On the Intimate Structure of Crystals. 305 



have jiist studied. Thus comparing Kopp's volumes in the two cases 

 we have : 



Cuprite (Cu a O) m.v., 24-77, deduct Cu 2 (14-1) = 10-67 (O). 



Tenorite (CuO) m.v., 12*67, Cu (7-05) = 5-62 (O). 



Thus by Kopp's method the volume of oxygen in cuprous oxide is 

 nearly twice that which it possesses in cupric t oxide, and as this is far 

 from being an isolated instance of this relation of the volumes of 

 oxygen in related compounds, Kopp very naturally came to the con- 

 clusion that the volume of oxygen varies in different compounds by 

 some multiple, and since he found it exhibiting a still less value in 

 some other cases, he imagined it might be reduced to one-half or one- 

 quarter of its normal value. In the present instance there is no need 

 to have recourse to such an explanation. In the crystalline structure 

 of cuprite open spaces exist, sufficiently large and numerous to contain 

 one more oxygen atom than the molecule possesses ; in this respect it 

 might be said that the volume of oxygen in cuprite is double that it 

 has in tennorite, but this would be a very illogical way of stating the 

 facts ; the vacant space is no more the property of the oxygen than of 

 the copper, and, if our conclusions are correct, the truer view would be 

 that in both oxides the volume of oxygen is identical, or very nearly 

 so, and that the apparent difference in volume is a natural result of 

 difference in configuration of the crystalline structure. 



Fluorspar, CaF 2 :m.v. 78; sp. gr. 3*15 to 3'18, mean (taken) 

 3-165 ;] m.v. 24-645 . ty (m.v. x 6) = 5-288, the edge of the cube of 

 reference. 



This mineral is of importance to our investigation, as it affords an 

 opportunity of obtaining a value for the volume of fluorine ; but we 

 are confronted by a difficulty at the outset, since the diameter of the 

 atom of calcium has been calculated from a single instance only, and 

 that a not very promising one, viz., calcium oxide ; it was concluded to 

 be 2 "2 7. If now we place an atom of calcium in octahedral contact 

 with five others about the centre of the cube of reference, we shall find 

 that it is too large to fit] in, the length of a tetragonal axis that it 

 would appropriate is 2*739, while the length on the axis from the 

 centre to the surface of the cube is only 2 '644; the atom would conse- 

 quently protrude for a distance of 0'095, and the greatest possible 

 diameter which it can possess to bring its surface just flush with the 

 face of the cube is 2-19. 



We may accept this provisionally as the approximate value for the 

 diameter of an atom of calcium ; it differs from that previously obtained 

 by .0-08. 



Since the outer surface of the atom of calcium contained within the 

 cube is in contact with the face of the cube, it follows that it also 

 touches the atom of calcium which lies outside the cube, and completes 



