[From the Report of Hie British Association, 1856.] 



XIV. On an Instrument to illustrate Poinsdt's Theory of Rotation. 



IN studying the rotation of a solid body according to Poins&t's method, we 

 have to consider the successive positions of the instantaneous axis of rotation 

 with reference both to directions fixed in space and axes assumed in the moving 

 body. The paths traced out by the pole of this axis on the invariable plane and 

 on the central ellipsoid form interesting subjects of mathematical investigation. 

 But when we attempt to follow with our eye the motion of a rotating body, 

 we find it difficult to determine through what point of the body the instantaneous 

 axis passes at any time, and to determine its path must be still more difficult. 

 I have endeavoured to render visible the path of the instantaneous axis, and to 

 vary the circumstances of motion, by means of a top of the same kind as that 

 used by Mr Elliot, to illustrate precession*. The body of the instrument is a 

 hollow cone of wood, rising from a ring, 7 inches in diameter and 1 inch thick. 

 An iron axis, 8 inches long, screws into the vertex of the cone. The lower 

 extremity has a point of hard steel, which rests in an agate cup, and forms the 

 support of the instrument. An iron nut, three ounces in weight, is made to 

 screw on the axis, and to be fixed at any point; and in the wooden ring are 

 screwed four bolts, of three ounces, working horizontally, and four bolts, of one 

 ounce, working vertically. On the upper part of the axis is placed a disc of 

 card, on which are drawn four concentric rings. Each ring is divided into four 

 quadrants, which are coloured red, yellow, green, and blue. The spaces between 

 the rings are white. When the top is in motion, it is easy to see in which quad- 

 rant the instantaneous axis is at any moment and the distance between it and 

 the axis of the instrument ; and we observe, 1st. That the instantaneous axis 

 travels in a closed curve, and returns to its original position in the body. 2ndly. 



* Trantactions of the Royal Scottish Society of Arts, 1855. 



