322 Mr. Tredgold on Mr. Dalton’s Speculations 
portant proposition in aérostatics: for if this proposition be true, 
the whole of his speculations are at variance from it, and mtst, 
therefore, be erroneous. Consequently, the labour of refuting 
them is reduced into a very narrow compass. 
Proposition I.—If an uniform mixture of gases or vapours, 
which mix without condensation, be confined in a close vessel, 
the elastic force of each gas on a given surface must be the 
same, and equal to the elastic force of the mixture on the same 
extent of surface. 
Let p be the elastic force of the mixture, and V the volume 
of the vessel. Also let A and B be the two gases, and v the 
volume of the gas A when its elastic force is p. 
It is obvious, that v must be less than V, otherwise the gas 
A would entirely fill the vessel, and a mixture could not be 
formed without condensation. 
But since v is less than V, and the gas A is uniformly dis- 
tributed throughout the greater volume of the vessel V, its 
parts must be kept asunder by a force which is not less than 
its own elastic force; and as the force which keeps separate 
the parts of the gas A, is the elastic force of the gas B, there- 
fore, the elastic force of the gas B in the mixture cannot be 
less than that of A. 
But by the same steps it may be proved that the elastic 
force of the gas A cannot be less than that of B, and conse- 
quently, that their elastic forces must be equal in the mixture, 
and also equal to the elastic force of the mixture. 
The addition of two other propositions will not only give 
the means of comparing the result of the preceding one with 
experiment, but also give the formule which will supply the 
place of Mr. Dalton’s. 
Proposition II.—If given volumes V, v, of gases of different 
elastic forces. F, £ be allowed to mix and occupy the volumes 
which previously contained them, the elastic force of the mix- 
VF +of 
; cee v- 
Let p be the elastic force of the mixture: and since it has 
been proved that each gas taken separately must be of the 
same elastic force-as the mixture, and the volumes are in- 
versely as the elastic forces, we have 
TE - 
mise |S se “s = the volume of the gas whose elastic force 
ture will be equal to 
p 
was f before mixture; and consequently, 
V+u— a = pV + JF _ the volume to be occupied 
by the other gas. Hence 
a ee a Ws yee ye ees ee 
V* p(V+v)—vf “* ‘P= 5(V40)=0f? V+u a 
