36 HISTOEY OF ACOUSTICS. 



changes of elasticity in the air, as dependent on its compression, cannot 

 be applied to those rapid vibrations in which sound consists, since the 

 sudden compression produces a degree of heat which additionally in- 

 creases the elasticity. The ratio of this increase depended on the 

 experiments by which the relation of heat and air is established 

 Laplace, in 1816, published 8 the theorem on which the correction 

 depends. On applying it, the calculated velocity of sound agreed 

 very closely with the best antecedent experiments, and was confirmed 

 by more exact ones instituted for that purpose. 



This step completes the solution of the problem of the propagation 

 of sound, as a mathematical induction, obtained from, and verified by, 

 facts. Most of the discussions concerning points of analysis to which 

 the investigations on this subject gave rise, as, for instance, the admis- 

 sibility of discontinuous functions into the solutions of partial differ- 

 ential equations, belong to the history of pure mathematics. Those 

 which really concern the physical theory of sound may be referred to 

 the problem of the motion of air in tubes, to which we shall soon 

 have to proceed ; but we must first speak of another form which the 

 problem of vibrating strings assumed. 



It deserves to be noticed that the ultimate result of the study of the 

 undulations of fluids seems to show that the comparison of the motion 

 of air in the diffusion of sound with the motion of circular waves 

 from a centre in water, which is mentioned at the beginning of this 

 chapter, though pertinent in a certain way, is not exact. It appears 

 by Mr. Scott's recent investigations concerning waves, 9 that the circu- 

 lar waves are oscillating waves of the Second order, and are gregarious. 

 The sound-wave seems rather to resemble the great solitary Wave of 

 Translation of the First order, of which we have already spoken in 

 Book vi. chapter vi. 



I 



CHAPTER IV. 



PROBLEM OF DIFFERENT SOUNDS OF THE SAME STRING. 



T had been observed at an early period of acoustical knowledge, 

 that one string might give several sounds. Mersenne and others 



Ann. Phy*. et Chlm. t. iii. p. 2SS. " Brit. Ass. Reports for 1844, p. 861. 



