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Any function of two independent angular coordinates (such as the direction angles 0, <1; of the radius vector) which satisfies equation (7) is called a Laplace's function. Thus Y is a Laplace's function of the order n. The corresponding function a when expressed in terms of (at, y, z) satisfies Laplace's equation and is a spherical harmonic, Art. 161. A Laplace's function when expressed as a function of the Cartesian coordinates of the point at which the radius vector intersects some given sphere with its centre at the origin is called a spherical surface harmonic.
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Excerpt from A Treatise on Analytical Statics, Vol. 2: With Numerous Examples
Any function of two independent angular coordinates (such as the direction angles 0, <1; of the radius vector) which satisfies equation (7) is called a Laplace's function. Thus Y is a Laplace's function of the order n. The corresponding function a when expressed in terms of (at, y, z) satisfies Laplace's equation and is a spherical harmonic, Art. 161. A Laplace's function when expressed as a function of the Cartesian coordinates of the point at which the radius vector intersects some given sphere with its centre at the origin is called a spherical surface harmonic.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Excerpt from A Treatise on Analytical Statics, Vol. 2: With Numerous Examples
1. Law of attraction. If two particles of matter are placed at any sensible distance apart, they attract each other with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance.
2. The reasons for believing the truth of this general law cannot be properly explained until the reader has advanced some way in the study of dynamics. At the same time a large number of theorems which are independent of all dynamical considerations follow from this law. Experience has shown that it is important for the student to acquire an early acquaintance with these results, as he cannot prosecute his studies in the higher dynamics without their assistance. It has therefore been found advantageous to study the attractions of bodies as a part of statics. For this purpose we assume the truth of the law of attraction as a working hypothesis and postpone its verification as a law of nature until the student has read dynamics.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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