The Dynamics of Particles And of Rigid, Elastic, And Fluid Bodies. Being Lectures On Mathematical Physics

Cover The Dynamics of Particles And of Rigid, Elastic, And Fluid Bodies. Being Lectures On Mathematical Physics
The Dynamics of Particles And of Rigid, Elastic, And Fluid Bodies. Being Lectures On Mathematical Physics
Webster, Arthur Gordon, 1863-1923
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We may make the space singly -connected by the insertion of a barrier in the shape of a diaphragm, closing the tube so that one of the paths is inadmissible. The connectivity of a portion of space is defined as one more than the least number of barriers or diaphragms necessary to make it singly connected. Thus the space in a closed vase with three hollow handles, Fig. 121, is quadruply- connected. We shaU always suppose the spaces loith which we deal in this took to he singly -connected, or to ...he made so hy the insertion of diaphra^fms, tmless the contrary is eocpresdy stated.
Suppose that W is a point -function which, together with its derivative in any direction, is uniform and continuous in a certain portion of space r bounded by a closed surface S. Then its dW derivative ^ is finite in the whole region, and if we multiply it by the element of volume dt and integrate throughout the volume r, the integral is finite, being less than the maximum value attained dW by -^— in the space r multiplied by the volume t.


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