546 Intelligence and Miscellaneous Articles. 



We thus get from the 



first twelve determinations, r=-00040, r f = -00048, -=1*2, 



r 



last nine determinations, r=-00032, r'=-00019, L=0'Q, 



r 



and from the weighted mean, —=-96; so that it appears from these 



r 



experiments that the photometric susceptibility of the eye is the 

 same for all colours. The result, however, is uncertain, because 

 it may be that R is chiefly due to other sources of error than the 

 limitation of sensibility ; still the experiments show as small a 

 value of B, as is usually obtained. I shall endeavour, by further 

 observations, to obtain a conclusive result. 



A further consequence of our hypotheses will be reached by dif- 

 ferentiating the expression for a light-sensation. We have 



d(I log x . i+ J log y .j+~K. log z . &)=- &x . li+- &y . J/+-ds . K£. 



x y z 



Now, as x, y, and z all exceed unity, the differential is greater the 

 nearer unity x, y, and z are. Hence, since the variation of the 

 proportions of the primary colours with a variation of position in 

 the normal spectrum is uniform, it follows that the change of 

 colour of the normal spectrum should be most rapid about A =582, 

 as it of course is. It is also obvious that, if the total quantities 

 of the three colours are nearly the same in different parts of the 

 spectrum (I here refer to these colours not as really objective, 

 but as measured in the usual objective way), then the part about 

 X = 582 must be the brightest — another familiar fact. 



I may observe that there is a modification of our formula for a 

 sensation of light, which probably better represents the relations of 

 the sensations. Writing, in the first place, 



the formula is 



t=B, )=Jj, fc=K&, 

 logx A+logy .j+logz .&. 



This loses its validity when any of the logarithms become nega- 

 tive. If z is the smallest of the three quantities, we may sub- 

 stitute 



X=-, Y=l-; 

 z ' z 



and the formula becomes 



logX . t + log Y . 3 + logz(t+j+fc). 



When x or y is smallest there will be two other formulae. Now, 

 as the variation in the brilliancy of the light affects only the last 

 term of the last formula, and not the first two depending on X and 

 Y, it is more than probable that the eye is habituated to separating 

 the element of sensation which this last term represents, and which 



