FREE and perfectly elastic molecules in a state OF MOTION. 41 
given to the molecules at its extremity can be conveyed through tire medium only by 
means of the molecular encounters, each of which contributes to this effect with 
different velocities resolved in the direction of the cylinder. It has been shown that 
the mean traversed distance in a given space during a given time due to any one 
molecular velocity is as the square of that velocity multiplied by the proportion of 
the number of molecules associated with it. Therefore, the united effect of all 
velocities must be equal to the sum of these products, and this sum is unity, or the 
whole medium multiplied by the mean square molecular velocity. But it was shown 
that if the molecular velocity were constant and ecpial to v, the absolute value of the 
mean resolved velocity, or traversed distance, during a constant time in one direction, 
would be v . Now, as the traversed distance or transmitting effect of this velocity 
in comparison to the other velocities u, &c., as they actually exist in the medium, is 
as -y 3 to u 2 , &c., we arrive at the conclusion that \v is actually the uniform velocity with 
which an impulse is transmitted through a medium. 
§ 41. According to the reasoning in §§ 27 and 28, the value of v is the velocity 
acquired in falling through three uniform atmospheres. This gives \v = 1122 feet per 
second at the temperature of melting ice, and 1176 at the temperature of 80°, being 
an increase of fth of a foot for each degree. In the article, “ Acoustics,” ‘ Penny 
Cycl.,’ it is stated that 1125 feet per second at 62° accords nearly with the mean of 
the best experiments, and that the difference for 1° is f-ths of a foot. The velocity 
hy the hypothesis is therefore about ^ part greater than is found by observation, 
which, in a distance of 8 miles, amounts to a difference of one second in the time of 
travelling that distance. This is probably a greater difference than can be allowed 
between observation and a correct theory. M. Moll’s observations, which seem to 
be standard authority, were taken with such precautions that an error of 1 in 
40 seconds can hardly be admitted. They likewise agree remarkably well with 
Mr. Goldingham’s observations at Madras. 
In taking astronomical observations of the same kind with the same instrument, 
it has lately been discovered that two individuals differ sensibly from each other. 
This has led to the suspicion that in all observations there is a personal error due to 
some obscure physiological cause that allows a small interval of time between 
sensation and perception, or volition. If this were the same for the sense of hearing 
as for vision, it could not affect the results of experiments on sound ; but it is quite 
possible that it may be different, and the very fact that such personal errors do 
exist, may justify a suspicion that such an effect might interfere and prevent a 
perfect degree of accuracy from being obtained. 
We have made no hypothesis of the nature of the impinging surfaces of the 
molecules. May the discrepancy arise from something omitted in this ? 
In other media, according to this theory, the velocity varies as the inverse square 
root of their specific gravity, and at different temperatures as the square root of the 
absolute temperatures. It depends wholly on the thermometer, and is quite inde- 
MDCCCXCII.—A. G 
