[ 285 ] 



XXI. Researches in the Theory of Machines. By the Rev. Henry Moseley, M.A., 

 F.R.S.f Prof. Natural Philosophy and Astronomy y King's College^ London. 



Received June 10, — Read June 18, 1841. 



JL HE work of a mechanical agent may be defined as the union of a continual 

 pressure with a continual motion. The work of overcoming a pressure of one pound 

 through a space of one foot, is in this country taken as the unit in terms of which 

 any other amount of work is estimated*. The work of any pressure operating 

 through any space is evidently measured in terms of such units, by multiplying the 

 number of pounds in the pressure by the number of feet in the space, if the direction 

 of the pressure be continually that in which the space is described. If not, it follows, 

 by a simple geometrical deduction, that it is measured by the product of the number 

 of pounds in the pressure, by the number of feet in the projection of the space de- 

 scribed-}-, upon the direction of the pressure ; that is, by the product of the pressure 

 by its virtual velocity. Thus then we conclude, at once, by the principle of virtual 

 velocities, that if a machine work under a constant equilibrium of the pressures 

 applied to it, or if it work uniformly, then is the aggregate work of those pressures 

 which tend to accelerate its motion, equal to the aggregate work of those which tend 

 to retard it ; and, by the principle of vis viva, that if the machine do not work under 

 an equilibrium of the forces impressed upon it, then is the aggregate work of those 

 which tend to accelerate the motion of the machine, greater or less than the aggre- 

 gate work of those which tend to retard its motion by one-half the aggregate of the 

 vires vivae acquired or lost by the moving parts of the system, whilst the work is 

 being done upon it. In no respect have the labours of the illustrious President of 

 the Academy of Sciences more contributed to the development of the theory of 



* The sense in which the term toork is here used, will be recognised to be that in which " dynamical effect," 

 " efficiency," " work done," " labouring force," &c. have been understood by different English writers, and 

 " moment d'activit^," " quantity d'action," " puissance mecanique," " travail," by the French. Among the 

 latter this variety of terms has at length given place to the most intelligible and the simplest of them, " travail." 

 The English word work is the obvious translation of " travail," and the use of it appears to be recommended 

 by the same considerations. M. Dupin has proposed the application of the term "d3mame" to a unit of 

 work. The author of this paper has gladly sheltered himself from the charge of adding to the vocabulary of 

 scientific words by assuming the term itself, " unit of work," to represent concisely and conveniently enough, 

 without translation, the idea which is attached to it. 



t If the direction of the pressure remain always parallel to itself, the space described may be any finite 

 space ; if it do not, the space is understood to be so small, that the direction of the pressure may be supposed 

 to remain parallel to itself whilst that space is described. 



2 p2 



