Objects and results of the investigation.-The results of this investigation have both a practical and a philosophical aspect. In their practical aspect they relate to the law of resistance to the motion of water in pipes, which appears in a new form, the law for all velocities and all diameters being represented by an equation of two terms. In their philosophical aspect these results relate to the fundamental principles of fluid motion; inasmuch as they afford for the case of pipes a definite verification of two principles, which are-that the general character of the motion of fluids in contact with solid suqfaces depends on the relation between a physical constant of the fluid and the product of the linear dimensions of the space occupied by the fluid and the velocity. The results as viewed in their philosophical aspect were thte primary object of the investigation. As regards the practical aspect of the results it is not necessary to say anything by way of introduction; but in order to render the philosophical scope and purpose of the investigation intelligible it is necessary to describe shortly the line of reasoning which determined the order of investigation.
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