242 Mr. Crichton on Expansions. [April, 



rent dilatation of mercury in glass, which they effect in the usual 

 way, by subjecting a known weight of that fluid, contained in a 

 glass vessel carefully deprived of air and humidity, to the 

 increase of temperature in the same thermic unit ; then dividing 

 the weight of the quantity contained in the vessel at freezing, by 

 the weight of the quantity expelled by boiling, they obtain the 



quotient 64*8, and thence infer, that -rr^ is the apparent dilata- 

 tion of mercury in glass. 



These very able experimenters justly insist on the great pre- 

 cision of which this method is susceptible. In trials I have 

 made, with vessels holding from 200 to 500 grains, the capillary 

 opening was so small, that a quantity, corresponding to less than 



— of a degree could be detached when expelled ; yet minute as 



this portion is, it was very palpably noted by the balance, which 



turned with y— of a grain. 



Every one who knows the difficulty of obtaining tolerably 

 uniform results from pyrometrical measurements, will readily 

 admit the advantages of the method adopted by MM. Dulong 

 and Petit, when with them we recollect, that " dans les mesures 

 directes de dilatation des solides, l'incertitude se trouve triplee 

 en passant de l'expansion lineaire a Pexpansion en volume." 

 An error, however, of considerable importance has entered into 

 all computations from the data thus obtained, which unac- 

 countably remains hitherto undetected ; for, though that portion 

 of a fluid, detached by increase of temperature, from a glass 

 vessel of known volume, is indeed the fraction expelled, yet this 



fraction (taking: the case of MM. Dulono; and Petit — — as " le 



v ° f 64'8, 



poids du mercure qui en sortait," does by no means denote the 

 dilatation of mercury in glass ; consequently the dilatation they 

 deduce as that of glass itself must be erroneous. 



To illustrate this, let us suppose that a vessel, containing 

 64*8 parts by weight of a fluid, throws out one of those parts by 

 increase of temperature ; it is evident that the dilatation of that 

 one part has not been taken into account, for were it put into 

 another vessel just holding it at 32°, then would another dilata- 

 tion take place of - ,,„ - , of the original volume, and still with 



r 419904 a 



this last portion must the operation be repeated, and so on to 

 infinity ; the successive expansions resolving themselves into a 



series, the sum of which is — -, or real dilatation. Or, to take 



another view of the matter, the vessel havingbeen heated to 212°, 

 there will remain within 63-8 parts ; these cooled to 32° leave at 

 top an empty space = 1, which heating to 212° will fill up; this 



one part, therefore, or 7^ of the volume of the mercury, will be 



