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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. 1910 Excerpt: ...of the points /, V. The angular velocity at each point on the moving»wheel may then be found and with this data we may finally obtain the lbsolute velocity and the absolute waterway by the following methods: On the conical surface 0-1, whose vertex lies on the axis of revolution at the point 01, there moves a particle of water whose relative velocity is given in amount and direction by u'o. As the assumed relative path of the water has the length 0-1, therefore the time required for the water to flow through this path is equal to u'o By multiplying this time by the peripheral velocity v0 we obtain the length of the path through which the water flows in said time as such path is measured on the periphery,. This path is to be drawn on a circle passing through 0 and having the center 01 (the vertex of the cone for both the absolute and the relative path of the water). By uniting the relative path and the peripheral path we obtain the point / of the absolute waterway. We may now proceed from point / to point // in a manner similar to the above except for the fact that the movement is now considered to take place on the conical surface /-//, whose vertex is at /-// on the axis of revolution. We must also consider the path /-// through which the water flows and the relative velocity at the point /. We thus find the time required for the passage of a particle of water from point / to point //, and with it a new section of the true curve through which the water flows. The union of the relative path with this section of curve gives the desired point // on the absolute waterway, and so on. At the same time we may obtain the absolute velocity Ce at the point / by combining the relative velocity «v with the peripheral velocity Ve, etc. If we then use as absci...
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