FIRED GUN-POWDER 69

B. is equal to, or greater than the greatest pressure of the fluidin A E: but if R be not capable of resisting the action of thefluid, it will begin to move towards B as soon as there is asufficient quantity of elastic fluid produced to overcome itsresistance. Thus, not only the pressure on each physicalpoint of the space ACE will be expressed by a right lineshorter than EF; but if the weight of R be so diminished,that it makes the least resistance possible, the line that willexpress the pressure of the fluid when R begins to move, willbe the shortest of all the lines that can be drawn between Eand F.

147. The column of air contained in the bore of the gun,and communicating with the external air, is the least resist-ance which can be opposed to the expansion of the fluid.

Now expressing by E V the pressure of the fluid that beginsto move the resisting body, and by H T its pressure in thespace A H, the line H T will be longer than a fourth propor-tional to A H, A E, E V, since the fluid in passing fromE to H is continually acquiring greater elasticity from thesuccessive generation of fresh matter. It will be the samewith the lines that express the pressure in the spaces A G,A I, &c. till the powder be entirely consumed: thus the lineV T S 2 passing through the extremities of these perpendicu-lars, will be a scale to determine the limit of the weakestpressure that the fluid can exert in the space A B C D.

148. But when the powder is entirely consumed, the pro-portion between the lines that express the pressure of the fluidwill be changed. Suppose that all the grains are consumedwhen the fluid reaches I, and that the pressure in the spaceAI be expressed by I 2, this line will be necessarily shorterthan IN; for according to supposition, IN represents notonly the effect of all the fluid, but also of the greatest degreeof heat that can be produced by the entire consumption of allthe combustible substances : but in 12, if the mass of thefluid be the fame, the degree of heat is less, whence its elasti-city and of course its pressure will be less: the scale V T S 2can never touch the hyperbola F L M N O, which maytherefore be considered as the limit of the greatest pressure ofthe fluid. When the fluid reaches K, the pressure K Q_ willbe less than a fourth proportional to AK, Al, 1 2; foras no fresh fluid will be generated between I and K, and theheat is decreasing, the elasticity will be less. At 3 and theother points in succession, the same reasoning will hold good.

E 3 Tha