The Messenger of mathematics Volume 1 - Tapa blanda

Reseña del editor

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. 1862 Excerpt: ... which becomes the ellipse or hyperbola as usual when n = 0, it being observed that we have an additional disposable constant introduced by the method employed in obtaining equation (1). It is evident that results of this kind may be multiplied indefinitely. To classify the cases in which the equations for r and 6 in terms of t can be completely integrated would be an interesting, but by no means an easy problem. T. SHORT PROOF OF THE MULTINOMIAL THEOREM FOR A POSITIVE INTEGRAL EXPONENT. In order to find the product of (a, + + c, +...+ pt) (a, + b, + c +...+pi) (a, + + ca +...+pi)-K + h + Cn+..'+P«), we have by continued multiplication to combine each member of the first group with each member of the second group, and to combine each of these combinations with each member of the third group, and so on till we arrive at the last group. Each of the final combinations will evidently be of the nth order, and the sum of them will be the product required. The number of combinations containing n as is one. A METHOD OF FINDING THE LATITUDE OF A PLACE BY DIRECT DIFFERENTIAL OBSERVATIONS. By A. Freeman, B.A., Scholar of St. John's College, Cambridge. This method is a modification of one given in Loomis' Practical Astronomy. By one additional observation on each occasion of the star's crossing the prime vertical, we obviate the necessity of knowing the star's declination. Suppose a transit circle placed so that its graduated circle is parallel to the prime vertical. Every star whose declination is less than the latitude will cross the prime vertical twice in 24 hours, at an interval (varying for different stars) of from 0 to 24 hours. By observing the star each time it crosses, we know the time between the two observations; and the arc of the prime vertical cut o...