/. G. Barnard on the Gyroscope. 



71 



i 



At first sight, tlie undulatory motion attending tlie precession, 

 known as '* nutation" (nodding) would seem identical witli the 

 undulations of the gyroscope. But the identity is not easily indi- 

 cated ; for the earth's motion of nutation is mainly governed by the 

 moon, with whose cycles it coincides ; and the solar and lunar 

 j)recessions and nutations are so combined, and affected by causes 

 which do not inter into our problem, that it is vain to attempt 

 any minute identification of the phenomena, without reference 

 to the difficult analysis of celestial mechanics. 



On a preceding page, I said that a horizontal motion of the 

 rotating disk around its point of support, without descending 

 undulations, was at variance with the laws of nature. This as- 

 sertion applied however only to the actual problem in hand^ in 

 which no other external force than gravity was considered, and 

 no other initial velocity than that of axial rotation. 



Analysis shows, however, that an initial impulse may be ap- 

 plied to the rotating disk in such a way that the horizontal mo- 

 tion shall be absolutely without undulation. An initial horizon- 

 tal angular velocity such as would make its corresponding de- 

 flective force equal to the component of gravity, g sm i5, would 

 cause a horizontal motion without undulation. 



If the axial rotation n, as well as the horizontal rotation, is 

 communicated by an impulsive force, analysis shows that it may 

 be applied in any plane intersecting the horizontal plane in the 

 line of nodes ; but if applied in the plane of the equator (where 

 it can communicate nothing but an axial rotation n\ or in the 

 horizontal plane, its intensity must be infinite. 



My announced object does not carry me further into the con* 

 sideration of the gyroscope than the solution of this peculiar 

 phenomenon, which depends solely upon, and is so illustrative 

 of, the laws of rotary motion. 



K I have been at all successful in making this so often ex- 

 plained subject more intelligible — in giving clearer views of some 

 of the supposed effects of rotation, it has been because I have 

 trusted solely to the only safe guide in the comphcated phenom- 

 ena of nature, analysis. 



