Vol,. 7, 1921 
PHYSICS: E. C. KEMBLE 
285 
It is easy to show from (9) by the application of well-known formulae that 
K T vanishes for odd values of r; that K 0 is tH; and that for even values 
of r greater than zero K T is given by the equation 
■ + 2 
where 
Now (6) becomes 
1.3.5. . . .(r- 1) 
2.4.6.... (r-f 2) 
00 
7 = [do + 2 2 ^ (2r)H T ] . 
We proceed to the evaluation of the coefficients a 0 , a h a 2 , . 
may be regarded as a function of either £ or w, let 
di/du = *(«) - x (f). 
Then 
(r) 
«r = i *(0). 
(10) 
(11) 
(12) 
As 
(13) 
Since w and f vanish together, the derivatives of ^ at the point u = 0 
can be calculated from the derivatives of X at the point £ = 0. The 
following method of procedure is perhaps the simplest. Let 
Then 
Let 
Then 
, . H -f(q) 
w , du v + l / 2 
/'(* + <*) 
(14) 
(140 
(15) 
Differentiating, 
vfr '(«) = x' (*) X ft) 
<A (w) M=xft) |{^ (M W } 
(16) 
In some cases these successive derivatives of \p are simple and easily 
calculated functions of £. In others the successive derivatives rapidly 
become complicated. If f(q) is given as a power series in £ the process 
of differentiation can be performed conveniently as follows : 
