342 APPENDIX CALCULATION OF THE 



RIGHT RECTANGULAR PRISM. 



different kinds of decrement, of which the general 

 symbols would be 



A, P A, A p , and(Cp G q Br). 



The unit of comparison will be different in each of 

 these cases. 



Let a b, a c, b c, fig. 347, be three diagonals, and 

 o d, oj\ o e, three perpendiculars drawn from those 

 diagonals to the angle o. 



The edges a b, a c, be, might be the edges of a 

 plane produced by a decrement by 1 row of mole- 

 cules, which plane would intercept the three edges 

 o a, o by o c> together with the three perpendiculars 

 drawn on the diagonals. The ratios of those perpen- 

 diculars to the edges may therefore be assumed as 

 the units of comparison for simple and mixed decre- 

 ments on the angles. Thus for decrements on the 



p 

 angle a o h, whose symbol is A, our unit will be 



o d : o c. For those on the angle a o c, whose symbol 

 is P A, the unit is of : o b. And for those on the 

 angle b o c, whose symbol is A p , the unit is o e : o a. 

 To find a constant ratio between these perpen- 

 diculars and the primary edges, let us suppose m, n, 

 and o known, and from these quantities, the plane 

 angles o a b being also known and called A v 



o a c A t 



o b c A 3 



we have o a : o d : : R : sin . A l 



o a : o c :: R : tang. AI 

 .-. o d : o c :: sin.A l : tang. A z 

 We also find of : o b :: sin. A z : tang. A l 



o e : o a :: sin. A 3 : tang. (90 A^) 

 The units for intermediary decrements are the 

 ratios of ?w, w, and o, and the methods for deter- 

 mining the several laws of decrement will be similar 

 to some of those already employed. 



