310 Col. Sir H. James and Capt. A. R. Clarke on Projections 



must be a minimum with respect to h and Jc. Effecting the in- 

 tegration, we get 



M = FH 1 -f2m 2 + 4sin 2 f, 



where the symbols H 1; H 2 are 



_J+/* 2 h(h*-l) (7i 2 -I) 2 1 (l-A) 9 

 i- N N 2 + 3N 3 3* 1 + A ~ ' 



N 7* 2 — 1 

 H^l+AJlog^ + ^i-A + l, 



and N = A + cos /3. Now 



^=0; ...*H 1 + H,=0j 



Sty ■■•'3-t'-. 



hence 



S H 2 

 M = 4sin 2 §-^-; 



and h must be determined so that 



H 2 



-~- = maximum. 



This is most easily determined by calculating the values corre- 

 sponding to assumed values of h. We have the following : — 

 h. logH^-logHj. 



1-35 . . . . . 0-420732 

 1-36 . . . . . 0-420756 



1*37 0-420762 



1-38 ...... 0-420747 



1-39 ..... 0-420665 



By interpolation the maximum is found to be 



h. logH^-logHx. 



1-36763 .... 0-4207623 



.-. ^ 2 - 2 = 2-634889; 



and consequently 



M=0-16261; 



and in this case the misrepresentation is to that in the Balance 

 of Errors as 103-6 : 1000. The point of sight or of projection 



