M. F. M. Osborne argue that in equation(2)the symbol E for estimate could be dropped since in such buying and selling the decisive estimates are definitive of actual value Or to put It differently, If enough people decide and act on the belief that something is valuable it Is valuable at that time 5. The above contains a critical point n our argument, Ie, the most probable ondition under which a transaction 1s recorded is given by equation(2) In words, this states that the contestants are unlkely to trade unless there is equalty of opportunIty to profit, w hether an indivdual happens at the moment to be a buyer or a seller, of stock, or of money The Exchanges are certainly governed but we also feel that this condtion must have obtained prior to any regulation, since every buyer, once having consummated his trade now finds himself as a potential seller in the virtual postion of his opponent wIth whom he was so recently hagghng The converse sltuation apples to the seller, now a potential buyer Under these circumstances It 1s difficult to see how trading could persist unless pnces moved in such a way that equalty of op- tunIty most probably prevailed, and equation(2)expresses this quantitatively perhaps less as an assumption than as a consequence of assumptions 3 and 4 We now ask, what Is the effect of the condition(2)on the distribution function ultimately developed for Alog P? Our argument follows closely one originally given by giBBs for an ensemble of molecules in equilbrium The actual distrbution function Is determined by the conditions of maxI- mum probabilIty (reference 3, p 79) 6. Assuming the decisions for each transaction in the sequence of transactions In a single stock are made independently (n the probabilty sense), then under fairly general condItions outlined below, we can expect that the distnbution func tion for y()logP(t+T/Po() will be normal, of zero mean wIth a dispersion or( which increases as the square root of the number of transactiong If these numbers of transactions (the volume )are fairly unIformly distributed in time, then or( will increase as the square root of the time interval, Ie, oy() will be of the form oVT, where a is the dispersion at the end of unIt time T. Mathematically we may express this as follows Suppose we have kin dependent random varables y(),飞=1,,配, y(o)=A. logo P=log(P(t+10)/P(+(1-1 8)J where P(e) Is the priee of a single stock at time t and 8 is the small time interval between trades t Assume that each y(i) has the same dispersion o(i)=o, then after k trades, a time T= k8 lat define Y() Y()=F(6)=∑=iy()=logP(t+)/P()=4logP() e8 1, g In parentheses will refer to independent random variables In a time As subscripts, 1, wlll refer to independent varables at the same rent stocks