This will be easily seen, if we consider that to bring a question within the field of mathematical analysis, we must first have discovered the precise relations which exist between the quantities which are found in the phenomenon under examination, the establishment of these equations being the necessary starting point of all analytical labours. This must evidently be so much the more difficult as we have to do with phenomena which are more special, and therefore more complicated. We shall thus find that it is only in _inorganic physics_, at the most, that we can justly hope ever to obtain that high degree of scientific perfection. The _first_ condition which is necessary in order that phenomena may admit of mathematical laws, susceptible of being discovered, evidently is, that their different quantities should admit of being expressed by fixed numbers. We soon find that in this respect the whole of _organic physics_, and probably also the most complicated parts of inorganic physics, are necessarily inaccessible, by their nature, to our mathematical analysis, by reason of the extreme numerical variability of the corresponding phenomena. Every precise idea of fixed numbers is truly out of place in the phenomena of living bodies, when we wish to employ it otherwise than as a means of relieving the attention, and when we attach any importance to the exact relations of the values assigned. We ought not, however, on this account, to cease to conceive all phenomena as being necessarily subject to mathematical laws, which we are condemned to be ignorant of, only because of the too great complication of the phenomena. The most complex phenomena of living bodies are doubtless essentially of no other special nature than the simplest phenomena of unorganized matter. If it were possible to isolate rigorously each of the simple causes which concur in producing a single physiological phenomenon, every thing leads us to believe that it would show itself endowed, in determinate circumstances, with a kind of influence and with a quantity of action as exactly fixed as we see it in universal gravitation, a veritable type of the fundamental laws of nature. There is a _second_ reason why we cannot bring complicated phenomena under the dominion of mathematical analysis. Even if we could ascertain the mathematical law which governs each agent, taken by itself, the combination of so great a number of conditions would render the corresponding mathematical problem so far above our feeble means, that the question would remain in most cases incapable of solution.