116 AN EMPIRICAL STUDY OF GYRATING BODIES. 



would be a slow, continuous motion without acceleration. 



In this case, where the diameter of the wheel subtends 

 an arc of 90°, taking the point of support as the centre, 

 it is not difficult to see that there will be no accelera- 

 tion ; but it is not so clear in case the instrument is 

 differently proportioned, if, e. g., the wheel is very 

 small ; nor why the bare axle will not stay up. 



There are various other questions that suggest them- 

 selves. I shall now, therefore, make the discussion so 

 general that all these may be included. 



Let fig. 8 represent our tee-square with the leg PO 

 horizontal, and the arms vertical, and, for simplicity, 

 suppose the mass concentrated in the ends A and B. By 

 giving proper values to these, we can even make one 

 section represent the whole wheel. Let O be a fixed 

 point resting on the standard. Draw the lines O A and 

 O B. The initial movement of A falling in the vertical 

 plane A O B will be represented by the tang A x. 

 Measure off any convenient distance, as A m, to represent 

 the force of gravity. It will be resolved into A x and x 

 m, both being really applied at A. The latter, x m, be- 

 ing opposite to the line A 0, and consequently expended 

 upon the fixed point O, may be neglected. 



To find Ax, AOw + AOP or a-OAm + mAx. But 

 wOA = OAm. '. mAx = a. 



From the triangle m x A, we have mA •• Ax - 1 ■■ 

 cos x Am or cos a. \Ax = cos amA ; or, taking Am as 

 unity. Ax = cos a. 



Suppose, now, our tee-square to be instantly reversed, 

 and that the time of the fall, A to x, was so short that 

 no sensible change occurred in the position of P, and, 

 for the present, suppose gravitation to cease. Fig. 9 

 will represent the new conditions. 



The mass A continues to be affected by Ax, which, on 

 its part, is unaffected in amount and direction. The 



100 



