NOTICES AND ABSTE>ACTS 



OP 



MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. 



MATHEMATICS AND PHYSICS. 

 Mathematics. 



Oil Plane Stigmaiics. Bij Alexan;)ee J. Ellis, F.E.S. 



This paper is a continuation of that read at the Bath Meeting- (Report of tlie Brit. 

 Assoc. 1864, Trans, of Sections, p. 2). By means of diagrams the meaning of the 

 stigmatic line, stigmatic involution, stigniatic homography, and the stigmatic circle 

 was illustrated, and these were sho-wni to include the straight line and circle of 

 Descartes, and the involution and homography of C'hasles, as particular cases. The 

 imaginary points of intersection of a stright line and circle, the imaginary double 

 points, and imaginary double raj's of an involution and homography, &c. were, for 

 the first time, publicly exhibited on paper. And an attempt was thus made to show 

 that the principle of stigniatics, as explained in the papers cited, affords a complete 

 solution of the problem of the geometrical signification of iniaginaries in the 

 geometries of Descartes and Chasles, and establishes an imbroken agreement be- 

 tween ordinary algebra and plane geometrj'. 



On Practical Hyjisometr}/. Bif Alexander J. Ellis, F.P.S. 



If the heights of the barometer be B, b inches, the temperatures of the air A, a 

 degrees Fahr., and the temperatures of the mercury M, in degrees Fahr. at the 

 lower and upper stations respectively, then, for all British heights, the ditference of 

 the level of the two stations is 



r B-&)x52400 _g, .,. .-i^ A + «+830 



English feet to the nearest unit, with the same accuracy as by Laplace's complete 

 formula. Beyond the British isles, small corrections for the alteration of gravity 

 in latitude and on the vertical, have to be made, but when aneroid barometers 

 are used, these corrections may be neglected, as being- much inferior to the pro- 

 bable instrumental error. The heights must be taken in sections not exceeding 

 4000 feet eacli, both on account of the construction of the formula, and of tlie un- 

 known law of variation of temperature. When the decrease of the temperature of 

 the air does not vary nearly as the decrease of the height of the barometer, or 

 the observations at both stations, Avhen distant, are not simultaneous, or the two 

 stations are not nearly north-east and south-west of each other, the results of 

 barometric hypsometry must be received with great caution. 



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