52 DR. JAMES BOTTOMLEy's 



rY being the effective yellow after passing through the 

 screen. After using the screen, the left-hand expression 

 of (A) would become 



Since qt=g't', if we substitute q't' for qt in the last ex- 

 pression, we shall get the light transmitted by the other 

 cylinder after using a screen ; hence, if the columns be ad- 

 justed so as to produce equality of colour with white light, 

 they will still be in adjustment if the light should become 

 tinged with yellow. 



Let «/j and y^ denote the effective yellows in one of the 

 cylinders with white incident light and with yellow light ; 

 then we shall have 



y,=[iqYt, 



y^ = Yr—Yrm^qt-{-YpiiJi,qt. 



Now suppose the length of the column of coloured liquid 

 to be altered a little so as to become t + ^t ; let ^(/^ and dy^ 

 denote the alterations in the effective yellow in each case, 

 then 



h2.= {Yp,fMq-Yrm,q)dt, 



ly^^Y^qlt. 

 Hence 



^^-^^ = -{Yrm^q + tJiqY{i~-p^)}dt. 



Therefore %j is less than ly^ ; that is to say, we shall not 

 see so much difference of colour for a given alteration of 

 depth when the light is tinged with yellow as when it is 

 white; therefore the sensibility of the method is diminished. 

 This may be put in another way. When the incident 



