mm reply to Mr. Riddle. 51 
Example.—Leta = 76° 0! oO! 
b 
=1'76r 41480 
z= =48 26 45 
z! = 39 58 45 
VW) ie 
22 30 0 
2log. sin.a . . . 19°97380 
vers. 22 °30! . - - 8'88150 
21°49! = vers. c = 8°85530 
Lato ao! 7 eee . 9°58284 
Cin AA 9:98694 
ar.cO.sin.c ...-. 0.42972 
A = 87° 16) sin. = 9:99950 
sin. 3 (2 +2/—c) . 9°73959 
sin. $(23— z+).  9°06589 
ar.co.sin.c ... 0°42972 
ar. co.sin.z .... 0°12591 
2)19°36111 
= = 28° 38) sin, = 9:68055 
2 
57 16 = B 
87 16= A 
30 0 =C.. vers. 9°12702 
sin. @ 9°98690 
sin. z 9°87409 11342 nat. vers.(a—z) 
8°98801 .. log. 9727 
y = 37° 53! nat. vers. = 21069 
ole Tit. 516257 
The demonstrations of the third and fourth methods (which 
methods, I believe, have been given for the first time) we 
must, for the sake of brevity, omit for the present; but they 
cannot create any difficulty to those who understand the prin- 
ciples of spherical trigonometry, as delivered in Woodhouse’s 
or Legendre’s treatises. We must notice, however, that the 
change in declination is not considered in the first equation 
given above, which will seldom make a difference of more 
than 1! on the final result. The latitude deduced by the third 
method, which is rigorously exact, is 52° 5' 20". 
Thus the candour and truth of Mr. Riddle’s statements are 
apparent. I cannot but acknowledge, however, that there 
G2 Ig 
