On the reciprocal Action of Pendulums. 259 



two chronometers placed very near each other. Many very cu- 

 rious effects of these vibrations have been observed by philoso- 

 phers ; and among these may be particularly distinguished tlie 

 phaenomena observed by M. Chladni upon sonorous plates and 

 rods; from which this learned physician has deduced an ingenious 

 method of determining the swiftness of sound in different solid 

 bodies. The preceding researches have led me to the following 

 theorem, to determine that swiftness in solid, in liquid, and in 

 aeriform substances. 



I assume that it has been determined by experiment, what de- 

 gree of elongation a solid bodv placed horizontally, and fixed at 

 one of its extremities, receives from the action of a weight equal 

 to its own placed on its other extremity. If the substance is 

 fluid, I suppose that it has been determined what is the abbrevia- 

 tion of a horizontal column of this fluid of the length of a metre 

 and compressed bv a weigiit equal to its own. This settled : if 

 we divide by this degree of elongation or abbreviation double the 

 weight which will depress the bodies in a second sexagesimal, 

 the square root of this quotient will be the number of metres 

 which sound traverses in that substance during the same in- 

 terval. 



Thus Borda having observed that a brass rod of eleven feet 

 and a half in length, and 37 ounces in weight, was lengthened 

 by the action of a weight of twenty-four pounds five parts and 

 three-fourths, each part being a hundred-thousandth of a fa- 

 thom ; it follows that a rod of one metre will be lengthened 

 0"\000, 000,77379 by the action of a weight equal to its own. 

 Dividing by that fraction the space 9'""8088, the double of what 

 the weigiit draws at Paris, in the first second, the square root 

 3560"4 of the quotient will l)e tiie number of metres which sound 

 traverses during one second in brass. 



It is known that the swiftness of sound in the air is increased 

 about one-sixth by the heat which develops the approximation, 

 of the vibrating particles. The same cause must without doubt 

 alter that swiftness in all bodies, but it is difficult to determine 

 the exact influence of it. We may, however, approach near to 

 such a determination, by comparing the swiftness deduced from 

 the preceding theorem, with that resulting from the method 

 of M. Chladni ; for that method founded upon the sound pro- 

 duced by tlie longitudinal vibrations of sonorous rods, giving the 

 real velocity of sound, the excess of that velocity above the 

 preceding will lie the effect of the temperature alternately ele- 

 vated and reduced in the vibrations. The swiftness of sound, 

 according to the experiments of Chladni upon a brass rod, is 

 359()""'58 per second ; which only surpasses the preceding in 

 about a hundredth part. The influence of the cause alluded to 



R2 is 



