This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1843 edition. Excerpt: ... communication I shall merely give a brief general explanation of the conclusions at which I have arrived, without attempting to state fully the process of reasoning on which they are founded, as this could not be rendered intelligible without entering upon mathematical details, which must be reserved for a paper of greater length. In the first place, if the body considered be an ellipsoid of homogeneous matter, supported by its centre of gravity, it is clear that it will be in equilibrium with any one of its three principal axes in the direction of the lines of force; and if it be put into any other position, the action of the earth upon it will be a couple, of which the moment may be expressed very simply in terms of the quantities denoting the position of the axes with reference to the direction of the terrestrial force, and certain constant magnetic elements depending on the substance and dimensions of the body. In considering the corresponding problem for a body of any irregular form, we readily obtain for the components of the directive couple, round three rectangular / axes chosen arbitrarily in the body, expressions involving nine constant magnetic elements. I have succeeded in proving that six of these elements must be equal, two and two; so that the entire number of independent constants is reduced to six. I have thus arrived at the interesting theorem, that there are, in any irregular body, three principal magnetic axes at right angles to one another, such that if the body be supported by its centre of gravity, it will be in equilibrium with any one of these axes in the direction of the terrestrial magnetic force. If the body be held in any other position, there will be a directive couple of which the moment is expressible in...