227 
+ a m^ H + &C- If we use the letter I to denote incident 
light, T to denote transmitted light, and A absorbed light, 
Herschel’s formulae may be written more briefly as follows : 
2ct = I, 2aJc t = T, 
k will be a function of the quantity of colouring matter pre- 
sent in a unit thickness. If g be that quantity we may 
write Jc=f(g), or if we expand &=/( 0) — /'(())(/ + higher 
terms in g. Now, g is very small. Let then the terms 
higher than the second be neglected. The first term will 
be the light transmitted when no colouring matter is present. 
If the colouring matter were dissolved in an absolutely 
transparent medium, the first term would be unity. In 
practice water or some colourless medium is used ; but the 
amount of light absorbed by a thin layer of pure water is 
very small, so that we shall make only a very small error in 
writing /(0)=1. Hence k= 1 — f(0)g. Substituting this 
value in Herschel’s formula and expanding, we have 
2ct - 2af(Q)gt + &c. 
Now, as g is very small, .we may neglect terms beyond the 
two first (unless t be very large). Hence 
2 a f(Q)gt = I - T = A. 
If we assume the colour to be constant, A will be a constant 
term. Now, let Q denote the whole quantity of colouring 
matter in the cylinder, and L the whole length of the co- 
lumn; then g— A. and the formula may be written 
2af(tyj~== A, orQ* = = constant. 
