# From G. H. Darwin   [c. 16 October 1873?]1

Dear Father,

If the impact of a weight falling on a horizontal plane is unity—the following table will give it for the other inclinations2

Inclination Impact

of plane to

horizon

0o. 1.

10o .9848 = $\frac{9}{10}$ or $\frac{98}{100}$

20o .9397 = $\frac{9}{10}$ or $\frac{94}{100}$

30o .8660 = $\frac{9}{10}$ or $\frac{87}{100}$

40o .7660 = $\frac{8}{10}$ or $\frac{76}{100}$ or $\frac{3}{4}$

45o .7071 = $\frac{7}{10}$ or $\frac{71}{100}$

50o .6428 = $\frac{6}{10}$ or $\frac{64}{100}$ or $\frac{2}{3}$

60o .5000 = $\frac{5}{10}$ or $\frac{50}{100}$ or $\frac{1}{2}$

70o .3420 = $\frac{3}{10}$ or $\frac{34}{100}$ or $\frac{1}{3}$

80o .1736 = $\frac{2}{10}$ or $\frac{17}{100}$ or $\frac{1}{6}$

90o 0

This may be epitomised thus, less to 40o the impact is about $\frac{9}{10}$ at 40o it is $\frac{3}{4}$, 45o it is $\frac{7}{10}$, at 50o = $\frac{2}{3}$, at 60o = $\frac{1}{2}$, at 70o = $\frac{1}{3}$ at 80o = $\frac{1}{6}$ & at 90o of course 0o

Your affectionate Son | G H Darwin

## Footnotes

The date is conjectured from the relationship between this letter and the letter from G. H. Darwin, 16 October 1873.
George’s letter may have to do with CD’s question about the angle a waxy leaf ought to hold to the horizon in order that raindrops should bounce off as completely as possible (letter to G. H. Darwin, 12 October [1873], and letter from G. H. Darwin, 16 October 1873).

## Summary

Sends table showing relative force of impact of weight dropped on a plane inclined at different angles.

## Letter details

Letter no.
DCP-LETT-9078
From
George Howard Darwin
To
Charles Robert Darwin
Sent from
unstated
Source of text
DAR 162: 62
Physical description
2pp