230 THE ROYAL SOCIETY OF CANADA 



required. Hence l)ef()re calculating lecipiocals for the pui'pose of 

 showing sensibilit}', the various increments of light wei'e first reduced 

 to a common standard of intensity. This was the intensity of the 

 standard of brightness, viz., the intensity of light of wave length 

 •414^ as observed in the eye-piece while the principal sections of the 

 niçois were parallel. 



Method of Reducing to a Common Standard of Intensity. 



We may assume that the luminosity of any portion of the spec- 

 trimi is proportional to its intensity. But the luminosity is inversely 

 proportional to the fraction of total intensity, at the point considered, 

 that will give a luminosity equal to the luminosity of the standard of 

 brightness. But this fraction of total intensity is proportional to the 

 square of the cosine of the angle between the principal sections of the 

 niçois — the light going through giving a luminosity ec^ual to the lumin- 

 osity of our standard of brightness. That is: the luminosity of any 

 portion of the spectrum is inversely proportional to the square of the 

 cosine of the angle between the principal sections of the niçois when 

 the light going through from that portion gives a luminosity equal to 

 that of the standard. Therefore, taking the luminosity of the standard 

 as unity, the luminosity of the spectrum at any point considered in 

 terms of this standard is given by 1 / cos-/3 where ^ is the angle between 

 the principal sections of the niçois when just sufficient of the light 

 considered is going through to give a luminosity equal to the lumin- 

 osity to the standard. And since intensity is assumed propor- 

 tional to luminosity, the intensit}^ of light at any point in the 

 spectrum in terms of the intensity of the standard is given by 1/Cos^^. 



Again, a denotes the angle between the principal sections of the 

 niçois after the rotation already explained. Therefore, the fraction 

 of total intensity by which the initial intensity i.e., that represented 

 by Cos-/?, was increased to give the least perceptible change in the 

 sensation, may be represented by (Cos-a — Cos-/3). The intensity 

 of any given portion of light depends upon its position in the spec- 

 trum. Therefore, the fraction of total intensity will have an intensity 

 depending upon the position of the point in the spectrum at which it 

 was added, i.e. depending upon the value of the angle /?. But it has 

 been shown that the intensity of light from any portion of the spec- 

 trum may be expressed in terms of the standard of brightness by 

 multiplying by l/Cos.-/9. Henceit was thought that by multiplying 

 (Cos-a — Cos^/9) by l/Cos'^ the various increments of light added to 

 produce a perceptible change in the sensation in each case would be 

 of equal intensity i.e., they would have an intensity equal to the in- 



