The lecture concludes with a demonstration showing that a free body in hyperbolic non Euclidean space may be so fashioned as in real time to carry ou… - Carl Barus

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The lecture concludes with a demonstration showing that a free body in hyperbolic non Euclidean space may be so fashioned as in real time to carry out the actual motions of the top. The form of such a body and the forces to actuate it are specified. Klein lays great stress on the beauty of this generalization. ...The full geometry of this case is not carried out in these lectures, however, and Klein regrets that the development of the s has recently fallen into abeyance.

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About Carl Barus

(February 19, 1856 – September 20, 1935) was an American physicist and the maternal great-uncle of the American novelist Kurt Vonnegut. He was dean of the Brown University Graduate Department from 1903 until his retirement in 1926. In 1905 he became a corresponding member of Britain, a member of the First International Congress of Radiology and Electricity at Brussels, and a member of the Physical Society. Beginning in 1906 he was on the advisory board of physics at the Carnegie Institution in Washington state. He died in Providence, Rhode Island, U.S.A.

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Mathematicians will do well to observe that a reasonable acquaintance with theoretical physics at its present stage of development, to mention only such broad subjects as electricity, elastics, hydrodynamics, etc., is as much as most of us can keep permanently assimilated. It should also be remembered that the step from the formal elegance of theory to the brute arithmetic of the special case is always humiliating, and that this labor usually falls to the lot of the physicist.

[L]et me refer to my original work. Naturally, if a student has been hammering away ever since 1979... he must have accumulated a lot of litter, much of which, perhaps, should have long since been swept away. But the fates are not to be bribed either by pother or importunity. Out of 1,000 men who are called, one (probably the ratio is much smaller) is chosen to do glorious scientific work. The others? Their lot is failure. They may be equally or even more industrious, they may have equal or even greater brain power—the other 999 exist merely to make the illustrious one in whom they culminate, possible. After that, the world will say to each in words of poetic brevity: "The man has done his duty, the man can go." And they do, pretty quickly, to a gentler lethe, flowing between the banks of amaranth and asphodel.
Gentlemen, I am one of the 999 about to be forgotten.

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Looking over such famous old books as Montmort's 'Analyse des jeux de hasard' or Moivre's 'Doctrine of Chances' one regrets that so much excellent mathematics should have been wasted on games most of which are wholly obsolete. Coriolus in his '[Théorie Mathématique des Effets du] Jeu de billard' (1835) fared better, for the game is still very much alive and its dynamical terrors unsubdued.

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