the Force of Fired Gunpowder. 147 



drawn from the nature of the subject, have induced me 

 to assume the ratio of the increase of z to the increase 

 of x as constant. 



But if, while x increases with an equable velocity from 

 o to 1000, z is increased with an equable velocity from o 

 to T 4 -y, then it is everywhere z to x as -^ to 1000; or 

 1000 z = yL, and consequently z = yoVoo > an< ^ when 

 a? is = I, it is z = To~o7To~ == o - oo 4 5 an d when x is 

 greater or less than i, it is = 0.0004.2;; and z being 

 expunged, the general equation expressing the relation 

 of x to y becomes ^ i + 00 ^ = _y ; and this is the 

 equation which was made use of in computing the 

 values of y, expressed in the following Table. 



In order that the elasticities might be expressed in at- 

 mospheres, the values of y, as determined by this equa- 

 tion, were multiplied by 1.841. 



If it be required to express the elasticity in pounds 

 avoirdupois, then the value of y, as determined by the 

 foregoing equation, being multiplied by 27.615, will 

 show how many pounds avoirdupois, pressing upon a 

 superficial inch, will be equal to the pressure exerted by 

 the elastic fluid in the case in question. 



