72 Mr. G. J. Buret on a Method 



The resistance of the leads can generally be added as in 

 equation (4). In other cases one of the " dummy- lead " 

 methods of Siemens or Callendar must be adopted. 



In conclusion I have to thank Mr. E. H. Griffiths, Mr. W. 

 A. Price, and Prof. W. N. Stocker for their help in preparing 

 this paper ; and the Silvertown Telegraph Company, who 

 have kindly allowed me to carry out the experiments and 

 publish the results. 



VI. On a Method of Drawing Hyperbolas. 

 By George J. Burch, M.A. Oxon* 



rPHE ordinary methods of drawing hyperbolas fail when 

 J- the portion of the curve required lies some distance 

 from the vertex, small errors of measurement being then so 

 much magnified as to render the results practically useless. 

 Cunynghame's hyperbolagraph, an admirable instrument for 

 describing the parts near the vertex with a single movement, 

 is also, for the same reason, inapplicable to the cases dealt 

 with in the present communication. 



In using graphic methods for the investigation of a problem 

 in Optics, the author had occasion, in 1885, to draw a number 

 of hyperbolas all passing through a fixed point far away from 

 the vertices of most of them, the asymptotes and the vertex 

 of each being given. After vainly endeavouring to draw 

 the curves in the usual way, he devised the following method 

 which proved entirely successful, and which is, so far as he 

 has been able to ascertain, a new one. 



Given the asymptotes Ox and Oy, and the vertex A, to 

 construct an hyperbola. 



The equation of an hyperbola, when referred to its asym- 

 ptotes as axes of coordinates, is 



4xy = a 2 + b 2 . 



In the simplest case, that of the rectangular hyperbola, a = b, 

 and the equation may be conveniently written 



xy=c 2 = a constant. 



To any point C on Ox draw AC, and from A draw a line 

 parallel to Oy, cutting 0^' in B. 



Make CE upon the axis of x equal to BO, and from E 

 draw a line parallel to Oy, cutting AC in D. 



Then yOx being a right angle, and AABC and ADEC 



* Communicated by F. J. Smith, F.R.S, 



