bestowed great care 'not merely in carrying oat his investigations, 

 but in considering the form in which they are expressed : and his 

 reluctance to premature publication of incomplete work may be 

 gathered from the fact that, though, on quitting the Presidential Chair 

 of the London Mathematical Society on 12th November, 1874, he 

 made a brief statement of some results which he had obtained in the 

 theory of Correlation of Space, the full exposition of his results was 

 not communicated to the Society until 9th January, 1890. 



The work with which his name as a mathematician will be most 

 definitely associated is contained in his papers on the Correlation of 

 Planes and the Correlation of Space. The simplest space of two 

 dimensions is a plane, and the elements of such a space are a point 

 and a straight line ; a correspondence is established between two 

 planes when all the elements of one plane are connected by a relation 

 or relations with all the elements of the other. When the relations 

 are such that, in general, one element of one plane is associated with 

 one (and with only one) element of the other plane, and vice versy, 

 the correspondence is unique. If each point in one plane corresponds 

 uniquely with a point in the other, and likewise each line in one 

 plane uniquely with a line in the other, the correspondence is called 

 a homography : the theory of homography is considered at length by 

 Chasles in his ' Traite de Geometric Superieure.' If each point in one 

 plane correspond uniquely with a line in the other, and likewise each 

 line in the one plane with a point in the other, the correspondence is 

 a correlation. A few properties of correlative planes are proved by 

 Chasles in the treatise quoted : it is Hirst's distinction to have con- 

 structed the theory of correlation of planes and to have developed it 

 to a great degree of perfection. The extension of the theory of 

 correlation so that it may be applied to space of three dimensions 

 was adverted to by Chasles in his * Aper9u Historique'; the full ex- 

 tension was carried out by Hirst, whose investigations in this subject, 

 together with those of his friends Rudolf Sturm, Cremona, and others, 

 have resulted in important and substantial additions to the theory of 

 pure geometry. 



The following memoranda of Dr. Hirst are due to Professor 

 Tyndall ; the present state of tys health is sufficient to account for 

 their brevity. 



A. R. F. 



[Memoranda concerning Dr. Hirst."] 



The "railway mania" was at its height, and profitable employ- 

 ment was in prospect for young men trained to the use of the 

 theodolite, spirit-level, chain, and drawing-pen. Youths of well-to-do 

 families were articled in numbers to a profession offering so many 



