Page:Calculus Made Easy.pdf/175

 Also, we see that $$p$$ is the numerical value of the ratio between the height of any ordinate and that of the next preceding it. In Fig. 40, we have taken $$p$$ as $$\tfrac{6}{5}$$; each ordinate being $$\tfrac{6}{5}$$ as high as the preceding one.

If two successive ordinates are related together thus in a constant ratio, their logarithms will have a constant difference; so that, if we should plot out a new curve, Fig. 41, with values of $$\log_\epsilon y$$ as ordinates, it would be a straight line sloping up by equal steps. In fact, it follows from the equation, that

Now, since $$\log_\epsilon p$$ is a mere number, and may be written as $$\log_\epsilon p=a$$, it follows that

and the equation takes the new form