14G Me. E. Hu>"t on certain Phenomena connected with 



and if the wheel spins long enough the curve will ultimately become a 

 horizontal Hne. In my apparatus it is very noticeable that it is in the 

 ascending portion of the curve that the change takes place most markedly. 



I have made the gyroscope describe curves when placed with its 

 centre at only five inches from the point of support, no counterweight 

 being in this instance used. With an extremely low rotatory velocity 

 the curves can even be shown with the point of support coinciding with 

 the centre of the gyroscope ; but in this and similar cases they very 

 rapidly become prolate, and disappear in consequence of the rapid 

 accumulation of the individually insufficient effects of the centrifugal 

 resultant.* 



I will now proceed to discuss some incomplete or erroneous explana- 

 tions that have been published. Amongst these is one given by Pog- 

 gendorfF, in the volume of his Annals, in which Fessel's apparatus is 

 described. This explanation is confessedly incomplete, and it would bo 

 tedious for me to enter into detail concerning it, although I had pre- 

 pared some remarks upon it. Most continental writers on the subject 

 appear to consider Poisson's explanation complete and accurate. The 

 discussion of Poisson's theory is involved in that of Major Barnard ; for, 

 as the latter author says, " He follows the steps of Poisson, and arriving 

 at his analytical results, he endeavours to develop fully their meaning, 

 and to show that they are expressions not merely of a visible phenome- 

 non, but that they contain within themselves the sole clue to its 

 explanation." 



In Major Barnard's application of the analytical method in the 

 investigation of the gyroscopic phenomena, I understand him to assume, 

 first, that the body is any solid of revolution ; second, that its original 

 rotation is about its geometric axis ; third, that it is supported at a point 

 in the geometric axis, at a given distance, from the centre of gravity ; 

 and, fourth, that at starting, the body is in such a position that gravi- 

 tation tends to turn it about a horizontal axis in such a way as to 

 bring its geometric axis into a vertical position. 



Further, he does not appear in his investigation to have anticipated 

 any alteration in the phenomena arising from mere change of position 

 with respect to the point of support. 



Having worked out his analytical results, the interpretation of them 

 which he gives is to the effect (as I understand him) that the actual 

 axis of rotation which also continues to be the geometric axis of the 

 body, travels along a series of equal cycloidal curves, of which the cusps, 



• The enlargement of the cun'es as the distance from the point of support is increased, 

 may arise partly from the mass having to be moved an increased distance to obtain a given 

 angular adjustment, as well as partly from the diminution of the centrifugal resultant. 



