20 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



elementary portions, the area of auy one of which is hdx, and the pres- 

 sure that it experiences is 



dD=^{A-{-xfd.r 



consequently the pressure against the "wliole disk, found by taking the 

 integral from x = — ^h to jc = + ^h, is 



or the average normal pressure on a unit of surface is 



F a'e 

 If now I seek that value of x which belongs to the elementary area that 

 experiences a pressure the same as this average, then it represents tlie 

 center of pressure for the whole disk. The result is, 



A+x=B=^ A'-^^Kh'' 



For circular disks we again take A as the distance of the center from 

 the axis of rotation, while the radius of the disk is p. In the division 

 of the disk into elementary vertical sections I indicate the limits of 

 these by the angle tp which is measured from the horizontal diameter. 

 The area of such a section is then 



2 <^sin cp^ (1 q) 



and the pressure that it experiences is 



ai)J^(^±±J'^\' sin cp^dcp 



By expanding the binomial and converting the cos^<^ and cos'*^^ into 

 the sines of the multiple angle, the integration becomes very simple and 

 the greater part of the terms disappear since the integral is taken from 

 coS(p = — 1 to cos (^ = 4- 1. We obtain 



and the section that experiences this average pressure is that whose cp 

 satisfies the equation — 



A-\-p cos cp=B:=J A^-\-jp'^ 



It follows that in both kinds of disks the difference between A and 

 the desired B remains very small when, as in my apparatus, A is very 

 large compared with h and p. 



Next, a series of observations will be communicated, made with five 

 pairs of circular disks, whose diameters were 2.5, 3.5, 4.5, 5.5, 6.5 inches. 

 Each time only two diflerent weights were laid in the scale-pan ; with 



