CHAPTER VII 



NUMERICAL LAWS AND THE USE OF 

 MATHEMATICS IN SCIENCE 



NUMERICAL LAWS 



IN the previous chapter we concluded that density 

 was a measurable property because there is a 

 fixed numerical relation, asserted by a " numerical 

 law," between the weight of a substance and its volume. 

 In this chapter we shall examine more closely the idea 

 of a numerical law, and discover how it leads to such 

 exceedingly important developments. 



Let us first ask exactly what we do when we are trying 

 to discover a numerical law, such as that between weight 

 and volume. We take various portions of a substance, 

 measure their weights and their volumes, and put down 

 the result in two parallel columns in our notebook. Thus 

 I may find these results : 



TABLE I 



WEIGHX __ _ > voma/^fi WEIGHT VOLUME 



7 



2 14 



3 21 



4 28 



10 70 



29 203 



I now try to find some fixed relation between the corres- 

 ponding numbers in the two columns ; and I shall succeed 

 in that attempt if I can find some rule whereby, starting 

 with the number in one column, I can arrive at the corres- 

 ponding number in the other. If I find such a rule 

 and if the rule holds good for all the further measure- 

 ments that I may make then I have discovered a 

 numerical law. 



In the example we have taken the rule is easy to find. 



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