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There remains the further extension to what may be called “multiplicate proportion” (duplicate, triplicate, … n · plicate). This may be regarded as a limiting case of compound proportion, being a relation between variable quantities P, X of two different kinds such that measures p, x of these variables are in the proportional relation p α xn. (The definition can, of course, be expressed—like the definitions of direct and inverse proportion—in terms of ratios of any two quantities of the one kind and the two corresponding quantities of the other kind.)
* Right instinct, often the instinct of the greatest genius, combined with sketchy mathematics is characteristic of Physical writing. The blame lies not so much at the door of Physics as of Mathematics. Unfortunately the loose expression gets transmitted to the learner; frequently the accurate thought behind it does not, especially when the vehicle is not a great physicist but a book.