292 PROFESSOR MOSELEY ON THE THEORY OF MACHINES. 



In that large class of machines which present but one moving and one working point, 

 the relation between Pj and P2 (equation 3.) will be found to present itself under the 



form 



Pi = aP2 + E; (7.) 



where a is a function of the prejudicial resistances assuming a finite value, which may 

 be represented by a^^\ when these resistances vanish ; and where E is a function of 

 P2 and also of the prejudicial resistances, which vanishes with them. In this case, 



therefore, 



P/o)=:F<«>(P2,P3,&c.) = a<«>P2; 



and by equation 6, 



P 1 



£2 _ „(o) p . ^ i_, 



also 



Pi = F (P2, P3, &c.) = a P2 + E ; 

 therefore, by equation 4, 



w, 



= «^ + E; 



substituting for fOg its value ^5 



7; = ^-l; + E, (8.) 



by which equation the modulus of the machine, in respect to an exceedingly small 

 motion of its parts, is determined in terms of the relation expressed by equation 7, 

 between the moving and working pressures Pj and P, in the state bordering upon 

 motion. Assuming the moving pressure to be applied in the direction of the motion 

 of the moving point, observing that s^, u^, U2 are the increments of S^, Uj, Ug, and 

 passing to the limit, we have by equation (8.), 



.••Ui = ^.U2+/ErfSi, (9.) 



which is the modulus of the machine. If the working pressure be constant, both as 

 to its amount and its direction, E is constant, and the modulus becomes 



U, = ^.U2 + E.S, (10.) 



7. It remains now to consider on what general principles the relation expressed by 

 equation 3. between the moving and the working pressures in their state bordering 

 upon motion, may in each particular case be determined. Amongst these pressures 

 there is, in every machine, included the resistance of one or more surfaces. Did no 

 friction result from the pressure of the- surfaces of bodies upon one another, their mu- 

 tual resistance would be exerted in the direction of the common normal to their point 



