418 Mr. 11. H. M. Bosanquet on the Theory of Sound. 



Now -ji- is throughout very small, and varies very slowly, 



so that -rat- is extremely small. In fact, from Table II. we see 

 that at 100° C. j^ is somewhere about '00000048. 

 [To "be continued.] 



LVI. Notes on the Theory of Sound. By K. H. M. 



Bosanquet, Fellow of St. Johns College, Oxford. 



[Continued from p. 349.] 



4. On Combined Wave-systems. 



THE principle that a stream of sound may be regarded as 

 a flow of energy, which cannot of itself increase or di- 

 minish in quantity, enables us to deal with certain simple cases 

 of combined wave-systems. I restrict myself for the present 

 to the case of plane waves. 



Prop. I. — If two equal and similar pendulum wave-systems, 

 travelling in opposite directions, meet in air, they form a sta- 

 tionary wave which will carrv the whole energy of both. 

 Let 



y 1 = rtsm— {vt— x), 



. 2it , . 



y 2 = a sm— {vt + x ) 



A 



be the two equal systems travelling opposite ways ; the more 

 general equations can always be reduced to this form by suit- 

 able choice of the origins of space and time. 

 Then 



v . . 2trvt 2ir 



l =yi + y 2 = 2a sm— - — cos — #, 



A A 



dY Aairv 2irvt 2ir 

 -7- = -^— -cos^— cos— x. 

 dt a a a ; 



dY Aira . 2-rrvt . 2tt 



-j- = - — — sm — r— sm — - x. 



dx AAA 



When £=0, Y=0 and -y— =0, or there is no displacement 



and no pressure anywhere along the stationary wave, but 

 there is a maximum velocity, 



dY kaivv 2irx. 

 dt A A 



