LAWS OF DECREMENT, 389 



From the tables of logarithms we find 

 log. 2 . . . ; . 0-3010300 

 log. tang. 35 25' 54" = 9-8521719 



10-1532019 

 log. 74 .... 1-8692317 



log. tang. \ d . . 8-2839702 



Therefore 



^difference of the angles dbc and deb I 9 6' 6" 



and \ their sum being 35 25' 54" 



the greater angle dbc == 36 32' 



and v c b a is consequently 180 36* 32 / =143 28'. 

 If we turn to p. 382, we may observe that this 

 angle is the same we are supposed to have found by 

 measurement, and from which we have deduced the 

 law of decrement. 



We shall now deduce the inclination of the plane 

 efg to each of the adjacent primary planes, from 

 the known law of decrement producing it, and from 

 the known angles'/, and A t . 



The symbol of this plane being as we have already 

 seen (B'2 B4 B"3), the edges de, df, d g, of fig. 362, 

 are as follows, 



de 2 



df 4 

 dg - 3 



The angle c d /, or f d g*, corresponds to A t , which 

 has been found 101 55'. 



Consequently the sum of the unknown angles dfe 

 and d ef, or d /"g and d gf, is zz 78 5'. 



