The difference, as we have said, is connected with the fundamental principle that we do not perceive Secondary qualities directly, but through a Medium. We have no natural apprehension of light, or sound, or heat, as they exist in the bodies from which they proceed, but only as they affect our organs. We can only measure them, therefore, by some _Scale_ supplied by their effects. And thus while extended magnitudes, as space, time, are measurable directly and of themselves; intensive magnitudes, as brightness, loudness, heat, are measurable only by artificial means and conventional scales. Space, time, measure themselves: the repetition of a smaller space, or time, while it composes a larger one, measures it. But for light and heat we must have Photometers and Thermometers, which measure something which is assumed to be an indication of the quality in question. In the one case, the mode of applying the measure, and the meaning of the number resulting, are seen by intuition; in the {335} other, they are consequences of assumption and reasoning. In the one case, they are _Units_, of which the extension is made up; in the other, they are _Degrees_ by which the intensity ascends. 2. When we discover any property in a sensible quality, which at once refers us to number or space, we readily take this property as a measure; and thus we make a transition from quality to quantity. Thus Ptolemy in the third chapter of the First Book of his _Harmonics_ begins thus: 'As to the differences which exist in sounds both in _quality_ and in _quantity_, if we consider that difference which refers to the acuteness and graveness, we cannot at once tell to which of the above two classes it belongs, till we have considered the causes of such symptoms.' But at the end of the chapter, having satisfied himself that grave sounds result from the magnitude of the string or pipe, other things being equal, he infers, 'Thus the difference of acute and grave appears to be a difference of _quantity_.' In the same manner, in order to form Secondary Mechanical Sciences respecting any of the other properties of bodies, we must reduce these properties to a dependence upon quantity, and thus make them subject to measurement. We cannot obtain any sciential truths respecting the comparison of sensible qualities, till we have discovered measures and scales of the qualities which we have to consider; and accordingly, some of the most important steps in such sciences have been the establishment of such measures and scales, and the invention of the requisite instruments.