NATURE 
[ Aug. 17, 1871 


PENDULUM AUTOGRAPHS 
I, 
peas I shall best put the reader in possession of 
all that I have to say, and shall best explain the nature 
of the accompanying figures, by giving some account of 
the successive steps that first led me to their discovery — 


Fic. 5.—Proportion r : 2.—Cusped type. 1 
It was a happy chance that directed my fingers, in an 
idle mood, one day in March of last year, to the top of a 
stiff twig that sprang from the stool of an old acacia, and 
rose to a height of about three feet, where it had been 
lopped by the gardener’s knife. Pulling the twig aside, 
and letting it fly back by its own elasticity, I noticed the 
path which its top traced in the air ; it was not difficult to 
follow its course, for the raw section of the wood was white 
and caught the eye, and the motion was not very rapid, 
the twig being rather slender for its height. I had often 
1oticed—everyone must have noticed—odd behaviour in 
a genuine discovery, so far as I was concerned, though I 
know there must be many to whom these curves and their 
mathematical properties are familiar, and who will smile 
at the tardy stages of experiment through which I had to 
pass, while they cannot refuse to congratulate me on my 
final success, 
Fic. 4.—Proportion 2: 

Fic. 6.—Proportion 1 : 2.—Looped type.* 
springs of various kinds before this, but the motion had 
been too quick or too slow to show the law that governed 
it. On the present occasion I could see that the twig 
began at once to deviate from the plane of its first vibra- 
tion, and to describe an elliptic path, the ellipse growing 
wider and shorter till it was nearly circular, then still 
wider and still shorter, till its width exceeded its length, 
and it was again elliptic, but the long axis now occupied 
nearly the position of what was the short axis before. 
The new ellipse still grew narrower at every vibration, and 
* Figs. 7—12 will be found in the second part of this article. 
aaron 
