Mr. J. (ilaisilier's Remarks on the Weather. 137 



and under this form of enunciation, it is obvious that the theo- 

 rem must admit of being extended, by deformation, to ellip- 

 soids, and other surfaces of the second degree. We may then 

 enunciate also this other theorem, respecting the inscription 

 of rectilinear polygons in such surfaces (which theorem was 

 communicated to the Royal Irish Academy in March 1849): 

 — If, after iiiscribing, in a surface of the second degree, any 

 gauche polygon of 2m sides, pPi . . p^w-m ^''^ ^'''^^ inscribe in the 

 same surface another gauche polygon, of^m + 1 sides, pVj ..p^^j 

 under the follovoing 4-m conditions of parallelism : 



p'p'i 11 pPi ; p'lP'a II P1P2; • . • p'2m-iP'2m II Pim-iP ; (249.) 

 and 



P'2mP'2m + l|lPP,; P'2m + lP'2m + 2llPlP2; '"^4m-lV' iJl^Im-lP', (250.) 



(the first corner p' of the second polygon being assumed at 

 pleasure on the surface, and the other corners p'p &c., of that 

 polygon, being successively derived from this one, by drawing 

 two series of parallels as here directed ;) then the diagonal 

 plane p'p'.2„,p'4,„, which contains the first, middle, and last corners 

 of the polygon "with 4m + 1 sides, "will be parallel to the plane 

 •which touches the surface at the first corner v of the polygon with 

 2m sides. In fact, the two rectilinear diagonals, p'p^2m and 

 p'2/HP'4m» will, by a former theorem of the present article, be 

 parallel to that tangent plane. For example, if the first, 

 second, third, and fourth sides, of a gauche quadrilateral in- 

 scribed in a surface of the second order, be parallel to the first, 

 second, third, and fourth, and also to the fifth, sixth, seventh, 

 and eighth sides respectively, of a gauche enneagon inscribed 

 in the same surface; then that diagonal plane of the enneagon 

 which contains the first, fifth, and ninth corners thereof, will 

 be parallel to the plane which touches the surface at the first 

 corner of the quadrilateral. 



[To be continued.] 



XIX. On the Weather during the Quarter ending June 30, 

 1849. jRy James Glaishek, Esq., F.R.S., and of the Royal 

 Observatory, Greenwich *. 



DURING the past quarter I have inspected the locality 

 and the instruments at Exeter, Southampton, Latimer, 

 Aylesbury, Stone, Hartwell House, Hartwell Rectory, Ox- 

 ford, Cardington, Liverpool, Leeds, Stonyhurst, York, White- 

 haven and Newcastle. 



The residts furnished to the Registrar-General for the past 



* Connnunicaleil by the Author. 



