"It is not denied," he says, "that there is a portion of extension which to the naked eye appears an indivisible point; it has been called by philosophers the _minimum visibile_. This minimum we can indefinitely magnify by means of optical instruments, making visible the still smaller parts which compose it. In each successive experiment there is still a _minimum visibile_, anything less than which cannot be discovered with that instrument, but can with one of a higher power. Suppose, now, that as we increase the magnifying power of our instruments, and before we have reached the limit of possible increase, we arrive at a stage at which that which seemed the smallest visible space under a given microscope, does not appear larger under one which, by its mechanical construction, is adapted to magnify more, but still remains apparently indivisible. I say, that if this happened, we should believe in a minimum of extension; or if some _a priori_ metaphysical prejudice prevented us from believing it, we should at least be enabled to conceive it."--(P. 84.) The natural conclusion of most men under such circumstances would be, that there was some fault in the microscope. But even if this conclusion were rejected, we presume Mr. Mill would allow that, under the supposed circumstances, the exact magnitude of the minimum of extension would be calculable. We have only to measure the _minimum visibile_, and know what is the magnifying power of our microscope, to determine the exact dimensions. Suppose, then, that we assign to it some definite magnitude--say the ten billionth part of an inch,--should we then conclude that it is impossible to conceive the twenty billionth part of an inch?--in other words, that we have arrived at a definite magnitude which has no conceivable half? Surely this is a somewhat rash concession to be made by a writer who has just told us that numbers may be conceived up to infinity; and therefore, of course, down to infinitesimality.