167 



On the Velocity of Sound and Variation of Temperature and 

 Pressure in the Atmosphere, By John Herapath. 



I. — Velocity OF Sound. ^^^ J>r»;» >n 

 Having communicated the discovery of some theorems, rela- 

 tive to the velocity of sound and the decrease of temperature 

 and barometric pressure in ascending in the atmosphere, to 

 several scientific friends, I have been prevailed on to give 

 them to the public before the work of which they are intended 

 to form a part. 



It is pretty well known in the scientific world, that in pur- 

 suing Newton's hints of the cause of gravitation, I have been 

 led to a theory of the nature and constitution of airs very dif- 

 ferent from that generally embraced. This theory, after un- 

 folding to me the laws of an immense variety of phenomena, I 

 was anxious to apply to solving the celebrated problems of 

 sound and atmospheric temperature and pressure. No diffi- 

 culty whatever occurred in developing the general laws ; but 

 this was not enough. If the theory to which I had arrived 

 was right, I felt assured there must be some method of getting 

 at the exact quantities of the phenomena, without drawing on 

 experiments for more than indispensable elements. For in- 

 stance, in estimating the velocity of sound, I conceived no just 

 theory ought to require more from experiment than the elastic 

 force and specific gravity of the air. The same elements only, 

 I apprehended, ought to be sufficient for determining the exact 

 rate of diminution in temperature and pressure at any elevation. 

 For a long time my eflTorts were unsuccessful. At last, how- 

 ever, a very simple idea, which I am surprised should have so 

 long eluded my attempts to reduce the equations of comparison 

 I had previously used to equations of equality, enabled me to 

 solve the hitherto refractory problem of sound, and with it 

 several of much more importance and utility. 



What probably will appear not the least remarkable is, that 

 this problem, which has obstinately resisted the abilities of 

 Newton, Euler, Lagrange, Laplace, and other eminent mathe- 

 maticians for 150 years, and the highest powers of analysis, 

 should at last yield to a process scarcely requiring simple 



