8 MR. AIRY'S SUPPLEMENT TO A PAPER "ON THE THEORETICAL 



the diagram to be moved towards the right hand, the third to be moved further to 

 the right, &c., and taking the sum of the ordinates of the various curves which are 

 then placed vertically one below the other ; it is clear that the large ordinates of one 

 curve will be added to the small ones of another, so as to produce in every part an 

 approximate mean value. If we perform the same operation numerically, combining 

 the last number of the first column in the Table with the last but three in the second 

 column, the last but six in the third column, and so on, to the twelfth column (observing 

 that the numbers in the columns recur after the sixth, or that they may be supposed 

 to recur before the first), and if we remark that by adding the numbers from twelve 

 columns we do in fact combine the intensities from all the diffused images that are 

 in any degree superposed ; and if we then divide by twelve, we find the following 

 numbers to represent the intensities : 



6884, 6882, 6881, 6879, 6875, 6872, 6870, 6868, 6867, 6868, &c., 



the greatest number being 6884 and the least 6868. It is plain that no bands will be 

 visible here. 



2. Let the violet end of the external spectrum be on the same side as the retarding 

 plate. The same algebraic expression holds as in the other case, but there is this im- 

 portant difference in the interpretation, that R (which increases towards the violet 

 end of the spectrum) is greatest in the spectrum on the retina on that side on which 



]f is negative, or when k increases R diminishes. And if -r- be equal to the change 



of k corresponding to a change of 2 x in R, or if ^ • j (or r) be equal to the change 



of ^^ corresponding to a change of 2 or in R, or of or in ^^ ; then the changes of ^-— 



and of -^ exactly destroy each other ; -^ -f — = a constant C, and the whole inten- 

 sity of light on a given point will be found by aggregating all the quantities 





{'x-* ('-*)} 



COS' 



(^-c). 



giving different values to k. As the second factor is independent of k, and as the 

 changes of the first caused by changing the values of k will be similar (to the extent 

 to which the light is sensible), whatever be the value of /, it follows that the aggre- 

 gate will be expressed by the form B cos^ {^^^ - Cj. This expression denotes that 



there will be light of all degrees of intensity from the brightest B to zero or total 

 darkness ; and that the whole of the changes will recur (or the dark bands will 



recur) when ^^ has changed by 2 cr, or when / has changed by -r-^- 



This combination will be represented graphically by drawing back the second curve 



