16. There still remains a serious, and highly interesting speculative consideration. In the above argument we took it for granted, in calculating the chance alternative, that only _one_ of the 10,000 possible values was favourable; that is, we took it for granted that the ratio π was the only one whose claims, so to say, were before the court. But it is clear that if we had obtained just double this ratio the result would have been of similar significance, for it would have been simply the ratio of the circumference to the diameter. In fact, Mr Smyth's selected ratio,--the height to twice the breadth of the base as compared with the diameter to the circumference,--is obviously only one of a plurality of ratios. Again; if the measured results had shown that the ratio of the height to one side of the base was 1 : sqrt{2} (i.e. that of a side to a diagonal of a square) or 1 : sqrt{3} (i.e. that of a side to a diagonal of a cube) would not such results equally show evidence of design? Proceeding in this way, we might suggest one known mathematical ratio after another until most of the 10,000 supposed possible values had been taken into account. We might then argue thus: since almost every possible height of the pyramid would correspond to _some_ mathematical ratio, a builder, ignorant of them all alike, would be not at all unlikely to stumble upon one or other of them: why then attribute design to him in one case rather than another? 17. The answer to this objection has been already hinted at. Everything turns upon the _conventional_ estimate of one result as compared with another. Revert, for simplicity to the coins. Ten heads is just as likely as alternate heads and tails, or five heads followed by five tails; or, in fact, as any one of the remaining 1023 possible cases. But universal convention has picked out a run of ten as being remarkable. Here, of course, the convention seems a very natural and indeed inevitable one, but in other cases it is wholly arbitrary. For instance, in cards, "queen of spades and knave of diamonds" is exactly as uncommon as any other such pair: moreover, till _bezique_ was introduced it offered presumably no superior interest over any other specified pair. But during the time when that game was very popular this combination was brought into the category of coincidences in which interest was felt; and, given dishonesty amongst the players, its chance of being designed stood at once on a much better footing.[6]