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This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

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. 1917 edition. Excerpt: ...Similarly for the action of the other bodies on the mass Wi, etc. These familiar equations (12) show that the actions of the bodies always are mutual; and therefore no change can be made in the component velocities of one body without corresponding reactions on the component velocities of the other bodies. It is obvious therefore that changes of velocities due to inter-actions necessarily are mutual. It is only under interpenetration of waves that stress of the medium is developed, and the magnitudes of the changes produced in the energy of these masses depend upon the forces at work, under the stresses operating in the action of the attracting bodies to which any single mass may be subjected within the system. Accordingly the changes within the system, depending on the mutual actions of its component masses, necessarily will be such that the Action is in accordance with the Lagrange-hamilton Equation (12) And therefore, in a conservative system, free of collisions and devoid of friction Thus any system necessarily pursues the path of Least Action under its own forces; for this merely conserves the vis viva. If the bodies be started with the velocities r, and co-ordinates x(, yt, z(, the changes in the velocities due to the mutual wave action of the bodies of the system necessarily will be such as to conform to the forces which are appropriate to the given co-ordinates. No other changes are dynamically possible. Consequently the system always conserves the vis viva, and hence automatically pursues the path of Least Action; and therefore for any interval, f0 to t, we have the above integrals (13) and (14). But starting at any epoch U it is obvious that A = /(niiVAdt = / Cdt, C = a constant, (15) and therefore for any given interval of time t--to...

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