388 APPENDIX - CALCULATION OF THE 



Let us now require the inclination to the primary 

 planes, of the planes whose law of decrement we 

 havejust determined. 



And first of the plane e i c, fig. 362, whose symbol 

 is A. 



4 



The inclination of this plane to the primary is equal 

 to the angle a b c, fig. 362; to obtain which we must 

 first know the angle d b c. 



The law of decrement being 3 molecules in breadth 

 and 2 in height, and the decrement in breadth being 

 measured by f an oblique diagonal and an edge, it 

 follows that the ratio of the lines of the defect may 

 be thus expressed, 



db : dc :: 3 half oblique diagonals : Sedges. 

 But we have before seen that 



\ oblique diagonal : edge :: 12 : 19 

 we have therefore db : dc :: 3x12 2x19 - 36 : 38. 



The sum of the sides d b, d c, of the triangle d b c 

 is therefore 38 -j- 36 zz 74 ; and their difference is 

 38 36 = 2. 



The angle d b c which we require, is evidently the 

 greater of the two angles d b c and d c b 



Now the sum of these two angles is 

 180 A 5 = 180 109 1 8' 11" = 70 51' 49" of which 

 \ 35 25' 54". 



But to find the greater angle, we must also know 

 their difference, which we may discover by means of 

 the general formula given in p. 376. 



tang, \ d = d> ian , - H 



$ 



which formula in relation to this particular case be- 

 comes 



tang, i d = 



