1326 
§ 2. We shall now ascribe a greater mobility to the system by 
imagining that the outer particles too can be displaced, with the 
restriction, however, that for any instant their coordinates can be 
found by multiplying by ‘the same factor 1-+ q the coordinates 
which they had in the case considered in the preceding paragraph. 
Then, the quantity g, which we shall suppose to be very small 
compared with 1, will determine the position of the outer particles 
and by suitably extending the meaning of q,,....4qs, these para- 
meters may be made, together with g, to determine the position of 
the entire system. | 
Indeed; Jet’ P,P’: P's «bef the points which are found if 
the coordinates of P, P', P",... (§ 1) are altered in ratio of 1 to 
1-+q simultaneously with the coordinates of the outer points, let 
, 7,5, §',7',$’... be the components of the deviations of the particles 
from these positions P, P’, P",... and let g,, q,---qs be quantities 
connected with §&, 7,6, &',7',¢' in the way shown by equations (3), 
if we continue to-assign- toa, 8, y the values we had to give them in 
the preceding paragraph. Then it is clear that the configuration of 
the whole system is really determined by q,q,-..¢s. The quantity q 
being now considered as variable, so that, though the places of the 
outer particles 7 the surface S be prescribed, this surface, keeping the 
same form, may dilate or contract as a whole, a constant value of 
q, Le. a constant volume, can in general be maintained only by the 
application of an external force Qcorresponding to that coordinate. 
It is precisely this foree which we want to know, especially for the 
case q=0, i.e. for the configuration of the body with which we 
began in § 1. 
The value of Q is connected with that of the external pressure, 
for Q is defined by the condition that, for an infinitesimal variation 
dq of the coordinate g, the other coordinates remaining unchanged, 
the work of the external forces is Qdg. If now this change takes 
place starting from the value g — 0, all dimensions of the surface 
increase in ratio of 1 to 1 + dg. The volume increases by 3v. Òg 
and the work of the external pressure is — 3pv. dq. Hence 
QE BD peta SN 
$ 3. The force Q may be determined by means of the equations 
of LAGRANGE, as soon as the potential energy U and the kinetic 
energy J’ are known as functions of all the coordinates q and the 
corresponding velocities, 
Then we have . 
