8$ Mr. J. Stevenson on the Chemical and 



X cos \ Y cos fl Z cos v 



a -f cos a. d+ cos j3 d+ cos y 



*(rfD^A)(S (ilDl+miD2+niI)3+A)+ - + -) = °- 



Hence the first part of the theorem follows as in § 1. 

 The second part is proved as in § 2, if we notice that the 

 projection of the intersection of any two planes passes through 

 the projection of the intersection of the lines in which these 

 two planes meet the plane ABC. 



6. Similarly, the projection of the line of intersection 

 of the zone [U Y W j with the plane A' B' C is the line 

 XJ£ + Vrj + Wf = 0, and the projection of the normal through 



£ v K 

 to the face (u v iv) passes through = = — . where 



v U V ic 



(d + cosa)f =Xacos AOA' &.c. ; the vertices of the triangle 

 of reference being the projections of the poles of (10 0), 

 (010), (0 01). 



7. The most interesting cases are those in which d=0, 1, 

 or cc , corresponding to a gnomonic, stereographic, or ortho- 

 gonal projection. It may be readily shown that the theorems 

 still hold in these special cases. 



2 Bryn Teg Terrace, Bangor, North Wales. 



VII. The Chemical and Geological History of the Atmosphere, 



hfytt By John Stevenson, M.A., F.I.C* 



V) ^ ill. 



Variations in the Amount of Atmospheric Carbonic Acid, with 

 special reference to the subject of Geological Climate. 



IN the two former articles of this series (Phil. Mag. 

 Sept. 1900, p. 312; Oct. 1900, p. 399, and Oct. 1902, 

 p. 435), in which questions relating to the history of free 

 oxygen and the composition and extent of the primitive 

 atmosphere were discussed, we concluded that the atmosphere 

 was almost certainly many times more extensive in very pri- 

 mitive times than it is now; that it probably contained no 

 free oxygen; that it most probably contained very large quan- 

 tities of carbonic acid ; and that it possibly may have con- 

 tained large quantities of hydrogen and hydrocarbon gases 

 either in addition to, or instead of, the carbonic acid gas. 

 Assuming that the latter were the principal gases originally 



* Comrnmiicated by the Author. 



