880 DE. A. MATTHIESSEN ON THE EXPANSION 



Regnault frequently used a thermometre a poids. Let P be the weight of mercury 

 contained in it at 0° C, p the weight of mercury expelled when exposed to the tempe- 

 rature t by ordinary thermometer. 



At temperature t by ordinary thermometer the volume of mercury below 0° is 

 V(l+^^), and the volume of the mercury above 0° is K#(l+5'0- Therefore the 

 volume of the whole of the mercury is V(l+^^)-f-K^(l+^^)- 



Hence 



p _ K<(1 -\-g t') K^ 



, V-W[l-vgt') + Kt[\-\-gt')-y + Y^t' 



Therefore 

 Therefore 

 tlierefore 



y^=^. When ^=100 let ^=i. 



_6 KIOO. 



i'-b— V ' 



J P-6 P 



100"~P— j9 b' 



Kegnault uses jrj ^ as the measure of temperature, which is the same as tt^ , the 



indication of a common mercurial thermometer uncorrected for the effect produced by 

 the expansion of glass. 



A small error is generally made in taking the boiling-point of water, 100°, viz. the 

 influence of latitude is not taken into consideration. Professor Millek writes to me on 

 this point the following:— " Laplace, in the fifth edition of his ' Systeme du Monde,' 

 states that he regards 100° C. to mean the temperature of water boiling under a pressure 

 equivalent to that of a column of mercury at 0° and 760 millims. in latitude 45°. 



"DuLONG, and afterwards Regnault, assumed 100° to be that of boiling water under 

 normal pressure at Paris. Now the pressure at 760 millims. of mercury at the level of 

 the sea in latitude 45° is equivalent to a column in latitude x at ^ metres above the level 



of the sea, the height of which is 760 Tl — 1-32^) (1-0-0025659 cos . 2?.), where r = 



radius of the earth =6366198 metres. 



" The latitude of Paris (48° 50' 14") is not very different from 45°. Regnault's place 

 of observation was about 60 metres above the sea. Hence a column of 760 millims. 

 mercury at the level of the sea exerts the same pressure as a column of 759*75 millims. 

 in Regnault's laboratory." 



This will only make a difference in the boiling-point of 0*01, a difference which may 

 be neglected in ordinary work, but in normal researches ought to be brought into calcu- 

 lation ; as, for example, in Miller's normal research " On the Constraction of the 

 New Standard Pound"*. At Abo this correction would amount to upwards of 0''-25. 



In the text-books on chemistry and natural philosophy we find the coefficients of 



* Philosophical Transactions, 1856, p. 753. 



