390 A Method for ascertaining Latitude and Time 
garithms when h = A’, and ten when the’altitudes are un- 
equal. 
In the case of two equal heights, we would have cos W= 
tang 2 tang 3D, and this angle would not require more 
than six logarithms instead of nine. 
Here is the calculation of it : 
TaRE fy tisiiege- tesa 00113399 W = 52° 0’ 14",25 
Tang 3D= 30°57'10",25  9:7779636 «| V: «== 62 36 58 79 
Cos W 52 0 14,25 9°7813035 u = 10 36 44 ,54 
The same simplification could be obtaimed from the ana- 
lytical formula; but it could not be so easily perceived. 
Thus analysis, handled as it should be, conduces to the 
same solution as spherical trigonometry; but it 1s not al- 
ways easy to choose such modifications as would reduce to 
the least terms the calculation of a complicated formula. 
Analytical Calculation of the Horary Angle. 
Ceaser. hoe eT 00074926 Tangu........ Q:2726964. 
"Deine: --+. 00113399 CosG...... «+ 9°83986047 
Tan G. .46° 14’ 307,77 00188325 C sin ae - O'21109881 
d= 8 22 43,1 Tana=11°55'18",31 93245492 
G— d= 37:61 47 ,67 
Trigonometrical Calculation. 
LCF pee ee 9:9925074 .Tangwu...... -- 927260904 
a ES 99880061 Sin%.......... 98398047 
Tang % = 43°45'20’, 2 g-9g11075 Ccos(?+%).... 02114881 
Appae: 43 ,10 ‘Van A=11°55'18",31 93245592 
Which shows that hoth operations are identical, which also 
is the case of the following: 
Calculation of the Latitude. 
Analytic Method. Trigonometric Method. 
Casmgn ero w ute ae OO905300 "Cos Ale elo o's .- 9:9G05300 
Cot (G—92)...... 0 1093281 Tang (? +x) ...... 0°10g3281 
Tan @ 51°31’ 477,19 0 0998581 Tan ¢ 51°31’ eee 00998581 
The analytical method requires twenty-five logarithms in 
the case of A=A’, and twenty-seven in the more general 
case. 
The trigonomeirical method would require twenty-four 
logarithms i in the case of h= lr’, setting aside the facility 
offered by the isosceles triangle. It requires twenty-six, in 
the more commoncase. In fact i it only requires tw enty-two 
in the case of two equal altitudes, which, therefore, has the 
advantage by three logarithms. It is true that the analytical 
method 
