10 
will be WoR n (l — p) + W 0 p. If we suppose n to become 
infinite the whiteness becomes Wo p, being the whiteness or 
greyness of the so-called black body. We might also have 
deduced the formula as follows : take a white area 
A, then the quantity of white light given off we may 
denote, by g A ; now let a series of grey points to fall upon 
this, let a be the area of the spots, then the quantity of 
white light given off by this we may denote by fxi a, the 
uncovered white area will be A — a, and the quantity of 
white light given off by this will be g( A — a), therefore the 
whole quantity of white light will be /^(A — a)+yia, or 
juAR-P/iia if It be written for 1 - If we suppose another 
series of grey points distributed over the surface, the un- 
covered white area will be AR 2 , and the surface covered by 
the grey points will be A — AR 2 , so that the quantity of 
light will be /i AR 2 -f — AR) 2 . If the operation be 
repeated n times the expression for the residual whiteness 
will be juXR n + ij}(A — AR n ) which may be written in the 
form juA(R n (l — p)+p), when p—~, also g A=W 0 , the initial 
whiteness so that the expression is equivalent to the one 
previously given. 
On the Theory of Engraving. 
Another subject of Interest in Colorimetry is the theory of 
engraving, which I think has never been considered. In 
this art various shades of grey are given to white surfaces 
by aggregations of lines or dots, giving rise to line, mezzo- 
tint, and other varieties of engraving. If the tint be 
produced by lines, it may be estimated as follows. Take a 
white square area A and rule it with parallel lines. The 
quantity of white light given off initially we may denote 
by juA. Let b be the breadth of one of these lines and l its 
length ; also suppose that then an n of these lines, then the 
white area uncovered will be A — nhl. Suppose n to become 
