LAWS OF DECREMENT. 



Let us suppose we have found i k : i d : : R : sin. a, 



we should then have m 

 n 



and . . . Log. = Log. R Log. sin. a. 

 n 



Let us also suppose ib : ic *: s'm.\/icb :\/sin.ibc, 



then P m = shl ' V ' c b 



q n sin. N/ ib-c; 



and Log. ?_???_ Log. sin. Y/ 2 c ^ Log. sin.yf 6 c. 

 qn 



The division of J!? by is effected by sub- 

 q n n 



tracting the logarithm of the latter fraction from 

 that of the former. And the natural decimal number 

 corresponding to the resulting logarithm, will bear 

 the same ratio to 1-0, 1-00, 1-000, &c. according to 

 the number of decimal planes in the number found, 

 as the decrement in breadth bears to that in height. 



Examples of the application of this method of 

 deducing the values of p and q, will occur in the 

 course of this appendix. 



Fig. 329. 



Let us now enquire how we may determine the 

 ratios of the three edges, i ft, i c, i , fig. 329, of the 

 defect^ occasioned by a decrement on one of the angles 

 of a parallelepiped. 



2 p 2 



