Page:Popular Science Monthly Volume 63.djvu/545

$2.34{\sqrt {3}}2.9=13.+$

$2.62{\sqrt {2}}5.9=13.+$

and so on through the list, the result in each case being 13. $+$. In short, we have quite uniformly

$P{\sqrt {S}}=C$,

where $C=13.57$, the arithmetic mean of the slightly varying values 13. $+$, which are given in the last column of our table.

How nearly this equation fits our data may be best seen from the graphical representation. Fig. 1. The curve $P{\sqrt {S}}=13.57$, as well

as the P's and S's from our table, have been plotted in rectangular coordinates by using the values of S for abscissas, and for ordinates ten times the corresponding values of P. The resulting points have been numbered to correspond with the index numbers in our table.

The relation expressed by $P{\sqrt {S}}=C$ may be easily expressed in words. For if P₁ and P₂ represent two predication averages, and S₁, S₂, the corresponding simple sentence percentages, We have approximately

$P_{1}{\sqrt {S}}_{1}=C=P_{2}{\sqrt {S}}_{2}$

from which

$P_{1}:P_{2}={\sqrt {S}}_{2}:{\sqrt {S}}_{1}$

that is:

The predication averages of various works are approximately inversely proportional to the square-roots of their simple sentence percentages.