450 The Rey: S. Earnshaw on a new Theoretical 
denoted by /) is much greater than Dalton’s experiments warrant, 
and than what would have been conjectured apriori to be its value. 
In looking also at the determinations of its value, and also of the 
value of the velocity of sound, I am a little suspicious that modern 
experimentalists have suffered themselves to be biassed by a de- 
sire to make experiment and theory agree. At any rate, if we 
compare experiments made since 1816, when Laplace announced 
his theorem for the correction of Newton’s result, with those 
previously made, it is impossible not to notice a very sudden and 
startling change ; and in the same spirit the value of & has been 
gradually growing in the hands of experimentalists till it is now 
large enough really to justify the opinion which has been ex- 
pressed, that to Laplace is due the honour of having completed 
the solution, which was begun in England, of the problem of the 
propagation of sound. And, to speak candidly, it must be con- 
fessed that Laplace’s sagacious suggestion undoubtedly has the 
air of a vera causa, although it requires a larger development 
of heat by the sound-wave than seems probable. But its great 
defect, if I may be allowed to consider it defective, is that the 
result it gives does not come up to experiment. The theoretical 
velocity, after being amended by Laplace’s suggestion, still falls 
short of the experimental velocity by 24 feet, if we take this last 
to be 1090 feet ; and by 76 feet, if we take the velocity of sound 
to be 1142 feet as determined by Derham, Flamsteed, Halley, 
and the Florentine Academicians. It should be remembered also 
that theory might a priori be expected to give aresult exceeding, 
rather than falling short of, experiment ; for theory assumes the 
elasticity and fluidity of the atmosphere to be perfect, and we 
have reason to think both are really in a slight degree im- 
perfect ; and this is not likely to accelerate, but rather to retatd 
(if it at all affect) the propagation of sound-waves. Upon the 
whole, after considermg the matter in as impartial a spirit as 
possible, candour obliges me to confess that Laplace’s suggestion 
does not furnish a sufficient cause. I do not deny that it may 
be a cause; but it is not the whole. There is a cause; still 
unrevealed, for the defect of the theoretical velocity. Euler 
considered that some part of the error of theory might be due 
2 
to the incorrectness of analysis in assuming (%) = 1 previ- 
ously to integrating the differential equation ; and certainly, as 
this was an arbitrary step, it was reasonable to suppose it might 
in some way have the effect of making the theoretical result 
smaller than it would be were the equation integrated without 
making use of approximative steps. When therefore I sue- 
ceeded in integrating it without approximative steps, I was 
disappointed: to find that the theoretical velocity of a sounds 
