primarily rectilinear motion, by any steady deflecting force which the moving body carries, so to speak, along with it, and which continually gives a lop-sided tendency to its forward movement. For instance, we have been told that a man or a horse, travelling over a great prairie, is very apt to find himself, after a long dayãs journey, back again near to his starting point. Here some small and imperceptible bias, such as might for instance be caused by one leg being in a minute degree longer or stronger than the other, has steadily deflected the forward movement to one side; and has gradually brought the traveller back, perhaps in a circle to the very point from which he set out, {499} or else by a spiral curve, somewhere within reach and recognition of it.
We come to a similar result when we consider, for instance, a cylindrical body in which forces of growth are at work tending to its elongation, but these forces are unsymmetrically distributed. Let the tendency to elongation along AB be of a magnitude proportional to BBÿ£¢ãý, and that along CD be of a magnitude proportional to DDÿ£¢ãý; and in each element parallel to AB and CD, let a parallel force of growth, proportionately intermediate in magnitude, be at work: and let EFFÿ£¢ãý be the middle line. Then at any cross-section BFD, if we deduct the mean force FFÿ£¢ãý, we have a certain positive force at B, equal to Bb, and an equal and opposite force at D, equal to Dd. But AB and CD are not separate
structures, but are connected together, either by a solid core, or by the walls of a tubular shell; and the forces which tend to separate B and D are opposed, accordingly, by a tension in BD . It follows therefore, that there