In reality time, in the sense of the astronomer’s time, does not enter into the methods of the mathematical physicist. Let us suppose that he is investigating the change that occurs in a material system between the two moments of time _t_↓{1} and _t_↓{2}, these moments being separated from each other by a period of duration that we can feel. Let the system be, say, the earth and moon; the first body being supposed to be motionless, and the second being supposed to have a certain tangential velocity of movement. If the interval _t_↓{1} to _t_↓{2} is really an interval of astronomical time, the problem, what is the difference of position of the moon owing to the gravitation of the earth, is incapable of solution, and even if we reduce the interval of time indefinitely while still supposing that it is a finite interval, the mathematical difficulty remains. We then replace the finite interval _t_↓{1} to _t_↓{2} by the differential _dt_, which means that the two phases of the system, motionless earth and moving moon at the time _t_↓{1}, and motionless earth and moving moon at the time _t_↓{2}, are separated by an interval of time _dt_, which is smaller than any finite interval that we can conceive. We must then integrate the differential of the position difference so as to obtain the real difference in the condition of the system after the finite interval of time _t_↓{1} to _t_↓{2} has elapsed. Thus mathematics, incapable of dealing with real intervals of time, _evades_ this difficulty by considering tendencies, not real occurrences. Things that happen in a part of inorganic nature arbitrarily detached from the rest, and investigated by the methods of mathematical physics, do not endure. Let us suppose that we take some silver and add nitric acid to it: the metal dissolves. We can then add hydrochloric acid to the solution and precipitate the metal in the form of chloride; and we can then fuse this chloride with carbonate of soda, or some other substance, and so obtain the metal again. If we work carefully enough we can repeat this series of operations again and again and the original portion of silver will remain unchanged both in nature and in mass. All the chemical reactions into which it has entered have not affected it in any way; that is to say, these reactions have not endured.