l64 PHILOSOPHICAL TRANSACTIONS. [ANNO 1797. 



powder, from 1 grain, or 3g thousandth parts, to 18 grains, or 702 thousandth parts 

 of the capacity of the barrel, I found that while the density of the elastic fluid = x, 

 expressed in thousandth parts, is increased from O to 1000, or till the powder com- 

 pletely fills the space in which it is confined, the variable part z of the exponent of 

 x } (l + z), is increased from to X V- And though some of the experiments, and 

 particularly those which were made with large charges of powder, seemed to indi- 

 cate that while x is increased with an equable or uniform motion, z increases with 

 a motion continually accelerated; yet, as the results of by far the greatest number 

 of the other experiments showed the velocity of the increase of z to be equable, 

 this circumstance, added to some other reasons drawn from the nature of the sub- 

 ject, 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 to 1000, z is increased 

 with an equable velocity from O to T \ T then it is every where z to x as -^ to 1000; 

 or 1000 z = tV?, and consequently z = j^^i and when x is = 1, it is z = 

 1 * 00 = 0.0004; and when x is greater or less than 1, it is z = 0.0004,r; and z 

 being expunged, the general equation expressing the relation of x to y becomes 

 x i + 0.0004* _. y. f an d thi s i s the equation which was used in computing the values of 

 y, as expressed in the following table. In order that the elasticities might be ex- 

 pressed in atmospheres, the values of y, as determined by this equation, were mul- 

 tiplied by 1 .84 1 . If it be required to express the elasticity in pounds avoirdupois, 

 then the value ofy, as determined by the foregoing equation, being multiplied by 

 27.615, will show how many pounds avoirdupois, pressing on a superficial inch 

 will be equal to the pressure exerted by the elastic fluid in the case in question. 



Table II, General Results of the Experiments in Table I. on the Force of Fired Gunpowder. 



