﻿144 Dr. John Kerr on a Fundamental 



Here A is the ratio of twice the area of the hyperbolic sector 



IT 



to the square of the initial radius, and a% is the constant sum 

 of the angle from the initial radius to the tangent and that 

 from the initial radius to the radius-vector. This leads us to 

 consider the hyperbolic analogue of the equiangular spiral. 

 Let p 1 denote the corresponding hyperbolic quinion; then 



log JJp'=iA. ot w =iA (cos w + sin w . 02) . 



Here w denotes the constant sum of the angle between the 

 initial vector and the radius-vector and the angle between 

 the initial vector and the tangent. The scalar term iA cos w 

 is the logarithm of the radius-vector, while the vector term 



iA sin w . a 2 is the logarithm of the hyperbolic angle. Here 

 i is the scalar V — 1; in the papers on " The Principles of 

 Elliptic and Hyperbolic Analysis," and on " The Definitions of 

 the Trigonometric Functions," I have shown that a quantity 

 which is the sum of a scalar independent of i and another 

 scalar dependent on 1 is represented along one straight line. 



University of Texas, ALEXANDER MaCFAELANE. 



Austin, Texas, U.S.A., 

 May 10, 1894. 



XIY. On a Fundamental Question in Electro- Optics. 



To the Editors of the Philosophical Magazine. 

 Gentlemen, 



WILL you kindly afford me space for a few remarks in 

 connexion with Professor Quincke's letter, which 

 appeared in the May number of this Magazine. The object 

 of that letter was to draw attention to the fact that, in my 

 paper on Electro- Optics which appeared in the April number, 

 I made no mention of a paper of Professor Quincke's, pub- 

 lished eleven years ago, which gives an account of experi- 

 ments by him on the same subject and by similar methods. 1 

 think 1 should preface what I have to say on this matter 

 with an expression of regret for my forgetfulness. 



I was well aware of the existence of that paper. I received 

 a copy from the author, and perused it I think immediately 

 on receipt. With regard to the electro-optic effects there 

 described, as given by an interference-refractor, it was evident 

 to me then, as it is now, that they were in their nature and 

 immediate origin essentially different from those pure double 

 refractions that are given regularly by the common polari- 



