9,769 8.0 41 13.7 112 38 1,087 2,174 3,261 4,348 5,435 6,522 7,609 8,696 9,783 8.1 42 13.8 114 39 1,089 2,177 3,266 4,355 5,443 6,532 7,621 8,709 9,798 8.2 43 13.9 115 40 1,090 2,181 3,271 4,361 5,451 6,542 7,632 8,722 9,812 8.3 44 14.0 117 41 1,092 2,184 3,276 4,367 5,459 6,551 7,643 8, 735 9,827 8.4 45 14.1 119 42 1,093 2,187 3,280 4,374 5,467 6,561 7,654 8,748 9,841 8.5 46 14.2 120 43 1,095 2,190 3,285 4,380 5,475 6,570 7,665 8,760 9,856 8.6 47 14.3 122 44 1,097 2,193 3,290 4,387 5,483 6,580 7,677 8,773 9,870 8.7 48 14.4 124 45 1,098 2,197 3,295 4,393 5,491 6,590 7,688 8,786 9,884 8.8 49 14.5 125 46 1,100 2,200 3,300 4,399 5,499 6,599 7,699 8,799 9,899 8.9 50 14.6 127 47 1,101 2,203 3,304 4,406 5,507 6,609 7,710 8,812 9,913 9.0 51 14.7 129 48 1,103 2,206 3,309 4,412 5,515 6,618 7,721 8,825 9,928 9.1 52 14.8 130 49 1, 105 2,209 3,314 4,419 5, 523 6,628 7,733 8,837 9,942 9.2 53 14.9 132 50 1,106 2,213 3,319 4,425 5,531 6,638 7,744 8,850 9,956 9.3 54 15.0 134 51 1,108 2,216 3,324 4,431 5,539 6,647 7,755 8,863 9,971 9.4 55 15.1 135 52 1,109 2,219 3,328 4,438 5,547 6, 657 7,766 8,876 9,985 9.5 56 15.2 137 53 1,111 2,222 3,333 4,444 5,555 6,666 7,778 8,889 10, 000 9.6 58 15.3 139 54 1,113 2,225 3,338 4,451 5,563 6,676 7,789 8,901 10, 014 9.7 59 15.4 141 55 1,114 2,229 3,343 4,457 5,571 6,686 7,800 8,914 10, 029 9.8 60 15.5 142 56 1,116 2,232 3,348 4,464 5,579 6,695 7,811 8,927 10, 043 9.9 61 15.6 144 57 1,117 2,235 3,352 4,470 5,587 6,705 7, 822 8,940 10, 057 10.0 62 15.7 146 58 1,119 2,238 3,357 4,476 5,595 6, 715 7,834 8,953 10, 072 10.1 63 15.8 148 59 1, 121 2,241 3,362 4,483 5,603 6,724 7,845 8,966 10, 086 15.9 16.0 150 151 60 1,122 2,245 3,367 4,489 5,611 6,734 7,856 8,978 10,101 a For all distances under 1.6 miles the correction may be taken as + 5 feet. Height of instrument is assumed 4.5 feet. GEOGRAPHIC TABLES AND FORMULAS. 287 TABLE 27. For obtaining differences of altitude for any minute, etc. Continued. 12 1 2 3 4 5 6 7 8 9 Corrections for curva- ture, refraction, and height of instruments 1,122 2,245 3,367 4,489 5,612 6,734 7,856 8,978 10, 101 1 1,124 2,248 3,372 4,496 5,620 6,743 7,867 8,991 10,115 Miles. Feet. Miles. Feet. 2 1,126 2,251 3,377 4,502 5, 628 6,753 7,879 9,004 10, 130 1.6 6 10.2 64 3 1,127 2,254 3,381 4,508 5,636 6,763 7,890 9,017 10, 144 2.1 7 10.3 65 4 1,129 2,257 3,386 4,515 5,644 6,772 7,901 9.030 10, 159 2.5 8 10.4 67 5 1,130 2,261 3,391 4,521 5,652 6,782 7,912 9,043 10, 173 2.8 9 10.5 68 6 1J132 2,264 3,396 4,528 5,660 6, 792 7,924 9,056 10,188 .3.1 10 10.6 69 7 1,134 2, 267 3,401 4,534 5,668 6,801 7,935 9,068 10, 202 3.4 11 10.7 70 8 1,135 2,270 3,405 4,541 5,676 6,811 7,946 9,081 10, 216 3.6 12 10.8 71 9 1,137 2,274 3,410 4,547 5,684 6,821 7,957 9,094 10, 231 3.8 13 10.9 73 10 1,138 2,277 3,415 4,554 5,692 6,830 7,969 9,107 10, 245 4.1 14 11.0 74 11 1,140 2,280 3,420 4,560 5,700 6,840 7,980 9, 120 10, 260 4.3 15 11.1 75 12 1, 142 2,283 3,425 4,566 5,708 6,850 7,991 9,133 10, 274 4.5 16 11.2 77 13 1,143 2,286 3,430 4,573 5,716 6,859 8,002 9,146 10, 289 4.7 17 11.3 78 14 1, 145 2,290 3,434 4,579 5, 724 6,869 8,014 9,158 10,303 4.8 18 11.4 79 15 1,146 2,293 3,439 4,586 5,732 6,879 8,025 9,171 10,318 5.0 19 11.5 80 16 1,148 2,296 3,444 4,592 5,740 (i, NSS 8,036 9,184 10, 332 5.2 20 11.6 U2 17 1,150 2,299 3,449 4;599 5, 748 6. 898 8,047 9,197 10, 347 5.4 21 11.7 83 18 1,151 2,302 3, 4-54 4,605 5,756 6,907 8,059 9,210 10, 361 5.5 22 11.8 84 19 1,153 2,306 3,459 4,611 5,764 6,917 8,070 9,223 10, 376 5.7 23 11.9 86 20 1,154 2,309 3,463 4,618 5,772 6,927 8,081 9,236 10,390 5.8 24 12.0 . 87 21 1,156 2,312 3,468 4,624 5,780 6,936 8,092 9,249 10,405 6.0 25 12.1 89 22 1,158 2,315 3,473 4,631 5,788 6,946 8,104 9,261 10,419 6.1 26 12.2 90 23 1,159 2,319 3,478 4,637 5,796 6,956 8,115 9,274 10, 434 6.3 27 12.3 91 24 1,161 2, 322 3,483 4,644 5,804 6, 965 8,126 9,287 10,448 6.4 28 12.4 93 25 1,163 2, 325 3,487 4,650 5,812 6,975 8,138 9,300 10, 463 6.5 29 12.5 94 26 1,164 2,328 3,492 4,656 5,821 6,985 8,149 9, 313 10, 477 6.7 30 12.6 96 27 1,166 2,331 3,497 4,663 5,829 6,994 8,160 9,326 10, 491 6.8 31 12.7 97 28 1,167 2,335 3,502 4,669 5,837 7,004 8,171 9,339 10, 506 6.9 32 12.8 99 29 1,169 2,338 3,507 4,676 5,845 7,014 8,183 9,351 10, 520 7.0 33 12.9 100 30 1,171 2,341 3,512 4, 682 5, 853 7,023 8,194 9,364 10,535 7.2 34 13.0 102 31 1,172 2,344 3,516 4, 689 5, 861 7,033 8,205 9,377 10,549 7.3 35 13.1 103 32 1,174 2,348 3,521 4, 695 5, 869 7,043 8,216 9,390 10,564 7.4 36 13.2 105 33 1,175 2,351 3,526 4, 702 5, 877 7,052 8,228 9,403 10, 579 7.5 37 13.3 106 34 1,177 2,354 3,531 4,708 ! 5,885 7,062 8,239 9,416 10, 593 7.6 38 13.4 108 86 1,179 2,357 3,536 4, 714 5, 893 7,072 8,250 9,429 10, 608 7.8 39 13.5 109 36 1,180 2,360 3,541 4, 721 5, 901 7,081 8,262 9,442 10, 622 7.9 40 13.6 111 37 1,182 2,364 3,546 4,727 | 5,909 7,091 8,273 9,455 10, 637 8.0 41 13.7 112 38 1,183 2,367 3,550 4,734 5,917 7,101 8,284 9,468 10, 651 8.1 42 13.8 114 39 1,185 2,370 3,555 4,740 5,925 7,110 8,296 9,481 10, 666 8.2 43 13.9 115 40 1,187 2,373 3,560 4,747 5,933 7,120 8,307 9,494 10,680 8.3 44 14.0 117 41 1,188 2,377 3,565 4,753 5, 942 7,130 8,318 9,506 10, 695 8.4 45 14.1 119 42 1,190 2,380 3, 570 4,760 5,950 7,140 8,329 9,519 10,709 8.5 46 14.2 120 48 1,192 2,383 3, 575 4,766 5, 958 7,149 8,341 9, 532 10, 724 8.6 47 14.3 122 1 44 1,193 2,386 3,579 4,773 5,966 7,159 8,352 9,545 10, 738 8.7 48 14.4 124 45 1,196 2,390 3,584 4,779 5,974 7,169 8,363 9,558 10, 753 8.8 49 14.5 125 H 1,196 2,393 3,589 4, 785 ft, 982 7,178 8,375 9, 571 10, 767 8.9 50 14.6 127 47 1,198 2,3% 3, 594 4,792 5, 990 7,188 8,386 9,584 10, 782 9.0 51 14.7 129 48 1,200 2,399 3,599 4,798 5,998 7,198 8,397 9,597 10, 796 9.1 52 14.8 130 49 1,201 2,402 3,604 4,805 6,006 7,207 8,409 9,610 10, 811 9.2 53 14.9 132 50 1,203 2,406 3,608 4,811 6,014 7,217 8,420 9,623 10, 825 9.3 54 15.0 134 51 1, 204 2,409 3,613 4,818 6,022 7,227 8,431 9,636 10, 840 9.4 55 15.1 135 52 1,206 2,412 3,618 4,824 6,030 7,236 8,442 9,648 10, 855 9.5 56 15.2 137 53 1,208 2,415 3,623 4,831 6,038 7,246 8,454 9,661 10, 869 9.6 58 15.3 139 54 1,209 2,419 3,628 4,837 6,046 7,256 8,465 9,674 10,884 9.7 59 15.4 141 55 1,211 2,422 3,633 4,844 6,055 7,265 8,476 9,687 10, 898 9.8 60 15.5 142 56 1,213 2,425 3,638 4,8.50 6,063 7,275 8,488 9,700 10, 913 9.9 61 15.6 144 57 1,214 2,428 3,642 4,857 6,071 7,285 8,499 9,713 10, 927 10.0 62 15.7 146 58 1,216 2,431 3,647 4,863 6,079 7,294 8,510 9,726 10, 942 10.1 63 15.8 148 59 1,217 2,435 3,652 4,869 6,087 7,304 8,521 9,739 10, 956 15.9 150 16.0 151 60 1,219 2,438 3,657 4,876 6,095 7,314 8,533 9,752 10, 971 a For all distances under 1.6 miles the correction may be taken as + 6 feet. Height of instrument is assumed 4.5 feet. 288 GEOGRAPHIC TABLES AND FORMULAS. TABLE 27. For obtaining differences of altitude for any minute, etc. Continued. 13 1 2 3 4 5 6 7 8 9 Corrections for curva- ture, refraction, and height of instruments 1,219 2,438 3,657 4,876 6,095 7,314 8,533 9,752 10, 971 1 1,221 2, 441 3,662 4,882 6,103 7,324 8,544 9,765 10, 985 Miles. Feet. Miles. Feet. 2 1,222 2,444 3,667 4,889 6,111 7,333 8, 556 9,778 11,000 1.6 6 10.2 64 3 1,224 2,448 3,672 4,895 6,119 7,343 8,567 9,791 11,015 2.1 7 10.3 65 4 1,225 2,451 3,676 4,902 6, 127 7,353 8,578 9,804 11,029 2.5 8 10.4 67 5 1,227 2,454 3,681 4,908 6,135 7,362 8,590 9,817 11,044 2.8 9 10.5 68 6 1,229 2,457 3,686 4, 915 6,143 7,372 8,601 9,830 11,058 3.1 10 10.6 69 7 1,230 2,461 3,691 4,921 6,152 7,382 8,612 9,843 11,073 3.4 11 10.7 70 8 1,232 2,464 3,696 4,928 6,160 7,392 8,624 9,855 11, 087 3.6 12 10.8 71 9 1,234 2,467 3,701 4,934 6,168 7,401 8,635 9,868 11, 102 3.8 13 10.9 73 10 1,235 2,470 3,706 4,941 6,176 7,411 8,646 9,881 11,117 4.1 14 11.0 74 11 1,237 2,474 -3,710 4,947 6,184 7,421 8,658 9,894 11, 131 4.3 15 11.1 75 12 1,238 2,477 3, 715 ,954 6,192 7,430 8,669 9,907 11,146 4.5 16 11.2 77 13 1,240 2,480 3,720 ,960 6,200 7,440 8,680 9,920 11, 160 4.7 17 11.3 78 14 1,243 2,483 3,725 ,967 6, 208 7,450 8,692 9,933 11,175 4.8 18 11.4 79 15 1,243 2,487 3,730 ,973 6,216 7,460 8,703 9,946 11,190 5.0 19 11.5 80 16 1,245 2,490 3,735 ,980 6,224 7,469 8,714 9,959 11,204 5.2 20 11.6 82 17 1,247 2,493 3,740 ,986 6,233 7,479 8,726 9,972 11,219 5.4 21 11.7 83 18 1,248 2,496 3,744 4,993 6, 241 7,489 8,737 9,985 11,233 5.5 22 11.8 84 19 1,250 2,500 3,749 4,999 6,249 7,499 8,748 9,998 11,248 5.7 23 11.9 86 20 1,251 2,503 3,754 5,006 6,257 7,508 8,760 10,011 11,262 5.8 24 12.0 87 21 1,253 2,506 3,759 5,012 6,265 7,518 8, 771 10; 024 11,277 6.0 25 12.1 89 22 1,255 2,509 3,764 5,019 6,273 7,528 8,782 10, 037 11, 292 6.1 26 12.2 90 23 1,256 2,513 3,769 5,025 6,281 7,537 8,794 10,050 11,306 6.3 27 12.3 91 24 1,258 2,516 3,774 5,032 6, 289 7,547 8, 805 10,063 11, 321 6.4 28 12.4 93 25 1,260 2,519 3,779 5,038 6; 297 7, 557 8,816 10, 076 11,336 6.5 29 12.5 94 20 1,261 2,522 3,783 5,044 6,306 7,567 8,828 10, 089 11,350 6.7 30 12.6 96 27 1,263 2, 525 3,788 5,051 6,314 7,576 8,839 10, 102 11,365 6.8 31 12.7 97 28 1,264 2,529 3,793 5,057 6,322 7,586 8,851 10,115 11,379 6.9 32 12.8 99 29 1,266 2,532 3,798 5,064 6,330 7,596 8,862 10, 128 11,394 7.0 33 12.9 100 30 1,268 2,535 3,803 5,070 6,338 7,606 8,873 10, 141 11,409 7.2 34 13.0 102 31 1,269 2,538 3,808 5,077 6,346 7,615 8,885 10,154 11,423 7.3 35 13.1 103 32 1,271 2,642 3,813 5,083 1 6,354 7,625 8,896 10, 167 11,438 7.4 36 13.2 105 33 1,273 2,545 3,817 5,090 6,362 7,635 8,907 10,180 11, 452 7.5 37 13.3 106 34 1,274 2,548 3,822 5, 096 6, 371 7,645 8,919 10, 193 11,467 7.6 38 13.4 108 35 1,276 2,551 3,827 5,103 6,379 7, 654 8, 930 10,206 11,482 7.8 39 13.5 109 36 1,277 2,555 3,832 5,109 6,387 7,664 8,942 10, 219 11, 496 7.9 40 13.6 111 37 1,279 2,558 3,837 5,116 6,395 7,674 I 8,953 10, 232 11, 511 8.0 41 13.7 112 38 1,281 2,561 3,842 5,122 6,403 7, 684 8, 964 10, 245 11,526 8.1 42 13.8 114 39 1,282 2,565 3,847 5,129 6,411 7,693 8,976 10,258 11,540 8.2 43 13.9 115 40 1,284 2,568 3,852 5,135 6,419 7,703 8,987 10, 271 11,555 8.3 44 14.0 117 41 1,286 2,571 3.857 5,142 6,427 7,713 8,999 10, 284 11, 569 8.4 45 14.1 119 42 1,287 2, 574 3,861 5,149 6,436 7,723 9,010 10, 297 11,584 8.5 46 14.2 120 43 1,289 2,578 3,866 5,155 6,444 7,732 9,021 10, 310 11,599 8.6 47 14.3 122 44 1,290 2,581 3,871 5,162 6,452 7,742 9,033 10,323 11,613 8.7 48 14.4 124 45 1,292 2,584 3,876 5,168 6,460 7,752 9,044 10, 336 11,628 8.8 49 14.5 125 46 1,294 2,587 3,881 5, 175 6,468 7,762 9,055 10,349 11, 643 8.9 50 14.6 127 47 1, 295 2,591 3,886 5, 181 6,476 7,771 9,067 10,362 11, 657 9.0 51 14.7 120 48 1,297 2,594 3,891 5,188 6,484 7,781 9,078 10, 375 11,672 9.1 52 14.8 130 49 1,299 2,597 3,896 5,194 6,4^3 7,791 9,090 10,388 11,687 9.2 53 14.9 132 50 1,300 2,600 3.900 5,201 6,501 7,801 9,101 10", 401 11,701 9.3 54 15.0 134 51 1,302 2,604 3,905 5,207 6,509 7,811 9,112 10, 414 11,716 9.4 55 15.1 135 52 1,303 2,607 3,910 5, 214 6,517 7,820 9,124 10,427 11, 731 9.5 56 15.2 137 5a 1,305 2,610 3,915 5,220 6, 525 7,830 9,135 10, 440 11, 745 9.6 58 15.3- 139 54 1,307 2,613 3,920 5,227 6,533 7,840 9,147 10,453 11,760 9.7 59 15.4 141 65 1,308 2,617 3,925 5,233 6,541 7,850 9,158 10, 466 11,775 9.8 60 15.5 142 56 1,310 2,620 3,930 5,240 6,550 7,859 9,170 10,479 11,789 9.9 61 15.6 144 67 1,312 2,623 3,935 5,246 6,558 7,869 9,181 10,492 11,804 ' 10.0 62 15.7 146 58 1,313 2,626 3,940 5,253 6,566 7,879 9,192 10,506 11,819 10.1 63 15.8 148 59 1,315 2,630 3,944 5,259 6,574 7,889 9,204 10, 519 11, 833 15.9 150 16.0 | 151 60 1,316 2,633 3,949 5,266 6,582 7,899 9,215 10,532 11,848 | a For all distances under 1.6 miles the correction may be taken as + 5 feet. Height of instrument is assumed 4.5 feet. GEOGRAPHIC TABLES AND FORMULAS. 289 TABLE 27. For obtaining differences of altitude for any minute, etc. Continued. 14 1 '-> 8 9 Corrections for curva- ture, refraction, and height of iiistrument.a 1,316 2,633 3,949 5,266 6,582 7,899 9,215 10,632 11,848 1 1,318 2,636 3,954 5,272 6,590 7,909 9,227 10,545 11,863 Miles. feet. Miles. Feet. 2 1,320 2,639 3,959 5,279 6,599 7,918 9,238 10,558 11, 877 1.6 6 10.2 64 3 1,321 2,643 3,964 5,285 6,607 7,928 9,249 10,571 11,892 2.1 7 10.3 65 4 1,323 2,646 3,969 5,292 6,615 7,938 9,261 10,584 11, 907 2.5 8 10.4 67 5 1,325 2,649 3,974 5,298 6.623 7,948 9,272 10, 597 11,923 2.8 9 10.5 68 6 1,326 2,653 3,979 5,305 6,631 7,957 9,284 10, 610 11,93(5 3.1 10 10.6 69 7 1,328 2,656 3,984 5, 312 6,639 7,967 9,295 10, 623 11, 951 3.4 11 10.7 70 8 1,330 2,659 3,989 5,318 6,648 7,977 9,307 10,636 11,966 3.6 12 10.8 71 9 1,331 2,662 3,993 5,325 6,656 7,987 9,318 10,649 11, 980 3.8 13 10.9 73 10 1,333 2,666 3,998 5,331 6,664 7,997 9,329 10,662 11,995 4.1 14 11.0 74 11 1,334 2,669 4,003 5,338 6, 672 8,006 9,341 10, 675 12, 010 4.3 15 11.1 75 12 1,336 2,672 ,008 5,344 6,680 8,016 9, 352 10,688 12,024 4.5 16 11.2 77 13 1,338 2,675 ,013 5,351 6,688 8,026 9,364 10, 701 12, 039 4.7 17 11.3 78 14 1,339 2,679 ,018 5,357 6,697 8,036 9,375 10, 715 12,054 4.8 18 11.4 79 15 1,341 2,682 ,023 5,364 6,706 8,046 9,387 10, 728 12,069 5.0 19 11.5 80 16 1,343 2,686 ,028 5,370 6,713 8,056 9,398 10,741 12, 083 5.2 20 11.6 82 17 1,344 2,688 ,033 5,377 6,721 8,065 9,410 10, 754 12, 098 5.4 21 11.7 83 18 1,346 2,692 ,038 5,383 6,729 8,075 9,421 10, 767 12, 113 5.5 22 11.8 84 19 1,348 2,695 ,042 5,390 6,737 8,085 9,432 10,780 12, 127 5.7 23 11.9 86 20 1,349 2,698 ,047 5,397 6,746 8,095 9,444 10, 793 12, 142 5.8 24 12.0 87 21 1,351 2,702 ,062 5,403 6,754 8,105 9,455 10,806 12, 157 6.0 25 12.1 89 -22 1,352 2,705 ,057 5,410 6,762 8,114 9,467 10, 819 12, 172 6.1 26 12.2 90 23 1,354 2,708 ,062 5,416 6,770 8,124 9,478 10, 832 12,186 6.3 27 12.3 91 24 1,356 2,711 ,067 5,423 6,778 8,134 9,490 10,845 12.201 6.4 28 12.4 . 93 26 1,357 2,715 1 ,072 5,429 6,787 8,144 9,501 10,859 12, 216 6.5 29 12.5 94 26 1,359 2,718 ,077 5,436 6,795 8,154 9,513 10, 872 12, 231 6.7 30 12.6 96 27 1,361 2, 721 , 082 5.442 6,803 8,164 9,524 10,885 12, 245 6.8 31 12.7 97 28 1,362 2,724 ,087 5,449 6,811 8,173 9,536 10,898 12,260 6.9. 32 12.8 99 29 1,364 2,728 ,092 5, 455 6,819 8,183 9,547 10,911 12, 275 7.0 33 12.9 100 30 1,366 2,731 ,097 5,462 6,828 8,193 9,559 10, 924 12,290 7.2 34 13.0 102 31 1,367 2,734 ,101 5, 469 6,836 8,203 9,570 10, 937 12, 304 7.3 35 13.1 103 32 1,369 2,738 ,106 1 5,475 6,844 8,213 9,581 10,950 12, 319 7.4 36 13.2 105 33 1,370 2,741 ,111 i 5,482 6,852 8,223 9,593 10,963 12, 334 7.5 37 13.3 106 34 1,372 2,744 ,116 I 5,488 6,860 8, 232 9,604 10, 976 12, 349 7.6 38 13.4 108 36 1,374 2,747 ,121 ! 5.495 6,868 8,242 9,616 10,990 12, 363 7.8 39 13.5 109 36 1,375 2,751 ,126 5,501 6,877 8,252 9, 627 11,003 12. 378 7.9 40 13.6 111 37 1,377 2,754 ,131 5,508 6,885 8,262 9,639 11,016 12, 393 8.0 41 13.7 112 38 ! 1,379 2,757 ,136 5,514 6,893 8,272 9,650 11,029 12, 408 8.1 42 13.8 114 39 1,380 2,761 ,141 5,521 6,901 8,282 9,662 11,042 12, 422 8.2 43 13.9 115 40 1,382 2,764 ,146 5,528 6,910 8,291 9,673 11,055 12,437 8.3 44 14.0 117 41 1,384 2,767 ,151 5,534 6,918 8,301 9,685 11,068 12, 452 8.4 45 14.1 119 42 1,386 2,770 ;156 5,541 6,926 8,311 9,696 11,081 12, 467 8.5 46 14.2 120 43 1.387 2,774 ,160 5,547 6,934 8,321 9,708 11,095 12, 481 8.6 47 14.3 122 44 1,388 2,777 ,165 5,554 6,942 8,331 9.719 11,108 12, 496 8.7 48 14.4 124 45 1,390 2,780 ,170 5,560 6,951 8,341 9,731 11,121 12,511 8.8 49 14.5 125 46 1,392 2,784 ,175 5, .567 6,959 8,351 9,742 11,134 12, 526 8.9 50 14.6 127 47 1,393 2,787 4,180 5,574 6,967 8,360 9,754 11, 147 12, 541 9.0 51 14.7 129 48 1,395 2,790 4,185 5,580 6,975 8,370 9,765 11,160 12,555 9.1 52 14.8 130 19 1,397 2,793 4,190 5,587 6,983 8,380 9,777 11,173 12, 570 9.2 53 14.9 132 50 1,398 2,797 4,195 5, 593 6,992 8,390 9,788 11,187 12, 585 9.3 54 15.0 134 51 1,400 2,800 4,200 5,600 7,000 8,400 9,800 11,200 12,600 9.4 55 15.1 135 52 1,402 2,803 4,205 i 5,606 7,008 8,410 9,811 11,213 12, 615 9.5 56 15.2 137 53 1,403 2,807 4,210 5, 613 7,016 8,420 9,823 11,226 12, 629 9.6 58 15.3 139 54 1,405 2,810 4,215 5,620 7,024 8,429 9,834 11,239 12,644 9.7 59 15.4 141 55 1,407 2,813 4,220 5,626 7,033 8,439 9,8i6 Il,2o2 12, 659 9.8 60 15.5 142 56 1,408 2,816 4.225 5,633 7,041 8,449 9, 8o7 Il,2h6 12, 674 9.9 61 15.6 144 57 1,410 2,820 4,230 5,639 7,049 8,459 9,869 11,T9 12,689 10.0 62 15.7 146 58 1,411 2,823 4,234 5,646 7,057 8,465 9,880 11, 292 12, 703 10.1 63 15.8 148 59 1,413 2,826 4,239 5,653 7,066 8,479 9,892 11, 305 12, 718 15.9 1.50 16.0 151 60 1,415 2,830 4,244 5,659 7,074 8,489 9,903 11,318 12,733 a For all distances under 1.6 miles the correction may be taken as + 5 feet. Height of instrument is assumed 4.5 feet. 4606108- -19 290 GEOGRAPHIC TABLES AND FORMULAS. TABLE 28. HORIZONTAL DISTANCES AND ELEVATIONS FROM STADIA READINGS. This is a most generally useful stadia table for rods reading 1 foot to the 100 feet and with angles up to 30. The values of other measures than those given in the table are obtained by multiplying the quanti- ties under the proper vertical angle by stadia readings in hundreds of units. The quantity representing the focal distance is very small and is given at the bottom of each page for focal lengths between three- fourths and 1-f feet and is represented as a constant equal to c. For ordinary work it is not necessary to take the latter into account. The direct use of the table involves a multiplication for each result obtained. Example. Let rod intercept be 3.25 feet, and the angle of inclina- tion be 5 35'. Then the distance on the horizontal would be ^=325 feet. If we accept the focal distance /*+ c as 1.25 feet, we have from the tables APR 1 1932 30m-l,'15 YD066176