156 MEASUREMENT OF HIGH TEMPERATURES. [boJl 
The constants to which the values of this table refer are 
m = 0.0001939 i 0.0000233 n= 0.03778 ±0.00054 
The probable errors of m and n indicate that the inaccuracy is large 
incurred in the measurement of /'(0) :/(0), whereas n is much mc 
fully warranted. The equation is one, however, in which pairs of v. 
' ues. of m and w, either both larger or both smaller than the critic 
values above, readily compensate each other. As usual, the con star 
which may be derived with a little forethought from careful grapl 
representations of results are probably nearer the truth than the valu 
which are mechanically computed by the method of least squares. 
The final results of this chapter may therefore be stated as follow 
In endeavoring to describe the platinum alloys as a class possessii 
generic characteristics, it is permissible to abstract from the minu 
and individual behavior of the isolated alloy ; and it appears that ele 
trical temperature-coefficient /'(0) :/(0) varies as a linear function 
conductivity (1 :/(0)) throughout the whole enormous variation of i 
sistance (10 to 65 microhms, c. c.) which platinum alloys not too high 
alloyed (<10 per cent.) present. In other words, if at t° the specific r 
sistance of a platinum alloy be denoted by /(£), where t symbolizes tei 
perature, then 
/(0)(/ / (0):/(0)+0.000194)=0.0378 ( 
It is perhaps not superfluous to remark in passing that if instead of tli 
thoroughly arbitrary temperature 0° centigrade some other value mo 
in keeping with the qualities of platinum alloys had been selected til 
constants m and n would present different values ; and it is easily co 
ceivable that correlated values of '/(/) and/'(tf) may exist, for which tl 
constant m is annulled and for which equation (7) takes its simple 
form. The actual search for such a result involves more labor than 
can at j)resent apply. Clausius 1 was the first to call attention to tl 
approximate proportionality of the resistance of most pure metals witt 
their absolute temperature. 
Accepting Matthiessen's general relation 
s t =s Q {l+ at- fit 2 ) ^=0.00382 /?= 0.00000120 
and putting 
ds t _ s 
dt~21V 
it appears that at, say, 60° the said proportionality is accurate. Again 
since/(2) increases more rapidly than f'(t) decreases, with increasin 
temperature the passage of the equation 
/(0) (/'(0) :/(0)+«)=»into/(*)/'(t) :/(0)=n', 
may be looked for in the region of positive t. 
» Clausius: Pogg. Ann., 4th series, vol. 14, 1858, p. 650; ef. Bull. U. S. Geo!. Survey 
No. 14, 1885, p. 24. 
(810) 
