1051 



Principally it is therefore not necessary to be able to measure 

 microscopic coordinates nor to determine the form of the equations 

 A. The equations B are sufficient which only contain macroscopic 

 variables and macroscopic instantaneous values. 



The equations which have to be made up in physics can thus 

 be considered as the elimination results of the equalions J3 or, 

 strictly speaking, as approximations of these. 



^ 3. So the contradiction between the kinetic-microscopic and 

 the physico-macroscopic conception has been removed by transferring 

 all observations necessary for the perfect determination of the 

 microscopic processes to the macroscopic domain. This however 

 does not yet make it sure that the laws of nature worked out in 

 physics until now are not open to the same objections as before our 

 remark. Indeed : we have by no means made as many observations as 

 are requested by the number of molecules by which the world is built up. 



It may be allowed to answer this objection with an analogy. Let 

 a part of an algebraic curve of extremely high degree be drawn 

 and suppose we were asked to continue approximately its course 

 to a certain finite extent. If it were possible to determine the 

 coordinates for a sufficient number of points of the given part 

 of the curve we should be able to indicate the whole further course 

 of the curve. But let this be practically impossible because of the 

 high degree of the curve, so we must content ourselves with 

 a much smaller number of accurately determined coordinates. 

 Must we then quite give up the solution of the problem ? Firstly, 

 the relatively few points will serve to confine somewhat the multi- 

 tude of possible curves from which we have to choose. But we get 

 still further if we take into consideration all we .9^6 in the part of the 

 curve that is drawn out : that will give us many qualitative data, which 

 enable us to exclude a much greater number of curves than would 

 be possible by means of the accurately determined points and in this 

 way we may be able — at least to a certain finite extent — to 

 give a very good extrapolation of the curve. 



It might be possible that in the same way in the establishing 

 of physical laws the meaning of qualitative observations must not 

 be estimated too low. Continuing the line of these considerations, 

 the daily confirmation of the "intuitively" formed physical laws will 

 perhaps no longer appear like an astonishing accidentality in face 

 of the fundamental ideas of kinetics. 



^ 4. We must pay attention to one other objection -. what has been 



