208 Prof. H. L. Callendar on Platinum Thermometry. 



temperature is accurately known by definition, and is not 

 dependent on uncertain errors of the instrument. It is a 

 mistake, therefore, in reducing a series of observations of this 

 kind, to put all the observations, including the fixed points, 

 on the same footing, and then apply the method of least 

 squares, as Mr. Dickson has applied it in his reduction of the 

 results of various observers with platinum thermometers. For 

 instance, in order to make his formula fit my observations at 

 higher temperatures, he is compelled to admit an error of no 

 less than o, 80 on the fundamental interval itself, which is 

 quite out of the question, the probable error of observation on 

 this interval being of the order of o, 01 only. The correct 

 way of treating the observations would be to calculate the 

 values at the fixed points separately, and to use the remainder 

 of the observations for calculating the difference-coefficient. 

 Even here the graphic method is preferable to that of least 

 squares, because it is not easy to decide on the appropriate 

 weights to be attached to the different observations. Cor- 

 recting the method of calculation in this manner, we should 

 find a series of differences between my observations and 

 Dickson's formula, of the order shown in Table I. It would 

 be at once obvious that the deA^ations from (6) were of a 

 systematic type, and that it did not represent the results of 

 this series of observations so well as that which I proposed. 

 The deviations shown in Dickson's own table are of a syste- 

 matic character ; but they would have been larger if he had 

 treated the fixed points correctly. 



Limitations of the Difference-Formula. — The observations 

 of Messrs. Haycock and Neville at high temperatures may be 

 taken as showing that the simple parabolic difference-formula, 

 in which the value of d is determined by means of the S.B.P. 

 method, gives very satisfactory results, in spite of the severe 

 extrapolation to which it is thus subjected, provided that the 

 wire employed is of pure and uniform quality. If, however, 

 the S.B.P. method of reduction is applied in the case of impure 

 wires at high temperatures, it may lead to differences which 

 are larger than the original differences in the values of pt 

 before reduction. For instance, I made a number of pyro- 

 meters some years ago with a sample of wdre having the 

 coefficients c = '00320, d // = l'7b. My observations on the 

 freezing-points of silver and gold (Phil. Mag., Feb. 1892) 

 were made with some of these pyrometers. All these instru- 

 ments gave very consistent results, but they could not be 

 brought into exact agreement with those constructed of purer 

 wire by the simple S.B.P. method of reduction, employ- 

 ing either difference-formula (2) or (4). This is not at all 



