C. B. WARKTXG. 185 



3. If this vibration be stopped, the weight will hang- 

 down at rest, and the lower hook will be drawn out to a 

 distance proportional to the weight. 



4. In an absolutely frictionless instrument the vibra- 

 tion would continue forever. 



All these are stated explicitly except the first. As to 

 that, I infer it from his saying, "The gyrostatic model 

 spring-balance is arranged to have zero moment of mo- 

 mentum as a whole." 



By the instrument being "so arranged that it has zero 

 moment of momentum," I understand that the moment 

 of momentum of the upper two gyrostats neutralizes 

 that of the lower two. I am confirmed in this belief by 

 his saying in the next sentence : "But now let there be 

 a different 1 rotational velocity imparted to the jointed 

 square round the axis of the two hooks, such as to give 

 a resultant moment of momentum around any given 

 line through the centre of inertia of the system." 



It seems to me that Sir William meant that when the 

 gyrostats revolve all in the same direction there will be 

 no rotation of the whole instrument, bnt if the wheels 

 revolve in different directions, there will be rotation of 

 the whole. 



This statement of Sir William's is to me exceedingly 

 obscure, 2 and grows more so as I reflect upon it. I 

 wrote, therefore, to him while he was at Baltimore, 

 stating my difficulty, and asking whether I had cor- 

 rectly made out his meaning. 



Not having received a reply I am obliged to rely upon 



1 By " different rotational velocity " he may mean that the upper pair of wheels rotate to 

 the right, and the lower pair to the left, or he may mean that the npper wheels rotate faster 

 than the lower ones. I take the first to be what was intended. 



2 This obscurity is increased by a note at foot of page 419, of Natim . written, apparently. 

 after the body of the paper, and certainly after the diagrams had been made, in which he 

 says : •• Each of the hooks is connected to the framework through a swivel joint " — the di- 

 agram is made without such joints — " so that the whole gyrostatic framework may be ro- 

 tated about the axis of the hooks in order to annul the moment of momentum of the frame- 

 work about this axis, due to the rotation of the fly-wheels in the gyrostat." Yet. as quoted 

 above, he says the balance is so arranged as to have no moment of momentum. 



169 



