778 EEPOBT— 1886. 



variatious, which have been calculated by Jevoiis. But when we have taken 

 account of these regular disturbances, when we bave ' eliminated ' the ' tides/ 

 there still remain undvdations which are amenable to the principles of prob- 

 ability. It may be objected, however, that the irregular variations most important 

 to the banker depend, not on a number of small agencies, but on a few great causes, 

 such as weather destroying harvests, war, or adverse exchanges. It is submitted, 

 however, that such great causes, being themselves the results of a multiplicity of 

 varying conditions, may, to a considerable extent, and with due reservations, 

 be reduced imder the tlieory of errors. Proceeding upon this hypothesis the 

 •writer attempts to determine, by the formulje of Laplace and Poisson, the 

 amount of Bank of England notes which may be regarded as certain to remain 

 out in the hands of the pubUc. The reserve of private banks in ordinary times 

 may be similarly treated. The I'eserve of the Bank of England presents pecu- 

 liar difficulties. We may at least obtain from the rules of probability a presump- 

 tion in favour of an increased reserve. This indication is agreeable to the opinions 

 of many high authorities. But there is one argument frequently employed by 

 practical sagacity for which mathematical theory does not vouch. It seems to 

 be generally assumed that, if the volume of banking business increases, the 

 reserve should increase proportionately, if safety is to be maintained. But the 

 d priori presumption is the other way. A banker may be compared to the 

 manager of a club who undertakes to have dinner ready for auj' number of 

 members who may present themselves any evening. Suppose (as in a case with 

 which the wi'iter is conversant) the average attendance is 18; and suppose that 

 deviations in excess from that mean to the extent of 8 and 16 — that is, attendances 

 of 26 and 34 — correspond to diflerent degrees of improbability ( j^ and ~ respectively), 

 and different arrangements, such as keeping provisions in the house or sending out 

 to borrow them. Suppose, now, that two or three such clubs amalgamate. The 

 deviations (of probability ~ and j~) for which provision as before must be made 

 will not be two or three times the deviations found for the single club. The 

 theoretical ratio will be not 2 or 3, but the square root of 2 or 3. Similarly 

 if the liabilities of the Bank of Saturn should double, while the ratio between the 

 liabilities to the reserve should diminish from 52 to 41 per cent, (as here in Eng- 

 land between 1844 and 1873), this circumstance ^jer se would not there cause any 

 alarm. The same principle is applicable to the theory of banker's balances. If 

 several Saturnian banks should be subordinated to one bank of banks, with whom 

 they all keep their reserves, in estimating the safety of the system it would be 

 improper to deduct en bloc the balances of the bankers, and to be alarmed if the 

 remainder was inadequate to meet the liabilities of the prime bank, or even less 

 than nothing. A smaller reserve is required for a consolidated system, not only 

 in so far as the demands upon one bank correspond to payments into another — the 

 principle of clearing which is admitted — but also, what is less evident, in so far as 

 the demands upon one bank are independent of the demands upon another. How 

 far this condition is ftilfilled, or how far ' other things are equal,' in particular 

 whether the presumption raised by increased volume is counteracted by the in- 

 creased rapidity of drains upon the reserve, the writer does not pretend to decide. 

 The mathematical method supplies to practical men rather general ideas than exact 

 propositions. 



II. The mathematical theory of exchange, constructed by Gossen, Jevons, 

 and Walras, applies to the money market, at least as well as to the other bargains, 

 which are the subject of economics. From the abstract point of view may be dis- 

 cerned an unobvious, perhaps unimportant, reason why the money market should be 

 particularly sensitive, more so than the labour market. In an" ideal market, con- 

 sisting in its simplest type of two sets of dealers and two kinds of commodities 

 exchanged, each individual belonging to one of the sets should be free to enter 

 into contract at the same time with any number of dealers belonging to the other 

 set. But the workman cannot, or does not often, at the same time contract with 

 different employers — sell on the same day this week's work to one employer, and 

 next week's work to another. Accordingly, if the balance of supply and demand 

 should be turning in a sense unfavourable to the workman, a new equilibrium will 



