— 101 — 



you the books as to which you had given him a commission 

 The last payement you made me was I think up to Ns^ 24 of the 

 Journal, that just sent you was N^ 28, making a volume, the 

 price for which with the postage is 22 sh. or say 27 francs. 

 Pr. S. gave me a paper of your on the theory of rotation in 

 Space of n dim. , which has been just in the printers hands, and 

 which will I hope appear in the next number of the Journal. 

 I was much obliged to you also for the paper in Grelle on the 

 same subject which you kindly sent me, and which I received 

 a few days ago. 



The last thing I have been working at is a theory ot the 

 correspondance of points on a plane curve. Since in a unicursal 

 cur\ e or curve with the maximum number ~ (m — 1) (m — 2) 

 of double points, the coordinates are expressible rationally in 

 terms of a parameter Q, — it is clear that Chasles' theorem for 

 the correspondance of points on a line applies to any unicursal 

 curve whatever — and we have thence a theorem appling to 

 any curve, viz. if the correspondance of the two points is such 

 that to any point of the first System there correspond a' points 

 of the second System, and to any point of the second System a 

 points of the first System, then the number of seif corresponding 

 points is a -|- a' -|- 2 k D, if D be the deßciency of the given curve. 

 I have obtained a theorem which enables me to find, if not always, 

 at least in most cases, the value of the coefficient k. 



29 March 66. 



Dr. Salmon has given Orders at my request to a Dublin 

 bookseller to transmit to you a copy of his new edition of his 

 treatise on surfaces and I have given instructions through a 

 friend in London to forward to you the New Edition of Hamil- 

 tons Treatise of Quaternions which I beg of yOu to accept as a 

 friendly memento from me and as an infinitesimal compensation 

 for the delay occasioned by my unhappy and deeply bewailed 

 habit of procrastination amounting to a kind of mental paralysis 

 of a peculiar and distressing form. 



I have just sent to the Royal Society a short paper on the 

 rotation of a free rigid body about a fixed point and if publis- 



