Cherbuliez could not provide an adequate definition of profit, because he has provided no analysis of surplus value.
“Now the rate of profit ought to be explained. But once again nothing emerges except the vulgar definition.” (p 374)
So, just as Cherbuliez defines profit as the excess of value over the cost of production, so he defines the rate of profit as this profit as a proportion of the advanced capital.
“The distorted conception and bungling application of the approximately correct distinction between the elements of capital, and the vague idea that profit and rate of profit are directly connected with the ratio of these elements to one another, only lead to a repetition of the generally known phrases in a rather doctrinaire fashion, in fact merely to a statement that profit and rate of profit exist without, however, anything being said about their nature.” (p 374)
Marx sets out Cherbuliez' algebraic formula for these relations.
““Let P be the aggregate product of a given period of time, C the capital invested, π the profit, r the ratio of profit to capital (rate), c the capital used up, then P–c=π, r=π/C therefore Cr=π. Therefore P–c=Cr; therefore r=P–c/C” (loc. cit., p. 70, Note 1).” (p 374)
This only sets out algebraically what has been stated verbally that profit is the excess of value over cost of production, and rate of profit is profit as a proportion of advanced capital. In fact, profit, under capitalism, is not the excess of value over cost of production, because commodities do not sell at their values, but at their price of production. The price of production is the cost of production plus the average profit, calculated on the advanced capital.
When Cherbuliez talks about the difference between consumed and unconsumed capital, he is really talking about the fixed capital, as opposed to the circulating capital. Surplus value is created in production, but is realised, as profit, in circulation. Whatever happens in circulation cannot change the reality of what happened in the production that precedes it. The average profit that attaches to the output of different capitals, according to the size of the advanced capital, is a consequence of what happens in the sphere of circulation. In other words, it is competition between capitals, competition that exists in the sphere of circulation, to obtain the highest annual rate of profit, which results in capital migrating towards the most profitable spheres, and thereby leads to the development of the average rate of profit. But, that does not change the fact that the total mass of surplus value available to be distributed in this way was produced in the production process.
“Surplus-value is antecedent to circulation and no matter how much the differences arising out of circulation affect the rate of profit, they have nothing to do with the origin of profit.” (p 375)
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