TRANSLATOR S INTRODUCTION XXXI 



' The question, whether the force of a body in motion is to 

 be measured, with Leibnitz and others, by the product of 

 the mass, and the square of the velocity (wz> 2 ), or with 

 Descartes, Euler, and others, by the product of the mass, 

 and the simple velocity (mv\ is here termed by Kant the 

 source of one of the greatest schisms existing among the 

 geometricians of Europe ; and he expresses the hope that 

 he may be able to contribute to its composition. He 

 advances against the Leibnitzian view, then prevalent in 

 Germany, several objections which tend in favour of the 

 Cartesian, but admits, nevertheless, the former with a 

 certain limitation. Kant divides all motions into two 

 classes ; the one class including motions supposed to 

 persist in the body to which they are communicated, and 

 to continue in infinitum, unless opposed by some obstacle ; 

 the other consisting of motions which cease, though opposed 

 by nothing, as soon as the external force by which they 

 were produced ceases to operate. (This " division "... is 

 completely erroneous.) Kant affirms that the Leibnitzian 

 principle applies to the former class, and the Cartesian 

 to the latter. If the conception of force be regarded, as is 

 now customary, as merely an accessory conception, the 

 controversy itself can no longer exist, since then only the 

 determination of what are the phenomena of motion and 

 their laws is directly of objective importance, while the 

 definition of force becomes a question of methodical con- 

 venience. If by force is meant a cause proportionate to the 

 quantity of the motion of a body, the Cartesian principle, of 

 course, applies ; but if the power of the body in motion 

 to produce certain special effects, e.g., to overcome a con- 

 tinuous and uniform resistance, is what is meant by force, 

 the Leibnitzian formula is applicable, according to which, 

 the "work" performed by the "force" is equal to the 

 difference of the products of half the mass multiplied by 



