BS aca 
ee 9 
Reduction of Latitude. is 233 
planet is flattened, the greater will be the deviation between the 
normal and radius, at the place where the reduction of latitude is a 
4. The number 3 30]? the measure of the earth’s oblateness, being 
put for @ in formuta 6), we shall obtain 
tang. i=r5 ersyit 750 Xtang# y? from which we have con- 
structed the following table, in ah columns A contain the lati- 
tudes differing by 1°, and columns B the corresponding values of the 
reduction of latitude for the earth. 
Table of. as of Latitude—the 7—the oblateness being 3 a0Tt 
B FA A A B 
el o| ] H oll “ 
10 23. $78 166 02.737 3110 05.113 fet 26.064 619 43, 132 76| 5 23.198 
20 47.725 176 22.776 | 32/10 16.037 | 47|11 24.889 6219 30.116 177 | 5 01.803 
31 W1.514) 186 42.3875 | 33,10 26.199 | 48)11 22.944163)9 16.201} 78) 4 40.037 
41 35.216 197 01.488 34/10 35.630 | 49/11 20.038 [64/9 02.004] 79| 4 17.868 
5 1 58.804 } 20/7 20.090 35/10 44.274 1 50/11 16.367 tic 46.943 |] 80/3 55.501 
62 22.249 | 21/7 38.161 | 36/10 52.138 | 51/11 11.868 | 6 8 31.236] 81} 3 32.785 
7/2 45.523 | 22\7 55.678 | 37/10 204 | 52)11 06.551 | 67 4.901 | 82| 3 09.806 
8'3 08.596 [23/8 12.619 i 95.47 311 00.419 687 57.961] 83 | 2 46.595 
93 31.443 [24/8 28.964 139/11 10.939 | 54/10 53.479 | 6917 40.433 | 84| 2 23.178 
10 4.033 §25'8 44.686 4011 15.585 | 55/10 45.743 } 70/7 22.389]85!1 59.585 
114 16.341 ] 26/8 59.788 |} 4111 19.408 | 56/10 37.216 | 71/7 03.703 186! 1 35.848 
12\4 38.341 [279 14.228 | 42,11 22.405 | 57/10 27.910 7216 44.548 |87| 1 11.987 
1 5 i 89 27.997 | 43)1 72 10 17.825 a 24.894 188) 0 48.041 
145 21.304]299 41.078 | 44/11 .006 a 04.769 | 89| 0 24.045 
155 42.216 9130/9 53.500 | 45111 26.403 160! 9 55.4344}75'15 44.194] 90/ 0 00.000 
If the value of 6 be required for a latitude between any two con- 
secutive latitudes of the table, it will be sufficiently accurate for most 
purposes, to determine it by an interpolation as follows: Let it be 
required to determine by means of the table, the reduction of lati- 
tude ata place whose latitude is 41° 24’ 36”. We perceive from 
the table, that the difference between the values of 6, corresponding 
to latitudes 41° and 42°, is equal to 2.997”; we then say, as 1° 
is to 2.997”, so is 24’ 36” to a fourth term, which is equal to 
2.997" x 24’ 36” _ 2.997” x 1476” 
Ay 3600” 
the value of 4, corresponding to the latitude 41°, will give the value 
of the required reduction of latitude ; if the value of 6 had been re 
quired for a latitude greater than that at which 6 is a maximum, the 
term found by interpolation should have been subtracted. When 
the utmost degree of aia is required, then we must resort to the 
use of the formula from which the table is constructed, and deduce 
Vou. XXXI.—No. 2. 30 
= 1.229”, which, being added to 
