But speaking of the higher forces as subordinating the lower, suggests that there should be something more definitely explained regarding the hypothesis of "differentiation," on which Mr. Herbert Spencer hangs so much of his mathematical faith in the true explication of vital phenomena. The term "differentiation" is not so formidable as it might seem to the general reader at first sight. As applied to physiological problems it should have the same determinate value, in expressing functional differences, as in the higher operations of mathematics. Nothing can, of course, differentiate itself, nor can any two things differentiate each other, even when functionally allied. The actual coëfficient sought is the difference effected, in functional value, in one of two independent variables. For all formulæ in differentiation are constructed on the hypothesis that only one of two variables suffers change. The differential coëfficient has yet to be determined which shall express the developmental changes in two variables at once. When, therefore, we attempt to extend the formulæ of differentiation to plant and animal life, we are confronted by a very formidable difficulty at the outset--the impossibility of determining an invariable coëfficient for any two variables. Besides, all attempts at differentiating an ape-unit into anything else than an ape-unit would be as impossible as to multiply or divide cabbages by turnips, or sparrows by sparrowhawks. Such divisions would give us no quotients, any more than their differentiations would give us a coëfficient. Physiological differentiation will, therefore, never help us out of fixed species or nearly allied types. We can bridge no specific differences by it. In the differentiation of the horse and the ass for instance, the superior blood will predominate in the preservation of types, and even the mule will kick against further differentiation. Nature would so utterly abhor the practice as resolutely to slam the door in Mr. Spencer's face, if the obstinacy of the mule did not kick it off its hinges.