## Abstract

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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### Equations (16)

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(2)
$$\text{log}\phantom{\rule{0.2em}{0ex}}y=\text{log}\phantom{\rule{0.2em}{0ex}}a+n\phantom{\rule{0.2em}{0ex}}\text{log}\phantom{\rule{0.2em}{0ex}}x$$
(3)
$$y=a\phantom{\rule{0.2em}{0ex}}{10}^{\text{mx}}$$
(4)
$$y=a{e}^{\text{nx}}$$
(5)
$${\text{log}}_{10}y={\text{log}}_{10}a+mx$$
(6)
$${\text{log}}_{\mathrm{e}}y={\text{log}}_{\mathrm{e}}a+nx$$
(7)
$$\left(\begin{array}{ll}\text{Note}\phantom{\rule{0.2em}{0ex}}\text{that}\hfill & \phantom{\rule{1.5em}{0ex}}n=\frac{m}{.4343}\hfill \end{array}\phantom{\rule{1.5em}{0ex}}\right)$$
(8)
$$n=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$$
(9)
$$y=a\xb7{10}^{\text{mx}}$$
(10)
$$m=\frac{\text{Slope}}{k}$$
(11)
$$a=\text{value}\phantom{\rule{0.2em}{0ex}}\text{of}\phantom{\rule{0.2em}{0ex}}y\phantom{\rule{0.2em}{0ex}}\text{when}\phantom{\rule{0.2em}{0ex}}x=0.$$
(12)
$$y=a{e}^{\text{nx}}$$
(13)
$$y={x}^{\mathrm{n}}$$
(14)
$$\text{log}\phantom{\rule{0.2em}{0ex}}y=n\phantom{\rule{0.2em}{0ex}}\text{log}\phantom{\rule{0.2em}{0ex}}x$$
(15)
$$y={10}^{\text{mx}}$$
(16)
$${\text{log}}_{10}y=mx$$