Philos. Transactions.— Leyloum's Mat hem. "Repository. 457 



By Sir Everard Home, Bart.—Reasons for giving the name of 

 Protfo Saurus to the Fossil Skeleton which has been tlescriljed. 

 By the same.— Some Observations on the Peculiarity of the Tides 

 between Fairleigh and the North Foreland ; with an ExplaiTa- 

 tiou of the supposed Meeting of the Tides near Dungeness. By 

 Captain James Anderson, R.N.— On the Ova of the different 

 Tribes of Opossum and Ornithorhyncus. By Sir Everard Home, 



Bart The Results of Observations made at the Observatory of 



Trinity College, Dublin, for determining the Obliquity of tlie 

 Ecliptic, and the Maximum of the Alteration of Light. By the 

 Rev. J. Brinklev,D.D.— On some new Methods of iiivestigatmg 

 the Sums of several Classes of infinite Series. By Charles 

 Babbage, Esq.— On the Optical and Physical Properties of Ta- 

 basheer By Dr. Brewster.— An Account of a Membrane m the 

 Eve now first described. By Arthur Jacob, M.D.— A new Me- 

 thod of solving Numerical Equations of all Orders by continuoui 

 Approximation. By W. G. Horner, Esq.— An Account of Ex- 

 periments for determining the Variation ui the Length of t.ie 

 Pendulum vibrating Seconds at the principal Stations of the Tri- 

 gonometrical Survey of Great Britain. By Captain Kater. 



Notice.— IXie 17th Number of Leybourn's Mathematical Repo- 

 sitory, containing the Geometrical' Solution of the Problem of 

 inscribing a regular Polygon of seventeen Sides in a Circle. — This 

 Number also contains several other curious mathematical Pro- 

 blems and their Solutions, as well as original Papers on Mathe- 

 matical Subjects; together with the following Set of Questions to 

 be answered in a future Number (XIX). 



1. A and B travelled on the same road and at the same rate 

 from H to L. At the 50th mile stone from L, A overtook a 

 drove of geese, which were proceeding at the rate of three miles 

 in two hours ; and two hours afterwards met a stage waggon which 

 was moving at the rate of nine miles in four hours. B overtook 

 the same drove of geese at the 45th mile stone, and met the same 

 stage waggon exactly forty minutes before he came to the 31st 

 mile stone. Where was B when A reached L ? 



2 The curve AVR and semicircle APB have the same abscissa, 

 the ordinate MV = tan. { arc AP: prove that the area AMV=» 

 twice the segment AP. . . i • 



3. A parabola revolves round its axis, which is vertical, in a 

 given time, and the angular motion will just prevent a body at 

 any point of the curve from descending : required the parameter 

 of the parabola ? 



4. To divide a given arc (A), less than a quadrant, into two 



•uch parts (p) and (7) that tan '" /) X tan " 9 may = max. 



