Mathematical questions and solutions in continuation of the mathematical columns of "the Educational times" Volume Ñ‚. 63 - Tapa blanda

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1895 edition. Excerpt: ...+ 2m)4, A = JMA2 + 2mb B = M«2;.-. m/M =.e2/(l-2«2). This is the solution of an example given in Routh's " Rigid Dynamics." For the particular case in question, put e3 = J, and we have m = JM. 12460. (J. W. Russell, M.A.)--Show that, if the reciprocal of the conic S with respect to the conic S' coincides with S, then the reciprocal of S' with respect to S coincides with S'; and find the relations which hold in this case between the invariants A, O, @', and A'. 12510. (Professor Hudson, M.A.)--When wheat is Is. a bushel, bread is Jd-a lb. What should the 4-lb. loaf cost when wheat is 28s. a quarter p Solution by T. Savage; B. T. Brierley; and others. At 8s. a quarter, the 4 lbs. cost Id.; hence required price is 3Jd. 12577. (Professor Finkel.)--Between Sing-Sing and Tarry-Town, I met my worthy friend, John Brown, And seven daughters, riding nags, and every one had seven bags; In every bag were thirty cats, and every cat had forty rats, Besides a brood of fifty kittens. All but the nags were wearing mittens! Mittens, kittens--cats, rats--bags, nags--Browns, How many were met between the towns? Solution by H. J. Woodall, A.R.C.S. There were 8 Browns, 8 nags, 56 bags, 1,680 cats, 67,200 rats, 84,000 kittens, 611,552 mittens. Altogether, 764,504. 12572' (Professor Hudson, M.A.)--If 80 million equal and similar rectangles placed end to end extend 15,000 miles, and cover 1,300 acres, find the dimensions of one of the rectangles to the nearest half-inch. If their aggregate weight is 290 tons, find the weight of each. Solution by H. J. Woodall, A.R.C.S.; Professor Aiyar; and others. Length of one = 15,000 miles divided by 80 million = 12 inches, nearly. Breadth,, = 1,300 acres divided by 15,000 miles = 8J,,,, Weight,, = 290 tons...