§ 9 OF ARTS AND SCIENCES. 393 



measured than any of the rest, being equally subject to 

 thermometric error; if this be true, then, according to the 

 theory of probability, the mean error of the results of Kopp 

 and Pierre combined will be, not one-quarter of their mean 

 difference, as would be the case if the standards were 

 absolutely reliable, but one-half or three-quarters, according 

 as we assign to Regnault (or whatever standard they may 

 have used) the weight of two observers or that of only 

 one. 



Where, as in the present case, the mean difference of 

 theory and observation is equal to about two-thirds of the 

 mean difference of two observers, the discrepancy is 

 probably due to errors of observation. It would appear 

 that for ten out of the eleven liquids most closely exam- 

 ined, — the exception being butyric acid — the agreement 

 is actually greater than probability could require even if 

 the theory (as well as the standards) were known to be 

 absolutely true. 



In the case of solids, according to the results obtained 

 by Dr. Matthiessen, the law of expansion will need to be 

 modified. I have already pointed out that if the mole- 

 cule or atom were itself compressible, the indication of 

 the kinetic theory would not be strictly fulfilled; the 

 departure can easily be subjected to mathematical compu- 

 tation, and its value determined, constantly increasing 

 with the state of aggregation. 



It appears to me, however, that the facts do not justify 

 such a laborious calculation. It is to be observed that 

 in weighing in water, as in the experiments of Dr. 

 Matthiessen, any error in the determination of the density 

 of the water,* or of its temperature, will affect the results 

 by a proportionate amount. 



* The mean difference between Kopp and Pierre for water [see Table, Sharpies, page 73] is 

 a little more than .0005, or one-twentieth of one per cent., corresponding to an error of one-tenth 

 of one degree in temperature. 



