
366 

points, has a fine saw cut about jth of an inch deep, made 
lengthwise at both ends. The wires which form the sides of the 
first triangle are put into one cut, and those of the second tri- 
ancle into the other ; and the rod may then be slid up or down 
along the wires, to different heights, so that when the pendulum 
is at rest the rod is horizontal, forming the base of one isosceles 
triangle, with sides of double wire, and its vertex down at the 
bob, and also of other two isosceles triangles, equal and similar to 
one another whose sides are of single wire, and whose vertices 
are the points of suspension in the ceiling respectively. 
It is now evident that the rod is rigorously constrained to 
oscillate in a plane perpendicular to the line joining the suspen- 
sion points, while the vertex of the triangle below the rod, 
which is the point of suspension of the bob, is free to moye, at 
any instant, only in a plane at right angles to the plane of motion 
of the rod. As the amplitudes of the oscillations are practically 
made small compared with the lengths of the component pen- 
dulums, we thus obtain, with almost any desired degree of exact- 
ness, the composition of two simple harmonic motions of diffe- 
rent periods of adjustable ratio, and in rectangular directions. 
It is easy also to see how, by making the wires of unequal 
length, and dividing them proportionally at the point of suspen- 
sion of the bob, the simple component motions may be adjusted 
to different inclinations. In order absolutely to prevent the bob 
from creating indeterminate motions about its point of suspension, 
it would be needful to substitute, for the wires below the 
suspended rod, stiff pieces rigidly attached to the bob. But with 
due care in swinging the pendulum no yery sensible motion of 
the bob, relatively to its suspending wires, need occur. 
To record the motions of the pendulum, I have most frequently 
adopted the old plan of sand running out at a fine hole at the 
bottom of the pendulum bob. But for class experiments at the 
University of St. Andrews, I have also made the following 
arrangement :—A heavy bob of lead, in metallic connection with 
its suspending wires, has a metal point projecting from its lower 
end. Wires from an induction coil are connected, one with 
either of the suspension points in the ceiling, the other with a 
sheet of a tin foil which rests on a table, and oyer which is placed 
a sheet of paper, all but touching the point projecting from the 
bob. The pendulum having been first got to swing steadily, the 
induction coil is put in action, and the sparks, passing from the 
pendulum point tothe tin foil, trace on the paper, if it be suitably 
prepared, a record of the pendulum motion. I used one of 
Ruhmkorff’s original coils, which, with a single Grove’s cell, was 
quite sufficient. The rheotome acted automatically, and with 
considerable regularity. The dots on the paper made by the 
sparks showed distances varying from one element of the pen- 
dulum track to another, and thus exhibited in a very interesting 
manner the variation in the velocity of the pendulum bob. 
WILLIAM SWAN 
Ardchapel, Dumbartonshire, Aug. 24 
PERMIT me to state that the diagrams in No. 94 of the 17th 
June to Mr. Hubert Airy’s ‘‘ Pendulum Autographs,” are identi- 
cal with the ‘‘ Kinematic Curves”’ by Mr. Perigal, drawn by him 
upwards of thirty years ago, and discovered by Mr. Sang of 
Edinburgh two years previously (On the Vibration of an Elastic 
Spring, Ed. Ph. Tr.), autographic copies being in the posses- 
sion of the Royal Society, Royal Institution, and Royal Astro- 
nomical Society. Vide my application of the Binomial Theorem 
to Perigal’s Bicircloids (Lond. Phil. Mag. 1849-1850). Mr. 
Perigal calls these curves, Lemnoids, Paraboloids, &c. 
August 28 S.M. Dracu 

Thickness of the Earth’s Crust 
THE question in debate is not a mathematical one. Accepting 
Archdeacon Pratt’s calculations as correct, they would show that 
certain facts in the earth’s motion are what they would be if the 
earth were a rigid mass, or nearly so. But this at present is not 
disputed. What is disputed is the soundness of the inference 
drawn from these facts respecting the fluid or solid state of the 
earth’s interior, for it is contended that in either case the move- 
ments in question might be practically the same, provided only 
they were slow enough. I do not think this is replied to by 
Archdeacon Pratt in his letter in NaTuRE, August 31. 
Whatever the disturbing forces may be, they amount to a 
motive impulse given to some portion of the mass of the earth. 
NATURE 




This impulse may have two effects : either it may alter the shape 
of the mass by causing part of it to move in some direction faster 
than the rest can follow, or it may alter the position of the mass 
by causing the whole to move together. If the portion which 
receives the impulse is able to move the rest as quickly as it 
moves itself, the whole will move together ; and where there is 
any cohesion at all, there must be a degree of slowness at which 
this condition is attained. 
Mr. Pratt’s rope of sand, if dealt with here, is a system of 
particles between which there is no cohesion, They are not 
able, by attractive power, to move each other at all. But if 
hung out in free space, they would certainly assume a definite 
shape as a whole, and would retain it with complete ‘‘ rigidity ” 
in spite of any applied force which was not able to move any of 
them faster than they could move each other. 
Suppose the earth were projected bodily along the line of its 
axis towards the pole star, what would happen to a loose stone 
lying on the surface at the south pole? If the earth moved 
northward ten feet in a second, the stone would, at the end of 
the first second, be still upon the surface. If the earth moved 
twenty feet in a second, the stone, at the end of the first second, 
would be a yard behind it, but before the end of the next second 
it would be on the surface again. Are not the relations between 
the rigid, the fluid, and the elastic states all illustrated here? 
What would be the real cohesive force in a molten earth, as 
compared with a congealed one, is another matter. ‘‘ Molten” 
does not neccssarily mean ‘‘ limp,” and the question, if deter- 
minable, has not, I imagine, been determined. The molten 
earth would no doubt be less compressible ; and this, in some 
cases, may be equivalent to an increased cohesion. Let me add 
that I have no theory as to the earth’s interior. As) avis 
Sept. 5 

Spectrum of the Aurora 
May I call your attention to an error which has occurred in 
the engraving of the Spectrum of the Aurora which I sent you 
last week. The lines are marked in strength exactly the reverse 
of what they should be. Thus: No. 1 is the strongest, and is a 
sharp line easily seen, and in the drawing it is the weakest ; and 
so with the others. No. 1 is the brightest, No. 5 is the faintest. 
47, Brook Street LINDSAY 

Transparent Compass 
I BEG leave to draw your attention to a contrivance that I 
think very suggestive, of improvements in getting up compasses 
for iron and wooden vessels. This I propose to effect by using 
glass globes with transparent needle-cards, and thus making a 
transparent mariner’s compass, visible in all directions, that may 
be either supported or suspended by very simple and compact 
fittings wherever most convenient. 
In iron vessels this transparent compass can be readily placed 
beyond the local attraction of the iron. In appearance like a 
pearl, and in good taste. 
Please draw attention to this very simple remedy for so many 
real or alleged complaints of the deviation of the compass on 
board of iron vessels. GroRGE FAwcus 
North Shields, Sept. 4. 
A Substitute for Euclid 
Since Prof, Tait has given the weight of his authority to the 
| attack for #>me time past directed against Euclid, J, and per- 
haps some others who like me have sons whom they wish to 
educate as mathematicians, would be much obliged to Mr. 
Wilson, or any other of your correspondents, who would recom- 
mend 2 book which is suited to lay the foundation of geometry in 
the future. A FATHER 
Monolithic Towers of Cement Rubble for Beacons 
and Lighthouses 
Ir occurs to me to suggest the trial of common rubble set in 
Portland or other equally good cement in the construction of 
beacons and seamarks, as also for lighthouses. The advantages 
of employing cement rubble, not in prepared blocks but by 
continuous building, are the following :— 
1. The dispensing with all squaring or dressing of materials. 
2. The suitableness for such work of any stone of hard quality, 
thus rendering it unnecessary to bring large materials from a 
distance, or to open quarries for ashlar, 

hen the’ 
