67 



of the earth, that the plane of oscillation of a vibrating line remains 

 at rest with relation to the vertical component of the real axis of 

 rotation, maj not be unacceptable. With this view I have devised 

 the apparatus I am about to describe. 



A semicircular arch from one to two feet radius is fixed vertically 

 on a horizontal wheel, and may thus be moved with any degree of 

 rapidity from any one azimuth to another. A rider slides along the 

 inner edge of the arch, which is graduated, and may be fixed at any 

 degree marked thereon. A spiral spring wire, by means of which a 

 slow vibration is obtained v/ith a comparatively short length, is at- 

 tached at the lower end to a pin fixed in the axis of the semicircle, so 

 that the point of attachment may be in the axis of rotation, and at 

 the upper end it is fixed to a similar pin in a parallel position fixed to 

 the rider. The vertical semicircle is not placed in a diameter of the 

 horizontal wheel, but parallel to it, at such distance as not to inter- 

 cept, from the eye of the observer, the vertical plane passing through 

 the diameter, and in which plane the wire in all its positions 

 remains. 



When the upper end of the wire is placed at 90°, that is when it 

 coincides with the axis of rotation, if the wire be caused to vibrate 

 in any given plane, say from N. to S., it will continue to do so what- 

 ever rotation may be communicated to the wheel ; so that with re- 

 spect to the moving wheel, or the axis of the wire, the plane of vibra- 

 tion will move with the same velocity and in the opposite direction. 

 When the rider is fixed at 30°, and the wire makes therefore an angle 

 of 60° with the axis of rotation so as to describe in its motion the 

 surface of a cone having this inclination to the vertical, it will be 

 observed that the plane of vibration makes one complete rotation 

 during two rotations of the wheel : this is best observed by fixing 

 the eye so that its axis shall coincide with a line in the same vertical 

 plane with the wire, while walking round with the wheel during its 

 rotation. W^hen the rider is fixed at 19^°, the plane of vibration 

 makes one rotation during three rotations of the wheel ; when fixed 

 at 14-^°, it makes one rotation during four of the wheel, &c. ; and 

 when it is fixed at 0°, the wire lying horizontally, no rotation of the 

 plane of vibration occurs. It is needless to observe that the sines 

 of 90°, 30°, 194°, ^H"' 0°, correspond to the numbers 1, ^ ^, ^, 0, 

 the reciprocals of the numbers expressing the respective times of 

 rotation*. 



It is not necessary that the Vv ire should have one of its ends fixed in 

 the axis of rotation: if it be parallel to a wire so fixed, the rotation of 

 the plane of vibration will be exactly similar ; in such case the wire 



* When the dimensions of the apparatus are as above given, I find that hai'd- 

 ened brass wii-e (No. 26), coiled so as to form a helix of one-quarter of an inch in 

 diameter, shows the etfect well. The thickest spiral wire employed in the manu- 

 facture of artificial flowers, which can be procured of any wire-drawer, will also 

 answer the purpose. 



The best way of setting the wire in vibration is to press the finger upon it in the 

 middle, so as to deflect it in the plane in which the vibrations are requu-ed to con- 

 tinue, and then suddenly to withdraw the finger in the direction of the vibrations. 

 The deflection must not be too great, or the elasticity of the wire will be injured. 



