50 Prof. Cayley on the Projection of the Ellipsoid. 



Magnesium, by the combustion of \\ grain, or 1 equivalent, 

 will raise the temperature of 1000 grains of water 19°*2 F. 



This is the greatest amount of heat produced by an equivalent 

 of any substance with which we are acquainted. 



Potassium and sodium, hitherto the largest heat-evolvers 

 known, produce only a rise of 17°* 5 F. in 1000 grains of water 

 by the combustion of one equivalent, oxygen =1. Magnesium 

 produces 19°'2 F. 



The quantity of heat evolved by the combination of magne- 

 sium with chlorine is also greater than that of any other sub- 

 stance. By dissolving a metal in hydrochloric acid, the chlorine 

 unites with the metal, and decomposition of the acid of course 

 takes place, the hydrogen escaping. Taking, therefore, the rise 

 of temperature caused by the dissolving, and adding the amount 

 of heat absorbed by the decomposition, we get the heat actually 

 generated by the combination of the chlorine with the metal. 



In this way Ij find that when one equivalent of magnesium, 

 oxygen = 1, combines with chlorine there is heat produced suffi- 

 cient to raise the temperature of 1000 grains of water 25°*2 F. 

 One equivalent of zinc, by combining with chlorine, will evolve 

 heat sufficient to raise the same quantity of water 11°'25 F., 

 and potassium 22°"9 F. 



Parsonstown, June 1865. 



VII. Note on the Projection of the Ellipsoid. 

 By Professor Cayley, F.R.S* 



CONSIDER an ellipsoid, situate any way whatever in regard 

 to the eye and the plane of the picture ; the apparent con- 

 tour of the ellipsoid is an ellipse, the intersection of the plane of 

 the picture by the tangent cone having the eye for vertex ; this 

 cone touches the ellipsoid along a plane curve (the intersection 

 of the ellipsoid by the polar plane of the eye), which may be 

 called the contour section ; and the apparent contour is thus the 

 projection of the contour section. Consider any other plane 

 section ; the projection thereof has double contact (real or ima- 

 ginary) with the projection of the contour section : the common 

 tangents are the intersections with the plane of the picture of 

 the tangent planes of the tangent cone which pass through the 

 pole of the section ; or, what is the same thing, they are the tan- 

 gents to the projection of the contour section, or to the projec- 

 tion of the section, from the point which is the projection of the 

 pole of the section. The projection of the pole lies in the line 

 which is the projection of the diameter conjugate to the plane of 



* Communicated by the Author. 



