446 THE POPULAR SCIENCE MONTHLY. 



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 differ- 

 ent conditions. The former statement can only mean that the releas- 

 ing 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 compai'ison with 

 the mad force of the avalanche, it is still, there, a blow which corre- 

 sponds with the raising of a definite weight to a definite height. By 

 the nature of the escapement, the releasing and the released foi'ce are 

 independent of each other, connected by no law. Hence it is inac- 

 curate 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 ex- 

 ample, 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 (SehiceUenwerth) capable of an exj)ansion 

 that is dependent on circumstances. Therefore, to explain by the aid 

 of the principle of escapement how a spiritual substance can effect ma- 

 terial changes, is not to be thought of. 



As to the solution proposed by M. Boussinesq, the grave point re- 

 mains at the stationary position simjfly in unstable equilibrium, and it 

 was not necessary to raise it by integration to calculate the conse- 

 quences 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 



" Intra duo cibi distanti e moventi 

 Hun modo " 

 (" Between two kinds of food, both equally remote and tempting ") 



is in unstable equilibrium. No " directing principle " of immaterial 

 nature is competent to move the grave point at the apex of the pa- 

 raboloid 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 im- 

 pulse 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 



