180 



of the Council, at a short interval of time, deprecating further 

 delay, and censuring what had already occurred. 



One name in the list of contributors from the town of 

 Cambridge, that of Hobson the carrier, celebrated by some 

 lines of Milton, has, from that circumstance, attracted atten- 

 tion, from the sum demanded and the nature of his occupa- 

 tion. 



" The original papers have been injured by damp, and 

 rendered in some degree, but not materially, defective. 



" 111 order to render the papers more accessible for 



perusal, I have sketched out a table of reference which I 



enclose, and avail myself of the kindness of my valued 



friend, the Lord Bishop of Cashel, for their transmission to 



DubUn. 



" I am. Sir, 



" Your obedient Servant, 



" John Newport. 

 " Sir William R. Hamilton, 



President R. I. Academy, 



8(C. 8(C. 8fc" 



The special thanks of the Academy were voted to Sir 



J. Newport. 



A paper was read by William Roberts, Esq., F. T. C. D., 

 " on the Rectification of Lemniscates and other Curves." 



Let a curve be traced out by the feet of perpendiculars 

 dropped from a fixed origin upon the tangents to a given 

 curve: and from this new curve, let another be derived by a 

 similar construction, and so on. Also let a curve be imagined, 

 which is constantly touched by perpendiculars to the radii 

 vectores of the given curve, drawn at the points where it is 

 met by these radii, and from this let another be derived by a 

 similar mode of generation, and so on. 



Then if Sn denote the arc of the curve which is ??"' in 

 order in the former series, and *_„ that of the w"' in the lat- 

 ter, we shall have 



