Royal Institution. 291 



heat at the temperature T„, is 



Q, T,+To' 



The fourth section concludes with a system of formulae, illustrated 

 by numerical examples, for computing the power and efficiency of 

 air-engines. 



In the fifth section, the principles of the preceding sections are 

 applied to aggregates consisting of heterogeneous substances, or of 

 the same substance in different conditions, especially the aggregate 

 of a liquid and its vapour ; and the results are applied to the nume- 

 rical computation of the theoretical efficiency of steam-engines. 

 Jan. 26.— The Rev. Baden Powell, V.P., in the Chair. 



A paper was read, entitled " On the Vibrations and Tones pro- 

 duced by the contact of bodies having different Temperatures." By 

 J. Tyndall, Esq., F.R.S. [An abstract of this paper was given in 

 our last Number.] 



ROYAL INSTITUTION OF GREAT BRITAIN. 



March 3, 1854. — On certain Phaenomena of Rotatory Motion. 

 By the Rev. Baden Powell, M.A., V.P.R.S., F.R.A.S., F.G.S., 

 Savilian Professor of Geometry, Oxford. 



The mechanical principle of " the composition of Rotatory 

 Motion," originally discovered by Frisi about 1750 (see Frisius de 

 Rotatione, Op. ii. 134, 157, and Cosmographia , ii. 24), is equally 

 simple in its nature, important and fertile in its consequences and 

 applications, and susceptible of the easiest explanation and experi- 

 mental illustration ; yet it has been singularly lost sight of in the 

 common elementary treatises. It is, indeed, discussed and applied 

 in a mathematical form in Mr. Airy's Tract on Precession (Math. 

 Tracts, p. 192, 2nd ed.) ; and the theorem is stated by Professor 

 Playfair in his Outlines of Natural Philosophy (vol. i. p. 144), and 

 its application explained (ib. vol. ii. p. 308). These, however, are 

 not books of a popular kind, and the author is not aware of any 

 mention of it in other English works. In a more abstract analytical 

 form it has been discussed by several foreign mathematicians, espe- 

 cially by Poinsot, in a memoir read to the Academy of Sciences, 

 May 19, 1834, but of which only an abstract was published; as 

 well as by Poisson, in a paper in the Journal de I'Ecole Poly technique 

 (vol. xvi. p. 247). 



The principle is involved in the explanation of several important 

 phaenomena, some of which are, in fact, mere direct instances of it ; 

 so that a simple experimental mode of exhibiting it would be emi- 

 nently desirable ; and several such have accordingly been devised 

 which yet seem to have been but little generally known. 



An ingenious instrument of the kind was contrived some 3'ears 

 ago by Mr. H. Atkinson, a very brief account of which is given in 

 the Astronomical Society's Notices, vol. i. p. 43, though so brief 

 that it is difficult to collect what the precise mode of its action was, 

 — but it seems somewhat complex. 



A far more complete and instructive apparatus was invented by 

 Bohnenberger, and described in Gilbert's Annalen (vol. Ix. p. 60). It 



