10 
DR. TYNDALL ON VIBRATIONS AND TONES. 
than when it is a bad one. It cannot be denied that the greater the quantity of heat 
transmitted, the greater will be the expansion; and henee the eonelusion seems 
unavoidable, that, if the vibration be due to expansion, both rocker and bearer, other 
things being equal, ought to possess the power of conduction in the highest possible 
degree. 
Assuming then that the effects are produced by ordinary expansion, the argument 
of Professor Forbes stated in its severe logical form would be as follows : — 
The greater the expansion the greater will be the effect ; but, 
The greater the conducting power the greater is the expansion : therefore, 
The greater the conducting power the greater will be the effect. 
This, to all appearance, is conclusive. A slight inadvertence, however, in the use 
of the term ‘ expansion’ appears to deprive the argument of much of its force. In 
the first proposition the term means expansion in a vertical direction ; for if this be 
not meant the proposition would be untrue. In the second proposition, however, 
it is the total expansion that is referred to*. Now supposing the conductivity of the 
bearer to be infinite ; that is to say, that the quantity of heat which it receives from 
the rocker during contact is instantaneously distributed equally throughout its 
entire mass, then, although the total expansion might be very great, there would be 
no local expansion at all, and therefore none of the effects in question. The expan- 
sion we require is a sudden elevation of the point where the rocker comes into con- 
tact with the bearer, and it is manifest that “a rapid communication with the inte- 
rior” may, by suddenly withdrawing the heat from the point where it is communi- 
cated, almost, extinguish the requisite elevation, and thus prevent the vibrations. 
This appears to be the precise reason why Professor Forbes has failed to obtain the 
numerous results described in the foregoing pages. His bearers were of such a form 
that the mass of matter immediately surrounding the point of contact quickly abs- 
tracted the heat communicated to that point, and thus destroyed the condition upon 
which the vibrations depend. The success of the experiments described in this me- 
moir depends on the precaution, that the abstraction of heat was prevented, to some 
extent, by reducing the bearers to laminse and mere spikes ; and the fact that a thin 
edge gave a better tone than a thick one thus receives a full explanation. These 
considerations, 1 think, render it. clear that the cause of the superiority of lead assigned 
by Professor Faraday is by no means an “ oversight.” On the other hand it would 
not be safe to affirm generally, nor has it been affirmed by the philosopher last 
mentioned, that the less the conducting power the greater will be the effect. In the 
case of glass and earthenware the vibrations soon come to an end, for the requisite 
difference of temperature between rocker and bearer, as anticipated by Professor 
Forbes, soon ceases. Perfect non-conductibility would be just as inefficacious as per- 
fect eonductibility, and the region of practical results lies between these two extremes. 
* Seebeck makes use of the same argument. — J. T. 
Royal Institution, January, 1854. 
