ON GEAPHIC METHODS IN MECHANICAL SCIENCE. 



395 



both by indicating where improvements may be made, and in facilitating 

 the design of new types. By their means also several problems, such as 

 the Hmiting speed at which a shunt-wound motor will excite itself, are 

 readily solved. Besides the characteristic a large number of other curves 

 are in more or less use in dynamo and motor design, such as the curve 

 showing the relation between the speed of rotation of a motor and the 

 exciting current round the field magnets, when a constant difference of 

 potential is maintained at the brushes. The speed being the reciprocal 

 of the effective induction through the armature, the form of the curve 

 (fig. 22) is a combination of a rectangular hyperbola with the charac- 

 teristic of the machine, the saturation of the iron modifying the hyper- 

 bolic form as the exciting current rises. 



Fig. 22. 



Amper& tuTVzs rorZTidy .Field/ Mtgmeis . 



'Various problems in electro-magnets, as regards their attractive force, 

 may be solved and the results rendered clear by this method.' 



' In investigations on alternate-current machinery the graphic method 

 is largely used. The value of the current varying as to time necessitates 

 a more or less complicated expression. When the current follows a 

 simple law it may readily be treated analytically, but, owing to the effect 

 of induction in the circuit, in practice the law becomes very complex. 

 If, as is generally the case, any part of the field in the neighbourhood of 

 the dynamo or transformer coils or of the external circuit contains iron, 

 the expression for the induction will be a function of the value of the 

 induction of the iron, and this cannot at present be expressed in an equa- 

 tion in terms of the current alone. Hence we are forced to obtain the 

 values of the current at each moment experimentally, and we can only 

 make use of them by constructing the curves connecting the values of 

 the current and time. Many such curves have been made, and show 

 curious deviations from the simple law (fig. 23).^ 



' By another application we may plot the variation in phase between 

 the current and the impressed E.M.F., and the changes produced by the 

 introduction of condensers and choking coils into the circuit. The use of 

 these curves, even when hypothetical, is shown in Professor B. Thomson's 

 explanation of electro-magnetic repulsion.^ 



' Jenkin, ' Transmitting Power of an Electric Friction Clutch.' Froc. Itist. C.E., 

 vol. cii. 



^ J. Hopkinson, Electrician, June 24, 1892. 



' Electrical Engineer^ New York, 1887. 



