Finally, it may be asked whether, in the case of horses having unequal chances, it is possible that wagers can be so proportioned (just odds being given and taken), that, as in the former case, a person backing or287 laying against all the four shall neither gain nor lose. It is so. All that is necessary is, that the sum actually pending about each horse shall be the same. Thus, in the preceding case, if the wagers 9l. to 6l., 10l. to 5l., 12l. to 3l., and 14l. to 1l., are either laid or taken by the same person, he will neither gain nor lose by the event, whatever it may be. And therefore, if unfair odds are laid or taken about all the horses, in such a manner that the amounts pending on the several horses are equal (or nearly so), the unfair bettor must win by the result. Say, for instance, that instead of the above odds, he lays 8l. to 6l., 9l. to 5l., 11l. to 3l. and 13l. to 1l., against the four horses respectively; it will be found that he must win 1l. Or if he takes the odds 18l. to 11l., 20l. to 9l., 24l. to 5l., and 28l. to 1l. (the just odds being 18l. to 12l., 20l. to 10l., 24l. to 6l., and 28l. to 2l. respectively), he will win 1l. by the race. So that, by giving or taking such odds to a sufficiently great amount, a bettor would be certain of pocketing a large sum, whatever the event of a given race might be.

a man who bets on a race must risk his money, unless he can succeed in taking unfair advantages over those with whom he bets. My readers will conceive how small must be the chance that an unpractised bettor will gain anything but dearly-bought experience by speculating on horse-races. I would recommend those who are tempted to hold another opinion to follow the plan suggested by Thackeray in a similar case—to take a good look at professional and288 practised betting-men, and to decide ‘which of those men they are most likely to get the better of’ in turf transactions Two considerations must have caused Scheer the gravest possible anxiety.Two considerations.

(From Chambers’s Journal, July 1869.)
SQUARING THE CIRCLE.
There must be a singular charm about insoluble problems, since there are never wanting persons who are willing to attack them. I doubt not that at this moment there are persons who are devoting their energies to Squaring the Circle, in the full belief that important advantages would accrue to science—and possibly a considerable pecuniary profit to themselves—if they could succeed in solving it. Quite recently, applications have been made to the Paris Academy of Sciences, to ascertain what was the amount which that body was authorised to pay over to anyone who should square the circle. So seriously, indeed, was the secretary annoyed by applications of this sort, that it was found necessary to announce in the daily journals that not only was the Academy not authorised to pay any sum at all, but that it had determined never to give the least attention to those who fancied they had mastered the famous problem.