23] 



we have 



'ANGLE BETWEEN SUMMITS. 



53 



Now putting = 1, 



writing 



we have 



70) 



A = Y(l a) (I ft) , 



AS 



C 



J (l*- 



In order to find limits between which this integral lies for all 

 possible values of a and ft, we notice that the coefficient of z in 

 the last factor is positive, and that the value of the factor, varying 

 always in the same sense as z, necessarily lies between the two 

 values it would have when had its extreme values, I and I. But 

 these are B 2 and A? so that 



Substituting in the radical a value that is too great or too small 

 will make the integral have an error in the opposite sense, therefore 



C- 



J (i*- 



p 



The polynomial under the radical being now of only the second 

 degree, the integral can be easily calculated, as follows. 



idz _ j.^ r fa i r ^ 



