# Philosophical Transactions of the Royal Society of London

Royal Society of London., 1886 - Mathematics

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Page 332 - Such empirical formulae possess no advantage over the graphical method aided by algebraic processes, and tend to mask much that is of importance. One purpose of the present investigation is to give an approximately complete construction of the characteristic curve of a dynamo of given form from the ordinary laws of electro-magnetism and the known properties of iron, and to compare the result of such construction with the actual characteristic of the machine. The laws of electro-magnetism needed are...
Page 342 - The currents in the fixed coils around the magnets are not the only magnetising forces applied in a dynamo machine ; the currents in the moving coils of the armature have also their effect on the resultant field. There are in general two independent variables in a dynamo machine, the current around the magnets and the current in the armature, and the relation of EMF to currents is fully represented by a surface.
Page 331 - THEORETICAL CONSTRUCTION OF CHARACTERISTIC CURVE. OMITTING the inductive effects of the current in the armature itself, all the properties of a dynamo machine are most conveniently deduced from a statement of the relation between the magnetic field and the magnetising force required to produce that field, or, which comes to the same thing but is more frequently used in practice, the relation between the electromotive force of the machine at a stated speed and the current around the magnets.
Page 172 - CD be divided into 10 equal parts by vertical lines (fig. 6, dotted figure), and these lines supposed to move with the fluid, they will shortly after assume the positions of the curved lines (fig. 6), in which the areas included between each pair of curved lines is the same as in the dotted figure. In this case, as in Case 1, the distance QP will represent the motion at any point P, and the slope of the lines will represent the tangential forces in the fluid as if the lines were stretched elastic...
Page 181 - These two conditions determine the position of H and the value of JI. As the load increases it appears from the exact equations (to be discussed in a subsequent article) that OH reaches a maximum value, which places H nearly, but not quite, at the left extremity of the brass, but leaves JI still small as compared with GH. For a further increase of the load H moves back again towards 0. In this condition the load has become so great that the friction, which remains nearly constant, is so small by...
Page 180 - Since the fluid film is in equilibrium under the forces exerted by the two opposite surfaces, these forces must be equal and opposite, so that it is only necessary to consider the forces exerted by AB on the fluid. From what has been already seen in Cases 6 and 7 it appears that the resultant line of pressure JM always lies on the right or on side of GH. The resultant friction clearly acts to the left, so that if JM be taken to represent the resultant pressure and MN the resultant friction, N is...
Page 172 - Fig. 5. Case 2. Parallel Surfaces approaching with no Tangential Motion. — The fluid has to be squeezed out between the surfaces, and since there is no motion at the surface, the horizontal velocity outward will be greatest half-way between the surfaces, nothing at O the middle of CD, and greatest at the ends. If in a certain state of the motion (shown by dotted line, fig. 6) the space between AB and CD be divided into 10 equal parts by vertical lines (fig.
Page 183 - If the surfaces are not strictly parallel in the directions TU and VW, the pressure would be greatest in the narrowest parts, causing axial flow from those into the broader spaces. Hence, if the surfaces were considerably irregular, the lubricant would, by escaping into broader spaces, allow the brass to approach and eventually to touch the journal at the narrowest spaces, and this would be particularly the case near the ends. As a matter of fact, the general fit of two new surfaces can only be approximate...