Dr. Hutton, after applying some requisite corrections to Mr. Robins's numbers, and after remarking that the powder does not all inflame at once, as well as that about 7/10ths of it consist of gross matter not convertible into an elastic fluid, gives v = 125 [sqrt] ((n · q)/(16 + q) × log. of b/a) for the initial velocity of any ball of given weight and magnitude, and n = ((p + w)/3180 ad^2)v^2 ÷ log. b/a for the value of the initial force n of the powder in atmospheric pressures: when a = length of the bore occupied by this charge, b = whole length of the bore, d = diameter of the ball, w = its weight, 2 p = weight of the powder, q = a/d. In his experiments and results, he found n to vary between 1700 and 2300, and the velocity of the flame to vary between 3000 and 4732; specifying, however, the modification in his computations, which would give more than 7000 feet per second for that velocity. Taking 2200 for an average value of n, and substituting 47 for its square root in the above formula for v, it becomes v = 5875 [sqrt] (q/(16 + q) × log. of b/a) for the velocity of the ball, a theorem which agrees remarkably well with the Doctor's numerous and valuable experiments. (Tracts, vol. iii, p. 290, 315.) In a French work entitled, "_Le Mouvement Igné_ considéré principalement dans la charge d'une pièce d'artillerie," published in 1809, there are advanced, among other notions which we apprehend few philosophers will be inclined to adopt, some which may demand and deserve a careful consideration. The author of this work observes, that if a fluid draws its force partly from a gaseous or aeriform matter, and partly from the action of caloric, which rarefies that aeriform matter; then its density in proportion to its dilatation, will follow the inverse ratios of the squares of the spaces described. He then investigates two classes of formulæ: the first appertains to fluids which possess simply the fluid or aeriform elasticity, which are free from all heat exceeding the temperature of the atmosphere. Whether there be one or many gaseous substances signifies not, provided their temperature agrees with that of the atmosphere; for when these dilate they conform to the inverse of the spaces described. The second relate to those which derive their elasticity as well from the aeriform fluids, as from the matter of heat which pervades them, and which are denominated _fluids of mixed elasticity_, to distinguish them from those of simple or purely _aeriform elasticity_. These fluids, in dilating, conform to the inverse ratio of the _squares_ of the spaces described. Thus the celerity of action of mixed elastic fluids, is to that of simple elastic fluids as S^2 to S; whence it follows that mixed elastic fluids are more prompt and energetic in their action than others; and hence also is inferred why the fluid produced by the combustion of gunpowder, is more impetuous and more terrible in its operation than atmospheric air, however compressed it may be.