THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 25 



loe no doubt that this extension was actually effected in con- 

 nexion with ^he problem of measurement, which we have yet 

 to consider ; but it will be instructive to conceive a method 

 which might have been followed which involves no reference to 



this problem. 

 r / 



Let us take a concrete example. We will suppose that we 

 have undertaken the task of compiling a " subject index " to 

 a library a catalogue in which a reference is given to the 

 books dealing with each subject. Separate sections of ' the 

 catalogue will be devoted to the main divisions of the subjects 

 represented, and it will be necessary to interpolate between 

 these main headings, as the library developes, sub-headings 

 referring to the portions of the catalogue which, are devoted to 

 the sub-divisions of the subjects. Thus Section 518 may 

 contain the books on Analytical Geometry, Section 519 those 

 on Aids to Calculation. Later it becomes necessary to dis- 

 tinguish sub-sections devoted to Plane Loci, Trilinears, Conic 

 Sections, Loci in Space, Conicoids, &c. To mark the position 

 of these smaller divisions we need to interpolate between the 

 numbers 518 and 519 other symbols that will continue in this 

 new field the correlative properties of the integers. We arrive 

 at the idea of employing for this purpose the symbols 518*1, 

 518'2, 518*3, &c., symbols which are obviously not in 

 possession, directly, of! all the properties of the integers, but 

 can just as obviously be used to continue their unambiguous 

 correlative function. Thus the symbol 518*3 fixes .the position 

 of the sub-section dealing with Conic Sections quite unambig- 

 uously between the sub-sections dealing with Trilinears (518*2) 

 and Loci in Space (518*4) respectively. When the books con- 

 cerned with Conic Sections are themselves numerous enough 

 for classification, we can arrange the correlation of the 

 secondary sub-divisions without disturbing the existing dis- 

 tribution of symbols. It is necessary only to repeat the same 

 device at a further stage, and to correlate the new sub-sections 

 devoted (say) to the Ellipse, the Hyperbola, and the Parabola 



OF THE 



