165 
Measurement op temperature. 
cannot be well represented in an empirical formula. The simple parabolic formula 
(p), R/R 0 = 1 + at + fit 2 , corresponds exactly with ( d) (p. 163), namely 
t —pt = %{(t/iooy — (t/ 100)}, 
where 8 = 10,000/3/(a + 100/3), and gives an accuracy of the 1 °f Q order through a range 
of 600° C. Other formulae may readily be found which give nearer approximations in 
special cases, and through small ranges. For instance, the exponential formula 
log R = ai/(l + fit) corresponds to the dotted line, Plate 13, fig. 11, and exactly smooths 
out the characteristic inequalities in the platinum-iron comparison-curve, agreeing 
with it far more closely than the parabola ; but in most other cases the exponential 
formula has the disadvantage. Benoit and Matthiessen use the parabolic formula, 
but Matthiessen expressed his results as variations of conductivity (R 0 /B), so that 
his formulse are quite inapplicable except between 0° and 100 c C.] 
I have endeavoured to give the fullest data in each case for the verification of my 
results, and to make the calculations in each case accurate within the limits of 
probable error, but among so large a mass of figures I can hardly hope to have 
escaped an occasional slip. 
My most sincere thanks are due to the authorities at the Cavendish Laboratory for 
the facilities which they gave me for the prosecution of these experiments, and 
especially to Professor Thomson for the kind interest he has taken in the subject, 
and for valuable suggestions and assistance. 
In overcoming the mechanical difficulties which are always the most important part 
of an investigation like the present, I received great help from Professor Thomson’s 
assistant, Mr. D. S. Sinclair, though, owing to the many calls upon his time, he was 
unable actually to make much of the apparatus. I had intended to make many other 
experiments, but my progress has been much retarded by my own want of mechanical 
skill, and the necessity of making all my own apparatus. 
I am at present intending to pursue these experiments to higher temperatures ; and 
have already worked out the experimental details of the application of the platinum 
thermometer to questions in the theory of heat where I consider greater accuracy 
may be obtained by its use. 
Authorities consulted. 
On the variation of the electrical resistance of metals with temperature. All 
experiments almost up to date are collected in the first volume of the last edition of 
‘Die Lehre von. der Elektricitat,’ by G. Wiedemann. Original papers by Benoit in 
the ‘ Comptes Rendus,’ and Matthiessen in the ‘ Phil. Trans./ 1862, are of the chief 
importance, but nearly everything has been collated. 
In Thermometry the best general information up to date is to be found in the 
‘ Enc. Brit.,’ 9th edit., Articles “Heat” and “Pyrometers,” already referred to. I 
have also studied with great care the whole of the classical researches of R/egnault 
in the ‘ Memoires de l’lnstitut/ vols. 21, 26, &c. 
