228 
MR, H. L. CALLEMDAR ON THE PRACTICAL 
observations in Table II., we might naturally suppose that the parabolic formula 
accurately represented the phenomenon, and that the numbers in the “ deviation ” 
column were errors of observation ; and regret that after all our trouble the results 
were so inaccurate. On the other hand, had we only the observations in Table F.-i., 
we might be carried away (as I was) with the idea that the exponential formula was 
the true solution of the problem, and that the small deviations were accidental, as in 
this case they very well might have been. But, having both series, F.-i. and F.— II., 
in every way independent, and yet exhibiting such a marked similarity, we are led to 
inquire what it means. Each curve is marked by a small subsidiary wave at about 
400° before the final upward rush. This is not altogether fanciful, but is just such in 
position and magnitude as would be produced by an irregularity in the resistance- 
variation of the platinum of the order of 1° taking place between 200° and 300° ; for 
in calculating the value of t and (fe — pt) we have assumed smooth parabolic 
formulae, which take no account of the small irregularities which are shown to exist 
by the curves of comparison of platinum wires, and one of which is indicated also by 
the am thermometer observations. In the curve F.-n. the phase of this subsidiary 
wave is retarded. Now the curve P.-i., containing the comparison between platinum 
wires (l) and (2), which were used in the comparisons F.-i., F.-il, respectively, 
shows that the curve of pt 2 is affected by a deviation similar in magnitude and sign 
to that of pt lt but taking place about 100° later. If this curious correspondence of 
the curves had been foreseen, the comparisons between the platinum wires would 
have been made more extensive and complete, and, in particular, the form of the 
curves between 100° and 300° would have been carefully explored. 
Professor Tait has observed that at about a dull-red heat the resistance of iron 
increases very rapidly ; the thermo-electric and mechanical qualities of the metal also 
change suddenly about this point. It is well known that very slight impurities exert 
a very marked effect on the softening point of iron ; we need not be surprised, 
therefore, that the upward rush in the case of F.-ii. does not come within the limit 
of observation, like that of F.-i. I propose to make a direct comparison between the 
wires F.-i. and F.-ii. to confirm this. Unfortunately, my first impression on 
reducing the observations was that they disagreed completely ; the nature of the 
agreement was not noticed till the apparatus had been dismounted and the wires 
used for other purposes, so that no more observations could be taken with the same 
coils. 
The curves F.-i., F.-ii., sufficiently illustrate the futility of applying empirical 
formulae calculated from observations between narrow limits for purposes of extra¬ 
polation. I have known cases where an empirical formula, calculated by the method 
of least squares from observations at varying temperatures with a mercurial thermo¬ 
meter between 20° and 100° C., has been applied to estimate temperatures above 
1000°. This is an extreme instance of a method to be avoided. 
Between the limits 0° and 500°, however, the parabolas—- 
