Rotatory Motion, the Gyroscope, 4'C. 145 



of the moving frame and details carrying the wheel. In the thii-d 

 experiment (with the backward impulse), it is necessary to place the 

 wheel in an elevated position at starting, as the lower halves alone of 

 the curves then formed are equal in size to the ordinary curves, the 

 entire curves being deeper and requiring greater scope. "When the 

 gyroscope is moving along a curve, an impulsive acceleration acts like a 

 backward impulse at starting, and similarly an impulsive retardation 

 acts like a forward impulse at starting, — the former making the curve 

 less prolate or more curtate, and the latter making it less curtate or 

 more prolate. 



I must now mention another phenomenon always shown in these 

 experiments. Whatever curve is made by the instrument at starting, 

 it gradually changes to a less curtate or more prolate curve, in a 

 manner indicating, that in time, if the rotation of the wheel continued, 

 it would ultimately become horizontal and without undulation. Several 

 causes combine to produce these results, and it would be extremely 

 difficult to assign to each the precise value due to it. The frictional 

 and general resistances to the movements of the apparatus cause the 

 wheel to rise to a less and less height at each succeeding undulation ; 

 and they must also, to some extent, modify the form of curve described. 

 When the wheel is descending the curve (the common eusped cycloid, let 

 us suppose), it is also imparting a horizontal motion to the apparatus, 

 and the mass partaking of this horizontal motion having been just 

 previously at rest, necessarily absorbs a corresponding amount of force. 

 Then the centrifugal resultant, although unable to prevent some descent 

 of the wheel, must tend to modify the curve by rendering it more pro- 

 late or more nearly a horizontal line than it would otherwise be. In 

 the descending portion of the curve, the centrifugal resultant wiU assist 

 in giving horizontal motion to the moving frame, and this part of the 

 curve will be more nearly like what may be termed the true curve, than 

 if either the centrifugal resultant acted alone, or the mass of the frame 

 absorbed part of the force alone. The ascending portion, however, of 

 the curve will be different, for as the wheel rises its horizontal motion 

 diminishes, so that the forward momentum of the moving frame will 

 tend to elongate the curve and render it more prolate, without being 

 partly counteracted by the centrifugal resultant, which, on the contrary, 

 now assists it rather than otherwise. The result is, that on the wheel 

 arriving at the top of the curve, the horizontal motion is not whoUy 

 destroyed ; and, on the next descent, the curve is more prolate and 

 resembles what would be the result at starting, if a slight forward 

 horizontal impulse were imparted to the wheel. An additional incre- 

 ment of horizontal motion is gained in this way at each undulation. 



Vol. IV.— No. 1. u 



