192 Mr. Warrington on the Change of 



Rj sin (8 2 — e 3 ) = a (tan J 3 — tan 1 2 ) 

 R 2 sin (6 3 — e t ) = a (tan A 5,- tan J 3 ) 

 R 3 sin {e 1 — 6 2 ) = a (tan ^ 2 - tan £0,). 

 By addition of these, we have 

 R T sin (6 2 — e 3 ) + R 2 sin(e 3 -Oj) + R 3 sin (©i — ©a) = °» 

 which is the criterion of the circle through Rj 8j , R 2 6 2 , 

 R 3 6 3 passing through the polar origin, or, in this case, the 

 focus of the parabola. 



It may not be irrelevant to remark, that the geometrical 

 property expressed by the values of e„ 6 2 , 6 3 in terms of 

 0„ # 2 , 9 is the familiar one found in all works on the conic 

 sections ; as in Hutton's Course, for instance, at vol.ii. pp. 1 1 1, 

 135, 147 of the 11th edition, and nearly in the same places 

 in the edition now printing. 



Lines drawn to the focus of a conic section from the intersec- 

 tion of two tangents, bisects the angle formed by the radii vector es 

 drawn to the points of contact. 



The property in reference to the other conic sections is 

 deducible in the same way, as will be obvious on forming the 

 equations Of the tangent in each of them, and which are 

 put down here for the ellipse and hyperbola : — 



r {cos (0-0J0 + e cos } = a (1-e 2 ), 

 and r {cos (0— 0,)0— e cos } = a (e 2 — 1). 



Many other properties may be obtained by this method 

 with great simplicity and elegance; but the method being 

 once pointed out, the details are too elementary to require 

 further notice in this place. 

 Royal Military Academy, 

 July 5, 1842. 



XXXIII. On the Change of Colour in the Biniodide of Mer- 

 cury. By Robert Warington, Esq., Secretary to the 

 Chemical Society *. 



TT is well known that when a solution of the iodide of po- 

 ■*■ tassium is added to a solution of the bichloride or perni- 

 trate of mercury, a yellow precipitate, passing rapidly to 

 a scarlet, is formed ; this is the biniodide of mercury. It is 

 soluble in an excess of either of the agents employed for its 

 production, and if this act of solution be assisted by heat, the 

 biniodide may be obtained, as the solution cools in fine scarlet 

 crystals, having the form of the octohedron with the square 

 base, or its modifications. 



* Communicated by the Chemical Society, having been read Feb. 1, 

 1842. Some of the facts related in this paper had been previously ob- 

 served by Mr. Talbot, and described by him in Phil. Mag. Third Series, 

 vol. ix. p. 2. — Edit. 



