372 
NATURE 

of oscillation diminished. It was easy to see that a large 
oscillation would strain the cords toa greater height above 
the slider than would be called for in a smaller oscillation. 
The truth of this surmise was proved by the success of the 
remedy applied. Instead of cords I used two pairs of 
broad tapes, and instead of a solid slider I made one in 
two halves, embracing the rod in the centre and nipping 
the concurrent tapes on either side between their opposed 
faces, being clamped together by thumb-screws beyond 
the tapes on either side. Here the slider had no firm 
hold on the rod beyond the accuracy of its fit, which 
served to prevent torsion, but had firm hold on the pairs 
of tapes, pinching them with especial accuracy at the 
upper edge of the slit in which they lay between the two 
halves, and reducing the hinge there to a narrow line no 
thicker than the pairs of tapes instead of the gross thick- 
ness of the cords which they superseded. The improve- 
ment of the pendulum’s performance on paper was very 
striking. When well adjusted, it was scarcely possible 
from beginning to end to detect any change in the shape 
of the figure described ; scavcely possible, I say, for even 
now our hinge is not a mathematical line, and we do not 
obtain perfect mathematical accuracy in our results. 
Further improvement might be obtained by refinement in 
tapes and slider, or by increasing the total height of the 
pendulum, or by substituting some other form of hinge ; 
but the form which I have described is so simple, and its 
performance so good, that I am content to accept its one 
very small fault for the sake of its many excellent 
qualities. 
Figures 1-12 are the produce of this pendulum thus 
improved. They are only a few of the most interesting 
out of an endless variety of interesting curves, and are 
chosen as characteristic specimens of a series too exten- 
sive to be fairly represented except by a much larger 
number of illustrations. Figures 1 and 2 represent the 
proportion 1 : 3, the lowest that is easily attainable with- 
out a loftier pendulum ; and the following pairs of figures 
show successively the proportions 2 :5,1 :2,3:5,2:3,3:4. 
Each of these is illustrated by two figures exhibiting 
the two chief types of the curve proper to that propor- 
tion. They may be termed the cusped type and the 
looped type. It will be seen that the two cusps in the 
first figure of each pair are opened into loops in the 
second, and that each loop in the first is doubled in the 
second. Between these two typical forms we have an 
infinite series of intermediate forms possessing features 
of great interest, those nearest the cusped type especially 
being characterised by a peculiar “ watered” appearance, 
due to the intersection of two sets of lines very slightly 
inclined to one another. This is seen, for example, in 
Fig. 3, which errs a little from the perfect type. 
Accuracy of proportion between the two periods of 
vibration could only be arrived at by repeated trials. 
The sliding-clamp sufficed for coarse adjustment, but for 
fine adjustment it was found necessary to attach a sub- 
sidiary weight below the large one in some way admitting 
of considerable range of position, so as to alter minutely 
the position of the centre of gravity. A heavy iron nut 
travelling easily on a screw-thread cut on the depending 
shaft that carried the pen supplied this want, and greatly 
facilitated the attainment of the utmost accuracy at com- 
mand, 
With a pendulum only seven or eight feet high, there 
is great difficulty in obtaining the curves that correspond 
to any proportions lower than 1 : 3, because the slider 
cannot be brought within a certain distance of the centre 
of gravity, which lies somewhere in the middle of the 
lead. To obtain the proportion 1 : 3, that is, to make 
the pendulum swing three times across for every one 
swing to and fro, we must lower the slider within a foot 
of the centre of gravity (the length of the pendulum 
varying as the square of the period of oscillation), and to 
obtain the proportion 1:4, the distance between the 

slider and the centre of gravity must be 1-16th of the 
height of the pendulum, or only six inches in the present 
instance ; but three or four of those six inches are taken 
up with the thickness of the lead and the attachments of 
the tapes, and the rest with the depth of the slider, and 
so the curve cannot be obtained without a more lofty 
suspension for the pendulum. This greater elevation 
I found in the great octagonal room which Sir Christo- 
pher Wren built as the chief room of the Royal 
Observatory in Greenwich Park. By means of two 
hooks fixed above opposite windows in this room, from 
which my tapes converged to the middle, I got a 
height of eighteen feet, and was able to reach such pro- 
portions as 1 :4,1:5,1:6. At this extreme it was really 
amusing to watch the busy haste of the manifold cross- 
vibration over-riding the staid gravity that marked the 
slower oscillation toand fro. To obtain proportions lower 

# 
[ Supe, 7, 1871 
yet than these, I should want a great increase in height of — 
suspension ; but there is no great inducement to attempt 
this, as the nature of the curve may be foreseen at a glance, 
and is marked by extreme simplicity—merely a zigzag or 
a string of beads. 
Some of these experiments with lofty suspension were 
made on stormy days ; and while watching the travels of 
the delicate pen-point, I could see that their regularity 
was slightly disturbed by every gust of unusual violence 
that beat against the high walls. 
But this article would never end if I allowed myself to 
dwell on all the points that called for attention in the 
course of experiment which I have been describing, I 
fear I have exceeded due limits already, and feel that I 
owe an apology to the reader for so large a trespass on his 
patience. My apology must be the elegance and exquisite 
symmetry of these natural curves in their admirable obe- 
dience to a purely natural law, and the great pleasure I 
have enjoyed—the sense of high privilege I have felt—in 
their investigation. I understand that these curves, or 
some of them, have been demonstrated before, by means 
of a stream of sand flowing from a hole in the base of a 
vessel that was used as the weight of the pendulum, and 
I believe that steel springs of elliptic or oblong cross- 
section have beeir made to trace such curves as that which 
first attracted my attention in the vibration of my slender 
acacia-twig ; but Iam not aware that any specimens of 
the series have ever before been exhibited in a form that 
rendered them accessible to the public eye. 
HUBERT AIRY 

SOME SPECULATIONS ON THE AURORA 
Ts preparing a lecture on the Aurora Borealis some 
months ago, I was led to some speculations which may 
or may not be new, and may or may not be of some value. 
I will submit them to the readers of NATURE. 
I assume of course that the auroral rays extend to great 
heights above the surface of the earth, that they are 
sensibly parallel, and that their apparent point of con- 
vergence is, generally speaking, that to which the freely- 
suspended magnet points. In the great aurora of October 
24, 1870, this point was close to 7 Pegasi at 8.30 P.M., co- 
inciding very weli with the direction of the magnet.* 
Remembering that this aurora was witnessed over a large 
part of the northern hemisphere, and that there was a 
contemporaneous aurora in the southern hemisphere, and, 
assuming that at each place the direction of the auroral 
streamers is approximately parallel to the magnet, we must 
conceive the earth, during such an auroral display, asa 
globe with streamers of light radiating and diverging from 
its polar regions, and spreading far out into space. The 
general direction of these streamers at different spots on 
the earth will be got by placing a magnet below a sheet of 
paper and getting the magnetic curves with iron filings, 
* To-night it isa few degrees below a Cygni (but not clearly defined) at 
1I P»My 
