In much laboratory work simultaneous observations are made on two dependent quantities, all others being kept constant. A relation is then sought between these quantities. One of the first recourses is to logarithmic and semi-logarithmic plotting. By dimensional reasoning, relations involving other quantities may then often be inferred, even without further experimentation. A device that combines speed, accuracy, and simplicity for this sort of plotting is therefore desirable as a laboratory adjunct.

In this paper the theory of logarithmic and semi-logarithmic plotting is reviewed, and a device is described which, it is thought, meets the above demands.

The theory of power and exponential finding, especially as the inverse of logarithmic and semi-logarithmic plotting, respectively, is also reviewed, and a simple addition to the above apparatus is described, by which one can read powers and exponentials.

© 1923 Optical Society of America

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Figures (2)

Fig. 1
Fig. 1

Power and exponential finding apparatus.

Fig. 2
Fig. 2

Log and semi-log plotting apparatus.

Equations (16)

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y = a x n
log y = log a + n log x
y = a 10 mx
y = a e nx
log 10 y = log 10 a + m x
log e y = log e a + n x
( Note that n = m .4343 )
n = y 2 y 1 x 2 x 1
y = a · 10 mx
m = Slope k
a = value of y when x = 0.
y = a e nx
y = x n
log y = n log x
y = 10 mx
log 10 y = m x