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This volume comprises a collection of scientific papers presented before the Royal Society of London, focusing on mathematical and physical sciences. As part of Series A, Volume 81, these 'Proceedings' offer a detailed snapshot of cutting-edge research and scholarly discussions from the period. The papers cover a diverse range of topics, reflecting the breadth of scientific inquiry prevalent at the time. Researchers and historians of science will find this compilation invaluable for understanding the development of mathematical and physical theories, experimental methodologies, and the evolution of scientific thought. The 'Proceedings' serve as a primary source for tracing the intellectual lineage of numerous scientific advancements and provide context for contemporary research. 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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.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.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
