526 POPULAR SCIENCE MONTHLY 



cedure is always the same. The primitive law enunciated a relation 

 between two facts in the rough, A and B; between these two crude 

 facts is introduced an abstract intermediary C, more or less fictitious 

 (such was in the preceding example the impalpable entity, gravita- 

 tion). And then we have a relation between A and C that we may 

 suppose rigorous and which is the 'principle; and another between C 

 and B which remains a law subject to revision. 



The principle, henceforth crystallized, so to speak, is no longer 

 subject to the test of experiment. It is not true or false, it is con- 

 venient. 



Great advantages have often been found in proceeding in that way, 

 but it is clear that if all the laws had been transformed into principles 

 nothing would be left of science. Every law may be breken up into 

 a principle and a law, but thereby it is very clear that, however far 

 this partition be pushed, there will always remain laws. 



Nominalism has therefore limits, and this is what one might fail 

 to recognize if one took to the very letter M. LeEoy's assertions. 



A rapid review of the sciences will make us comprehend better 

 what are these limits. The nominalist attitude is justified only when 

 it is convenient; when is it so? 



Experiment teaches us relations between bodies; this is the fact 

 in the rough; these relations are extremely complicated. Instead of 

 envisaging directly the relation of the body A and the body B, we 

 introduce between them an intermediary, which is space, and we 

 envisage three distinct relations : that of the body A with the figure A' 

 of space, that of the body B with the figure B' of space, that of the 

 two figures A' and B' to each other. Why is this detour advantageous ? 

 Because the relation of A and B was complicated, but differed little 

 from that of A' and B', which is simple; so that this complicated rela- 

 tion may be replaced by the simple relation between A' and B' and by 

 two other relations which tell us that the differences between A and A' y 

 on the one hand, between B and B', on the other hand, are very small. 

 For example, if A and B are two natural solid bodies which are dis- 

 placed with slight deformation, we envisage two movable rigid figures 

 A' and B' . The laws of the relative displacements of these figures 

 A' and B' will be very simple; they will be those of geometry. And 

 we shall afterwards add that the body A, which always differs very 

 little from A', dilates from the effect of heat and bends from the effect 

 of elasticity. These dilatations and flexions, just because they are 

 very small, will be for our mind relatively easy to study. Just imagine 

 to what complexities of language it would have been necessary to be 

 resigned if we had wished to comprehend in the same enunciation the 

 displacement of the solid, its dilatation and its flexure? 



The relation between A and B was a rough law, and was broken up ; 



