Dr. 0. Lodge on Electric Radiation. 

 them parallel, is as follows : — From fig. 2, 



51 



fj,= 



sin (6 + <£) 

 sin (j) 



dy 

 y=(x +/) tan 6 ; -j- = cot <£. 



dx 



vanish 



or 



Solving these equations, and making 6 and 

 together, we get, as the curve of the lens, 



r = (#+/) sec 



r - ■/»-!) . 

 />t cos — 1' 



a hyperbola with one focus as origin, with eccentricity /x, 



f 

 semi-latus rectum f(/x — l), and semi-axis major -^— • 



Taking fi as 1*7 for pitch (according to the measurement 

 of Hertz with a prism), and calling the semi-axis major unity, 

 the focal length of the lens is 2*7, the semi-latus rectum 

 1*89, and half the angle between the asymptotes, being 



cos -1 -, is 54°. 

 A* 

 Using these data, and taking six inches as unit of length, a 

 curve was drawn as shown in fig. 3, where F, the focus of the 

 hyperbola, is to be also the principal focus of the lens ; its 

 distance from the lens is 41 centim. 



Fig. 3. 



This curve was given to the laboratory assistant, Mr. Da vies, 

 who cut out a pair of wooden templates to the pattern, 

 nailed sheet zinc to them so as to make a mould, propped it up 

 in an outhouse, and proceeded to cast it full of pitch — the 

 upper fluid surface constituting the plane surface of the lens. 



All went well till the mould was nearly filled, when the 



E 2 



