1918] on The Spinning-Top in Harness 291 



tefciMhedron, equivalent to sfcretchiiii^ the simple pendulum length 

 threefold. The beat from Y to VII o'clock is the same as the 

 beat from I to XE, when the axle is held horizontal a^ain. 



Professor Perry has written a popular book on " The Spinning- 

 Top," in stimulating kindergarten style, but it is doubtful if he has 

 ever seen a top, leastways of this size. And I wonder if he has ever 

 seen this gyroscope, although it is the present I made him many 

 years ago. 



As in skating over thin ice, the novice can progress swiftly, never 

 stopping to look down at the black water underneath ; whereas if he 

 paused to consider the depth below, he would break through and go 

 down ; so in the theory of the top the analytical difficulties would 

 drown the beginner, if not kept out of sight as long as possible. 



The kindergarten explanation of the spinning-top is ample in 

 answer to the beginner's question of the How and "Why ; but 

 in mathematical treatment it is the How Much. That is the 

 question. 



Crabtree's " Gyroscopic Motion" goes more deeply into the mathe- 

 matics of the subject ; and here my " Report on Gyroscopic Theory, 

 1914," is intended to serve for reference on the complete theory, 

 where no analytical difficulty is avoided, when any practical problem 

 arises for solution. 



I should like to avail myself of the privilege of addressing this 

 learned audience, but I fear time will not allow it, to quote from my 

 Report the statement of the exact theory in a few lemmas, given in 

 Poinsot's style, recommended by Maxwell (I. p. 248), as a power of 

 mathematics more searching than the Calculus, where ideas take the 

 place of symbols, and intelligible propositions supersede equations. 

 This would be in preference to the purely analytical treatment of 

 Lagrange in his " Mecanique Analytique," not so much to Maxwell's 

 taste. The translation of the lemmas into analytical equations intro- 

 duces the elliptic integral in all its forms, first, second and third ; 

 and the further development could not be compressed into a lecture 

 of one hour, so I refer you to my Report. 



But I call your attention to these model deformable Henrici 

 hyper boloids, passing through the shape of a confocal system. They 

 were employed by Darboux for the material representation by geo- 

 metrical constants of a state of top motion. Calculation was thereby 

 replaced by measurement on a drawing. 



Then there is Kirchhoff's '• Kinetic Analogue," of the bent and 

 twisted wire, to assist in making a mental picture of the top motion 

 in all its complexity. The "Analogue" states that if an elastic round 

 wire, rod, or shaft is bent and twisted into its most general tortuous 

 curve under the action of an equal opposing wrench at each end, 

 the shape of the curve is such that if a point moves along the curve 

 with constant velocity the hodograph of its motion is a spherical 

 curve which can be identified as the curve described by a point 



