175 



April 15, 1858. 



The LORD WROTTESLEY, President, in the Chair. 

 Major-General Boileau was admitted a Fellow of the Society. 

 The following communications were read : 



I. " On Tangential Coordinates." By the Rev. JAMES BOOTH, 

 LL.D., F.R.S. Received March 20, 1858. 



Many years ago, after I had taken my degree, I was much inter- 

 ested in the study of the original memoirs on reciprocal curves and 

 curved surfaces, published in the ' Annales Mathematiques ' of Ger- 

 gonne, and in the works of such accomplished geometers as Monge, 

 Dupin, Poncelet, and Chasles. In the course of my own researches, 

 it occurred to me that there ought to be some some way of express- 

 ing by common algebra the properties of such reciprocal curves and 

 surfaces, some method which would, on inspection, show the relations 

 existing between the original and derived surfaces. I was then led to 

 the discovery of a simple method and compact notation from the fol- 

 lowing considerations. But before I state them, it is proper to men- 

 tion that I published the discovery in a little tract which I printed 

 at the time, of which the title was, ' On the Application of a New 

 Analytic Method to the Theory of Curves and Curved Surfaces.' 

 This little tract, which is now out of print, as only a few copies were 

 printed, excited but little attention. Nor is this to be wondered at. 

 Mathematical researches, and, indeed, I might add, scientific pur- 

 suits in general, command but small attention in this country, unless 

 they promise to pay. The obscurity of the author, and the remote- 

 ness of a provincial press, still further account for the little notice it 

 obtained. Besides, it must in fairness be added, that the materials 

 were hastily and crudely thrown 'together ; that to save space, the 

 demonstrations were for the most part omitted, and that the prin- 

 ciples on which the method rests were not so clearly explained as to 

 enable an ordinary reader, who had to incorporate with his own 

 thinking the notions of another, to pursue the train of argument, or 



VOL. IX. O 



