Molecular Constants. 323 
or by an endless succession of masses A 1 moving at the rate r x at 
a distance d apart, and an endless succession of masses A 2 
moving at the rate r 2 at the same distance d apart : or by the 
same masses A x and A 2 returning at equal intervals with the 
velocities r x and r 2 . 
These statements may be illustrated as follows: — Let there 
be (Plate IV. fig. 1) an annular tube b of 12 cub. centim. 
capacity, and let there be 1 cub. centim. of water at a. At 
whatever rate a may pass round b, the density of the path is 
the same, namely ^. If it move round at the rate of once 
in a second, let its path-density be Pd. If, now, it moves round 
n times in a second, then in expression (1) r becomes nr, and 
I becomes nl; so that Vd remains unchanged. 
Again, if the tube b be doubled in length, the path-density 
will be halved at whatever rate a may move. 
§ 6. "When an irregularly* shaped mass of uniform density 
moves with uniform velocity in a straight line, the path is of 
uniform density longitudinally but varies in density trans- 
versely (like a sword-stick). 
Taking the case of a triangle moving on its base (fig. 2, 
PL IV.), we have at once 
Pda = a_ 
Vd b b' 
The distances a and b are here indeed nothing more than 
the expression I in § 3, equation (1). 
§ 7. If Z be constant, that is if the moving matter have 
equal thickness all over in the direction of its motion, varia- 
tion in density at different parts will of course produce corre- 
sponding and proportional variation in the path-density. 
It follows that a heavy sector of a circle of unit density 
revolving about the centre of the circle will give rise to a path 
a 
which is of uniform density, and whose density is Qp AO , if 6 be 
the angle of the sector. The shadow of such a disk is uni- 
formly dense or the moving disk is equally transparent to light. 
If a heavy line revolve about one of its ends, the density of 
the path, which is a circular surface, varies inversely with the 
distance from the centre. The shadow of such a revolving line 
(or narrow strip) varies in density according to the same rule. 
§ 8. The path-density of a heavy plane moving parallel to 
itself, as in § 3 (/3), but inclined to its path at an angle 6, is 
— — g , if ^d be, as before, the path-density, when the plane is at 
* Any shape excepting a prism haying parallel back and front faces. 
2A2 
