Prof. H. L. Callendar on Platinum Thermometry. 207 



on the platinum scale, just like a mercury thermometer, or 

 any other instrument intended for practical use. The quantity 

 directly observed is not the resistance in ohms, but the tem- 

 perature on the platinum scale, either pt, or j)t+pt°. The 

 advantage of this method is that the indications of different 

 instruments become directly comparable, and that the values 

 of pt for different wires agree very closely. If this method 

 is not adopted, the resistances in ohms of different instruments 

 at different temperatures form a series of meaningless figures, 

 which cannot be interpreted without troublesome reductions. 



(2) The second advantage of the difference-formula lies in 

 the fact that the difference is small, more especially at mode- 

 rate temperatures, and can be at once obtained from a curve 

 or a table, or calculated on a small slide-rule, without the 

 necessity of minute accuracy of interpolation or calculation. 

 In many cases, owing to the smallness of the difference 

 between the scales, the results of a series of observations 

 can be worked out entirely in terms of the platinum scale, 

 and no reduction need be made until the end of the series. 

 For instance, in an elaborate series of experiments on the 

 variation of the specific heat of water between 0° and 100° C, 

 on which I have been recently engaged, by a method de- 

 scribed in the Brit. Assoc. "Report, 1897, all the observations 

 are worked out in terms of the platinum scale, and the re- 

 duction to the air-scale can be performed by the aid of the 

 difference-formula in half an hour at the end of the whole 

 series. As all the readings of temperature have to be taken 

 and corrected to the ten-thousandth part of a degree, and as 

 the whole series comprises about 100,000 observations, it is 

 clear that the labour involved in Mr. Dickson's method of 

 reduction would have been quite prohibitive. It is only by 

 the general introduction of the method of small corrections 

 that such work becomes practicable. 



On the Method of Least Squares. — There appears to be a 

 widespread tendency among non-mathematical observers to 

 regard with almost superstitious reverence the value of results 

 obtained by the method of least squares. This reverence in 

 many cases is entirely misplaced, and the method itself, as 

 commonly applied, very often leads to erroneous results. For 

 instance, in a series of observations extending over a con- 

 siderable range of temperature, it would be incorrect to attach 

 equal weight to all the results, because all the sources of 

 error increase considerably as we depart further from the 

 fixed points of the scale. In a series of air-thermometer 

 observations, the fixed points themselves stand in quite a 

 different category to the remainder of the observations. The 



