380 



temperature ; and, like it, is represented by a single oscillation. 

 Inthemeanof theyears hitherto examined the minimum occurs, 

 both for the intensity and temperature, in the month of Febru- 

 ary. The epochs of the maxima do not accord quite so closely, 

 that of the intensity taking place about the beginning of July, 

 while that of the temperature occurs a month later ; but as the 

 amount varies very little near the epoch of the maximum, and 

 as there is considerable difference in this respect in the results 

 of different years, we may reasonably expect a closer agree- 

 ment in the means deduced from a greater number of separate 

 years. The mean amount of the annual variation of the inten- 

 sity is about "0014 of the vphole. 



The author concluded by some remarks on the bearing of 

 these facts upon the physical explanation of the phenomena. 



Sir William Rowan Hamilton communicated to the Aca- 

 demy some results, obtained by the quaternion analysis, re- 

 specting the inscription of gauche polygons in surfaces of the 

 second order. 



If it be required to inscribe a rectilinear polygon p, Pi, 

 P2« • -Pre-i in such a surface, under the conditions that its n 

 successive sides, pPj, p, Pg, . . . p,j.i p, shall pass respectively 

 through n given points, Ai, A3, . . . a„, the analysis of Sir W. 

 R. H. conducts to one, or to tivo real right lines, as contain- 

 ing the first corner p, according as the number n of sides is 

 odd or even : while, in the latter of these two cases, the two 

 real right lines thus found are reciprocal polars of each 

 other, with reference to the surface in which the polygon is 

 to be inscribed. Thus, for the inscription of a plane triangle, 

 or of a gauche pentagon, heptagon, &c., in a surface of the 

 second order, where three, five, seven, &c. points are given 

 upon its sides, a single right line is found, which may or may 

 not intersect the surface; and the problem of inscription ad- 

 mits generally of two real or of two imaginary solutions. 

 But for the inscription of a gauche quadrilateral, hexagon, 



