58 
Mr. W. Baily's Illustration 
from which it appears that in every case the shifting is in the 
direction of propagation of waves of higher pitch, or towards 
the source of graver pitch. 
According to Matthiessen, the shifting takes place with a 
velocity equal to half the difference of velocities of the com- 
ponent trains, i. e. 
"-1-* < 13 > 
and in the direction of that component train which moves with 
greatest velocity. So far as regards the direction merely, the 
two rules come to the same thing for the range of pitch used 
by Lissajous and Matthiessen, since over this range the velo- 
city increases with pitch. If, however, we have to deal with 
waves longer than the critical value (1*7 centim. for water), 
the two rules are at issue, since now the velocity increases as 
the pitch diminishes. The following are a few corresponding 
values, in C.Gr.S. measure, of wave-length, velocity, and fre- 
quency of vibration calculated by Thomson's formula (A). 
Wave-length., 
Velocity 
Frequency .. 
•5 
31-48 
62-97 
1-0 
24-75 
24-75 
1-7 
23-11 
13-60 
2-5 
23-94 
9-579 
3-0 
24-92 
8-306 
5-0 
29-54 
5-908 
I have examined the matter experimentally with the aid of 
vibrators making from 12 to 7 complete vibrations per second, 
and therefore well below the critical point, with the result that 
the transference is towards the source of graver pitch, although 
this is the direction of propagation of the component which 
travels with the smaller velocity. I reserve for the present a 
more detailed description of the apparatus, as I propose to 
apply it to the general verification of Thomson's law of ve- 
locities. 
VIII. An Illustration of the Crossing of Rays. 
By Waltek Baily*. 
[Plate I.] 
WHEN rays of light are passing through a point, the re- 
sultant motion of the rether is in general far too com- 
plicated to be conceived; but if the light is homogeneous, it 
can readily be shown that the motion at each point is simply 
harmonic motion in an ellipse ; so that in that case the 
* Communicated by the Physical Society; read May 2G, 1833. 
