The Theorem of Definite Proportions

This theorem can be usefully employed to make clearer certain arguments regarding the science of organisation (the study of the administrative apparatus, of demographic composition, etc.), giving them a plainer pattern, and also politics generally (in analyses of situations, relations of forces, in the problem of the intellectuals, etc.). It is understood that one always needs to remember how recourse to the theorem of definite proportions has a schematic and metaphorical value, that it cannot be applied mechanically, since in human aggregates the qualitative element (or the technical and intellectual ability of individual members) has a predominating function, whereas it cannot be measured mathematically. Therefore it can be said that every human aggregate has its own particular best principle of definite proportions.

The science of organisation especially can usefully refer to this theorem, and this can be seen clearly in the army. But every form of society has its own type of army and every type of army has its own principle of definite proportions, which also changes even for the different arms or specialities. There is a determined relationship between the troops, the non-commissioned officers, subalterns, superior officers, High Commands, the General Staff, etc. There is a relationship between the various arms and specialised bodies among them, etc. Any change in one part determines the need for a new balance for all, etc.

Politically the theorem can be seen applied in parties, trade unions, factories, and it can be seen how each social class has its own law of definite proportions, which varies according to the level of culture, of mental independence, spirit of initiative and sense of responsibility and of the discipline of its more backward and borderline members.

The law of definite proportions is summed up by Pantaleoni in this way in his Principles of Pure Economics: "... Bodies combine chemically only in definite proportions and each quantity of an element which exceeds the quantity required for combination with other elements, present in definite quantities, remains free; if the quantity of an element is too little in relation to the quantity of other elements present, combination only takes place to the extent to which there is sufficient quantity of the element which is present in lesser quantity than the others."

Use could be made metaphorically of this law in order to understand how a "movement" or a trend of opinion, becomes a party, that is, a political force which is effective from the point of view of the army of the governing power: precisely to the extent to which it possesses (has produced inside itself) leaders at various levels, and to the extent to which these leaders have acquired certain abilities. The historical "automatism" of certain premises (the existence of certain objective conditions) is potentialised politically by parties and by men of ability: their absence or weakness (quantitively and qualitatively) neutralises the "automatism" itself (which is therefore not automatism): the premises exist abstractly but the consequences are not realised because the human factor is lacking. Therefore parties can be said to have the task of elaborating capable leaders, they are the function of the masses which selects, develops, multiplies the necessary leaders in order that a definite social group (which is a "fixed" quantity, since it can be established how many members there are of each social group) articulates itself from confused chaos, becomes an organically predisposed political army. When a party in successive elections at the same level or at different levels (for example in pre-Hitler Germany: elections for the president of the republic, for the Reichstag, for the diets of the Länder, for the communal councils, and so on down to the factory committees), fluctuates in its mass of votes between a maximum and a minimum which appear strange and arbitrary, it can be deduced that its cadres are deficient in quantity and quality, or in quantity and not in quality (relatively), or in quality and not in quantity. A party which has many votes in local elections and less in those of greater political importance is certainly qualitatively deficient in its central leadership: it has many subordinates or at least a sufficient number, but it does not possess a High Command which is adequate for the country and for its position in the world, etc.