58 Mr. S. T. Preston on an Acoustic Thermometer. 



only be one form for each velocity. In the light of equation 

 (16) above, the oversight in discarding the "imaginary" 

 value is obvious. It is too hastily concluded that such a 

 value would imply infinite velocity &c. either when x=. + <x> 

 or when #=.. — <x> , but this is not necessarily so, though it is 

 too frequently assumed in such like investigations, for in fact 

 the value of <j> given in (5) above gives a well-known expan- 

 sion of the form %Ke ax+bz such as is considered by Stokes, 

 but the " real " coefficients p are discontinuous, changing sign 

 with X, so that eP x vanishes both for a= + oo , and for os= — go . 

 We may conclude, then, that we have obtained just as 

 satisfactory evidence for the unchanging propagation of the 

 solitary wave as there is for that of the infinite train investi- 

 gated by Stokes. In a Supplement to his paper published in 

 1880*, he has carried his approximation one step further, and 

 we may with advantage employ a somewhat similar method 

 in proceeding to higher degrees of approximation for the 

 solitary wave. Proceeding on the same principles by which 

 we obtained (1) and (2), we may take instead 

 U(^ + ^)=-(^ + ^) + 2Aa +1 tan 2f+1 4m(^ + ^)/U. (55) 

 which leads to the higher approximations with considerably 

 less labour, though to the order with which we have been 

 occupied it offers no advantage, in fact rather the reverse from 

 its indirect character. 



VIII. Acoustic Thermometer — a Suggestion. 

 By S. ToLVER PRESTONf. 



THE following may have more theoretical than practical 

 interest (illustrative of a connexion between acoustics 

 and heat); but perhaps ingenuity might give the suggestion 

 also a practical value. The idea is simple enough, and relates 

 to the varying note afforded by a resonance-tube according 

 to the temperature of the enclosed air or gas; the notion 

 being to employ this in some way as a measure of tempera- 

 ture. I shall only illustrate, however, the simplest aspect of 

 the case. 



Thus, for mere theoretical illustration, we may suppose a 

 tube, closed at its inner end, to be inserted somewhere in the 

 wall of some furnace, or buried in some less heated object, 

 whose temperature is to be estimated. Of course a tuning- 

 fork of a certain vibrating period will, at normal temperature, 



* Collected Papers, vol. i. 



t Communicated by the Author. 



