Page:Popular Science Monthly Volume 20.djvu/462

446 that the releasing force may be infinitely small passes to the assertion that it may be really null, it seems to make an unwarrantable use of a process in the infinitesimal calculus which is usual under quite different conditions. The former statement can only mean that the releasing force may be vanishingly small in comparison with the released force. The force of the wing-flapping of a crow which starts an avalanche thus vanishes in the face of the force of the avalanche as it finally plunges through the valley; that is, the former may be neglected in the measurement of the latter, because the influence it exerts can not be indicated by any figures, and because it may fall within the range of errors of observation. But, however insignificant, as regarded from the valley, the wing-flapping above may seem in comparison with the mad force of the avalanche, it is still, there, a blow which corresponds with the raising of a definite weight to a definite height. By the nature of the escapement, the releasing and the released force are independent of each other, connected by no law. Hence it is inaccurate to say that "the ratio of the releasing force to the released force approaches zero," without adding that this depends on an accidental increase, so far as relates to the former, of the latter; as in our example, the wing-stroke being the same, the increase depends on the greater height, steepness, and smoothness of the mountain-slope, on the ever-mightier piling up of snow, etc. So little can the releasing force be in itself really null, it can never, unless we deny the releasing, fall below a certain something (Schwellenwerth) capable of an expansion that is dependent on circumstances. Therefore, to explain by the aid of the principle of escapement how a spiritual substance can effect material changes, is not to be thought of.

As to the solution proposed by M. Boussinesq, the grave point remains at the stationary position simply in unstable equilibrium, and it was not necessary to raise it by integration to calculate the consequences of that situation. The case, in fact, differs only in its abstract form of expression from Buridan's or Dante's paradox, which may be so formulated that the hungry creature—

is in unstable equilibrium. No "directing principle" of immaterial nature is competent to move the grave point at the apex of the paraboloid in the slightest degree; a mechanical force, though it be ever so little, is necessary even upon a wholly frictionless surface. If this could be a force equivalent to nothing, then our second transcendental difficulty, of the origin of motion, would disappear at once; for an impulse equivalent to nothing would never be wanting.

M. Boussinesq also brings up the question of what would be the consequence of the reversal of all the motions of the world. If we