Rotatory Motion, the Gyroscope, ^-c. 143 



ance of the air, or friction, on the other hand, causes the weight to rise 

 if the gyroscope is set in a certain position. I will speak more fully of 

 some of these effects when discussing Mr. Elliot's paper. 



In the course of my investigations it occurred to me to consider 

 whether any difference would be produced in the phenomena exhibited 

 by placing the gyroscope farther from the point of support. In com- 

 paring two cases with the view of ascertaining what difference arises 

 from difference of position, with reference to the point of support, we 

 must assume that the other conditions are precisely alike in both cases ; 

 that the form of wheel, and the original rotatory velocity are the same ; 

 and that gravitation tends to produce an equal amount of precessional 

 motion in both cases. In fig. 5, which may represent one case, the 

 point of support is supposed to coincide with the centre of the wheel, 

 and a vertical plane passing through what may be termed the preces- 

 sional axis, c c, divides the wheel into two equal halves. The centrifugal 

 resultants represented by the arrows, e e, act on opposite sides of the 

 point of support, and both in the same direction of rotation. Fig. 9 

 will represent the conditions of the second case we ai'e now considering. 

 Here the point of support, F, is away to one side of the wheel. The 

 centrifugal resultants represented by the arrows, e e, both act on the 

 same side of the point of support, and in opposite directions of rotation 

 round that point. However, if they are equal to those in the first case, 

 and to each other, they will have precisely the same effect as in the first 

 case, for the conversion of one of them into a backward strain, is exactly 

 compensated for by the increased leverage of the other. But are they 

 equal to each other ? The precessional axis, c c, must necessarily pass 

 through tlie point of support, p ; and it will be obvious on inspecting 

 fig. 9, that a vertical plane through c c, divides the wheel into two 

 MJiequal parts. It will also be easily seen that the final resultant in the 

 direction of the precessional motion will be lessened in consequence of 

 this unequal division, and it follows, that a gyroscope, under circum- 

 stances in which it would exhibit a horizontal precessional motion with- 

 out undulations, if placed \Vith its centre coinciding with the point of 

 support, can be placed at such a distance from the point of support that 

 the centrifugal resultant shall be insufficient to render the precessional 

 motion horizontal. In such a case, the modified phenomena shown wHl 

 resemble what I have said would be exhibited by a sphere in which no 

 centrifugal resultant arises, — that is to say, the wheel will move along 

 an undulatory curve. This phenomenon is shown in a very remarkable 

 manner by a common gyroscope, a, set as represented in fig. 14, at ten 

 or twelve inches' distance from the point of support, upon a light lever, 

 n, free to turn in every direction about that point. It is necessary to 



