a very different kind of instance. The loss against which the insurance was directed was death by small-pox, the premium paid was the illness and other inconvenience, and the very small risk of death, from the inoculation. The disputes which thence arose amongst writers on the subject involved the same difficulties as to the balance between certain moderate loss and contingent great loss. In the seventeenth century it seems to have been an occasional practice, before a journey into the Mediterranean, to insure against capture by Moorish pirates, with a view to secure having the ransom paid. (See, for an account of some extraordinary developments of the insurance principle, Walford's Insurance Guide and Handbook. It is not written in a very scientific spirit, but it contains much information on all matters connected with insurance.)
2 All that is meant by the above comparison is that the ideal aimed at by Communism is similar to that of Insurance. If we look at the processes by which it would be carried out, and the means for enforcing it, the matter would of course assume a very different aspect. Similarly with the action of Trades Unionism referred to in the next paragraph.
3 One of the best discussions that I have recently seen on these subjects, by a writer at once thoroughly competent and well informed, is in Mr Proctor's Chance and Luck. It appears to me however that he runs into an extreme in his denunciation not of the folly but of the dishonesty of all gambling. Surely also it is a strained use of language to speak of all lotteries as ‘unfair’ and even ‘swindling’ on the ground that the sum-total of what they distribute in prizes is less than that of what they receive in payments. The difference, in respect of information deliberately withheld and false reports wilfully spread, between most of the lotteries that have been supported, and the bubble companies which justly deserve the name of swindles, ought to prevent the same name being applied to both.
4 “A fire insurance is a simple bet between the office and the party, and a life insurance is a collection of wagers. There is something of the principle of a wager in every transaction in which the results of a future event are to bring gain or loss.” Penny Cyclopædia, under the head of Wager.
5 Encyclopédie Methodique, under the head of Tontines.
6 Of course, if we introduce considerations of Political Economy, corrections will have to be made. For one thing, every Insurance Office is, as De Morgan repeatedly insists, a Savings Bank as well as an Insurance Office. The Office invests the premiums, and can therefore afford to pay a larger sum than would otherwise be the case. Again, in the case of gambling, a large loss of capital by any one will almost necessarily involve an actual destruction of wealth; to say nothing of the fact that, practically, gambling often causes a constant transfer of wealth from productive to unproductive purposes.
7 Choice and Chance, Ed. II.[** TN: space] p. 208.
8 It was, I believe, first treated as a serious problem by Mr Galton. (See the Journal Anthrop.[ TN: space] Inst.[ TN: space] Vol. IV.[ TN: space] 1875, where a complete mathematical solution is indicated by Mr H. W. Watson.)
9 Bernoulli himself does not seem to have based his conclusions upon actual experience. But it is a noteworthy fact that the assumption with which he starts, viz.[ TN: space] that the subjective value of any small increment (dx) is inversely proportional to the sum then possessed (x), and which leads at once to the logarithmic law above mentioned, is identical with one which is now familiar enough to every psychologist. It is