312 Mr E. Sang cm a new Solution of 



The determination of the other angles from y is so simple, 

 that it is quite needless for me either to indicate or to illus- 

 trate it. 



As the cosines of obtuse angles have to be taken, it is advisa- 

 ble to inscribe on the pages of the Canon the proper angles all 

 the way up to 360°, and also, instead of a subtractive cosine, to 

 write the versed sine of the angle with a 9 prefixed, in order to 

 avoid subtractions. These remarks will suffice, to render the 

 following processes quite intelligible. 



Example I. 



The two sides being 37° 18' and 6Q° 23', and their included 

 angle 71° 38', required the third side and the remaining angles. 



log sin 

 log sin 



9.782 4643 

 9.920 5200 



log sin = 9.977 2934 



log cos = 0.096 6707 



log sin = 9.756 4284 

 log sin => 9.994 4841 



Example II. 



At noon, Greenwich, on July 1. 1832, the moon's place will 

 be N. P. D =^ 74° 53' 08", AR = 1 47° 33' 36" ; required 

 her angular distance from the star Spica Virginae, at that in- 

 stant. 



This question corresponds exactly with that for the solution 

 of which the method that I have given was originally intended, 

 and serves at once to exhibit the aptitude of the calculus. 



iWiii ;<:. 



