98 Lord Rayleigh on the Regularity of 



avoid confusion. Thus along the shorter side measurements of 

 the overlap were made at the ends L, N and at the middle M, 



M 



and on the parallel side at P, Q, R. The differences of these 

 overlaps, suitably averaged by the formulae of the calculus 

 of finite differences, give b' —b. It is hardly necessary to 

 explain the process further. The results were 



= -•0032, 



= +•0379 



and thence 



a'V—al> _ a' -a V -b (a! —a)(b' -I) 



ab a b ab 



= +'0379--0032--0001 = -0346. 



This is the fraction by which the area of marked exceeds 

 that of plain. The difference between this fraction and that 

 found above for (w f —w)lw indicates that marked is thinner 

 than plain by the fraction '0010. 



The total thickness is most easily found from the weight 

 and area with the aid of an assumed specific gravity (2*8) . 

 For plain we get 



thickness = '0306 mm. = '00120 inch. 



The difference of thickness in the two pieces resulting from 

 the observations on weight and area is thus little over a 

 millionth part of an inch, and might perhaps be considered 

 as devoid of significance. But it is difficult to admit that 

 either the weights or the areas could be in error to the extent 

 of a thousandth part. I am disposed to think that the dis- 

 crepancy is real in the sense that it would not be eliminated 

 by repetition. Possibly it may be attributed to differences 

 in the condition of the surfaces which had been handled 

 more than was good for them. There are also scratches and 

 other minor irregularities to be considered. 



