﻿368 Canon Moseley on the Mechanical Impossibility 



Weight of vertical lamina VmnQ, = Jw?(PQ f mn) Ym dec. 

 Normal pressure of weight on mn = weight x cos i. 

 Friction of weight of Pm n Q on mn = /weight x cost. 



... , . , , dmn 7 



Distance traversed by m n over mn = — 1 — ay. 



Work of friction of P m n Q on mn 



= \wf cos i{YQ, + mn)¥m—j—dxdy. . . , (5') 



_ g/3+*7(*-/3) , [ fl/3+^(«-ffl] [ 6y + y(/3-y)] 

 r^ + mn- ^ + ^ 



_ [*j8+a<a-|S)][(|3+7)& + y(0-y)] 



^77m _ (/3— y)[fl|3 +#(*-- /3)] . 

 dy ~ ab(3 ' 



.'. work of friction of PmwQ on /«w 



= Wf 7ail~ 7) N3+*("-fflTO+y)a+ (g-y)y] (b-y)dxdy, 



+ {P-7)y~\(b-y)doc dy, 



u 4 / cos ,= ^1=^ [i> 3 « 3 -«W LiO+r> 3 

 +i(/3-y)i 3 ]], 



Work of friction of lamina P p q Q on p q 



= weight YpqQ x cos o xfx \pq> 



(8) 



weight TpqQ = w; P/? . ^ PQ + jsg rfa? 



_ 1 ^[fl/3 + <a-/3)"j(/3 + 

 " 2 a/3 



