Page:Proceedings of the Royal Society of London Vol 69.djvu/321

Rh have just 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