914 
Physics. — “An interpolation-formula for resistance-thermometry 
at low temperatures’. By Dr. F. Zernike. (Communicated by 
Prof. H. Haga). 
(Communicated in the meeting of October 31, 1914.) 
1. Introduction. In using resistance-thermometers to measure low 
temperatures with some accuracy one is often hampered by the 
difficulty to deduce the temperatures from the measured resistances. 
This difficulty is partly due to a want of fixed points which could 
reproduce the absolute scale of temperatures with the required 
accuracy. 
To a great extent the difficulty mentioned must be ascribed to the 
lack of an interpolation-formula which enables us to use a resistance- 
thermometer, after calibration at a few standard-temperatures, at all 
intermediate temperatures. For the following reasons such a formula 
is much more necessary in our case, particularly for the commonly 
used platinum-resistance than in that of most other physical measures. 
First of all the resistance is not a “simple” function of the temperature, 
ie. the higher derivatives of this function are large, which makes 
linear interpolation impossible even in small intervals, or quadratic 
interpolation in somewhat larger intervals. Ordinarily graphical in- 
terpolation will be used in such a case. However this will not 
remove the difficulty here, at least if an accuracy of 0.°O1 or 0.°02 
is required — as we shall suppose in the following. For a large: 
scale drawing would then be required and the few known points 
would not allow to trace the curve unambiguously. 
Some years ago considerations of this kind made me try the 
suitability to this purpose of many different formulae. I made use of 
the experimental data of Onnes and Cray’), in particular of those 
concerning the platinum wire Pt, and the very pure gold wire Au777. 
Temperatures were used after reduction to the thermodynamic scale 
and resistances reduced as far as possible to the values for pure 
metals by subtracting from everyone the resistance at the absolute 
zero, which was found by extrapolation. This was done in accord- 
ance with the well-known experiments of KaAMERLINGH ONNEs at 
the temperatures of liquid helium, which had refuted the current 
opinion that the resistance would become infinite at the absolute 
zero of temperature. Thus these experiments explained the failure 
of former attempts to find adequate formulae for the resistance 
1) Leiden Communications No. 95 and 99, these Proceedings 9, 207 and 10, 200. 
