PROFESSOR MOSELEY ON THE THEORY OF MACHINES. 
289 
Substituting this value in the preceding equation (1.), 
+ + ( 2 .) 
This equation expressing a relation between the work 2 Uj done upon the moving 
point of a machine, and that 2 U 2 yielded at its working points, it is proposed to call 
the Modulus of the machine. 
If the velocity V x of the moving point be constant, or if it return to the same value 
at the expiration of each period, then 
Vj = V 2 , and 2 Uj = 2 U 2 + 2 m. 
This may be called the modulus of uniform or periodical, and the other that of 
variable motion. The modulus is thus in respect to any machine, the particular form 
applicable to that machine of the above equation, and being dependent for its amount 
upon the amount of work 2 u expended upon the friction, and other prejudicial re- 
sistances opposed to the motion of the various elements of the machine, it measures 
in respect to each such machine, the loss of the work due to these causes, and 
therefore constitutes a true standard for comparing the expenditure of moving power 
necessary to the production of the same effects by different machines, and (c ceteris pa- 
ribus) a true measure of the working qualities of such machines. It has been the 
principal object of the researches which the author proposes to submit to the Society, 
in this and a subsequent paper, to develope these properties of the modulus under a 
general form, to determine the particular moduli of some of those elements which 
enter most commonly into the composition of machinery, and to deduce the moduli of 
various compound machines, by a general method, from the moduli of their component 
elements. 
4. Solving equation (2.) in respect to V 2 , we obtain 
V 2 *-V 1 * = 2 g 
f 2 U 1 — 2 U 2 — 2 m 
2 
}• 
It is evident from this equation, that any inequality between the work 2 U x done 
upon the moving point, and that 2 U 2 + 2 u yielded upon the work done, and upon 
the prejudicial resistances, produces a greater or less variation in the velocity of the 
machine, according as the quantity represented by 2 w X 2 is greater or less. 
It is proposed to call this quantity, which has a different value under every different 
mechanical combination, and which is here, it is believed, first introduced into the dis- 
cussion of the theory of machines, the coefficient of equable motion. Being determined 
in respect to any machine, it measures (every other consideration being excepted) the 
greater or less steadiness of the motion, which is maintained by that machine under 
a given variation of the power which impels it. 
5. General form of the Modulus of a Machine. 
Let P x represent the pressure upon the moving point of a machine, and P 2 P 3 P ( 
