430 M. Berthelot on a New Thermometer for measuring 

 that is, 



h 



which is the relation signified. 



If this capacity were indeed constant, it would be simply neces- 

 sary to trace by the side of the scale of pressures a scale of tem- 

 peratures in which the divisions were proportional to those of 

 the pressures. Strictly speaking, however, the condition which 

 determined this relation is not exactly fulfilled in the new ther- 

 mometer, and for the following reasons : — (1) From the expan- 

 sion of the glass envelope ; and (2) from the expulsion of a por- 

 tion of the air contained in the reservoir, which impinges upon 

 the mercury in the capillary tube. But if the dimensions given 

 below are observed, it will easily be seen that this theoretical con- 

 dition is but slightly altered in practice ; the very small diver- 

 gence renders the accurate construction of the instrument still 

 perfectly possible. 



In the first place, we will calculate the possible amount of 

 variation in the capacity of the envelope. 



Admitting ttoWit for the coefficient of cubical expansion of 

 glass, then from 0° to 500° the capacity of the reservoir will in- 

 crease by 3-7WOJ or by y^. It results, therefore, that the length 

 of a degree on the instrument slightly diminishes from 0° to 

 500°, being, of course, least at the latter point. 



It is needless to calculate the amount of this diminution ; it 

 is sufficient to remark that any objection to our method of gra- 

 duation, arising from the fact of the gradually increasing capa- 

 city of the glass envelope, is nullified when it is considered 

 that this graduation is the result of direct experiment, and is 

 obtained by means of certain empirically fixed points. 



We will now consider the effect due to the small portion of 

 air expelled from the reservoir. It will be seen, from the dimen- 

 sions adopted, that the capacity of the cylindrical reservoir is 

 about 4 cubic centims., and also that the air at zero occupies 

 some 500 to 550 millims. in length of the capillary tube. At 

 500° this air will occupy about double the length. Let us cal- 

 culate the increase in volume under the extreme condition, that 

 is, at 500°. Supposing the tube to be \ of a millimetre in in- 

 ternal diameter, then the capacity of 1 metre in length of this 



tubing is equal to ir -^r 2 1000 cubic millims., or about 31 cubic 



millims. 



Now this volume represents only the j^w part of the capacity 

 of the reservoir. But the weight of this air represents a much 

 larger fraction of the weight of the air contained in the reser- 



