Prof, Challis on a Theory of Magnetic Force. 93 
each of the order of the square of the velocity, as is shown by 
the general differential equations involving the pressure, no 
extraneous force being supposed to act. Nowif w, v,, w,; 
Up) Voy Wo, &e. be velocities due to different disturbances acting 
separately, and each set of valucs satisfy separately the second 
of the above equations, it is evident that if w=u,+u + &ce., 
v=v,+2,+ &e., w=w,+w.+ &e., u,v, w will satisfy the same 
equation. From this reasoning it follows that when several 
causes of steady motion coexist, the velocity they produce con- 
jointly at any point, is the resultant of the velocities which they 
would produce at the same point by acting separately. Hence 
since the component motions, being steady, are constant in 
magnitude and direction at each point, the resultant motions 
will be constant in magnitude and direction at each point; that 
is, the whole motion will be steady. 
16. Hence in the general hydrodynamical equation applicable 
strictly to steady motion, when no extraneous force acts, viz. 
2 
a* Nap. log p= c-¥ 
we may assume, since terms involving the square of the velocity 
have been taken into account, that V is the resultant of several 
velocities, v', vo’, &c., given in magnitude and direction. Take, 
for instance, the two velocities v! and v”, and suppose their direc- 
tions to make an angle a with each other. Then 
V2=0? +y!? + 20'v! cos a. 
From this equation it is seen that if the value of C be given, 
the velocity is greatest and the density and pressure least, where 
a=0, that is, where the two streams coincide in direction; and 
that the velocity is least, and the density and pressure greatest, 
where a=7 and the two streams are in opposite directions. 
In general the constant C will be different for different lines 
of motion. But in the cases of convergent streams flowing from 
an unlimited distance, and divergent streams flowing to an un- 
limited distance, at remote points p=1 where V=0, and con- 
sequently C=O for each of the lines of motion. 
17. The hydrodynamical theorems above demonstrated are 
those which have been used in accounting for electric attrac- 
tions and repulsions, the mutual action between two electrodes, 
that between an electrode and a magnet, and the mutual attrac- 
tions and repulsions of magnets. It is to be remarked that in 
these explanations the moving forces of the ether acting on the 
ultimate atoms of bodies have been supposed to be due to varia- 
tions of its density, producing statically differences of pressure 
at different points of each atom. But if motion resulted solely 
from variation of the density of the ether from point to point 
