404 Mr. S. U. Pickering on the Expansion 



My determinations were not nearly numerous enough to 

 establish either of the changes bere suggested, and were taken 

 only as hinting the possibility of the existence of such ; but 

 they showed the advisability of examining the more numerous 

 results of other physicists in the same manner. 



In all cases except one the differentiation of tbese was per- 

 formed on the experimental values themselves. The exception 

 was that of Kopp's determinations, which, though they may 

 approximate to the truth more nearly than in several other 

 cases, show such experimental errors in consecutive determina- 

 tions as to be useless for purposes of direct differentiation. 

 The smoothed curve representing the experiments was there- 

 fore differentiated in this case. In other cases also the 

 smoothed experimental curves were differentiated, but only 

 with the view of supplementing the evidence derived from a 

 direct differentiation. 



The differentiation of the several results requires some 

 manipulation in order to combine the various series which 

 several of the experimenters have made, and in order to get 

 fairly equal differences between the consecutive determina- 

 tions. One or two determinations which were evidently 

 erroneous have been omitted. I have not considered it neces- 

 sary to reproduce here the voluminous tables containing these 

 results. 



It, is scarcely necessary to point out that only the experi- 

 mental values themselves were taken, and that values calcu- 

 lated from equations purporting to represent them would be 

 of no use for such purposes as the present. 



Some of the results refer to volumes, others to weights : 

 in some water at 0° is taken as unity, in others water at 4°: 

 in some, again, the weights or volumes are uncorrected for 

 the expansion of the glass. None of these differences will 

 affect the question at issue — the existence or position of sudden 

 changes of curvature — they will only affect (and that to a 

 very small extent) the inclination, and, possibly, the curvature 

 (if the coefficient of expansion of glass is represented by a 

 curve instead of a straight line as is generally assumed) of the 

 differential. Where densities are taken, the sign of the dif- 

 ferential will be the opposite of what it is where volumes are 

 taken : in the Plates I have represented them so that this dif- 

 ference shall not interfere with a comparison of the various 

 figures. 



It must be remembered that the figures here given illustrate 



