157 



from the theorem of Cotes. Maclaurin's theorem is: "If 

 any transversal be drawn through a fixed point o, in the 

 plane of a curve of the n"'- order, so as to meet the curve in 

 n points, the tangents drawn at these points will cut off upon 

 any fixed right line passing through o, segments OTi, 0T2 . . . 

 OT„, the sum of whose reciprocals is constant." 



The following is a more general theorem for plane curves : 

 ^^ If any two transversals be drawn through a fixed point o^ 

 in the plane of a curve of the w"' order, so that one meets the 

 curve in n points Mi, M2 . . . m„, and the other in n points m'i, 

 M'2, . . . m'„ ; the right lines MiM',, MaM'a, . . . m„m'„, will cut 

 off, upon any fixed right line passing through o, segments ot,, 

 OT.,, . . . OT,„ the sum of whose reciprocals is constant." 



And we have an analogous one for surfaces : " If any 

 three transversals be drawn through a fixed point o, the first 

 meeting a surface of the n"' oi'der in n points, jvij, Mj, . . . M„ ; the 

 second meeting it in m'i, m';,, . . . m'„ ; the thirdin m",, m"<i, . . . 

 w,/' ; the planes MiM'iM"2, MaM'sM^a, • • • m„m'„m"to will cut off, 

 upon any fixed right line passing through o, segments, the sum 

 of whose reciprocals is constant. 



The Rev. Dr. Drummond read a paper on the authorship 

 of the poem entitled " The Exile of Erin," 



This subject was taken up in consequence of a provincial 

 newspaper having been sent to Sir William Hamilton, accom- 

 panied by a letter setting forth the claims of George Nugent 

 Reynolds, Esq., to the authorship of that poem, and request- 

 ing that the matter might be brought under the consideration 

 of the Royal Irish Academy. This task was at first declined, 

 as unworthy of serious attention ; but the claims of Reynolds 

 continuing to be urged in several publications, and Thomas 

 Campbell, the reputed author, represented as a plagiarist, 

 Dr. Drummond, lest the silence of the Academy should 

 be construed into an admission of the validity of Reynolds' 



