380 
MESSRS. W. E. AYRTON AND H. K1LGOUR ON THE 
Next, with the object of ascertaining the magnitude of the error that would be 
introduced into the values of r 0 , a, and j3 by a small error having been made in 
reading the temperature, the preceding calculation was repeated on the assumption 
that the second temperature instead of being 153 0 ‘3 C. was 155° C. The values then 
obtained were 
r 0 ■— 0'2488 ohm ~ 
a = 0'00354 „ > 
/?= — 0*000000896 „ 
( 2 ). 
Thirdly, the method of least squares was applied to all the observations made on 
May 10th, and given in Table I. In this way there were obtained the values 
J3 = 
0-246987 
0-003560 
0-000000645 
ohm " 
” I ' 
5 ? _ 
(3). 
Lastly, the method of least squares was applied to all the observations made on 
May 14th and 15th, and given in Table II., the values thus obtained being 
r 0 = 0'247338 ohm j 
a — 0-003650 „ l 
/3 = — 0-0000001091 „ 
( 4 ). 
To compare the values of r 0 , a, and (3 obtained from the curve recording the obser¬ 
vations of May 14th and 15th with the values obtained by applying the method of 
least squares to the same observations, we may examine the value of the difference 
between r l0Q , the resistance of the wire at 100° C., and r 0 , the resistance at 0° C. ; 
using the values of r 0 , a, and /3 given in (1), we find 
Aloo r 0 — 0*0862, 
whereas, using the values of r 0 , a, and /3 given in (4) we have 
t'loo — r 0 = 0"086325. 
Again the mean coefficient of increase of resistance per 1° C., between 15° C. and 
85° C. when obtained from the curve alone, is 0"00350, whereas the mean coefficient 
per 1° C., between 0° C. and 100° C., using the means of the values of r 0 , a, and ft 
given in (l), (3), and (4), is 0"00348. 
We may, therefore, conclude that it is not necessary to use the lengthy method of 
least squares to obtain the values of r 0 , a, and /3, and that the values obtained by 
