SECTIONAL TRANSACTIONS.— J. 489 



where A is a positive constant, t is time and x and y, when positive, are the 

 intensities of hate in the two persons and, when negative, the intensities of 

 love. The solution of (i) is 



X = A^ + Be**, y = A^- Be-*' (2) 



where A and B are constants ; so that, as t becomes large, x and y both 

 increase with the same sign. The point a; = o, y = o is a point of balance ; 

 but the balance is unstable. The instinctive drift may lead in one or other 

 of two opposite directions. 



The expression can be made more lifelike by the introduction of positive 

 fatigue-and-expense coefficients a and of positive or negative grievances g 

 so that 



dx/dt = ki2y — XiX + gx, dy/dt = ki^x — a^j + ^2 (3) 



The terms in a have a stabilising effect ; so that instability only occurs if 



^12 • ^21 > «i a2 (4) 



There are still two opposite kinds of drift. For nations, the positive infinity 



may be called ' war ' ; and we have to find a name for the negative infinity, 



which is obviously not tranquil exclusiveness, but may be called ' united 



organisation,' or ' close co-operation.' 



Foreign trade is the commonest form of co-operation between nations. 



Alfred Marshall in his discussion of foreign trade, when near to zero, gave 



an argument closely related to equations (3). Accordingly, on looking for 



something objectively measureable which might serve to represent x and 



y, the author has formed two statistics of ' threats minus co-operation.' 



One is 



, / 1 ^- \ 1 r (warlike expenditure) ] 



<]> = (population) logio i ,r . f , —\ \ 



I (foreign trade) . (constant)) 



the constant being adjusted to make ip zero for an average nation in the year 

 1926. 



So far it appears that assumptions of type (3) are a credible approximation 

 to actuality. Accordingly they have been generalised for n nations thus 

 , i = n 



-jj = 8i + S kij Xj (t = I, 2, 3 . . . n) 



at ;■ = I 



and the criterion of stability has been deduced. In many cases there is 

 an instinctive barrier separating two regions of opposite drift ; the barrier 

 goes through a point of balance, the position of which depends on the 

 grievances g. 



The relation between g and objective facts is very peculiar. A halting 

 apology may be received as though it were a fresh insult. 



The practical conclusion is that the traditional policy of the balance of 

 power is now futile, because the balance is unstable. To bring the point 

 (x, y) into the region where the instinctive drift goes towards more co- 

 operation, two actions can be taken : (i) the barrier can be heaved to the 

 positive side by abolishing grievances g, and (ii) the point {x, y) can be 

 heaved to the negative side by decreasing threats. Neither of these actions 

 is instinctive ; both would require national efforts of will. 



Miss D. Gandine-Stanton. — An examination of behaviour in attempting 

 difficult tasks (12.15). 



Difficult tests, problems and puzzles have been presented to several 

 groups of children. About six hundred individuals have been examined, 



R 2 



