72 THE ANATOMY OF SCIENCE 



at the next one. This I take to he the whole 

 significance of a mathematical proof in physics. 



However, if we find that our geometry fails 

 even in the slightest degree to coincide with our 

 observations in kinematics, we must beware, for 

 it will surely fail again; and when it does we 

 must not say that our mathematics is wrong, 

 but only that we have chosen the wrong mathe- 

 matics ! Supposing that in some plot of experi- 

 mental data we have a number of points repre- 

 senting different measurements. We have on 

 our desk a box of circles, ellipses, hyperbolas 

 and parabolas cut out of cardboard, and by 

 trial we find that a parabola fits the points. 

 We then run a pencil along its edge and by this 

 extrapolation we hope to predict a new obser- 

 vation ; but performing our experiments we find 

 a point which does not at all fit the curve we 

 have drawn. We do not throw our cardboard 

 parabola into the waste basket and say it is no 

 good ; we put it back into the box to be used on 

 another occasion and select a new curve, per- 

 haps a hyperbola, which now fits all the old 

 points and also the new. 



Was the simple mathematics of Newtonian 

 kinematics going to continue to be adequate 

 with the advance of experimental physics? The 



