32 Kcv. W. Whewell on the principles of Dynamics, 



whicli, T confess, appears to me entirely fallacious, but which 

 must, I think, at least be allowed to be unscientific and un- 

 philosophical. The idea of instantaneous force is introduced 

 merely to be got rid of. It is not deduced from nature, but 

 it is borrowed from the imagination, and made the foundation 

 of the science ; and must again be dismissed before we can 

 apply our conclusions to any of the phenomena of the universe. 



It is true that we may conceive physical impact after the 

 manner in which it is generally understood ; that is, as con- 

 tinuing during a small definite time, for instance one-tenth of 

 a second ; and we may then imagine such impact to represent 

 all other forces. By this means the force will be a pressure of 

 the kind which really exists ; but then we shall lay the reason- 

 ing open to the objections which the assumption of instantane- 

 ous force seems intended to avoid, namely, the necessity of 

 introducing the time during which the force is supposed to act. 



II. Supposing, however, we allow this substitution of im- 

 pulsive for permanent forces, we shall, I think, find ourselves 

 met by new difficulties. It is to be proved or assumed, (Law 

 3,) that this impulsive force is proportional to the velocity 

 which it produces, and this is proved from experiment, in a 

 demonstration (Laplace, Art. 5,) which assumes that these 

 forces thus producing velocity may be compounded according 

 to the law of composition of forces which is established in sta- 

 tics. Now nothing can be clearer than that the statical com- 

 bination of forces cannot apply to the composition of impacts, 

 without complete alteration of the use of terms, and the 

 meaning of the proposition. The definition of statical force, 

 and every step of the process^ supposes the forces to be em- 

 ployed in producing equilibrium^ which cannot in any manner 

 apply to impulsive or instantaneous forces. And this objec- 

 tion is so obvious, and apparently so insurmountable, that I 

 am at a loss to imagine how reasoners so acute as those whose 

 demonstrations I am considering, can have passed it over ; at 

 the same time, I think no person can examine the proofs to 

 which I have referred, without seeing that they are altogether 

 dependent upon this vicious reasoning. 



The fact, perhaps, may be, that the authors who have 

 adopted this fallacious train of reasoning have not sufficiently 



