396 Scientific Proceedings, Royal Dublin Society. 



known to be about a uno-eighteen (10 18 ),(/) and there are of course 



500,000 times this number in a column 500 metres long, and a 



square mm. in section ; *. e. there are 5 uno-twentythrees in this 



column. One-third of all the molecules in the column are the 



squadron that we are to regard as travelling lengthwise — half of 



these advancing towards one end, and the other half retiring from 



it. It thus appears that the number of molecules within the 



column to be taken as travelling at any instant towards one end is 



5 



- . 10 23 . This, accordingly, is the number that will strike against 



a square millimetre of the wall in one second. Now the time r 



being, as we have found, - of an eleventhet of a second I - x — — 



of a second j , it follows that y^ 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 r. 



This is on the supposition that the molecules are divided into 

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

 ingly all the strokes delivered against the square millimetre 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 : (j) so that the real number of blows 



delivered upon the square millimetre is about — x 10 12 . 



(i) See footnote (d), above. The uno-eighteen means the number represented by 1 

 with eighteen cyphers after it. It accordingly is the same as 10 18 . 



(j) If 2V be the number of downright blows delivered on a surface * in the time T, 

 and if a be the momentum communicated by each blow ; then the pressure they will 

 occasion j^ 



If, on the other hand, the blows arrive from all quarters indifferently, and if dn' be 

 the number reaching s from inclinations between and 6 + do, 6 being measured from 

 the normal, then will 



dn' = k . s cos . 2nd cos d, (2) 



where k is such that k . dcr 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 



= a co . 2irks cos 6d cos d. 



