368 Prof. G. C. Foster on Graphical Methods of 



refracted wave-plane within the crystal, viz. when the plane of 

 incidence contains the optic axis or axes, and the wave-normal 

 corresponding to the two coincident refracted wave-planes coincides 

 with an optic axis. If the cap of the tube A be replaced by a Nicolas 

 prism with a small orifice, the images may he four, three, two, or 

 one as the stage B is rotated (the last corresponding to the same 

 arrangement as that which gives two images in the previous 

 case) when in addition the Nicol's prism is so adjusted as to 

 polarize the incident light in such an azimuth as to cause the 

 intensity of one of the reflected vibrations to vanish. The planes 

 of polarization of the several refracted rays may be determined 

 by examining them by means of a NicoPs prism introduced into 

 the tube E. If the tubes A and E be made of the same dia- 

 meter, one NicoPs prism will be sufficient for all purposes. 



Queen's College, Galway, 

 April 1875. 



XLII. On Graphical Methods of solving certain simple Elec- 

 trical Problems. By Prof. G. Carey Foster, F.R.S* 

 [With a Plate.] 



IT is probably very seldom that the geometrical representation 

 of the mathematical relations between physical quantities 

 is as convenient, for purposes of investigation, as the correspon- 

 ding analytical expression ; but for purposes of exposition, as 

 distinguished from those of investigation, geometrical construc- 

 tions often possess considerable value. In particular, whenever 

 they can be put into a simple form, their physical significance 

 is more easily understood, than that of an algebraical formula, 

 by those who are but little accustomed to mathematical modes 

 of expression ; and they generally exhibit with greater clearness 

 the effect of a variation of any one of the related magnitudes. 

 I have therefore thought that it might be worth while, for the 

 sake of trying to draw increased attention to the utility of 

 geometrical methods in elementary physical teaching, to point 

 out in detail their application to a few important electrical 

 problems, such as some of the simplest cases which come under 

 Ohm's law of the relations between electromotive force, strength 

 of current, and resistance. 



If the equation which expresses Ohm's law be written in the 

 three following ways — 



0=11, |-C, Cll=E, 



* Read before the Physical Society, November 7, 1874. Communicated 

 by the Society. 



