xxxii KANT'S UNIVERSAL NATURAL HISTORY 



the squares of the velocity at the commencement, and at 

 the end of the motion. (At the present time, as is known, 

 mv is used to designate the " quantity of motion," and mv 1 

 " the living force." In the case of a body falling freely, the 

 final velocity after n seconds = 2g, and the distance 

 traversed in n seconds = n 2 g. One half of the product 

 of the mass by the square of the velocity = 



%mv~ = \m . 4n 2 g 2 = 2mn^g 2 = 2gm . w*g, 



or the product of the "moving force" (2gm) by the distance 

 (n^g). The heights to which bodies rise when thrown 

 upwards vary, therefore, as the squares of their initial 

 velocities ; and in like manner, generally, the " work " 

 performed by a moving body is measured by half the 

 product of the mass into the square of the velocity.) 

 D'Alembert showed as early as 1743, that analytical 

 mechanics can leave the disputed question on one side, since 

 it is only a dispute about words. From the present stand- 

 point of science, B. W. H. Lexis, in an inaugural dissertation 

 (Bonn 1859), expresses the following judgment : "Kantius, 

 gravidis quidem erroribus laborans, tamen multis locis pro- 

 fundiorem rei ostendit perspicientiam." Yet at the bottom of 

 the discussions lay concealed by the contest of words the 

 problem, how to combine the principle of the equality of 

 cause and effect with facts. A characteristic affirmation is 

 made by Kant in 19, that metaphysics, like many other 

 sciences, had only reached the threshold of well-grounded 

 knowledge.' History of Philosophy, Vol. n., p. 142. 



When Kant published his first work, he had left 

 the University, and he was engaged thereafter as a 

 private tutor for about ten years, till he completed 

 his Cosmogony in 1754-5. In the winter session of 

 1755, he qualified as a lecturer in the University of 

 Konigsberg, and thus entered on his great public 



