Royal Society. 49 



if from any point in the circumference there be drawn two lines, 

 one to the point without the circle, and another to the foot of this 

 perpendicular, the former of these lines will be to the latter, as the 

 distance of the point without the circle from the centre, is to the ra- 

 dius of the circle. By means of this property, and assuming that 

 the ellipse is the curve whose ordinate, at right angles to its axis, is 

 to the corresponding ordinate of the circle, described upon this axis 

 as a diameter, in a constant ratio, the author proves the following 

 propositions relating to this curve : — 



1. The rectangle of the abscissae is to the square of the ordinate, 

 as the square of the semiaxis major to the difference of the squares 

 of the semiaxis major and the excentricity. 



2. The distance of any point in the curve from the focus, is to 

 its distance from the directrix, as the excentricity is to the semiaxis 

 major. 



3. The sum of the distances of any point in the curve from the 

 two foci is equal to the axis major. 



By a method nearly similar to that employed for the ellipse, and 

 assuming that the hyperbola is a curve in which the rectangle of the 

 abscissas is to the square of the ordinate, as the square of the ordi- 

 nate in a circle, described upon the axis major as a diameter, is to 

 the square of the subtangent, the author shows, first, that the distance 

 of any point in the curve from the focus is to its distance from the 

 directrix, as the distance between the foci is to the axis major ; and 

 secondly, that the difference of the distances of any point in the curve 

 from the two foci is equal to the axis major. 



3. " On the diurnal Temperature of the Earth's surface, with the 

 discussion of a simple formula for ascertaining the same." By S. M. 

 Drach, Esq., F.R.A.S. Communicated by John Lee, Esq., LL.D., 

 F.R.S.* 



The author investigates the several causes which influence the 

 daily temperature of any point at the earth's surface. He employs 

 the term Thermal establishment to denote the retardation of the effects 

 of solar light caused by atmospherical conduction and by local cir- 

 cumstances, in the same manner that the term Tidal establishment 

 has been used to express the local constant by which the astronomical 

 effects on the waters of the ocean are delayed. After explaining the 

 formation of the tables and diagrams given at the end of the paper, 

 and detailing the conclusions derivable from them, the author enters 

 into a review of the perturbing causes, investigates the analytical 

 expression for the daily heat, and concludes with some observations 

 on isothermal lines, on the influence of the friction resulting from 

 the rotation of the earth about its axis, and on the agency of elec- 

 tricity. 



March 2. — 1. A paper was read, entitled, " On the laws of Indi- 

 vidual Tides at Southampton and at Ipswich." By G. B. Airy, Esq., 

 M.A., F.R.S., Astronomer Royal. 



The author gives the results of his own personal observations of 

 the tides at Southampton and at Ipswich, in both of which places 



• See Phil. Mag., S. 3. vol.xx. p. 511.— Edit. 

 Phil, Mag. S. 3. Vol. 23. No. 149. July 1843. E 



