382 APPENDIX CALCULATION OF THE 



i horizontal diagonal : perpendicular b n (fig. 358 & 9) 

 :: sin. \ A, : cos. (^ 5 90) :: sin. 50 57' 30" 

 : cos. 19 8' 11" :: '7766881 : -9447409 :: 46 : 56 nearly. 

 or log. sin. 50 57' 30" = 9-8902466 

 log. cos. 19 8' 11" = 9-9753128 



0-0850662 



Having thus determined the elements of the 

 rhomboid of carbonate of lime, which we may re- 

 mark are all deduced from the single angle /,, we 

 may proceed to determine the laws of decrement 

 producing any of its observed secondary planes. 



Let us now suppose that we have measured the 

 inclination to the plane P, of a plane belonging to 

 class b of the rhomboid, and that we have found it 

 143 28'. 



We have already seen in p. 366, that the ratio of 

 those lines of the defect occasioned by the planes , 

 from which the law of decrement is to be deduced, 

 may be expressed by the fraction 

 sin. (I a A.) 

 sin. ( 180 / 3 ) 



In relation to the plane we have measured we find 



/ 3 = 143 28' 

 and we have found . A & = 109 8' 11" 



therefore I 3 A 5 . . = 34 19' 49" 



and 180 7 3 is evidently zn 36 32'. 



The ratio of those lines of the defect from which 

 the law of decrement may be deduced, is therefore 

 in this particular case 



sin. 34" 19' 49" 

 sin. 36 32 ; 



