In reply to this we may observe, that the circumstance of _our not seeing_ in the nature of the case anything which determines for us the coefficients above spoken of, cannot prove that they have not some certain value _in nature_. We do not see in the nature of the case anything which should determine a body to fall sixteen feet in a second of time, rather than one foot or one hundred feet: yet in fact the space thus run through by falling bodies is determined to a certain magnitude. It would be easy to assign a mathematical expression for the velocity of a body, implying that one-hundredth of the velocity, or any other {239} fraction, is lost in each second[22\3]: and where is the absurdity of supposing such an expression really to represent the velocity? [Note 22\3: This would be the case, if, _t_ being the number of seconds elapsed, and _C_ some constant quantity, the velocity were expressed by this mathematical formula, _C_(99/100)^_t_.] Most modern writers on mechanics have embraced the opposite opinion, and have ascribed our knowledge of this first law of motion to experience. Thus M. Poisson, one of the most eminent of the mathematicians who have written on this subject, says[23\3], "We cannot affirm _à priori_ that the velocity communicated to a body will not become slower and slower of itself, and end by being entirely extinguished. It is only by experience and induction that this question can be decided." [Note 23\3: Poisson, _Dynamique_, ed. 2, art. 113.] Yet it cannot be denied that there is much force in those arguments by which it is attempted to show that the First Law of Motion, such as we find it, is more consonant to our conceptions than any other would be. The Law, as it exists, is the most simple that we can conceive. Instead of having to determine by experiments what is the law of the natural change of velocity, we find the Law to be that it does not change at all. To a certain extent, the Law depends upon the evident axiom, that no change can take place without a cause. But the question further occurs, whether the mere lapse of time may not be a cause of change of velocity. In order to ensure this, we have recourse to experiment; and the result is that time alone does not produce any such change. In addition to the conditions of change which we collect from our own Ideas, we ask of Experience what other conditions and circumstances she has to offer; and the answer is, that she can point out none; When we have removed the alterations which external causes, in our very conception of them, occasion, there are no longer any alterations. Instead of having to guide ourselves {240} by experience, we learn that on this subject she has nothing to tell us. Instead of having to take into account a number of circumstances, we find that we have only to reject all circumstances. The velocity of a body remains unaltered by time alone, of whatever kind the body itself be.