290 
PROFESSOR MOSELEY ON THE THEORY OF MACHINES. 
the pressures upon its different working points, and let that relation which obtains at 
any period of the motion between the moving pressure P x and the working pressures 
P 2 , P 3 , &c., when in the state bordering upon motion, and subject to the various 
prejudicial resistances under which the machine works, be represented by 
Pi = F (^2’ P35 & c -) ( 3 -) 
Let q, s 2 , s 3 , &c. represent the spaces described in the same exceedingly small time 
by the points of application of P l5 P 2 , &c., if these points move in the directions in 
which those pressures severally act, and if not let them represent the projections of 
these spaces on the directions of the pressures. Then are these spaces, q, q, & c., evi- 
dently related to the space q by equations of the form 
^ 2 ^2 = ^3 S 3 = ^ 1 > l Jj 4 tV 4 = ^ 1 ? & C - & c *, 
where p 2 , [* 3 , fq, Sec. are certain constant quantities determined by the forms and di- 
mensions of the moving elements of the machine and their combination, or certain 
functions of these and of the space q which the moving point has described from 
the commencement of any given period of its motion. Let now u x represent the 
work of the pressure P x through the space q, u 2 that of P 2 through s 23 Sec. 
Mi 
= Pj q, u 2 = P 2 q, m 3 = P 3 q, &c. 
Pl = 
I ) 
i > “ 5 
P3 = Ac. 
= F (^^ J&C ) ( 4 .) 
Which equation, — expressing a relation between the work u x at the driving point, 
through a small increment q of the space described by that point, and the work 
m 2 , m 3 , See. yielded during the same period at the several working points — is the 
modulus of the machine in respect to an exceeding small motion of its elements. 
If the pressures Pu P 25 &c. remain constant during any given period of the opera- 
tion of the machine, and act continually in the same directions, it is evident that the 
above reasoning obtains whatever may be space q through which the work u l is done ; 
so that the exceeding small quantities u l3 u 2 , Sec. q may in this case be replaced by the 
finite quantities U l5 U 2 , &e. S 1 * ; Sj representing any finite space through which the 
work Uj is done at the driving point, whilst the work U 2 , U 3 , Sec. is yielded at the 
working points of the machine. 
If the pressures P l5 P 2 , P 3 , &c. be variable during any given period of the continuous 
operation of the machine, as it respects their several amounts, or their directions, or 
as to both these elements, then are they (in every case presented in the operation of 
machinery, simply and without the interposition of any voluntary agent) functions of 
the spaces S 1? S 2 , S 3 , &c. traversed by their points of application, and therefore of the 
* If the direction of the pressure P, be other than that in which its point of application is made to move, S, 
must be taken to represent the projection of the space described by that point on the direction of the force. 
