Rotatory Motion, the Gyroscope, ^c. 153 



equal angulai* distance measured in the direction of the fall round the 

 point p from the positions which the rotation alone would have given. 

 In plain words, the top will have fallen through a certain distance ; this 

 result being the reverse of what Mr. Elliot tries to show. In proceed- 

 ing with his explanation, he assumes that the particle at the lowest 

 point B, is stiU the lowest point after it has moved to 6. Could he 

 prove this, he would certainly prove too much, for he would prove that 

 one particular particle moves round in a horizontal plane, and is always 

 the lowest point, under which cu'cumstances the top would not rotate 

 on its axis at all, but be merely moving in an inclined position round 

 the vertical o p ! Before assuming, however, that b is the new lowest 

 point, it is necessaiy to prove that no other point is lower than it. 

 This Mr. ElUot does not attempt to do, but proceeds to explain by 

 means of his second diagram (fig. 13), how the actual rising or faUing 

 of the top depends on the velocity of rotation. The eUipse a B is the 

 projection of the ring, in which the mass of the top is supposed to be 

 concentrated, on a vertical plane touching its lowest point. The short 

 verticals above the horizontal line d e, and extending from it to the 

 ellipse, are intended to measure the heights through which the point at 

 B would rise, during given intervals, by the rotation alone. The verti- 

 cals below the horizontal line D E, extending to the parabolic curve r 6, 

 are intended to represent the heights through which the point B would 

 fall in the same intervals by gravity alone. The paii's of verticals next the 

 lowest point B, are all that are compared ; and it is obvious that whilst 

 the lower ones are always the same, the upper ones are longer or shorter 

 according to the rotatory velocity of the ring. Mr. EUiot says if the 

 rotatory velocity is such that the upper and lower verticals are equal, 

 the top will not fall, because the forces represented by the pairs of 

 verticals are opposite and equal ; but this is only true of the ascending 

 side. Thus the point B would not absolutely fall whilst on the ascending 

 side of the ring ; but if we consider a point behind it, and on the 

 descending side, as at n, we find that the motions or forces represented 

 by the verticals above and below the horizontal d e, have both the same 

 direction ; and, therefore, instead of opposing and neutralizing each 

 other, as on the ascending side, they will be added together, and the 

 point at H will move to a position below b ; whereas, for the new point 

 b in advance of the point B to be the new lowest point, the point at h 

 should not have descended below B, nor even have reached as far! 

 Nothing is gained by supposing half the ring to be concentrated in the 

 point B, and the other half in the opposite point A ; for if, when the 

 point B is on the ascending side, gravity prevents it from ascenduig as 

 far as it would otherwise have done, gravity will also make the point 

 Vol. IV.— No. 1. x 



