PROJECTILES HOT-AIR ENGINES.] 



APPLIED MECHANICS. 



841 



matter, which may with advantage be sub-divided . We 

 may here merely notice the branches which this division 

 of the subject embraces. 



Both heat and electricity appear to be universally the 

 result of chemical action. They are not new forces 

 created by the combination or separation of materials, 

 but are merely the manifestations of force already 

 stored up in bodies, and elicited by changes in their 

 constitution. Practically speaking, however, heat may 

 be said to be the force produced by the chemical action 

 of combustion, or the union of oxygen with inflammable 

 matter a force which universally manifests itself as a 

 repulsion, acting upon the particles of matter exposed to 

 it. A pound of coal or carbon, or any other combustible, 

 uniting with ita proper equivalent of oxygen, produces a 

 certain amount of heat, which is capable of expanding 

 the bulk of any solid, liquid, or gaseous body exposed 

 to it ; of changing a solid into a liquid, or a liquid into a 

 vapour, apparently by forcing the particles to a greater 

 distance from each other. Combustible bodies are uni- 

 versally found throughout the earth ; oxygen abounds in 

 the atmosphere ; and man has only to bring these two 

 kinds of matter together, under proper conditions, in 

 order to obtain the force developed by their union, which 

 he can apply in many different ways as a motive power. 



The various modes of thus applying heat may be dis- 

 tinguished under three heads. 



1 The combustion of explosive substances, or sub- 

 stances like gunpowder, which very rapidly change from 

 a c adition in which they occupy small space, to one in 

 which they occupy a very large space. The chief uses 

 made of such forces are for blasting, and for giving 

 motion to projectiles. The enormous force applied to 

 these purposes may be best understood by observing, that 

 any particular quantity of gunpowder, when ignited, 

 expands to about 2,000 times its volume, in an interval 

 of time so inappreciably small, that its expansion may 

 almost be said to be instantaneous. Let us suppose, for 

 instance, that a cannon of six inches bore is charged 

 with a quantity of powder occupying about six inches of its 

 length, and, on the powder, an iron ball is placed, weigh- 

 ing 32 Ibs. Before the ignition of the powder, the surface 

 of the ball is pressed on equally in ail directions by the 

 pressure of the atmosphere, about 15 Ibs. on every square 

 inch, or, its sectional area being 28 square inches, the 

 total atmospheric pressure tending to push it in any 

 direction is 28 X 15 = 420 Ibs. ; and as this pressure is 

 exerted equally in every direction, no motion ensues. 

 On the ignition of the powder, the pressure on one side 

 is suddenly increased from that of one atmosphere, 

 420 Ibs., to that of 2,000 atmospheres, or 840, 000 Ibs. ; 

 and thus a force is applied, at one side of the ball, ex- 

 ceeding 26,000 times its weight. Were this force con- 

 tinued for 1" of time, the ball would acquire, in that 

 time, a velocity 26,000 times that which gravity would 

 give it, because the force is 26,000 times the weight or 

 force of gravity ; and as gravity gives in 1" a velocity of 

 32 feet per second, the force of the gunpowder would in 

 the same time give it a velocity of 26,000 X 32 = 

 832,000 feet per second, or nearly 570,000 miles per hour. 



But, as the gun is comparatively short, seldom exceed- 

 ing 9 or 10 feet in length, the pressure acts only during 

 the short time which the ball occupies in traversing that 

 distance. Also the elastic gases generated from the 

 explosion of the gunpowder, instead of maintaining 

 their enormous initial pressure during even this short 

 period, lose more and more of it as they are permitted 

 to expand by the forward motion of the ball ; so that by 

 the time it reaches the muzzle of the gun, their pressure 

 would probably be reduced to less than 100 atmospheres. 

 * Let V be the volume at 32 



p t ,, at < t of temperature 

 Va ,, at < 3 of temperature 



Then since P, = V + V ' ~ Q 32 = 



Moreover, as the ball does not precisely fit the gun, a 

 considerable leakage is permitted round it, so that the 

 pressure is still farther reduced, and even a certain back- 

 pressure is caused by the gas which thus gets in front of 

 the ball. From all these causes there results a dimi- 

 nished velocity of the ball, which seldom exceeds 2,000 

 feet per second, or about 1,360 miles per hour. 



The whole subject of projectiles, and of the apparatus 

 used for applying the combustion of explosive substances 

 to give them motion, may be said to be in a transition 

 state ; and although of late years very great ingenuity 

 has been displayed in contriving implements for this 

 purpose, it would scarcely suit the limits of a work like 

 the present to enter upon their discussion. 



2. The combustion of fuel, without explosive violence, 

 has been applied to cause the expansion of air for the 

 purpose of producing motive power. T* it principle of 

 this action is of a very simple character. Any volume 

 of any gas, such as a cubic foot - ' air at a temperature 

 of 32 (Fahr.), on receiving accessions of heat, increases 

 in temperature and expands in bulk, and the amount of 

 expansion depends on the increase of temperature, ac- 

 cording to the following law : For every added degree 

 (Fahr.) of temperature, the volume expands Tro^h part 

 of itself. Thus, if the cubic foot were heated from 32 

 up to 72, the increase of temperature being 40 (the 

 difference between 32 and 72), the increase of volume 

 would be j^ths, or j^ths, or T Vth of a cubic foot ; that 

 is to say, 144 cubic inches. Or the volume at 72 would 

 be 1 and j*g%ths, or |ths of a cubic foot. If, now, 

 this volume were heated up to 73, or 1 more, its ex- 

 pansion would be jijyth, and its total volume would be 

 {|$ths and j^th ; in all, Ijj^ths. Or its volume at 72 

 would be increased by y^g-th of itself, on the accession of 

 another degree of temperature. Now, if we observe that 

 480, the divisor which gives the expansion per degree of 

 a volume at 32, is 448 added to 32, and that 520, the 

 corresponding divisor for 72, is 448 added to 72, we 

 readily see that the expansion per degree of any volume 

 at any temperature is found by adding the constant 

 number 448 to the temperature, and using the same as 

 a divisor.* This leads to a rule by which, knowing the 

 volume at any temperature, "we can readily find the 

 volume at any other temperature: thus 



Rule. Add the constant number 448 to each of the 

 temperatures, and state the proportion : as 448 + the 

 temperature of the given volume is to 448 -f- the tem- 

 perature of the required volume, so is the given volume 

 to the required volume. 



Example. Required the expansion of 10 cubic feet, 

 when heated from 60 to 212. 



60 



448 



508 : 



Given volume. 

 10 cubic feet 



Required volume. 

 13 cubic feet nearly. 



508)6600 



13 nearly. 



Hence the expansion is nearly 3 cubic feet. 



It may now be understood that, having the means of 

 largely expanding any volume of air by adding heat, 

 and of again contracting it by taking beat away, we have 

 a force within our reach, capable of being applied as a 

 motive power. Several contrivances for utilising this 

 force have been made from time to time, but they all 

 present so strong a similarity to the steam-engine, and 

 they have, as yet, met with so little success in their 



and since r s = V -j- V 



f t 32 



480 "' 



eliminating V, we hare 



480 



448 



TOt. I. 



