in the Theory of Sound. 101 



and colder by rarefaction. The want of acquaintance with this 

 circumstance, has led him and many others into the erroneous 

 conclusion, that the particles of elastic fluids repel each other 

 with forces inversely as their central distances, which could never 

 be the case, if the capacity be affected, no matter in what manner 

 or degree, by a change of density. Newton himself has shewn in 

 his Principla^ that, if the cube of the pressure in an elastic fluid 

 were as the fourth power of the density, the particles must re- 

 pel each other with forces inversely as the squares of their central 

 distances. Now, the experiments of the French philosophers near- 

 ly agree with such a relation subsisting between the pressure and 

 density of air. Numerous experiments which I have m'ad^on this 

 subject, answer almost exactly, and this was far from my expecta- 

 tion ; for, till these experiments were made, I had conjectured 

 that the true result would lie quite on the contrary side of those 

 obtained in France; but on perceiving that my result accorded 

 with the existence of a repulsion between the particles of air in- 

 versely as the squares of their distances, which is such a general 

 law of nature, I was led to adopt this as the true law of gaseous 

 repulsion. MM. Desormes and Clement have given a particu- 

 lar description of their apparatus and mode of experimenting, in 

 the 89th volume of the Journal de Physique. But I am not 

 aware that any intelligible account has been published of the 

 apparatus employed by MM. Gay-Lussac and Welter; though, 

 from the brief and obscure hints given in the 12th book of the 

 Mecanique Celeste^ I still suspect they are liable to some of the 

 inaccuracies which I hinted at in the Number of this Journal 

 for April last, and used every means to avoid, in my own ex- 

 periments. 



The late celebrated Marquis Laplace had often directed his 

 attention to this subject ; and reflecting that sound is propagated 

 by aerial undulations, which cause a compression of the air as 

 they move along, he conjectured that such compression, by ge- 

 nerating an increase of temperature, augmented the elasticity of 

 the air, and consequently the velocity of sound ; and that this 

 was the reason why Newton'*s result fell short of experiment. 

 According to Laplace, the velocity of sound, as deduced by 

 Newton s theory, and which is about 91().3 feet, should be mul- 

 tiplied by the square root of the quotient obtained by dividing 



