The Theory of Elliptic Integrals and the Properties of Surfaces of the Second Order; Applied to the Investigation of the Motion of a Body Round a Fixed Point

by James Booth

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. 1851 ...(102). XLIX. If we multiply the first of (100) by, the second by n, v the third by-, and add the results, the sum will be CO CO zero, or-I'p + m'q + n'r =0;.. (103); whence it follows that, the plane of the centrifugal couple always passes through the instantaneous axis of rotation. L. Multiply together line by line the groups in (95) and (100), add the results, the sum will be cypher; or KG W + mm'+ nn' =0... (104) Whence we infer that the planes of the impressed and centrifugal couples are always at right angles to each other. LI. If we compare the formula (84) with (100), we shall find the second members identical, if we assume as, in (97), P=f% =fv r=/X; whence G = rnco2... (105). We may hence infer that the triangle between the radius vector, the tangent plane, and the perpendicular on it from the centre, coincides in position with the plane of the centrifugal couple. The centrifugal couple is also equal to the centrifugal triangle multiplied by the mass and the square of the angular velocity. The reader will not fail to have observed the ease and simplicity with which the properties of the ellipsoid, treated generally, without reference to the principal axes, by the method of tangential coordinates, may be used to illustrate and establish the corresponding states of a body in motion round a fixed point. The subsequent investigations might in most cases have been discussed with the same generality and facility; but as the principles of this new analytical geometry, the method of tangential coordinates, is probably but little known, it may be more satisfactory to conduct our investigations on principles universally admitted. To simplify the results, we shall adopt a particular system of coordinates which will render the formulae much more manageable. If...

38 pages, Paperback

Published January 1, 2012

About the author

James Booth has written extensively on Philip Larkin. Booth has recently retired from the Department of English at the University of Hull, where he had been Larkin's colleague for seventeen years.

The distinction between Booth's and Andrew Motion's biographies is, in Booth's own words:

"His (Motion's) biography is a magnificent achievement, but he is not on Larkin's wavelength when it comes to humour".

However, despite praising Motion's achievement in this regard, Booth adds that:

"I think Motion took Larkin too much at his own word. When Larkin said he was a sour brute who didn't treat his mother well, he believed him. In fact, Larkin wrote two letters to his mother every week for 40-odd years."

Booth's writing is defined by his admiration for one of Britain's most beloved poets of the twentieth-century:

"I have always loved his poetry and love is the right word"