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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 P 2 (equation 3.) will be found to present itself under the 
form 
Pj = a P 2 -j- E ; (7-) 
where a is a function of the prejudicial resistances assuming a finite value, which may 
be represented by a (0) , when these resistances vanish ; and where E is a function of 
P 2 and also of the prejudicial resistances, which vanishes with them. In this case, 
therefore, 
P/o’ = F (0) (P 2 , P 3 , &c.) = « (0) P 2 ; 
and by equation 6, 
also 
- 2 = « ( o’ P 2 
^2 1 
1^2 — a ( 0) 5 
Pj = F (P 2 , P 3 , &c.) - a P 2 + E ; 
therefore, by equation 4, 
— = a 
+ E ; 
substituting for (a 2 its value — 
( 0 )’ 
u j a 
? + 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 2 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 q, u l} u 2 are the increments of S l5 U l5 U 2 , and 
passing to the limit, we have by equation (8.), 
d F i a d U 2 p 
~ a {0) ' dS, ^ 
••• u, = ^ . U 4 + fEdS,, (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, . u 2 + E.Sj ( 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 
