146 M. F. M. Osborne deductions wIth observations on prices The fundamental facts, as sumptions, and critical points in the derivation of the properties of this ensemble, are given in the numbered paragraphs below These facts and assumptions are sufficient, but not necessary to obtain agreement of theory with observation 1. Prees move in discrete unIts of 1 of a dollar From this it immedate follows that the natural logarithms of prices also move in discrete unIts, approxi mately 1/(8xprce) We shall call loge-unts ratio units A ratio unt of +100 orresponds to a ratio of +2 817/1 We point out for the convenience of the reader, that percentage changes of less than +15 per cent, expressed as fractions from unIty, are very nearly natural logarithms of the same ratio Thus logr(100+15)/1001≈+015 2. There 1s a finIte, Integral number of transactions, or decisions, per unIt me This number may vary from zero to a thousand or more per day for a single stock Hence the decisions also are separated by discrete units of time Observationally, the number of decisions per day may be estimated to be not more than the volume in round lots It may be less, for there may be more than one round lot per trade 3. The stimulus of price in dollars, and the subjective sensation of value in the mind of the trader or investor, are related in accordance with the weber-Fechner aw As this assumption has engendered some controversy, let us specify pre- Isely its meanng The Weber-Fechner law states that equal ratios of physical tumulus, for example, of sound frequency in vibrations /second, or of lght or sound intensty in watts per unt area, correspond to equal intervals of subgectue ensation, such as pitch, bnghtness, or noise The value of a subjective sensation, lke absolute position in physical space, Is not measurable, but changes or differences In sensation are, since by experiment they can be equated and reproduced thus fulfilling the criteria of measurablity The Weber- Fechner law Is best applicable when there is a single dor nant, or prmary stimulus Thus in comparing two sounds, or two light es, the frequency distrbution(pitch or color) must be nearly the same, or the errors of comparison are large Thus, in assuming the Weber Fechner law, we are relegating earnings, dividends, management, etc and their future outlook to postions of secondary Importance These factors may be Important, Just as the intermolecular force law 1s Important In molecular problems, In determining departures from the steady state For determining the steady state, we ignore them in the molecular problem and we ignore their analogs in this problem also The hypothesis that price and value are related by the Weber-Fechner law can be reached Inductively from the raw data by the following rather sImple-minded argument Let us imagine that a statistician, trained perhaps in astronomy and totally unfamiliar wnth finance, Is handed a page of the Wall Street Journal containing the n y Stock Exchange