THE HIGHEST AIM or THE PHYSICIST 675 



the investigation is the same as we started with. Hence we can never 

 predict the result in the case of velocities beyond our reach, and such 

 calculations as the velocity of the cathode rays from their electro- 

 magnetic action has a great element of uncertainty which we should do 

 well to remember. 



Indeed, when it comes to exact knowledge, the limits are far more 

 circumscribed. 



How is it, then, that we hear physicists and others constantly stating 

 what will happen beyond these limits? Take velocities, for instance, 

 such as that of a material body moving with the velocity of light. There 

 is no known process by which such a velocity can be obtained even 

 though the body fell from an infinite distance upon the largest aggrega- 

 tion of matter in the universe. If we electrify it, as in the cathode 

 rays, its properties are so changed that the matter properties are com- 

 pletely masked by the electromagnetic. 



It is a common error which young physicists are apt to fall into to 

 obtain a law, a curve or a mathematical expression for given experi- 

 mental limits and then to apply it to points outside those limits. This 

 is sometimes called extrapolation. Such a process, unless carefully 

 guarded, ceases to be a reasoning process and becomes one of pure 

 imagination specially liable to error when the distance is too great. 



But it is not my purpose to enter into detail. What I have given 

 suffices to show how little we know of the profounder questions involved 

 in our subject. 



It is a curious fact that, having minds tending to the infinite, with 

 imaginations unlimited by time and space, the limits of our exact 

 knowledge are very small indeed. In time we are limited by a few 

 hundred or possibly thousand years: indeed the limit in our science is 

 far less than the smaller of these periods. In space we have exact 

 knowledge limited to portions of our earth's surface and a mile or so 

 below the surface, together with what little we can learn from looking 

 through powerful telescopes into the space beyond. In temperature 

 our knowledge extends from near the absolute zero to that of the sun 

 but exact knowledge is far more limited. In pressures we go from the 

 Crookes vacuum still containing myriads of flying atoms to pressures 

 limited by the strength of steel but still very minute compared with the 

 pressures at the centre of the earth and sun, where the hardest steel 

 would flow like the most limpid water. In velocities we are limited to 

 a few miles per second; in forces, to possibly 100 tons to the square 

 inch; in mechanical rotations, to a few hundred times per second. 



