It is generally allowed that the great objects of the atomic system are, 1st to determine the relative weights of the simple elements; and 2d to determine the _number_, and consequently the weight, of simple elements that enter into combination to form compound elements. The greatest _desideratum_ at the present time is the exact relative weight of the element hydrogen. The small weight of 100 cubic inches of hydrogen gas, the important modifications of that weight by even very minute quantities of common air and aqueous vapour, and the difficulties in ascertaining the proportions of air and vapour in regard to hydrogen, are circumstances sufficient to make one distrust results obtained by the most expert and scientific operator. The specific gravity of hydrogen gas was formerly estimated at ⅒ that of common air; it descended to ¹/₁₂.₅, which is the ratio we adopted in the Table at the end of Vol. 1. it is now commonly taken to be ¹/₁₄.₅, and whether it may not in the sequel be found to be ¹/₁₆.₅ is more than any one at present, I believe, has sufficient data to determine. The other factitious gases have mostly undergone some material alterations in their specific gravities in the last twenty years, several of which I have no doubt are improvements; but when we see these specific gravities extended to the 3rd, 4th, and 5th places of decimals, it appears to me to require a credit far greater than any one of us is entitled to. In the mean time, it may be thought a fortunate circumstance, that the weight of common air has undergone no change for the last thirty or forty years; 100 cubic inches bring estimated to weigh 30.5 grains at the temperature of 60°, and pressure of 30 inches of mercury: (whether this is exclusive of the moisture I do not recollect.) It is also a fortunate circumstance, (provided it be correct) that this weight is nearly free from decimal figures. I may be allowed to add, that according to my experience, the weight of 100 cubic inches of air is more nearly 31 grains than 30.5. I apprehend these observations are sufficient to shew that something more remains to be done before we obtain a tolerably correct table of the specific gravities of gases; the importance of this object can not be too highly estimated. The combinations of gases in equal volumes, and in multiple volumes, is naturally connected with this subject. The cases of this kind, or at least approximations to them, frequently occur; but no principle has yet been suggested to account for the phenomena; till that is done I think we ought to investigate the facts with great care, and not suffer ourselves to be led to adopt these analogies till some reason can be discovered for them. The 2d object of the atomic theory, namely that of investigating the _number_ of atoms in the respective compounds, appears to me to have been little understood, even by some who have undertaken to expound the principles of the theory.