398 Mr airy, ON THE INTENSITY OF LIGHT 



and so on, we find for the integral generally 



(v^ - v., + v., — i',; + &:c.) sin it + («, — V3+ Vn — V: + &c.) cos 11. 



The first limit of the integration being w, and the last being infinity, 

 and the quantities %, ^i, &c. vanishing for w = infinity, the value of the 

 integral between these limits is, 



( — Vo + »a — v., + V6 — &c.) sin « + (-»! + I's — -iij + -t), — &c.) cos n. 



2 1 



It will be observed here that v = -. 



IT Sw" — m 



The following are the expressions for »„, y„ &c. 



2 1 



24 w 



■n''(_3w'-my' 



240 1 288 Hi 1 



'■'! = —5- 77:— 5 -t^i + 



7r> '{3m'-my^ m" '{Sw^-mf 

 11520 w _ 17280 >« w 



253440 1 725760m 1 483840hi' 1 



21288960 H/ 69672960 Hi W 52254.720 iii' W 



V- = - 



TT^ ■(3w'-m)'' Tr" '(3w=-Hi)'° ,r" '{Sw'-mY" 



723824640 1 3413975040 m 1 4981Cl(;640m= 1 22a!l207e80 m ' 1 



t' ■(3w"-.n)'""'' ^^ (3w'-m)" ■*■ ^^^ (Sw^-m)'-'*' ^r^ (¥»•-- m)"'" 



86858956800 w 450644705280 m w 717352796I60»i- w 3586J639U0K0m' m 



it' ■(3w''-m)'= T» '(Sw'-m)'" t° (Sw^-w)'* •t» ' (3!ir-m)'- 



Making w — 2'00, computing these expressions for every value of 'w, 

 and substituting them in the expression for the integral from ir = 2-00 

 to w = infinity, the numerical value of the integral for each value of 

 m was found. 



This process was exceedingly accurate for all the negative values of m, 

 and for the positive values about as far as m = + 3-0, when a difficulty 

 presented itself. It must be remarked that when 3w- — m (or in the 



