LAWS OF DECREMENT. 383 



If we recur to the tables of natural sines, we shall 

 find the numbers constituting this ratio to be nearly 



1 , which fraction being reduced to its lowest 



18 

 terms will be 



This, as we have already shewn, is to be divided 

 by the unit of comparison ; which in this instance is 

 the ratio of \ the oblique diagonal to an edge, and 



12 

 has been found equal to _. 



X. \J 



But to divide by , we must invert the terms 



of the latter fraction, and then multiply the first 

 by it. 



18 19 18 3 , . , . c 



rience x zz zz , which gives a law or 



decrement by 3 rows in breadth and 2 in height pro- 

 ceeding along the plane P. 



If however instead of using the natural sines, &c. 

 we use only logarithms, the law of decrement may be 

 thus determined. 



log. sin. 34 19' 49" = 9-7512503 

 log. sin. 36 32' zz 9-7747288 



- 0-0234783 



To divide this by the unit of comparison, we must 

 subtract the logarithm of that unit, which is given in 

 p. 381, from the above logarithm of the ratio of the 

 edges of the defect; this may be done' by the ordi- 

 nary method of subtracting algebraic quantities, by 

 changing the sign of the quantity to be subtracted 



and then adding ; 



. 



