1825.] Royal ISociety. 67 



Brande, Esq.; S. Goodenough, Lord Bishop of Carlisle ; Major 

 T. Colby; J. W. Croker, Esq. ; D. Gilbert, Esq.; C. Hatchett, 

 Esq. ; Sir E. Home, Bart. ; J. Pond, Esq. ; W. H. WoUaston, 

 MD. ; T. Young, MD. 



Of the New Cou)iciL—W. Babington, MD. ; F. Baily, Esq.; 

 J. G. Children, Esq. ; J. W. Viscount Dudley and Ward ; 

 J. F. W. Herschel, Esq. ; Capt. H. Kater ; T. A. Knight, Esq. ; 

 A. Mac Leay, Esq. ; SirT. S. Raffles, Knt. ; Edward Adolphus, 

 Duke of Somerset. 



President. — Sir H. Davy, Bart. 



Treasurer. — D. Gilbert, Esq. 



Secretaries. — ¥/.T. Brande, Esq. ; and J. F.W. Herschel, Esq. 



Dec. 9. — Charles Mackintosh, Esq. was admitted a Fellow ; 

 M. Thenard was elected a Foreign Member ; and the following 

 communications were received. 



Three extensive series of Astronomical Observations made at 

 the Observatory of Paramatta, New South Wales ; communi- 

 cated by Sir Thomas Brisbane. 



Explanation of an Optical Deception in the Appearance of 

 the Spokes of a Wheel seen through Vertical Bars. By P. M. 

 Roget, MD. FRS. 



A portion only of this paper was read. 



Dec. 16. — The name of Dr. John Thomson, of Edinburgh, was 

 ordered to be inserted in the printed lists of the Society ; and 

 the reading of Dr. Roget's paper was concluded. 



The spokes of a revolving wheel appear curved when viewed 

 through the intervals of a series of vertical l>ars, such as those 

 of a palisade, or a Venetian window-blind. The spokes on each 

 side of the upper one, which has arrived at the vertical position, 

 appear bent upwards ; and the curvature of each spoke increases 

 accordingly as it is more distant from the uppermost one. The 

 direction of the curvature is the same, whether the wheel be 

 moving to the right or to the left of the spectator. The appear- 

 ance takes place only when the wheel is revolving with a certain 

 velocity, and remains the same whatever greater velocity is giveir 

 to the wheel, as long as the spokes continue visible. 

 author states the results of experiments illustrating the influence 

 of various circumstances on these illusive appearances ; and 

 infers from them that the combination of a progressive with a 

 rotatory motion is essential to their production. He explains 

 them on the well-known physiological principle of the conti- 

 nuance for a certain time of an impression made on the retina; 

 and shows that not only all the ordinary phenomena accord 

 witli his theory, but that, by means of it, the result of more 

 complicated combinations may be anticipated. The paper con- 

 cludes with a mathematical investigation of the curves thus 

 generated ; of which the general equation and leading properties 



are given. 



r 2 



