THE MATHEMATICAL QUESTIONS, PROPOSED IN THE LADIES' DIARY, AND THEIR ORIGINAL ANSWERS, TOGETHER WITH SOME NEW SOLUTIONS, FROM ITS COMMENCEMENT IN THE YEAR 1704 TO 1816. IN FOUR VOLUMES. BY THOMAS LEYBOURN, OF THE ROYAL MILITARY COLLEGE. VOL. IV. London: PRINTED BY W. GLENDINNING, HATTON GARDEN; AND PUBLISHED BY J. MAWMAN, LUDGATE STREET MATHEMATICAL QUESTIONS PROPOSED IN THE LADIES' DIARY, AND THEIR ANSWERS. Questions proposed in 1802 and answered in 1803. I. QUESTION 1089, by P. Panglos. A pendulum vibrates as often in a minute as it is inches in length. Query, what that length is ? Answered by Master John Golding, at Mr. Gregory's Academy, Cambridge. Put x for the pendulum's length in inches, and also its number of vibrations in a minute; the length of the second's pendulum being 39 inches. Then, the number of vibrations being inversely proportional to the square of the lengths, as √ √39: 60x; hence, multiplying extremes and means, xx=6039; and, by squaring, 3600 × 39 140850; therefore x=140850 = 52·02982 inches, the length required. The same by Mr. J. H. Hearding, Adderbury School. The lengths of pendulums are to one another reciprocally as the squares of their vibrations made in the same time: therefore, putting x for the length required, x: 39:: 602: x2; hence, x3 60 × 391 140850, and x = 140850 = 52.02982 inches, The same by Mr. Jos. Kaye, Aldmonbury. It is demonstrated by mathematician's (Hutton's Course of Mathematics, vol. 2, pa. 174, &c.) that the times of vibrations of pendulums are as the square root of their lengths; or the number of vibrations in a given time reciprocally as the square root of their lengths. Let the number of vibrations in a minute, and also the length; then VOL. IV. |