Non-existence of Density in the Elemental ^Etlier. 471 



ingly is the number that will strike against a square millimetre 

 of the wall in one second. Now the time t being, as we have 



found, k of an eleventhet of a second (^ x ^Tm °f a second), 



it follows that ^ x 10 12 is the number of downright blows 



that would be delivered by these molecules upon one square 

 millimetre of the wall in the time t. 



This is on the supposition that the molecules are divided 

 into three squadrons. They are not so divided in reality, and 

 accordingly all the strokes delivered against the square milli- 

 metre of the wall are not downright blows, but are many of 

 them oblique. An easy computation shows that this will 

 increase the number of blows in the ratio of 3 to 2 * ; so that 



* If N be the number of downright blows delivered on a surface 5 in 

 the time T, and if ct be the momentum communicated by each blow, then 

 the pressure they will occasion 



= N" (1) 



sT ^ ; 



If, on the other hand, the blows arrive from all quarters indifferently, 

 and if dri be the number reaching s from inclinations between 6 and 0-t-dO, 

 6 being measured from the normal, then will 



dn' = k. scosO. SndcosB, (2) 



where k is such that k . da is the number of blows coming from directions 

 lying within an element da- of solid angle, that would be received in the 

 time T, by a unit of surface presented perpendicularly to the shower. 

 These dn' molecules communicate to s a momentum 



= at, cos 6 . 2nks cos 3d cos 6. 



Therefore the whole momentum communicated in this way from all 



inclinations 



f 1 2 



= 27rksoc J cos 2 6d cos 6 = - irkset ; 



and the pressure thus caused 



IT (3) 



This is to be equal to the pressure produced by N downright blows ; 

 whence, equating (1) and (3), 



N=|rf (4) 



Again, N', the number of blows that reach s, when molecules fly in all 

 directions, 



= J dn' = 27rsk . J cos 6d cos 6 ; 



whence fr-Mid (5) 



Comparing (4) and (5), we find that 



N' = 3 

 as in the text. N 2 



202 



