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494 Mr. J. J. Waterston on the Theory of Sound. 



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eives — : and the ratio of this to 8 is also -: thus the increment 

 ° n n 



of vis viva is equal to the decrement of distance, irrespective of 

 the velocities and distance, and is equal to the mechanical force 

 exerted by the plate. In an elastic medium, the increment of ab- 

 solute temperature is equal tg one-third the decrement of volume, 

 and the increment of- temperatui-e is the equivalent of the force 

 expended in the act of'bornjiression. We thus gain a knowledge 

 of the mechanical - equivateiit of heat, and further deduce the 

 amouut of vis viva in ag^s to be equal to the work performed 

 by its pressure acting 'thcoilgh three times its volume. 



The diminution of teftiperature found when ascending the 

 atmosphere may be illustrated by supposing a series of 

 elastic balls, a, b, c, d, &c., to be arranged in a vertical, 

 and moving in the vertical so that those adjacent shall 

 alternately strike against each other at the extremity 

 of their up-and-downi motion without any transference © << 

 of vis viva, which requires that they should encounter 

 each other with equal velocities, e. g. b in its up-motion 

 striking c, and in its down-motion striking a. Now 

 we have to mark, that, between the upper and lower 

 impact, b receives an accession of vis viva from the 4 

 force of gravity which is proportional to the vertical 

 distance traversed ; so that comparing the vis viva of 

 b with any other of the series, such as z, we shall find 

 that the higher ball z has less vis viva than Z», and the 

 diflPerence is equal to gravity acting through bs. Thus in the 

 atmosphere we might expect the decrease of temperature to be 

 uniform if its constitution agrees with this hypothesis. 



The strict demonstration represents this to be the case, and 

 that the gradient of temperature is 1° in 319 feet; also that the 

 absolute height of the atmosphere is six times the height of a 

 uniform atmosphere, the density in a stratum as the fifth power 

 of the depth of that stratum below the summit, and the elastic 

 force or height of barometer as the sixth power of that depth. 



Here we find that the diminishing temperature, in ascending 

 the atmosphere, is represented as the natural condition of ver- 

 tical equilibrium ; and the question occurs, may not the increas- 

 ing temperature found in descending through the earth's crust 

 be also its natural condition of vertical equilibrium ? This may 

 be cited as one of many instances of the suggestive power 

 of the vis viva theory, marking it as specially the natural intro- 

 duction to the dynamic theory of heat, and as likely to promote 

 a beneficial change in the application of mathematics to mole- 

 cular physics generally. Upon this account it seems to merit 

 the attention of the educational authorities in the higher depart- 



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