550 THE POPULAR SCIENCE MONTHLY. 



retardation so caused, implies the belief that there can be no retarda- 

 tions without proportionate retarding causes ; which is itself the as- 

 sumption otherwise expressed in the first law of motion. 



Again, let us suppose that, instead of inexact observations made on 

 the movements that occur in daily experience, we make exact experi- 

 ments on movements specially arranged to yield measured results ; 

 what is the postulate underlying every experiment ? Uniform velocity 

 is defined as motion through equal spaces in equal times. How do we 

 measure equal times ? By an instrument which can be inferred to 

 mark equal times only if the oscillations of the pendulum are isochro- 

 nous ; which they can be proved to be only if the first and second 

 laws of motion are granted. That is to say, the proposed experimen- 

 tal proof of the first law assumes not only the truth of the first law, 

 but of that which Prof. Tait agrees with Newton in regarding as a 

 second law. Is it said that the ultimate time-measure referred to is 

 the motion of the Earth round its axis, through equal angles in equal 

 times ? Then, the obvious rejoinder is, that the assertion of this simi- 

 larly involves an assertion of the truth to be proved ; since the undi- 

 minished rotatory movement of the Earth is itself a corollary upon the 

 first law of motion. Is it alleged that this axial movement of the Earth 

 through equal angles in equal times is ascertainable by reference to 

 the stars ? I answer, that a developed system of Astronomy, leading 

 through complex reasonings t'o the conclusion that the Earth rotates, 

 is, in that case, supposed to be needful before there can be established 

 a law of motion which this system of Astronomy itself postulates. 

 For, even should it be said that the Newtonian theory of the Solar 

 System is not necessarily presupposed, but only the Copernican, still 

 the proof of this assumes that a body at rest (a star being taken as 

 such) will continue at rest ; which is a part of the first law of motion, 

 regarded by Newton as not more self-evident than the remaining part. 



Not a little remarkable, indeed, is the oversight made by Prof. 

 Tait, in asserting that '" no a priori reasoning can conduct us demon- 

 stratively to a single physical truth," when he has before him the fact 

 that the system of physical truths constituting Newton's " Principia," 

 which he has joined Sir William Thomson in editing, is established by 

 a priori reasoning. That there can be no change without a cause, or, 

 in the words of Mayer, that " a force cannot become nothing, and just 

 as little can a force be produced from nothing," is that ultimate dictum 

 of consciousness on which all physical science rests. It is involved 

 alike in the assertion that a body at rest will continue at rest, in the 

 assertion that a body in motion must continue to move at the same 

 velocity in the same line if no force acts upon it, and in the assertion 

 that any divergent motion given to it must be proportionate to the 

 deflecting force ; and it is also involved in the axiom that action and 

 reaction are equal and opposite. 



The reviewer's doctrine, in support of which he cites against me 



