154 ON MR. EWART’S PAPER ON THE 
therefore, given to the principle of vis viva, when 
applied to the motion of machines, the following 
new enunciation :—‘ The difference between the 
aggregate work done upon a machine, during 
any time, by those forces which tend to accelerate 
the motion, and the aggregate work during the 
same time of those which tend to retard the motion, 
is equal to the aggregate number of units of work 
accumulated in the moving parts of the machine 
during that time, if the former aggregate exceeds 
the latter, and lost from them during that time if 
the former aggregate fall short of the latter.”— 
(Preface p. 9.) 
Professor Moseley expresses this by the follow- 
ing formula, which is in agreement with those of 
Poisson: 
1 
2 U,==0,+ Du+ 9g ue (v2 —v,) 
Where =U, represents the number of units of 
work done upon the machine by the moving 
power, =U, the units of useful work performed, 
wu the work consumed in overcoming friction and 
other resistances, v, and v, the velocities at the 
commencement and termination of the period of 
: 1 
working, and ag2 ( v—v;) half the aggregate 
difference of the vires vive of the moving ele- 
