244 Si7- George Greenhill and Dr Bennett, 



When the circuit is complete, the solid angle described will be 

 represented by the spherical area; but there is a discrepancy of 

 2iT to be considered, according as the area encloses the nadir z or 

 not, when ifj increases by 2??, or oscillates and returns to its original 

 value ; but we will not delay over this here. 



When the circuit of the pole Z is incomplete, the geometrical 

 interpretation of + j/r is not simple, as will be seen on reference 

 to (6), p. 71, E. Gr. T. ; and the angle does not appear in an in- 

 spection of the model. But cjy and ifj separately are visible in the, 

 chalk-marks and their divergence; but the angles are in different! 

 planes. * 



It is only in the complete circuit, where the stalk OZ is brought 

 back to its original position, that the angle can be visualised 

 through which the flywheel has turned relative to the frame. 



In the statement of E. G. T., § 14, criticized by Dr Bennett inl 

 his § 4, where in the model the stalk is hanging vertical, d = 0, ■ 

 and the stalk is then revolved in azimuth, the solid angle ct = 0^ 

 + = 0. But in a complete revolution of the stalk, »/f = 2^, 

 and (fi = -Itt; that is, the wheel has rubbed once round the axle 

 mside; and </> does not represent the angle the wheel has turned in 

 space; the wheel remains stationary with respect to the frame and 

 the stalk turns round inside the wheel; but + i = at any 

 intermediate stage. 



Dynamics were never studied at Cambridge as an experimental 

 science, so it is not likely that the model of E. G. T., Fig. 3, should 

 exist there, to place on the lecture-table between the lecturer and 

 his class, for him to show off the variation of Euler's angles, and 

 to handle and feel an actual state of gyroscopic motion. ' The 

 non-spmnmg gyroscope is imitated by a plummet at the end of a 

 thread, as a spherical pendulum, when the wheel has no rotation • 

 and by giving the wheel a spin R, the extension is made to the 

 most general state of the spinning gyroscope. 



But a penholder is always at hand, to serve as an illustration 

 of the angular creep in ^. The action is not frictional as has been I 

 objected Butter the finger to acquire the perfect smoothness of ^ 

 the text-book jargon, and the creeping action is not arrested. 



The experiment is not inapt, as it shows the relative motion 

 apparently reversed, where the axle is fixed in the wheel and runs 

 m outside bearings; here the finger and thumb, perfectly buttery 

 bo too with the other homely famiHar experiments cited by 

 Dr Bennett. • 



Euler's angles require to be interpreted on the altazimuth 

 suspension of the stalk in Fig. 3. But Prandtl suppresses the com- 

 phcation of the hub and vertical spindle on ball-bearings, and 

 replaces It by the simple economical arrangement of a fixed hook 

 to which the stalk is hooked up, with the rubbing surfaces well 



I 



