146 Experiments to determine 



is done, the value of z, and the law of its increase as x 

 increases, will be known ; and this will show the relation 

 of X to _)', or of the elasticities of the generated fluid to 

 their corresponding densities, in a clear and satisfactory 

 manner. 



Without increasing the length of this paper still more 

 (it being perhaps already too voluminous), by giving an 

 account in detail of all the various computations I 

 made, in order, from the results of the experiments in 

 the foregoing table, to ascertain the real value of z, and 

 the rate at which it increases as x is increased, I shall 

 content myself with merely giving the general results of 

 these investigations, and referring for farther informa- 

 tion to the following Table II., where the agreement of 

 the law founded on them, with the results of the fore- 

 going experiments, may be seen. 



Having, from the results of the experiments in Table 

 I,, computed the different values of z, corresponding to 

 all the different densities, or different charges of powder, 

 from I grain, or 39 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 = at, expressed 

 in thousandth parts, is increased from o to 1000 (or till the 

 powder completely fills the space in which it is confined), 

 the variable part x of the exponent of ;^, (i -[- z), is in- 

 creased from o to y^Q. And though some of the experi- 

 ments, and particularly those which were made with 

 large charges of powder, seemed to indicate that v/hile x 

 is increased with an equable or uniform motion, z in- 

 creases with a motion continually accelerated; yet, as the 

 results of by far the greatest number of the other experi- 

 ments showed the velocity of the increase of z to be 

 equable, this circumstance, added to some other reasons. 



