11. An indefinitely large plane area is ruled with parallel equidistant lines, the distance between consecutive lines being c. An ellipse whose major axis is less than c is thrown down on the area. Shew that the chance that the ellipse falls on one of the lines is where 7 denotes the perimeter of the ellipse. пс 12. A messenger M starts from A towards B (distance a) at a rate of v miles per hour, but before he arrives at Ba shower of rain commences at A and at all places occupying a certain distance z towards, but not reaching beyond, B, and moves at the rate of u miles an hour towards A; if M be caught in this shower he will be obliged to stop until it is over; he is also to receive for his errand a number of shillings inversely proportional to the time occupied in it, at the rate of n shillings for one hour. Supposing the distance z to be unknown, as also the time at which the shower commenced, but all events to be equally probable, shew that the value of M's expectation is, in shillings, EDUCATIONAL MATHEMATICAL WORKS. By I. TODHUNTER, M.A. Fellow and Assistant Tutor of St. John's College, Cambridge. 1. A Treatise on the Differential Calculus: And the Elements of the Integral Calculus. With numerous "TO THE DIFFERENT CHAPTERS WILL BE FOUND APPENDED EXAMPLES SUFFICIENTLY NUMEROUS TO RENDER ANOTHER BOOK UNNECESSARY. The examples have been selected almost exclusively from the College "A TREATISE WHICH WILL TAKE ITS PLACE AMONGST OUR STANDARD "FOR THE GREAT BULK OF MATHEMATICAL STUDENTS-ESPECIALLY AT 2. A Treatise on the Integral Calculus, And its Applications; with numerous Examples. Crown 8vo. cloth, 10s. 6d. 3. A Treatise on Analytical Statics. With numerous Examples. Crown 8vo. cloth, 10s. 6d. 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