A SYSTEM OF PARTICLES. 257 



hence pressure from tlie air in tlie tube 



C depending on the size of the tube. 



23. If it be allowable thus to suppose an action on the tube, this 

 j^ives the elastic force 



Let now a given mass of air be supposed compressed, as in Pro- 



2 7 



fessor Robison's experiments, then since the mass oc ~ 



Il 



The conclusion then at which we have arrived is that E= CD {I +qD); 

 q being small. 



Now tlie external air, acting in the same manner, produces a force 

 which is C n {^ + qD)\ subtracting these we get for the pressure 



p = CD{l+aD)- cn'. 

 Now if D' = Z) = 1, p = 0\ 



.: C(l + «)= C; 



p = C\n(l + aD) - (1 +a)\. 



Also if Z) = 0, « = -l; ■•■ C= ^ 



\ + a 



p = D\\ + a(D -\)} -\; 

 but )) •(- ] is the actually measured pressure, hence calling this P, 



P = D{1 + a(D- \)} (a) 

 which, however, supposes a to depend on the volume of tlie tube. 



