226 Capt. Abney and Lieut.-Col. Festing on the Relations 
the current and p the potential. The first term of the right- 
hand member seems to represent the amount of current which 
would pass if the filament could be kept at some particular 
temperature (probably the absolute zero), and the second the 
additional current due to increased conductivity caused by in- 
crease of temperature. 
We append in a tabular form the results of typical experi- 
ments with four different patterns of lamps in which the dimen- 
sions of the carbon filaments differ considerably. These tables 
give the observed potentials and currents, together with the 
resistance and energy deduced from them, as well as the results 
obtained by the application of the above equation to the ob- 
served potentials ; and it will be seen that these results cor- 
respond very closely with those deduced from the observed 
currents when the resistances have any considerable range. It 
should be remembered that for small currents, the deflections 
of the measuring instruments being very small, the percentage 
error of observation is liable to be large ; these observations 
are therefore not so trustworthy as those of larger currents. 
It is probable that for these lower temperatures another term 
should be introduced into the equation, which may be disre- 
garded at temperatures above, say, 400°. 
From the above-stated equation another may be deduced for 
the value of the energy in watts: this would be it? = p 2 (a + bp^); 
and the resistance in ohms would be r . The form of 
a + bp* 
equation between energy and resistance would be rather more 
complicated, w=l—f — ) X -. 
If the curve of current in relation to potential be plotted, it 
will be found to be fairly smooth. It is, however, evident 
that a result obtained by the combination of two observations 
each of which is liable to a small error will probably be further 
from the truth than that obtained by a direct observation. 
On this account, in the curve of potential and resistance, the 
points indicating resistance are more unevenly distributed than 
those indicating current in the former curve. Similar irre- 
gularity will be found in a curve of potential and energy, and 
still greater in the case of a curve of energy and resistance 
(see diagram, curves C and D). An inspection of curves 
A and B in the diagram will show that, as stated above, the 
radiation is directly proportional to the energy when the latter 
is above 30 watts ; the deviation from the straight line below 
this point is doubtless due to the temperature of the sur- 
roundings being commensurate with that of the filament. 
