302 Scientific Intelligence. 
in its state of rest or motion for the time being, and which is 
always proportional to the force employed in overcoming it. 
follows from this, that, under = circumstances referred to, the 
t each epoch 
orn throughout the motion. But if the body is at rest to start 
with, and T is divided into equal intervals, the work done at the 
end of the first interval a according to the above measure, will be 
3 = Br = ; that done at the end of the second interval will be 
; F? fe: 2; that at the end of the third interval will be 
1 8T\2 ‘ A 
5 re = )» ete.: and therefore the work done in the first interval 
T [2 1 
- , Will be = = Fa that during the second interval will bes op 
n® 
that saa the third interval will be 5 °F? ei sete. It has ae 
been pointed out, however, that the egal definition of work 
implies that the amount of work done in equal intervals of time 
ill be the same. "it £ ollows, therefore, that the definition and 
measure of work above ee pours each other in the 
case we pete ane considerin 
that, if during the small time T the body moves through the space 
s, and has acquired at the end of T the velocity V, we shall have 
Fs= 4 (MV3-—MV}), 
an equation, be it remembered, which holds independently of the 
magnitude of T, provided F be uniform 
If we put V=V,+2, we shall have 
work = Fs = 4M (v?-L20V, ) (1) 
entirely idence si alike of F, of M 
(3.) The right side of the expression “) wil ‘always be pa 
so long as V, and v have the same sign, i. é so long as the 
tions of the force and the initial nite des conspire. : 
*. 
Spee eed eee Ree SES wo eS 
