310 Professors Ayrton and Perry on the most Economical | 
where there is a sudden bend and an absence of points, deter- 
mined from experiments to guide us in drawing the curve. 
Instead of plotting w and y, and obtaining a curve which it 
would be very difficult to draw correctly, we may by using 
some simple function of y obtain points which obviously 
lie in a curve which it is easy to draw. ‘Thus we may plot 
Vy and x, or “Wy and 2, or logy and w. When the curve 
connecting y and & is not roughly asymptotic to the axis of a, 
but to some line parallel to this axis, it is obvious that there 
is a greater likelihood of obtaining simple curves by plotting 
Vy--eand x, or Wy+aand 2, or log (y+) and 2, where 
ais some constant obtainable by inspection, than by simply 
plotting the function of y alone. 
The following table gives M. Foussat’s lives in terms of v 
and the corresponding values which we have calculated of 
log f(v), log @(v), and of log f(v)@(v) from the values of @(v) 
given in the previous table. 
TABLE IT, 
v. f(v). log f(2). log 6(v). log f(v)A(w). 
95 | 3595 3:5557 0-9729 4-5286 
96 2751 3-4395 1:0119 4-4514 
97 2135 3:3294 1:0485 43779 
98 | 1645 32161 1-0851 43012 | 
99 1277 31062 1:1199 4-261 
100 1000 3-0000 11556 41556 
101 785 2:8949 1:1898 4-0847 
102 601 2:7789 1:2216 4-0005 
103 ATT 2-6785 1:2531 39316 
104 375 2-5740 1:2852 83-8592 
105 284 9-4533 13152 3°7685 | 
When log f(v) @(v), and v are plotted as coordinates of 
points, these points are found to lie so nearly on a straight 
line that the formula 
if 
He)Ae) 
is found to be true with considerable accuracy, and such a 
formula lends itself with great ease to calculation. 
It is quite true that we might have obtained a still more 
accurate formula than (2) since, as published by Mr. Wright, 
one of the members of our class, in the ‘ Electrician’ for 
February 21st, the logarithm of the life of a lamp is shown 
to be a line-function of the difference of potentials at which 
it is worked. 
We may in fact with this particular type of lamp put 
I(r) =]0'4-Olle Sg al aie aa os 
with very great accuracy indeed. 
— LOG ge v—11-697 , : : i : (2) 
(3) 
