Prof. Cavalleri on a New Seismometer. 109 
the earth’s crust. Let us imagine a spiral formed by an iron 
wire, hard as from the draw plate, with rings of equal size, form- 
ing a cylinder the spires of which are separated from each other. 
Let the spiral be attached at one extremity to a fixed point, sus- 
pended with its axis vertical, and let a moderate weight be placed 
at the other extremity. The spiral will lengthen and stretch a 
little, and then remain motionless. Now if the weight be pushed 
up and then left free, the spiral will oscillate like a common pen- 
dulum, only vertically. The elasticity of the spiral performs the 
same office as attraction in common pendulums. The descend- 
ing weight acquires an accelerated motion, which tends to stretch 
the spiral more than it would do were it at rest; hence follows 
the reaction of the elastic spiral, which tends to draw the weight 
up more than it would do were it motionless; and this continues 
until, after a certain time, the resistance of the air and the im- 
perfect elasticity of the spiral stop the vertical pendulum. Such 
is the apparatus which I have constructed for noting vertical up- 
heavals or elevations of the earth’s crust. But as the number 
of the oscillations of the spiral within a given time must depend 
on the weight which is attached, the size of the rings or turns, 
the thickness of the wire, and the number of the rings, I consi- 
dered it necessary to institute a series of experiments in order to 
give to the spiral, conditions capable of fulfilling our intention, 
and thus to render complete a work which, so far as 1 am aware 
of, has not been done by another. 
The following laws are the result of my experiments :— 
1st. The vertical oscillations are isochronous. 
2nd. With the same length of wire, the number of oscillations 
in a given time is in the inverse ratio to the diameter of the 
spiral. 
8rd. The number of oscillations with the same number of 
rings is in the inverse ratio to the square root of the weights 
which stretch the spirals, subtracting the weight of the spiral 
itself, which acts as a weight and tends somewhat to retard the 
oscillations. 
4th. The number of the oscillations in a given time is in 
inverse ratio to the square root of the number of rings or coils 
in the spiral. 
5th. With the same weight, length of wire, and diameter of 
spiral, the number of oscillations is in the inverse ratio @ the 
diameter of the wire. 
The first and fifth of these laws agree fully with those dis- 
covered by Coulomb relative to the elasticity of torsion. The 
second (note being taken that the spirals used in my experiments 
are cylindrical) arises from the constant relation between the 
length of the wire and the number of rings in the spiral, and 
