1648. J 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



339 



they are carried from the temperature 0" to that of 100° (32° to 

 212° Fahrenheit). This law, so remarkable for its simplicity, 

 naturally led them to think that the dilatation of the gases ought 

 to be in a more simple ratio to the quantities of heat than that 

 of solids or liquids. Some, more bold, even concluded that the 

 dilatation of gases must be rigorously proportioned to the quan- 

 tity of heat, and that the gas thermometer was the true normal 

 thermometer to which all the' phenomena of heat ought to be 

 referred. 



M'e now know that this great simplicity in the law of the dila- 

 tation of tlie gases is far from existing. I have shown in the 

 memoir upon the dilatation of gases that not only the different 

 gases have not the same coefficient of dilatation, but that even for 

 the same gas this coefficient varies , with its density. The indica- 

 tions of gas thermometers then, can only be considered, like those 

 of other tliermometets, aj functions more or less complicated of 

 the quantities of beat. : 



But the gas thermometers present an advantage over the mer- 

 curial,, and in general over all liquid or solid thermometers, an 

 advantage which arises from the gi-eatness of the dilatation of the 

 thermometric substance. In any thermometer formed l)y a li(iuid 

 or gaseous substance, the indications of the instrument depend 

 upon the dilatation of this substtince, and of that of tlie substance 

 in which it is inclosed. Now, the dilatation of mercury is only 

 about seven times greater than that of the glass which Iiolds it; 

 and the variations which we remark in the law of the dilatation 

 of the dift'erent glasses, form very appreciable fractions of the 

 apparent dilatation of the mercury, and consequently influence in 

 a notable manner the indications of the instrument. In the gas 

 thermometer, on the contrary, the dilatation of the gas being one 

 hundred and sixty times greater than that of the glass, the viria- 

 tions of the law of dilatation of the different glasses no lonuer 

 sensibly influence the indications of the apparatus, and do not 

 prevent tlie instruments from being comparable. 



If, then, we wish to proiit by this important property, and adopt 

 the gas tliermometer as a standard, we must study se\'eral impor- 

 tant questions, so as to fix the conditions under which the instru- 

 ment will remain comparable. 



The present memoir has for its object the study of the difl^erent 

 methods which have been imagined for measuring temperatures in 

 experiments which require great precision. I will divide it into 

 three parts : in the first part, I will treat of the gas thermometer; 

 in the second, of the mercurial tliermometer ; and in the third, of 

 tlie measurement of temperatures by means of thermo-electric 

 currents. 



Part I. — 0/ Gas Thermometers. 



When a gas enclosed in a mathematically-elastic envelope is 

 submitted to an elevation of temperature, its volume increases, and 

 the gag retains the same elastic force. But if we prevent this 

 dilatation of the gas, by exerting a proper degree of pressure over 

 tlie whole surface of the envelope, the gas retains the same volume, 

 but its elastic force increases. 



Tliere are then two modes of employing a gas as a thermometric 

 substance. The gas may be placed under circumstances such, 

 tliat the pressure which retains it remains constant, and its increase 

 of bulk be observed ; or the gas maybe compelled to keep the 

 same bulk, and its increase of elastic force be examined. 



First Method. — In order that a gas should realise the conditions 

 prescribed by this method, which are very nearly those found in 

 the mercurial thermometer, it would be requisite that the gas sub- 

 mitted always to the same pressure, should expand freely in a 

 gauged reservoir, kept throughout at the same temperature. But 

 these indications cannot be fulfilled in practice — at least, if the ap- 

 paratus is to be submitted to high temperatures. 



The thermometer must therefore he composed of a reservoir 

 which is to be exposed to the temperature which it is desired to 

 measure, and a gauged tube, united to the reservoir by a capillary 

 tube, which removes tlie other from the place where the tempera- 

 ture is to be measured. This gauge tube fulfils the purpose of 

 the graduated stem of the mercurial thermometer, and serves to 

 collect the gas which the rising of the temperature drives out of 

 the reservoir. This tube may also be kept at a constant tempera- 

 ture differing but little from that of the surrounding air. At any 

 moment during the experiment, the gas is composed of two parts : 

 the first, contained in the reservoir, is at tlie temperature to be 

 found, the other in the tube is at the surrounding temperature. 

 These two portions are at the same pressure, whicli may be brought 

 as nearly as is desired of that of the atmosphere. The equations 

 derived from these conditions permit us to calculate the required 

 temperature. 



This arrangement is the one adopted by M. PouiUet, in his air 

 pyrometer, and M. Regnault himself employed it in his fifth 

 series of experiments made to determine the dilatation of gases. 

 It presents a very serious inconvenience when the apparatus is to 

 be used for the measurement of high temperatures. In fact, it will 

 easily be seen that in this case the far greater part of the air will 

 already be in tlie gauged tube, and but little will remain in the 

 reservoir, so that a further elevation of the temperature will cause 

 but a very small portion to pass over into the tube, and this will 

 with difficulty be measured with the proper degree of accuracy. 



In fact it can be easily shown that, calling the temperature .r, 

 and the coefficient of dilatation of the gas a, the sensibility of the 

 apparatus will vary very nearly inversely as (1 -|- ax)". This cir- 

 cumstance led M. Regnault to reject this arrangement for a gas 

 thermometer. 



Second Method. — In the second method the gas is kept constantly 

 of the same volume, and the elastic force which it presents under 

 different circumstances is measured ; then from these, by the law of 

 Marriotte, we may calculate the dilatations which the gas would 

 have undergone if the pressure had been kept constant. 



The apparatus founded upon this second method are much more 

 easily managed, and give greater precision than those constructed 

 according to the first method : they have moreover the advantage 

 of presenting the same sensibility at high as at low temperatures. 

 By placing in these appai'atus air of atmospheric pressure when 

 the reservoir is surrounded by melting ice, we are sure to have in- 

 struments rigorously .comparable. Nevertheless, if we: desire 

 to measure very higlr temperatures— if for instance the instrument 

 is to be used as an fiir pyrometer — it is to be feared tliat the elastic 

 force of the gas within, becoming very considerable, the envelope 

 may experience a permanent change of form under the great 

 interior pressures. This inconvenience may be avoided by intro- 

 ducing into tire apparatus, air under an initial pressure less than 

 that of the atmosphere, when the reservoir is at 0'. In this way 

 the elastic force may be kept within limits as low as may be de- 

 sired, but it is evident that the apparatus becomes less sensitive in 

 proportion as the elastic force of the gas at 0° is feebler ; still, as 

 the measurement of the elastic force may be made with extreme 

 precision, the indications of the apparatus will be in the gi eater 

 number of cases sufficiently exact, even though the initial pressure 

 of the gas at 0^ was but one-fourth of that of the atmospliere. 



But here a very important question presents itself: arc air ther- 

 7nomelers filled with air at very different densitiei comparable with each 

 other ? That is, will such instruments agree at all temperatures 

 when their scales have been made to accord at 0° and 100" .'' We 

 ha^/e before seen (p. 240) that the absolute value of the coefficient 

 of dilatation of a gas changes very notably with its density ; it is 

 required to know whether the changes of density will not produce 

 besides, sensible differences in the law of dilatation. It is abso- 

 lutely indispensable to decide this question in order to fix the con- 

 ditions under which air thermometers shall be established in order 

 to be comparable with each other. M. Regnault also proposed for 

 himself a second question, which he thinks not le^s important than 

 the first — viz., do gas thermometers, filled with gases of different kinds 

 accord with each other when they have been adjusted at 0° and 100° ? 



The apparatus used in these investigations consisted essentially 

 of two gas thermometers placed side by side in the same boiler. 



Each of these thermometers was composed of a globe of flint 

 glass (crystal), of from 700 to 800 cubic centimetres content, ter- 

 minated by a re-curved capillary tube, and a manometric apparatus. 

 The two globes were kept, by copper wires, side oy side on a 

 metallic support, consisting of two metallic plates of lozenge form 

 placed, one below, the other above the globes, and united by iron 

 rods which were permanently fixed to the cover of the boiler ; the 

 upper plate was pierced witli two holes through which passed the 

 stems of the air thermometers, and with two other holes, situated 

 in a line at right angles to that joining the first, through which 

 passed the stems of two merciu-ial thermometers. 



The boiler-cover was permanently fixed to a solid partition, and 

 the copper boiler was attached to it by screw bolts, so that it could 

 be removed or replaced without disturbing the thermometers. 



The manometric apparatus was composed of two glass tubes of 

 12 or 14 mm. interior diameter, cemented into an end piece of 

 cast-iron provided with a stop-cock, so arranged, that by properly 

 turning it, you could at pleasure either cause the two tubes to 

 communicate together, or dicharge the mercury from either of 

 them, or intercept the communication of the tubes with each other 

 and with the open air. The manometers were fixed to the side of 

 the partition opposite to the boiler. 



The capillary tubes of the air reservoir were connected with 

 the capillary tubes of the manometers, by bringing these tubes 



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