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false. In fact, the very meanings assigned to ${\displaystyle x}$ and ${\displaystyle y}$, as being a number of cubic feet and a number of pounds sterling, are indifferent. During the mathematical investigation we are, in fact, merely considering the properties of this correlation between a pair of variable numbers ${\displaystyle x}$ and ${\displaystyle y}$. Our results will apply equally well, if we interpret ${\displaystyle y}$ to mean a number of fishermen and ${\displaystyle x}$ the number of fish caught, so that the assumed law is that on the average each fisherman catches twenty fish. The mathematical certainty of the investigation only attaches to the results considered as giving properties of the correlation ${\displaystyle 20y=x}$ between the variable pair of numbers ${\displaystyle x}$ and ${\displaystyle y}$. There is no mathematical certainty whatever about the cost of the actual building of any house. The law is not quite true and the result it gives will not be quite accurate. In fact, it may well be hopelessly wrong.

Now all this no doubt seems very obvious. But in truth with more complicated instances there is no more common error than to assume that, because prolonged and accurate mathematical calculations have been made, the application of the result to some fact of nature is absolutely certain. The conclusion of no argument can be more certain than the assumptions from which it starts. All mathematical calculations about the course of