and the Observed Velocity of Sound in Air and Gases. 9 



in relation to the velocities of the three kinds of waves : — 



w. Minute waves, velocity varies from to %v. 



x. Ordinary waves, ,, „ „ \v to v. 



y. Violent waves, „ ,, „ v to infinity. 



I do not presume to offer an opinion in relation to the legiti- 

 macy of the mathematical processes by which these extraordinary 

 results have been reached ; but the physical aspects of the sub- 

 ject seem to warrant two queries. First, is it admissible to 

 assume the law of force, according to which the molecules of the 

 atmosphere act on each other, to be that of the 4th power of the 

 inverse distance ? The only reason given for this assumption is, 

 that it is " the lowest power of the inverse distance which the 

 mathematical expressions themselves would permit us to try." 

 Secondly, does not the fact that the analytical processes lead to 

 two entirely distinct types of waves (w and x belonging to the 

 circular type, and y to the exponential type) indicate that there 

 must be some error in the assumptions of the mathematician ? 



Restricting ourselves to the general physical bearings of Mr. 

 Earnshaw's deductions, it seems to me that the difficulties in 

 the way of their admissibility are absolutely overwhelming. Is 

 it not almost a physical impossibility that the same elastic medium 

 in which a disturbance occupies ten or twenty minutes in reaching 

 a point ten miles distant from the source of agitation, should, 

 by the mere increase in the violence of the genesis, propagate it 

 through the same space in an infinitesimal portion of time ? In 

 a medium (as the luminiferous aether) in which the elasticity is 

 enormous as compared with the density, we may imagine a pulse 

 to be propagated with incredible velocity ; but that the same 

 elastic medium should transmit waves varying in velocity, accord- 

 ing to the violence of their genesis, from zero to infinity, is 

 scarcely conceivable. It is true there may be nothing a priori 

 improbable in the assumption that the velocity of sound might be 

 related to the violence of the disturbance ; but the fact that the 

 analytical investigations conduct to such extreme results as to set 

 at nought all our physical conceptions, originates a strong pre- 

 sumption that they belong to that class of mathematical fictions 

 which have frequently sharpened the ingenuity and brightened 

 the imagination of some of the most eminent geometers. 



Nevertheless it will be granted that all such general objections 

 as the foregoing must fall to the ground whenever the deductions 

 of theory are found to be accurately accordant with experiments. 

 Let us turn our attention to this aspect of the question. At first 

 sight, as this theory demands an indefinite range of velocity, it 

 would seem to be very readily susceptible of experimental veri- 

 fication. According to Mr. Earnshaw, however, sound-waves 

 belonging to the first class, or minute waves, whose velocities 



