M. Poinsot on the Percussion of Bodies, 349 



vapour ; and the higher it is swelled up the more the barometer 

 falls under the cloud, because the higher it swells up the more 

 runs off at the top. I am now nearly seventy-three yeai's of 

 age, and it would gratify me much to see my theory universally 

 received before I die; but my gratification is a small matter 

 compared with the interest of all mankind in adopting the true, 

 instead of a false system. It is painful to me to see the whole 

 meteorological world groping in the dark, for more than twenty 

 years after the true system has been developed. 



Again I most earnestly entreat that the subject be taken up 

 by many of the numerous learned societies in Great Britain and 

 Ireland. Very respectfully, &c., 



James P. Espy. 



P.S. I have left some copies of my 'Fourth Report' at the 

 Smithsonian Institution, at Washington City, to be sent to any 

 Society that will promise to investigate the subject carefully and 

 repoi't upon it. — J. P. E. 



XLIV. On the Percussion of Bodies, By M. Poinsot. 



[Continued from p. 290.] 



cokollary iii. 



On the points at which the body is capable of producing 

 the same percussion. 

 23. ^T^O find the points at which the body strikes with a given 

 JL force nP, we have merely to make 



Q=nP 



in the general expression for Q. By so doing, the equation of 

 the locus of these points will be found to be 



By transforming to parallel coordinate axes of X and Y whose 

 origin is at the point x= ^, y= ^, this equation becomes 



4«2(«2X2 + /S'^Y^) = «2«^ + /3%^-4a^^%n^-n), 

 or, in a simpler form. 



When the second part of this equation is positive, the curve 

 is evidently an ellipse similai', and similarly placed to the central 

 ellipse, but having its centre at the point whose abscissa is 



x= 7Z-, and whose ordinate is y=Tr-. 

 %n An 



