babus.J PYRO-ELECTRIC PROPERTIES OF ALLOYS. 153 
To avoid complete recalculation of a it is desirable to investigate 
some method for passing from a m and » 357 to a. If the values 
s, s', s" correspond to t, t', t", 
and if I accept 
1 + at+p? l + at'+p t ,2 ~l + at" + p t " 2 
there follows : 
_ (s'-s)(st" 2 -s"t 2 )-(s"-s){st /2 -s , t 2 ) 
a -(st'-s't){st" 2 -s"l 2 )-(st"-s // t)(st ,2 -s't 2 
from which it is easy to deduce 
™ 100 „, 356 
St' 
—S"f iSV'—S'f 6 
W>*7 st'—s't 
Now, st"—s"t=;D" and st'—s't=D' are already known from the earlier 
computations ; and for the present purpose, where a correction only is 
sought, s"t 2 and s'f may be neglected as compared with st" 2 and st' 2 , 
respectively, t being small in- comparison with V and t". Hence 
n 100 ™ 35fi 
„ n 100 "o ^0 
t ,2 J)/t 
which, since t" 2 /t' 2 is a constant, is a sufficiently convenient form, and 
much of the correcting may be done mentally. Finally, the three quan- 
tities tf 100 > ar 100 357 > and a 3b7 have a similarly simple approximate relation 
;o each other ; for 
100 ° ° o sv 357 
whence 
"o 100 (t'-t)+a m ™ (t"-V)=a™ (t"-t\ 
whence, furthermore, for instance, 
+ii // 
^100 ^357 V t/Y 10 ° rv * b7 \ 
a "0 +// j. \ U Q "100 / 
md since {t" —t')/{t"—t) is a constant these reductions are also mental. 
It has been observed that the corrections throughout affect only a 
•ew units of the last figure, and it is for this reason that the reductions 
ire simple. As a matter of corroboration a for Nos. 0, 1, 2, 3 was cal- 
ulated directly by the quadratic formula. The results were : 
No. ^=0.002328 
1 <r =0.001827 
2 .<* =0.001492 
3 ^ =0.001323 
vhich agree substantially with the other values in Table 34. 
(807) 
