3. Of course this conventional estimate is nothing different in kind from that which may attach to _any_ order or succession. Ten heads in succession is intrinsically or objectively indistinguishable in character from alternate heads and tails, or seven heads and three tails, &c. Its distinction only consists in its almost universal acceptance as remarkable. 4. _Our Inheritance in the Great Pyramid_, Ed. III. 1877. 5. Made in _Nature_ (Jan. 24, 1878) by Mr J. G. Jackson. It must be remarked that Mr Smyth's alternative statement of his case leads up to that explanation:--"The vertical height of the great pyramid is the radius of a theoretical circle the length of whose curved circumference is exactly equal to the sum of the lengths of the four straight sides of the actual and practical square base." As regards the alternatives of chance and design, here, it must be remembered in justice to Mr Smyth's argument that the antithesis he admits to chance is not human, but divine design. 6. See Cournot, _Essai sur les fondements de nos connaissances_. Vol. I. p. 71. 7. It deserves notice that considerations of this kind have found their way into the Law Courts though of course without any attempt at numerical valuation. Thus, in the celebrated De Ros trial, in so far as the evidence was indirect, one main ground of suspicion seems to have been that Lord De Ros, when dealing at whist, obtained far more court cards than chance could be expected to assign him; and that in consequence his average gains for several years in succession were unusually large. The counsel for the defence urged that still larger gains had been secured by other players without suspicion of unfairness,--(I cannot find that it was explained over how large an area of experience these instances had been sought; nor how far the magnitude of the stakes, as distinguished from the number of successes, accounted for that of the actual gains),--and that large allowance must be made for skill where the actual gains were computed. (See the _Times_' report, Feb. 11, 1837.) 8. _Metretike_. At the end of this volume will be found a useful list of a number of other publications by the same author on allied topics.