184 
DBS. A. MATTHIESSEN AND C. VOGT ON THE INFLUENCE OF 
in iron could not be made, owing to the brittleness of the alloys ; the high percentage 
decrement in the conducting-power of the first two indicating something abnormal, 
which it would have been interesting to have followed out. 
On account of the probability of the arsenic and phosphorus being chemically com- 
bined with the copper, we have not considered it worth while to calculate the percentage 
decrements, and therefore no Table corresponding to the last has been made for these 
alloys. 
If the above proportion, 
Po . Pc . : X 100 o X 100 o, (1) 
be converted into terms of resistance, the following formula is obtained, 
ru* __ /y* — — n/J . . _ nJ /9 ] 
7 100° 7 0° 7 100° 7 0° ? \^J 
where r m a , r 0 o, and P l00O , 
0°; for 
but 
and 
r' 0 o represent the observed and calculated resistances at 100° and 
Po ^100° . 
•Pc a' 100 o 
Po=100-^°- 100=^2(X r -X M r), 
Pc= 100 ■ 100= 
XqO X 0 O 
And substituting these values in the above, we have 
a„° A 0 o — A 10 o° ^ioo 0 
A 0 ° A a ° — ^ioo° ^100° 
°r , , 
A 0 ° A| 00 q A 0 ° — Ai 00 ° 
^0° • ^100° V • ^100° 
or 
1_J_ 1 1 
A ioo° ^o° ^ioo° V 
which is equal to 
y ’l00 o — ^ , 0 c ’ ::=: ^100 o K°, (2) 
for the reciprocal values of the conducting-powers of bodies are their resistances. The 
formula (2) expresses the fact that the absolute difference between 0° C. and 100° C. in 
the resistance of an alloy is equal to the absolute difference between 0° C. and 100° C. in 
the calculated resistance of the alloy. 
The formula (2) may be written 
^*ioo° ^ioo* — r 0 ° 'dfp , (3) 
which is equal to saying that the absolute difference in the observed and calculated resist- 
ances at 100° C. is equal to the absolute difference between the observed and calculated 
resistances at 0°C. Tables XIV., XV., and XVI. contain examples of these deductions 
taken from the three groups of alloys, taking the resistance of silver at 0° equal to 100. 
