298 APPENDIX CALCULATION OF THE 



As an example of this method, let us suppose 

 we have found 



i k : id :: 11 : 8 



therefore = i!. 



n 8 



And let us suppose the ratio of 



ib : ic :: sin. y icb : sin. \/ ibc :: 33 : 16; 



then we should have P m zz . 



q n 16 



If we divide the second fraction by the first, the 

 quotient will be |? X ~ = ~ = -, which would 



give a law of decrement by three rows in breadth, or 

 in the direction of i k, and two in height, or in the 

 direction of the edge i d. 



If we now suppose the edges i k, and if, to be 



equal, it is evident that becomes equal to 1. 



n 



Under this supposition the ratio of i b to ic might 

 be expressed by a fraction of the form . . 



q 



Let us now imagine the ratio of i b : ic to have 

 been found as 1 : 3. 



This would indicate a decrement proceeding along 

 the terminal plane by 3 rows of molecules in height. 



If we find i b : i c : : 4 : 3, the law of decrement 

 producing the plane from which that ratio is deduced, 

 is by 4 rows in breadth, and 3 in height, on the termi- 

 nal plane. 



The second method of dividing the proposed frac- 

 tion -J? by is by means of the logarithms of the 

 q n n 



quantities from whence those ratios are deduced. 



