294 EEPORT— 1887. 



used in modern industry, by way of reserve, to meet tlie residues of claims 

 not mutually compensated. It is shown by the present writer in his 

 paper on TJie Atathematical Theory of BanJcing ' that, theoretically and 

 abstractedly, reserves tend to vary as the square root of the volume of 

 transactions which they support. The reserve of material money and 

 the mass of credit transactions are to each other, as Mr. Gififen says, as 

 the little weight and the big weight at the ends of the unequal arms of 

 a lever. But it is a lever of a very peculiar mechanism, such that, 

 when you increase the big weight, you lengthen the long arm. It will 

 be understood, of course, that this doctrine is quite abstract and ideal ; 

 related to banking business very much as the ' quantity theory ' to hard- 

 cash transactions — ' the most elementary proposition,' as Mill says of 

 the latter theory, and without which ' we should have no key to any of 

 the others.' 



The proper factor, therefore, is no longer P. The mildest expression 

 for the correction now required is of the form (1 — K)P + KJv'P, 

 where J is a new and probably unascertainable constant. That is 

 theoretically - the sort of ratio by which, when the volume of trade in- 

 creases, the mass of metallic money should be increased, in order to drive 

 the trade at an unaltered level of price. 



Now introduce the attribute that the ratio of credit to hard cash 

 varies with time, and the varying ratio of the mass of metal to the volume 

 of transactions, as we have good reason to believe.^ Superadd the 

 circumstance, which we have no reason to deny, that the rapidity of 

 circulation also varies, and it is evident that the investigation which we 

 have attempted is blocked by insurmountable statistical difficulties. 



We might get a little farther no doubt if we assume an additional 

 datum, R, the ratio of gold in reserve to gold in actual circulation ; then, 

 with the help of P and K and R, as it were rail off from the indvistrial 

 world a zone of hard-cash transactions to which the abstract formula of 

 the text-books is applicable. This method has been pursued by Professor 

 Neumann Spallart and Dr. F. Krai in the elaborate monograph OeJdwert 

 unci Preisbeioegung.* It certainly seems possible by this method^ to explain 

 the fact, if not to measure the magnitude, of a rise or fall of general 

 prices ; to predict the direction of the change, whether positive or 



' Report of the British Association, 1886. 



^ K and C being still supposed constant. 



' Cf. Giffen, Stock Exchange Securities, ' To give it [the abstract theory] 

 validity, it must be assumed that a scarcity of money produces no expedients for 

 economising money, and that an abundance of money does not lead to want of 

 economy, which can hardly ever be the actual condition of life.' 



■* Staatswissensohaftl. Studien, n. v. Dr. Ludwig, Elster, Jena, 1887. 



* The modest hope of explaining accomplished facts is not encouraged by Dr. 

 Krai's success. For a priori be finds that the store of gold in Germanj- during the 

 last few years has been fully adequate to the work which it has had to do — account 

 being taken of rapidity of circulation and the amount of credit transactions. 

 There have been no symptoms of a ' Geldmangel,' that is to say (see p. 262, top) no 

 reason to expect a rise of the purchasing power of money, a general fall in prices. 

 Yet a posteriori it seems to be admitted that there has been such a fall of prices. 

 That this fall has originated 'auf Seiten der Waren,' that it is due to the development 

 of industry rather than the introduction of the ' Goldwahrung ' into Germany, may 

 be a fact. But that fact does not seem to annul the right we have to expect a 

 correspondence between the two lines of investigation ; namely (1) the comparison 

 between the supply of money and the amount required in order that the level of 

 prices may be steady ; and (2) the observed level of prices. 



