442 The Hon. J. W. Strutt on Curves professing to represent 



independent variable, is really a kind of average corresponding 

 to values grouped together in a small cluster. 



For the sake of simplicity, let us suppose that the spectrum 

 is originally pure, and that the true curve giving the relations 

 between the two quantities is P Q R. Also let M N be the range 

 over which the independent variable changes in each observation 

 — in our case the width of the thermopile. Then the observed 

 curve is to be found from the true by taking m, the middle point 

 of M N, and erecting an ordinate^? m, such that 



p m . M N = area of curve PQNM. 



The locus of p will give the curve expressing the result of the 

 observations. It remains to find a convenient method of passing 

 from the one curve to the other. 



In the figure P It Q represents the true curve, M N the range 

 as before; Mm=mN=A;jois the point on the observed curve 

 found in the manner described ; Om=x Q) Rm; 



Now 



areaMPK,QNM=i ydh 



:y , pm=y'. 



h 



dy 



Thus 



y'=pm= Vo + „, 





dh 



(A) 



which shows how to deduce y' from y. 

 To pass backwards, we observe that 



d*?/_d*y tfdy # 

 dx 2 ~" dec* 6 dx ' 



h*<Py_ &(dfy _ & d*y\ _ h* d*y ! 

 '"' 6 dx 2 ~ 6 W 6 dxV~ 6 dx*> 



