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chance of A's winning a single counter from B is to the chance of B's getting one from A :: a : b. What is the probability that A will win all B’s counters?

16. Explain the method of finding the velocity with which a bullet struck a pendulous body.

17. If a ponderous cylinder is put in motion about its axis by a weight p, descending through a spaces; and, p being taken off, the moment thus generated be employed to elevate another weight q: the space through which the cylinder's motion elevates q can

p never be so great as sx even if the effects of friction are neglected. 18. Find the fluent of vmmni, when v is the hyp. 1

2%. Also the fluent of

2 - 3x +2

pi 18. Find the relation of 'x and y, when + rý, ami

, cj and also when ay + 20. Having given the velocity of projection, greater than that acquired by falling from an infinite

1 distance, when the force oc and also the distance

from the centre of force; find the proper direction of projection so that any one of Cotes's three last spirals may be described.

21. Having given the fluents of , yri, yxor,

..yřn-l.c; find the fluents of À =yi, B=, CBC. R=2.1, the number of the last equations being .

22. S is the pole of the logarithmic spiral, and P any point in the curve; if with centre P, and radius

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PS, a circle be described, and 2D taken equal to n times 2R, then DT may be expressed by a series of cosines of R2 and its multiples, the variable coefficients of the series being those of a +al"

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23. Suppose both sun and moon in the equator, and prove that the momentary change in the height of the whole tide is proportional to the sine of twice the moon's distance from the place of high water.

24. Let y=arn + b.xn-- +cx?-?+ &c. be the equation to the parabolic curve whose axis is AE. Prove that the continued product of the greatest ordinates will be equal to

multiplied into BC% x BD x CD X &c.

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FINI S.

ERRATA.

P. 23. I. 18. for a body, read, a falling body.
P. 30. I. 4. read, the equation a'y- xy-a=0.
P. 84. 1. 17. for vertices, read vortices.
P. 108. I. 2. for field view, read field of view.
P. 113. 1. 9. for x cosec. p. sec. l. read Xcosec, p. sec. l,
P. 142. I. 11. for consines, read cosines.

HODSON, PRINTER, CAMBRIDGE.

Tutor in starvard University

1816 1818

THE

LITERARY AND SCIENTIFIC

PURSUITS

WHICH ARE ENCOURAGED AND ENFORCED

IN THE

University of Cambridge,

BRIEFLY DESCRIBED AND VINDICATED.

WITH VARIOUS NOTES.

BY THE

Rev. LATHAM WAINEWRIGHT, A.M. F.A.S.

OF EMMANUEL COLLEGE, IN THAT UNIVERSITY;

AND

RECTOR OF GREAT BRICKHILL, BUCKS.

Πολλών δ' έφθίμοισι δεδώρηται βασιλένσι, ,
Πολλών δέ Πολίεσσι, πολυν δ' αγαθοίσιν εταίροις.

Theoc. Idyll. 17.

LONDON:

PRINTBD FOR J, HATCHARD, BOOKSELLER TO THE QUEEN,

NO. 190, OPPOSITE ALBANY, PICCADILLY.

S. Gosnell, Printer, Little Queen Street, London.

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