388 Mr Murphy on the Inverse Method of 



which we get m = f, (A) (putting 3 =°)> as also that for internal 

 points, where - is a proper traction 



a "J, {a 2 + /3 2 + 2a/3.(l-2<)j ' 



from which premised observations, the question takes this form : 

 To find (A), such a function of t, that we may have 



lw+ 



\a 2 + (l 2 + 2,al3.(l-2t)\l 



= the least of ^ 



m 



a 



m 

 .(3 



The left-hand member of this equation 



- ' ./ah- ■*•' »' 4 



2 



?)■ 



when expanded becomes 



^\« + /3 + * • (« + /3)' "' + 2.4 • („+/3) s f &C 1 



The right-hand member expanded by Section II, Art. 17, 

 becomes 



f 1 1.1 2 3 a<3 1.1.3 2V/3' , ^ \ 



,W la + /3 + 2.4 ■ (a + /3) 3 + 2.4.6 ' («+/3) 5 +&c -}' 



and comparing the general terms in both series, we have 



■" 2. 4. ..2a; 2.4.6...(2# + 2) 



or jtA.f = 



x + 1 ' 



and therefore by the principles of Section I, A = the constant 

 quantity »«. 



