I. ON THE ROTATION OF A SOLID BODY ROUND 

 A FIXED POINT; BEING AN ACCOUNT OF THE 

 LATE PROFESSOR MAC CULLAGH'S LECTURES ON 

 THAT SUBJECT.* COMPILED BY THE REV. SAMUEL 

 HAUGHTON, FELLOW OF TRINITY COLLEGE, DUBLIN. 



[Transactions of the Soya I Irish Academy, VOL. xxn. p. 139. Read April 23, 1849.] 



I. COMPOSITION or ROTATIONS. 



LET be the intersection of two axes of rotation, OR, OR' ; 

 and let the magnitudes of the rotations be represented by o>, w'; 

 then the motion impressed upon the body by these two rotations 

 will be the same as the motion produced by a single rotation 

 round an axis, which is represented in magnitude and position 

 by the diagonal of the parallelogram formed by w, o/. For, 

 draw through any point I of the body a plane perpendicular to 

 the line 01, and project upon this plane the parallelogram 

 formed by w, a/ ; the sides of this parallelogram will be <u sin 

 ROI and a/ sin R'OI. Now the velocities impressed upon the 



* This Essay " On the Rotation of a Solid Body round a Fixed Point," 

 has been compiled from my notes of Professor Mac Cullagh's Lectures, delivered 

 in the Hilary Term of the year 1844, in Trinity College. A short account of some 

 of the results contained in it was published by Professor Mac Cullagh himself, in 

 the Proceedings of the Royal Irish Academy. t As it has appeared to many of Mr. 

 Mac Cullagh's friends desirable that a somewhat more detailed account of his re- 

 searches in this subject should be published, I have, in accordance with this desire, 

 drawn up and presented to the Academy an account of his Lectures on 

 Rotation. I have endeavoured to arrange the subject in a systematic order, and 

 to give tha results proved by him during the course of the Lectures, carefully ex- 

 cluding all theorems and proofs of theorems, which were not originally given by 

 him, as here stated. SAMUEL HAUGHTON. 



+ Vol. n. pp. 520, 542. 



