Mb. Edmund Hunt on Rotatory Motion. 203 



being put in a general form, but for the sake of simplicity, I will here 

 give it as applicable to a sphere free to turn about any axis passing 

 through its centre. " If a plane passes through a given axis of rotation 

 the orthographic projection on that or a parallel plane, of a line repre- 

 senting the tangential velocity of a given point on the surface, will be 

 equal to V" sin 6; V representing the tangential velocity of a point on 

 the equator, and d the angle formed with the plane, by a line from the 

 given point to the centre of the sphere." It follows as a corollary 

 that, if in a sphere two or more diametrical axes of rotation lie in 

 a plane, the relative velocities of any point about such axes will be 

 represented as orthographically projected on such plane by lines at right 

 angles to the respective axes, and having the ratios to each other of 

 the respective angular velocities ; for each projection is as the corre- 

 sponding equatorial or angular velocity multiplied by sin 6 — that is, the 

 projections are equimultiples of the angular velocities, and having there- 

 fore the same ratios to each other that such velocities have. 



Since my first paper was read, I have seen a second article by Major 

 Barnard in Sillimans Journal for January, 1858 ; and as in this paper 

 the mode of showing the enlarged " cycloidal " motions is described, 

 I think it proper to mention that I wrote three several times to the 

 editors of SillimarCs Journal respecting my paper, the last time on 4th 

 December, 1857, describing the " cycloidal " experiments. I have 

 received answers to every letter but this last and most important one. 

 The parts of Sillimans Journal generally reach here about the 20th of 

 the month they are for ; but that for January, 1858, was not received 

 until the 3d March. I have thus reason to think that an account oimy 

 experiments was in America before that of the Major's was published ; 

 however, as far as I can learn, the experiments I exhibited before the 

 Society on the 2d December, 1857, had not then been shown elsewhere. 



Major Barnard's first paper conveys the impression that in practice, 

 as well as theory, the gyroscope never moves horizontally — that there 

 are always undulations, but that with high velocities they are " too 

 rapid and too minute to be perceived." In the second paper, however, 

 wo are told that the undulations speedily vanish, and that the gyroscope 

 moves horizontally, or nearly so ! We are not told how the undulations 

 are made larger on mounting the gyroscope farther from the point of sup- 

 port, nor why thej' are not sensible with the gyroscope arranged in the 

 common way, as they ought to be, by the Major's theory. He attri- 

 butes the gradual change in the form of the curve mainly to the decreas- 

 ing rotatory velocity of the lly-wheel. To test the correctness of this 

 arrange the apparatus, fig. 14, with the centre of gravity of the lever, 

 wheel, and weight at the centre of the ring d, and set the wheel spin- 



