CHANGE OF LAMP VOLTAGE 
335 
that reason the minimnni change here considered objectionable 
is perhaps a little higher than one meets in reality. 
If carbon lamps had been used the permissible change would 
I /V \k 
f ® B 
be much less. When calculated from the formula^ = j 
where lo is the C. P. at a voltage expressed by Yo and 1st is 
the C. P. at a rated voltage Yst, the exponent k is about 3.6 
for all tungsten lamps requiring 1.25 watts per M. H. C. P. 
and 4.8 for gem lamps requiring 2.5 watts per M. H. C. P. each 
at the rated voltage. From this it is noted that a change of 
3.67 volts on the gem lamp produces as much change in the 
illumination as a change of 5.5 volts on the tungsten, which was 
the change noticed by practically every one. From the same 
formula it can be shown that only 7 1-3 volts change is required 
on the gem lamp to correspond to an objectionable change of 
11 volts on the tungsten. 
We have a right to use 3.6 for k when we deal with tungsten 
lamps whose efficiency is 1.25 _ and 4.8 when dealing 
with carbon lamps whose efficiency is 2.5 This was 
tried out by an auxiliary experiment in which tungstens were 
used ranging from 100 watts to 25 watts and carbons ranging 
from 100 watts (40 G. P.) to 20 watts (4 C. P.). For the 
carbons the efficiency is much less and hence the value of k 
greater ; but for tungsten lamps the value of k is very nearly a 
constant. 
For the older forms of carbon lamps the value of k is much 
higher, and hence the permissible change in voltage would be 
much less. For that reason much better regulation is required 
for the older types of lamps than for those most commonly used 
at present. 
A 100-watt tungsten, also a 200-watt, and a 300-watt tung- 
sten, all gas filled, having an efficiency of about 0.8 ^ 
were also tried, with the result that the change in C. P. for a 
given change in voltage was a little more marked than for the 
vacuum tungstens. For the g£^ filled lamps the value of k in the 
formula was very close to 4. The above statements are borne 
out by the accompanying table showing experimental results. 
^Trans. I. E. S. 3., p. 459. 
