Page:Proceedings of the Royal Society of London Vol 60.djvu/537

502 frequency it is seen that they coincide with the diagonal from the O/O corner; also th at the entries of minimum frequency are disposed symmetrically on either side of th at diagonal and converge towards the same corner. Consequently, the existence of spurious correlation is manifest here. If B he the constant, and A and 0 the variables, the general results will of course be the same.

Secondly, let both A and B be constant and equal to I, and C the only variable ; then there are only three possible combinations of A/C and B/C. In one of them both values are equal to I, in another to I/II, and in the th ird to I/III, all of which lie along the diagonal from (0, O), and thus testify to intimate correlation.

Lastly, let C be the only constant and equal to 1. Then A/C, B/C, become A and B, and the table of frequency of their various combinations is th at shown in Table I and by the large figures in fig. 1, whose symmetrical disposition in all directions proves that there is no correlation.

In presenting, as desired by the Committee, Professor Sollas’s reporton the attempts to ascertain, by boring, the structure of the atoll of Funafuti and on other investigations simultaneously undertaken, I avail myself of the opportunity of expressing the gratitude which is felt by its members to our friends in New South Wales, who have given such real and substantial help, especially by the loan of machinery and skilled wmrkmen, in putting the project into execution ; and among’ them chiefly to Professor Anderson Stuart (who has been practically another secretary in Australia), Professor Edgeworth David, Mr. W. H. J. Slee (Chief Inspector of Mines), and Sir Saul Samuel (the Agent-General of the Colony in England). I shall venture also to acknowledge gratefully the services of Captain Field and the officers of H.M.S. ** Penguin,5' and the unstinted labour which has been given by Mr. W. W. W atts, F.G.S., our Secretary in London, in carrying out our plans. In conclusion, may I express, speaking for myself, my earnest hope that another attempt will be made to determine the true structure of an atoll. I think, however, that our experience on this occasion shows that the attempt can be