Relation of Mass to Energy. 3 
vector is, however, zero. The energy transfer is not through 
space in the ordinary sense, but is along the constraint which 
holds the condenser-plates apart. The plate in the rear picks 
up, as we may say, the energy of the field, and after it has 
been transmitted to the forward plate by means of the constraint 
it is there set down again. On the other hand, when the 
condenser is mosdng parallel to the plane of the plates, there 
is no energy flow along the constraint and the Poynting 
vector adequately represents the transfer of energy. So also 
in the case of a single moving electron, the rate of transfer 
of energy is not given by the integration of the Poynting 
vector through all space, but differs from this by an amount 
corresponding to the energy- flow along the constraints in the 
body of the electron. This does not mean that there is any 
energy associated with the constraints, for of course rigid 
constraints can neither absorb nor give out energy; there is 
no storing up, but merely a transfer. 
5. It is not difficult to find an expression for this rate of 
transfer. If the constraint is a simple linear one the transfer 
of energy along its direction is evidently 
-nv, 
where (/) is the length of the constraint, (V) the velocity with 
which it is moving along its length, and (T) the tension 
along it. The amount of energy (TV) per sec. is put at the 
forward end, and is instantly available at the rear end at a 
distance (I). If the velocity (v) makes an angle (0) with the 
constraint, v'=v cos 0, and the transfer in the direction of v is 
-ZT«cos 2 0. 
Another type of transfer enters when there is shearing- 
stress in the constraint, a transfer that is which is in a 
direction perpendicular to that of velocity. It must be 
remembered that the constraints~Hre described in no way 
except geometrically. 
If we consider therefore the general case where the stress 
in the body of the constraint is represented mathematically by 
the nine stresses commonly used in the theory of elasticity, 
namely, Xx, Y x , Z x , X y , Y y , Zy, X~, Y% Z 2 , then there is a 
rate of transfer of energy in the a?- direction through unit 
volume given by 
ft == — (v x + X x ^ Y x 4- v z Z x ) . 
B2 
