118 Prof. D. Mendeleeff on the Variation in the 



water, corresponding to one degree, and after are shown the 

 corrections AS for the specific gravity of water which must he 

 introduced, in order to obtain from the observed quantities 

 these specific gravities as referred to the hydrogen thermo- 

 meter. Here also the corrections for the figures given by 

 the experimenters apparently affect the fifth decimal. And 

 since in the constancy of the temperatures and in the readings 

 of the thermometers we must allow, besides, their own inevi- 

 table errors, and seeing that, in addition to this, these errors 

 differ with different observers and thermometers *, it may 

 be considered as demonstrated that in general in the data 

 existing at present for the density of water, at 20° for instance, 

 not only the sixth but the fifth decimal place is subject to 

 correction. 



But what is the magnitude of possible error in perfected 

 determinations of the density of water, if we reckon that 

 insignificant and individual errors disappear on taking a 

 mean result, and making the figures more uniform by the 

 method of interpolating introduced by all observers in their 

 experiments, by expressing them in the form of densities 

 referred to entire degrees ? 



I have devoted much time to the consideration of the best 

 answer to this question ; having endeavoured to determine by 

 an examination of the original investigations, the measure of 

 the errors of each experimenter by introducing into his results 

 all the possible corrections, and calculating the mean quadratic 



* Many investigators on the expansion of water at various tempera- 

 tures have determined, if not all the possible error, at least the value of 

 the deviations of the formulas expressing the expansion from their experi- 

 mental results. Thus, for instance, Hagen {I. c.) found for his observa- 

 tions, that the so-called " probable error," or more precisely the measure 

 of the discrepancies between the experimental results and those given by 

 formula, may be expressed in fractions of degrees of the temperature, 

 which we translate into millionths of the volume. 





In degrees. 



In volumes. 



From 0° to 8° 



+0-1033 



+ 0-000002 



» 8 „ 14 



0-1085 



11 



„ 14 „ 20 



0-0479 



8 



„ 20 „ 30 



0-0788 



20 



„ 30 „ 40 



0-0439 



14 



„ 40 „ 60 



0-0526 



24 



„ 60 „ 80 



0-0592 



36 



„ 80 „ 100 



0-1249 



+ 0-0000086 



The greater portion of the errors of this kind (accidental) are elimi- 

 nated in the majority of the investigations by the help of interpolation, by 

 the method of least squares, and therefore in the sequence I avoid dwelling 

 upon such errors, and pay chief attention to the constant errors in con- 

 nexion with the fundamental methods of research, which cannot be 

 removed by interpolation. 



