The Multiplication and Division of Concrete Quantities 1

Abstract

I HAVE recently been laying stress on the fact that the fundamental equations of mechanics and physics express relations among quantities, and are independent of the mode of measurement of such quantities; much as one may say that two lengths are equal without inquiring whether they are going to be measured in feet or metres; and indeed, even though one may be measured in feet and the other in metres. Such a case is, of course, very simple, but in following out the idea, and applying it to other equations, we are led to the consideration of products and quotients of concrete quantities, and it is evident that there should be some general method of interpreting such products and quotients in a reasonable and simple manner. To indicate such a method is the object of the present paper.