331 



lands in the county Tipperary, allotted in 1656 to Colonel Henry Prettie, 

 ancestor of theDunally family, for military services rendered by him in 

 this country. 



He observed that the original maps, although on varying scales of 

 320 and 160 perches to the surface square inch, were by the photogra- 

 phic process, at will and without the necessity of any calculating medium, 

 reduced to a size suitable for illustrating his paper in the Transactions;" 

 that the scales of the reductions cannot be represented in the usual way 

 by numbers ; that the paramount advantage of the photographic over 

 all other methods of reduction is the ready facility it possesses of repre- 

 senting the original picture on any prescribed area, and that the accu- 

 racy with which that operation is performed far exceeds all other known 

 methods, and amounts to perfection. 



He further observed, that these photographs may be zincographed 

 to any number; and that he hoped that, as the subject in reference to 

 the publication of his MS. mapped townland survey narrative is, by an 

 understanding between the Council of the Academy and himself, soon to 

 be submitted to the Treasury for publication as a public document of 

 much interest and value, the propriety and utility of illustrating the 

 narrative with these photozincographed maps will be admitted; and 

 that the Lords of the Treasury will authorize Colonel Sir Henry James, 

 who so kindly supplied the photographic specimens exhibited to the Aca- 

 demy, to complete the requisite number for that purpose — a result that 

 would be alike beneficial to science, literature, and the public service. 



The following letter, addressed to the President, by Sir W. K. Ha- 

 milton, was read : — 



Observatory, April 27, 1863. 

 My dear Mr. President, — I have been wishing for your permission 

 to report, through you, to the Eoyal Irish Academj^, some of the results 

 to which I have lately arrived, while extending the applications of 

 Quaternions, in connexion with my forthcoming Elements. 



I. One set of such results relates to those gauche curves of the third 

 degree, which appear to have been first discovered, described, and to 

 some extent applied, by Professor Mobius, in the Barycentric Calculus 

 (1827), and afterwards independently by M. Chasles, in a JN'ote to his 

 Apergu Historique (1837); and for which our countryman, Dr. Salmon, 

 who has done so much for the Classification of Curves in Space, has pro- 

 posed the short but expressive name of Twisted Cuhics. 



II. A particular curve of that class presented itself to me in an in- 

 vestigation more than ten years ago, and some account of it was 

 given in my Lectures, and (I think) to the Academy also, in connexion 

 with the problem of Inscription of Polygons in surfaces of the second 

 order. I gave its vector equation, which was short, but was not sufii- 

 ciently general, to represent all curves in space of the third degree : nor 

 had I, at the time, any aim at such representation. But I have lately 



