THEORY OP ENGRAVING. 81 



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 sur- 

 faces by aggregations of lines or dots, giving rise to line, 

 mezzo-tint, and other varieties of engraving. Tf 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 fiA. Let b be the breadth of one of these lines 

 and / its length; also suppose that there are n of these lines ; 

 then the white area uncovered will be A — nbl. Suppose 

 n to become very great and b very small, so that we no 

 longer have the impression of black lines on a white sur- 

 face, but see a uniform grey surface ; then the expression 

 for its degree of whiteness will be fjL(A — nbl) or W (i — nr) 



if r denote -r. 



A 



Sometimes an engraver, instead of using parallel lines 

 only, crosses the lines (cross hatching). With a given 

 number of lines the tint will not be the same if he draws 

 them all parallel, and if half are drawn at right angles to 

 the others. Suppose we have in lines. If drawn parallel, 

 the degree of whiteness will be W (i — inr) ; but let n of 

 these lines be drawn perpendicular to the remaining n. 

 Take the case of one of these perpendiculars : it will inter- 

 sect one of the first series in a square whose area is b z ; and 

 as it is cut by n lines, the sum of these will be nb z ; the 

 additional white area blotted out by this line will be 

 lb — nb z ; and since there are n such lines, the total area 

 they blacken will be n(lb — nb z ). Hence the remaining 

 white area will be A—nlb—(nlb — nb z ), which may be 

 written A(i— nr) z , since l z = A. If W x denote the white- 



SER. III. VOL. VIII. G 



