The London, Edinburgh and Dublin philosophical magazine and journal of science . p=av. pv=K2. p = av pv2 = K3. W dv v2> .*. at the vertex, where^9=v=K, =— 1 ; and at this point, on the bisector of the axes, the curve isinclined downwards at 45°. (2) dp K3 ~r- = — 2—5-= —2 sit vertex : dv v3 curve at vertex is inclined downwards at 634°. Similarly the inclination downwards at the vertex increases rapidly; and for dp K>+1 (n) dv +- the tangent of the downward-pointing angle is n. We can approximately represent most governing relationsby a straight line meeting such a hyperbolic curve. Thep
The London, Edinburgh and Dublin philosophical magazine and journal of science . p=av. pv=K2. p = av pv2 = K3. W dv v2> .*. at the vertex, where^9=v=K, =— 1 ; and at this point, on the bisector of the axes, the curve isinclined downwards at 45°. (2) dp K3 ~r- = — 2—5-= —2 sit vertex : dv v3 curve at vertex is inclined downwards at 634°. Similarly the inclination downwards at the vertex increases rapidly; and for dp K>+1 (n) dv +- the tangent of the downward-pointing angle is n. We can approximately represent most governing relationsby a straight line meeting such a hyperbolic curve. Thepart which represents the state of things where the governoris in action is on the curve beyond the point of junction withthe straight line. Consider first the straight line from 0; p = av. Thepower is proportional to the velocity. This will be the caseso long as the steam is supplied at constant pressure. Forpower is pressure on piston x velocity. But pressure onpiston is constant; .*. power varies as velocity. The hyper-bolic curves represent governors which are
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Keywords: ., bookcentury1800, bookdecade1840, booksubjectscience, bookyear1840
