]2 
PROFESSOR G. H. DARWIR OR THE MECHANICAL CONDITIONS OF 
We cannot, then, rely on this method of procedure beyond the region included 
tetween x = oo and x — S, and must now make a new departure. 
Since 
d“7/ _ e'J 
~ ^ ’ 
cPy\ 
therefore, 
Noav, let 
lot 
dx^ J 
= y — 4 log X ; 
fPy d^y fdy 4 
dx^ dx~ \dx X 
" nl dx” ’ 
(17) 
where, after differentiation, x is put equal to c, a constant. 
Then (17) may be written— 
2 ! / 4 ^ 
'^3 — Nl ^3 (^1 
Now, it is clear that 
dPA,i n + p! 
dcP 
oil 
- A 
, -^n+p 
■ ( 18 ) 
Hence-, differentiating (18) n — 3 times, we have 
, = o n 
'L±JL'm - 1 - i— r 
3 -ry!(7!3! 2! ] n ? + l "T I / c? +1 
•’ ^ ^ n — 3\ 2\ n — g — 1\ . 
~ A = S - - - A 
31 " ^ .. 
or 
i-' V (^n_g_ij(n-q-2)A„_,_,l(qA- l)+ i + (-)^^,4i ^ 
n.7l — 1.71 — O o- 
9 = 0 
or 
' ;; 12 . iHo r (n — 2) A ^_2 -h (—)" 
71. 71 — 1 . 71 — 3 I ^ c" 
+ 3 . 2.4. 
(n — 3)H„_3 —(—)” +...|_. (19) 
Now, if, for a given value of x, viz., c, we know y, or Aq, and dyldx, or A^, then we 
can compute A .2 from the formula — and, by the formula (18), viz. ;— 
^ 3-3 
2 . 1 
zlg may be computed. 
Mterwards, A^, A~, &c., may be computed by successive applications of (19). 
being so, 
This 
