I IK AT 



607 



an electrified conductor. By the helpof the 'specific 

 li.-.ii ni liodies (which will be II-MI---! later) we can 

 determine I'nnii their change of temperature how 

 much heat they gain or lose. The scientific or 

 nfi.ni/ itfr measurement ni temperature can only l>e 

 alluded to hen'. It depends up<n theoretical con- 

 siderations for which see THERMO-DYNAMIO& 



Ifttuvre <>f llmt. Whether it be a vibration, 

 -ii. -h .-is lixht and sound (as in Home cases it cer- 

 tainly is), or consist in independent motions of the 

 particle* of a body, leading to a succession of 

 iiniiiK-ts on each other and on the walls of the con- 

 taining vessel (as is almost certainly the case in 

 ), it is none the less certain that the amount 

 of heat in a lx>dy is to be measured by the energy 

 oi moving particles. But as we cannot observe 

 those particles so as to ascertain their vis-viva, we 

 niu-t have as a preliminary some artificial unit in 

 terms of which to measure heat. This will be 

 de-cribed later. But in order that this process may 

 he applied we must have some means of measuring 

 the temperature of a body, depending upon an effect 

 of heat. Whatever that effect may be, it is obvious 

 that, as the laws of nature are uniform, it will 

 afford us a reproducible standard, by which we can 

 estimate at any time and at any place an amount 

 of heat, and compare that amount with another 

 observed somewhere else ; just as the French Metre 

 (q.v.) is reproducible at any time, being (at least 

 by its original definition ) the ten-mittionth part of 

 a quadrant of the meridian. 



Dilatation or Expansion. Now, one of the most 

 general and notable effects which heat produces on 

 matter is to expand it. The length or a metallic 

 bar varies with every change of temperature, and 

 is ever the same at the same temperature. The 

 fixing of the tire of a cart-wheel is a very good 

 instance. No hammering could fit an iron hoop so 

 tightly on the wood-work of the wheel as does the 

 simple enlarging of the tire by heat, and its subse- 

 quent contraction by cold. It is thus possible to 

 slip it on, and an enormous force is secured to bind 

 the pieces together. In almost every kind of struc- 

 ture the expansion and contraction from changes 

 of temperature require to be guarded against. In 

 the huge iron tubes of the Britannia Bridge the 

 mere change of the seasons would have produced 

 sufficient changes of length to tear the piers asunder, 

 had each end of a tube been fixed to masonry. 

 Watches and clocks, when not compensated (see 

 PENDULUM), go faster in cold weather, and slower 

 in hot, an immediate consequence of the expansion 

 or contraction of their balance-wheels and pendu- 

 lums. 



If a flask full of water or of alcohol be dipped 

 into hot water or held over a lamp, the flask is 

 heated first, and for a moment appears not quite 

 full, hut as heat reaches the liquid it expands in 

 turn, and to a greater degree than the flask, so that 

 a portion of the liquid runs over ; a glass shell 

 which just floats in a vessel of water, sinks to the 

 bottom when the water is heated ; and as water is 

 gradually heated from l>elow, the hotter water con- 

 tinually rises to the surface. Indeed, if this were 

 not the case, it would be impossible to prevent 

 explosions every time we attempted to boil water 

 or any other fluid. If a bladder, partly filled with 

 air, and tightly tied at the neck, be heated before a 

 fire, the contained air will expand, and the bladder 

 will be distended. As it cools it becomes flaccid 

 again by degrees. 



These and like instances are sufficient to show us 

 that in general all bodies expand by heat. In order, 

 then, to prepare a reproducible means of measuring 

 temperature, all we nave to do is to fix upon a sub- 

 stance ( mercury is that most commonly used ) by 

 whose changes of volume it is to be measured, and a 

 reproducible temperature, or rather two reproducible 



temperature*), at which to measure the volume. 

 ThoHe usually selected are that at which water 

 freezes, or ice melts, and that at which water IK. IK. 

 In both of these cases the water must l>e pure, an 

 any addition of foreign matter in general change* 

 the temperature at which free/ing or Wiling takes 

 place. Another important circumstance in the 

 In it/lit of tin; liuromcter (see BOIMNC;). The second 

 reproducible temperature in therefore defined as 

 that of water boiling in an open vessel when the 

 barometer stands at 30 inches. In absolute strict- 

 ness, this should also be said of the free/ing-jMint, 

 but the effect on the latter of a change of baro- 

 metric pressure is practically insensible. The 

 practical construction of a heat-measurer or ther- 

 mometer on these principles, the various ways of 

 graduating it, and how to convert the readings 

 of one thermometer into those of another, are 

 described in the article THERMOMETER. In the 

 present article we suppose the Centigrade thermo- 

 meter to be the one used. 



If we make a number of thermometer tubes, fill 

 them with different liquids, and graduate as in the 

 Centigrade, we shall find that, though they all give 

 in freezing and 100 in boiling water, no two in 

 general agree when placed in water between those 

 states. Hence the rate of expansion is not generally 

 uniform for equal increments of temperature. It 

 has been found, however, by very delicate experi- 

 ments, which cannot be more than alluded to here, 

 that mercury expands nearly uniformly for equal 

 increments of temperature. However, what we 

 sought was not an absolute standard, but a re- 

 producible one ; and mercury, in addition to fur- 

 nishing this, may be assumed also to give us 

 approximately the ratios of different increments 

 ot temperature. 



We must next look a little more closely into the 

 nature of dilatation by heat. And first, of its 

 measure. A metallic rod of length / at increases 

 at t by a quantity which is proportional to t and 

 to 1. Hence, k being some numerical quantity, the 

 expanded length I' = l( 1 + kt ). Here k is called 

 the coefficient of linear dilatation. For instance, a 

 brass rod of length 1 foot at becomes at t 

 (1 + -0000187*) feet ; and here k, or the coefficient 

 of linear dilatation for one degree ( Centigrade ), is 

 0000187 ; or a brass rod has its length increased by 

 about one fifty-three thousandth part for each 

 degree of temperature. 



If M ? e consider a bar (of brass, for instance) whose 

 length, breadth, and depth are I, b, d then, when 

 heated, these increase proportionally. Hence 



/'= 1(1 + kt), 



b' = b(l + kt), 



d' = d(l + kt), 



and therefore the volume of, or space occupied by, 

 the bar increases from V or Ibd to V or I'b'a". 



Hence V' = V(l+to) 8 , 



= V( 1 + Skt) nearly, since k is very small. 



Therefore we may write V = V( 1 + Kt ), where we 

 shall have as before K, the coefficient of cubical 

 dilatation for 1 of temperature. And, as K = 3k, 

 we see that, for the same substance, the coefficient 

 of cubical dilatation is three times that of linear 

 dilatation. 



In the following table these coefficients are 

 increased a hundredfold, as it gives the propor- 

 tional increase of length for a rise of temperature 

 from to 100 Centigrade. It must also be 

 remarked that, while the linear dilatation of solids 

 is given, it is the cubical dilatation of liquids and 

 gases which is necessarily given. Moreover, as the 

 latter are always measured in glass, which itself 

 dilates, the results are only apparent ; they are too 

 small, and require correction tor the cubical dilata- 

 tion of glass. This, however, is comparatively very 



