resting upon a Vibrating Support. 55 
is required of it; and after a few successes repetition becomes 
easy. If w e wish not merely to see the progressive waves, 
but to measure the velocity of propagation with some approach 
to accuracy, further assistance is required. In my experi- 
ments an endless string, passing over pulleys and driven by a 
small water-engine, travelled at a small distance above the 
plate so that its length was in the direction of wave-propaga- 
tion. A piece of wire was held at one end by the fingers, and 
at the other rested upon the travelling string and was carried 
forward with it. In this way, by adjusting the water supply, 
the speed of the string could be made equal to that of wave- 
propagation; and the former could easily be determined from 
the whole length of the string, and from the time required by a 
knot upon it to make a complete circuit. Thus (on February 7) 
the velocity of propagation was found to be 5*4 inches per 
second. At the same time, by measurement of the pattern as 
seen by ordinary vision, 14 X =4§ inches. Hence frequency 
= -^— =15 - 5 per second; exactlv one half the observed fre- 
A. 
quency of the bar, viz. 31. 
In addition to the phantoms which may be considered to 
represent the four component progressive waves, others may 
be observed travelling in directions inclined at 45°. If we 
take coordinates f , rj in these directions, (5) may be written 
4 cos — ^r cos — -.cos nt; (7) 
V2 V2 v 
in which if we put 
V2 V2 + 
(i. e. if we suppose the eye to travel with velocity V2 . n/ic), 
we get 
2 cos —~ cos — ^r + terms in 2nt. 
The non-periodic part may be supposed roughly to represent 
the phenomenon. 
In order if possible to settle the question beyond dispute, I 
made yet another comparison of the frequencies of vibration 
of the fluid and of the support, using a plan not very different 
from that originally employed by Faraday. A long plank 
was supported on trestles at the nodes, and could be tuned 
within pretty wide limits by shifting weights which rested 
upon it near the middle and ends. At the centre was placed 
a beaker 4£ inches in diameter, and containing a little mer- 
cury. The plank was set into vibration by properly timed 
