1824.] Mr. Crichton on Expansions. 243 



alternately occupied by it, or vacant, as the temperature is 32° 

 or 212° ; so that weighing in this experiment, serves merely to 

 determine what parts the vessel contains at boiling. 



MM. Dulong and Petit having fixed the absolute dilatation of 



mercury at -rr^r, and its apparent dilatation in glass at — — , pro- 

 ceed to determine that of their vessel. But here an error has 

 been committed not less important than the other ; for in order 

 to obtain the dilatation in question, they adopt a common but 

 false assumption ; that if the absolute dilatation of a fluid, and 

 its apparent dilatation in a vessel be known, the difference 

 between these must represent that of the vessel itself, and of 



course give ( — r — jr-gj gj= as the number ; the result here is 



far from the truth, and would still have been so, though the 



proper number — - had been used instead of — — ; the difference, 



in neither case, giving the real dilatation which the vessel must 

 have undergone, in the interval of temperature between 32° and 

 212°. 



To learn the true dilatation in this instance, we have only to 

 recollect, that whatever quantity is expelled from a vessel, by a 

 given increase of temperature, something more would be expelled 

 if the vessel itself did not expand ; and that this supposed por- 

 tion must be added to the quantity expelled at the higher tem- 

 perature (as found by experiment), and deducted from that then 

 remaining in the vessel, that each may represent what it would 

 be, if the vessel were not liable to expansion : the following 

 illustration will furnish a concise general formula, for all similar 

 dilatations of vessels. 



To find this correcting quantity, we may take the coefficient 

 of the dilatation of the vessel to express its capacity at any given 

 temperature, as 32°, consequently the same coefficient, plus 

 unity, will express its increased capacity at the higher tempera- 

 ture, 212°. 



Now, in the case of MM. Dulong and Petit, if g be that coef- 

 ficient, g and g + 1 will respectively represent the capacities at 

 the given extremes of temperature ; and from what is said above, 



63 # 8 — — ; must be the corrected contents, as 1 H — — ; is the 



true expelled quantity at 212°, then, making the former of these 

 divided by the latter = the coefficient of the absolute dilatation 



of mercury, that is, — ^ = 55*5, we obtain g = 433*301, or 

 for the absolute dilatation of the vessel used by MM. Du 



433-301 



long and Petit, and not „— as in the table, Annates, p. 138 



r2 



