ON THE PROPAGATION OF SOUND. 289 



be marked on the paper, and will correctly represent the progress of the 

 vibration. Whatever the nature of the sound transmitted through any 

 medium may be, it may be shown that the path thus described will also 

 indicate the situation of the different particles at any one time. The 

 simplest case of the motion of the particles is that in which they observe 

 the same law with the vibration of a pendulum, which is always found op- 

 posite to a point supposed to move uniformly in a circle : in this case the 

 path described will be the figure denominated a harmonic curve ; and it may 

 be demonstrated that the force impelling any particle backwards or for- 

 warfls, will always be represented by the distance of the particle before or 

 behind its natural place ; the greatest condensation and the greatest direct 

 velocity, as well as the greatest rarefaction and retrograde velocity, happen- 

 ing at the instant when it passes through its natural place. 



We are ready to imagine that very hard bodies transmit motion instan- 

 taneously, because we have no easy means of measuring the interval of 

 time that elapses between the action of pushing the end of a rod, and the 

 protrusion of an obstacle at the other end, or between the instant of pulling 

 a bell rope, and that of the ringing of the bell. But it is demonstrable that 

 in order to transmit an impulse in a time infinitely small, the hardness of 

 the substance must be infinitely great, and it must be absolutely incom- 

 pressible and inextensible by any force, which is a property not discover- 

 able in any natural bodies : the hardest steel and the most brittle glass 

 being very susceptible both of extension and compression. 



The least elastic substance that has been examined, is perhaps carbonic 

 acid gas,* or fixed air, which is considerably denser than atmospheric air 

 exposed to an equal degree of pressure. The height of the atmosphere, 

 supposed to be homogeneous, is in ordinary circumstances, and at the sea 

 side, about 28,000 feet, and in falling through half this height a heavy 

 body would acquire a velocity of 946 feet in a second. But from a com- 

 parison of the accurate experiments of Derham,t made in the day time, 

 with those of the French Academicians,^: made chiefly at night, it appears 

 that the true velocity of sound is about 1130 feet in a second, which agrees 

 very nearly with some observations made with great care by Professor 

 Pictet. This difference between calculation and experiment has long 

 occupied the attention of natural philosophers, but the difficulty appears 

 to have been in great measure removed by the happy suggestion of 

 Laplace, who has attributed the effect to the elevation of temperature, 

 which is always found to accompany the action of condensation, and to 

 the depression produced by rarefaction. It is true that a greater change 

 of temperature would be required than Mr. Dalton's experiments on the 

 compression of air appear to indicate ; but those experiments do not per- 



* It is sulphurous acid, in which the velocity is 229 -2 ft. Rees, Dissertatio de 

 Celeritate Soni, 4to. Trajecti ad Rhenum, 1819. Journal de Physique, 1821, p. 40. 



t Ph.Tr. 1708, p. 2, concludes that the velocity is 1142ft. per second. 



J Hist. etMem. del'Acad. 1738-9. Here the effect of the wind was first taken 

 into account: vel. = 1106ft. at 43 of temp. The actual velocity at the freezing 

 t&np. is about 1090 ft. per second. The increase of velocity is 1 '136 ft. for every 

 degree of temperature, on Fahrenheit's scale. 



See Poisson, Journal de 1'Ecole Poly technique, cah. xiv. Biot, Journal de Phy- 

 sique, Iv. 173. Mem. d'Arcueil, ii. 94. 



