facilities afforded by “time-bargains” to operators who have a little money, just sufficient to enable them to keep afloat as speculators in fair weather. The first serious disturbance that violently agitates prices sweeps them away in a shoal. The question which a sensible speculator will ask himself before he begins to operate is, What are the risks incurred of losing his all at one stroke? De Morgan, in his book on probabilities, says in Chapter V., on the risks of loss or gain, “A man should not hazard his all on any terms; but in ventures the loss of one of which would not be felt, we may suppose the venturer able to make a large number of the same kind; in which case the common notions of mankind reinforced by the results of theory, tell us that the sum risked must be only such a proportion of the possible gain as the mathematical probability of gaining it is of unity. For instance: suppose I am to receive a shilling if a die, yet to be thrown, give an ace; in the long run, an ace will occur one time out of six, or I shall lose five times for every time which I gain. I must, therefore, make one gain compensate the outlay of six ventures, or one-sixth of a shilling is what I may give for the prospect, one time with another. But one-sixth is the probability of throwing the ace. _Principle_—Multiply the sum to be gained by the fraction which expresses the chance of gaining it, and the result is the greatest sum which should be given for the chance.”[3] “A man should not hazard his all on any terms.” Does a man who enters upon a career of speculation take the trouble to consider at starting whether or not his first operation places him in a position in which he hazards his all? There is not probably one speculator in a hundred who ever thinks of it at all. We will suppose a man to be worth £200 in cash as his all, applicable to the payment; of losses. It may safely be stated that numbers of speculators open accounts with a less sum, in fact a considerable proportion of speculative operations are entered upon in reality without any funds at all; misfortunes in other vocations being frequently followed by gambling in the Stock markets. A speculator with £200 to pay losses with is in this position if he buys, for instance, for the rise £5,000 of any English railway stock; a fall of 5 per cent., which even in two or three days is nothing very extraordinary, carries him £50 “under water.” What can he reckon upon on the other side, by keeping the account open, that is a mathematical certainty like the occurrence of an ace one time out of six in the long run in throwing the die? If he be exposed to such a loss at any moment as that mentioned, the risk is an absurd one to run if there is not at least an equal chance of a similar rise, and several times £250 in reserve. But all experienced in Stock Exchange fluctuations know that upward movements are, as a rule, gradual, a rise of 1 per cent.