VEGÅ-EXPEDITIONENS V ET EN S K A FLI G A AltBETEN. ■ 261 



q =0.00018116 



in the first, case g is = O.00002753 [q = O.00017905 Reg.] 

 ;> » second g » =0.00002974 [q ^O.oooisiie Wiilln.] • 

 This uncertainty, which does not amount to more than 

 0.00000221, will perhaps seem to be verv unimportant but would 

 indeed be inost fatal, if it was not neutralized to a great degree 

 by a stratagem in the method. An easy calculation shx)ws 

 that the influence, which this uncertainty, as to the real coeffi- 

 cient of expansion of mercury, excercises upon the final result, 

 is in some cases abont 5 to 10 times greater than the distur- 

 bance caused by unavoidable errors of observation. I think, 

 that the original number O.00017905 of Regnault represents the 

 average coefficient of dilatation of mercury below zero more 

 closely than O.oooisiie. Therefore the following results are cal- 

 culated by means of the constants 



q ^= 0.00017905 g = 0.00002753 



The volumes of pure teater and ice are also calculated b}'' 

 means of 



q = 0.00018116 g = 0.00002974 



to facilitate the comparison with the calculations of Pliicker 

 and Geissler, which are founded upon a similar assump- 

 tion. ^ In both cases the values of q and g arg supposed to 

 be constant within the temperatures of observation. 



This assumption is of course not correct, but is an almost 

 unavoidable consecj[uence of the prevailing uncertainty. as to 

 the real dilatation of mercury - at low temperatures and from 

 the chosen standard of temperature, which involves: 



q — g = constant 

 from which it follows, that the variations of q and g must 

 be equaL The value of g being only Ve of q, it follows, that 

 the expansion of glass varies 6 times more rapidly than that 

 of mercury. In order to avoid the application of this conse- 

 quence, which is hardly acceptable, if q is supposed to vary 

 below zero in the ratio given by the formulae, I have sup- 

 posed both q and g to remain constant and consequently to 



^ q = 0.00018058. 



- In the course of this research the author has gained the conviction, 

 that the dilatation of mercury below zero is not exactly represented by the 

 formulae and the coefficients given by Regnault a. O. for higher tempera- 

 tures, and that this subject highly needs a repeated experimental research. 

 The alteration in the coefficient of dilatation, which begins to appear on 

 approaching the point of solidification of mercury, is the real cause of the 

 discrepancy between the air-thermometer and the mercury thermometers. 

 The author hopes to return to this subject in a future paper. 



