Dr. W. Pole on Colour-Blindness. 57 



old plan, would have been called the primary colours ; but 

 here they were only considered as preliminary elements ; the 

 new fundamental colours, say x, y, and z, being dependent on 

 them and connected with them by linear equations : thus 



^== ai . R + ^i . G + Ci.V, 



y = a 2 . R + & 2 . G + c 2 .V, . 



The nine coefficients having to be hereafter determined, 

 making, in each line, 



a + b + e=l. 



To arrive at these constants appears the crux of the problem, 

 it being necessary for this purpose to enter into the investi- 

 gation regarding the colour and luminosity relations before 

 referred to. The quantities dE 1} dE 2 , and dE 3 are taken to 

 represent the magnitudes of the differential perceptions for 

 the elementary observations, and rfE is the magnitude of the 

 difference in the colour resulting therefrom. This latter 

 quantity had to be expressed in terms of x, y, and z, and for 

 this purpose the following formula was arrived at (p. 453) : — 



'dx). 



d®^ BX //l dx_l dyv* /l d//^l*dz\* A ^_1 

 k ^ 3 V \x'dX y ' dX I \y dX 2 dXJ + \z \iX x 



where X = wave-length, SX = a certain mean error, and k a 

 constant found by multiplied observations. This equation 

 has to do with the sensitiveness to colour. 



With the aid of the constants, having given an observation 

 of the values of R, G, and V, at any wave-length, the values 

 of x, y, and z may also be found, and the constants must be 

 such that <£E, determined by the above equation, shall be 

 equal, or nearly so, at all points of the spectrum. 



Having got this constant value of <£E, it has then to be 

 compared with the equation for dE arrived at in a different 

 way, from dE ly dE 2 , and d,E 3 , viz. 



dE=k.e. V3J 



where e is a certain very small fraction, also arrived at by 

 observation. This second value of dE has to do with the 

 sensitiveness to luminosity. And if the two values are 

 equal or nearly so, the calculation maybe considered justified. 



* Probably this is a misprint for _. The book unfortunately contains 

 several typographical errors. 



