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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
bý, 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
Ꭴ 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 yö, yri, yxor,
..yřn-l.c; find the fluents of À =yi, B=AĆ, 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
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"
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.
P. 23. I. 18. for a body, read, a falling body.
HODSON, PRINTER, CAMBRIDGE.
Tutor in starvard University
LITERARY AND SCIENTIFIC
WHICH ARE ENCOURAGED AND ENFORCED
University of Cambridge,
BRIEFLY DESCRIBED AND VINDICATED.
WITH VARIOUS NOTES.
Rev. LATHAM WAINEWRIGHT, A.M. F.A.S.
OF EMMANUEL COLLEGE, IN THAT UNIVERSITY;
RECTOR OF GREAT BRICKHILL, BUCKS.
Πολλών δ' έφθίμοισι δεδώρηται βασιλένσι, ,
Theoc. Idyll. 17.
PRINTBD FOR J, HATCHARD, BOOKSELLER TO THE QUEEN,
NO. 190, OPPOSITE ALBANY, PICCADILLY.