254 Rev. Mr. Emmett on the Expansion of Liquids. [Oct# 



Article V. 



On the Expansion of Liquids. By the Rev. J. B. Emmett. 

 (To the Editors of the Annals of Philosophy.) 



GENTLEMEN, Great Ousebuni, Aug. 14, 1824. 



If the temperatures be taken in arithmetical progression, the 

 volumes of a liquid at those temperatures are the logarithms of 

 a certain series of numbers in arithmetical progression, which 

 latter are, of course, the reciprocals of a series of numbers in 

 harmonical progression. This estimate is sufficiently accurate 

 for the graduation of thermometers which require the true scale, 

 the approximation being so near the truth, that for mercurial or 

 alcoholic thermometers, the deviation will not be perceptible, 

 except very near the boiling and freezing points. The rigorous 

 law is connected with some mathematical investigations, which 

 have not yet been published, but which will appear as soon as 

 my health will allow me to make some requisite experiments and 

 calculations. The true law is this : if the temperature increase 

 in arithmetical progression, the volumes will increase according 

 to the following law, an increasing geometrical x increasing 

 arithmetical progression. As the common difference of the 

 latter series is very small, it may be neglected, except for 

 changes near to the two points named. This closely coincides 

 with the table of expansions given by Dr. Thomson : the first 

 column is the temperature ; the second, the volume of the liquid 

 from the above tables; the third, the numbers to which column 2 

 are logarithms ; the fourth, the differences of the successive 

 numbers of column 3. 



Mercury. 



Temperature. Volume. Log. of 



50° 100183 12594-5 



80 — 508 12603-98 



110 813 12612-8 



140 —1119 12621-7 



170 —1424 12630-6 



200 —1730 12639-5 



Sulphuric Acid. 



Temperature. Volume. Log. of 



50° 100000 12591-6 



80 806 12612-6 



110 —1540 12633-9 



140 —2320 12659-4 



170 —3116 12680-0 



200 —3911 12703-1 



