I found in Descartes' letters what you mentioned to me- namely, that he had tried to avoid the consideration of velocities in formulating the reasons for moving forces and had taken into account only the heights. If he had remembered this when he wrote his principles of physics perhaps he would have avoided the errors into which he has fallen with respect to the laws of nature, but he happens to have avoided the consideration of velocity there where he might have retained it, and to have retained it in the case where it could produce errors. For, with regard to the power which I call dead (as when a body makes its first effort to descend before it has acquired any impetus from the continuance of the motion), and with regard to the case when two bodies are in equilibrium (for then, the first efforts which the one exercises on the other are always dead), it happens that the velocities are as the distances; when, however, we consider the absolute force of bodies which have a certain impetuosity (and this is necessary for establishing the laws of motion), the calculation should be made from the cause or from the effect, that is to say, according to the height to which it can rise by virtue of this velocity, or according to the height from which it must descend in order to acquire this velocity. If we should attempt to employ the velocity, we should gain or lose a great deal of force without any reason for it. In place of the height we might suppose a spring or any other cause or effect, and the result would always be the same; viz., proportional to the squares of the velocities.

I find in The News of the Republic of Letters for the month of September, of this year, that someone named Abbe D. C., of Paris, whom I do not know, has replied to my objection. The trouble is that he seems not sufficiently to have thought over the difficulty. While pretending to contradict me vehemently he grants me more than I wish and he limits the Cartesian principle to the single case of isochronous powers as he calls them, as in the five usual forms of machinery, and this is entirely against Descartes' intention. Besides this, he thinks that the reason why in the case which I proposed one of the bodies has quite as much force as the other although it has a smaller quantity of motion, is the result of this body's having fallen for a longer period since it has come from a greater height. If this made any difference, the Cartesian principle which he wishes to defend would be ruined by that very fact. This reason, however, is not valid, for the two bodies can descend from those different heights in the same time, according to the inclination which is given to the planes along which they must descend; and my objection would still be entirely valid. I hope, therefore, that my objection may be examined by a Cartesian who shall be a Geometer and well versed in these matters.

Finally, M., as I honor you infinitely and am very much interested in whatever concerns you I will be delighted to learn from time to time of the state of your health and of the works which you have in hand; whose value I am proud to be able to recognize,

I am, with a passionate zeal,

XV: Leibniz to Count Ernst von Hessen-Rheinfels

[Taken from my letter of November, 1686.]

I take the liberty, Monseigneur, to beg your Serene Highness to have the enclosed sent to M. Arnaud, and, as it treats of matters far from the external senses and dependent upon pure intellection, which are not agreeable to and most frequently are looked down upon by persons who are, nevertheless, active and successful in the affairs of the world, I will say here something in favor of these meditations; not because I am so fatuous as to wish your Serene Highness to amuse himself with them (this would be as unreasonable as to wish that the general of an army should apply himself to algebra, however important this science may be to any one who is concerned with mathematics), but so that your Serene Highness may better estimate the purpose and the use of such thoughts that might appear unworthy of taking up a man's time; especially since all a man's moments ought to be so precious to him. As these matters are usually treated by the Schoolmen, they are only disputations and distinctions and plays upon words; but there are veins of gold among these barren rocks. I think in fact that thought is the principal and perpetual function of the soul. We shall always think, but we shall not always live here; this is why whatever renders us more capable of thinking about most perfect objects and in the most perfect way is what naturally contributes to our perfection. Nevertheless, the present state of our life compels us to a great number of confused thoughts which do not add to our perfection, such is the knowledge of customs, of genealogies, of languages, and even all historical knowledge of facts, whether civil or natural; these are useful for us in avoiding dangers and in taking care of the bodies and of the men whom we have around us, but they do not enlighten the mind. The knowledge of routes is useful to a traveller while he is on his journey, but whatever has a greater relation to the duties that lie before him in patria is more important for him. Now we are destined to live some day a spiritual life, where substances separated from matter will occupy us much more than do the bodies.