PROFESSOR MOSELEY ON THE THEORY OP MACHINES. 289 



Substituting this value in the preceding equation (1.), 



2Ui = 2U2 + 2t. + ^(Vi2-V/)?toX2 (2.) 



This equation expressing a relation between the work 2 Uj done upon the moving 

 point of a machine, and that 2 Ug yielded at its working points, it is proposed to call 

 the Modulus of the machine. 



If the velocity Vj of the moving point be constant, or if it return to the same value 

 At the expiration of each period, then 



Vi = V2, and 2 Ui = 2 U2 + 2 u. 



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 (cceteris 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 Vg, we obtain 





It is evident from this equation, that any inequality between the work 2 Uj done 

 upon the moving point, and that 2 Ug + 2 w 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 «/ X^ is greater or less. 



It is proposed to call this quantity, which has a diflferent 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 Pi represent the pressure upon the moving point of a machine, and Pg Pj — P^ 



