THE PHILOSOPHY OF PHYSICS 151 



connections are of the most universal character. A perfectly correct 

 " science " might be built up in which we connected extension (for example) 

 successively with terrestrial position (gravitation), the magnetic or electric 

 quaUties of neighbouring objects, rotations (as when the rod is whirled round), 

 etc. Each of these connections for its specification would require a knowledge 

 of the " laws " governing the individual phenomena. Modem science 

 proceeds, on the other hand, by inventing a quantity which it calls force 

 by aid of which a relation can be specified which is common to them all. 

 In much the same way the most modem science is connecting together 

 numerous atomic phenomena, in which the above form of unification appears 

 to break down, by means of the invention of quanta of action. Some day, 

 with Httle doubt, these two forms, which at present appear irreconcilable 

 with one another, wiU be found to conform to a common law. I wish to 

 argue that, wherever the complexity in laws is found to exist, it indicates a 

 defect in our scientific system which further investigation or a difierent 

 selection of fundamental quantities will ultimately put right. 



We must pass from this somewhat abstract portion to parts which are 

 more important for the practical worker. The question of units and dimen- 

 sions is discussed in Chapter XIV. Here again we meet with much with 

 which we can heartily agree ; but again the author is rather carried away, 

 in his search for procedure alternative to that usually adopted, into regions 

 bordering on the fanciful. There are many assertions with which we do 

 not agree (for various reasons). The equation, density equals mass -!- 

 volume, does not imply that the density (even of a given substance) is a con- 

 stant. To define volume as mass 4- density is to define the easily ascertain- 

 able in terms of a quantity (density) which cannot be directly determined. 

 To get over the difiSculty by taking the density of a particular substance 

 as an arbitrary unit is to do away %vith aU the advantages of absolute units. 

 The present definition of a litre in terms of a mass of water is clearly only a 

 secondary definition, and is on a par with the definition of an electric current 

 in terms of electrolytic deposition. Both these definitions are only adopted 

 for convenience in approximate measurements, and are inconsistent with 

 the International units also adopted. Campbell's dielectric constant K 

 (p. 383, etc.) is the reciprocal of what we have grown accustomed to : it 

 is small when the capacity is great. In the equation 



[charge] = [force]* X [length] X [dielectric constant]—* 



Campbell regards the charge and the dielectric constant as being on a different 

 footing. The dielectric constant is stated to be defined by the above equa- 

 tion while the charge requires other laws. Surely both are equally undefined 

 by the single equation. " Mass, length, and time are not the magnitudes 

 we habitually measure as fundamental magnitudes ; the practical fundamental 

 magnitudes are weight, length, time, and electric resistance." Surely the 

 fundamental magnitudes usually measured all consist of lengths : all the 

 rest is inference. In the footnote on p. 389 occur the two equations F — 

 fji i i^ ds ds'^/r^ and F = fi mm^/r^. Surely one of the quantities /j. is inversely 

 proportional to the other. Much discussion might take place about the 

 justifiabihty of inserting K and fi where modem usage introduces them in 

 connection with the dimensions of electromagnetic quantities. Campbell 

 advocates their omission, and tvvits some writers on priding " themselves on 

 their correctness in including K on every possible occasion." Is it not 

 true, however, that the only way of writing an equation in electromagnetics 

 so that it shall be true, whether electrostatic, electromagnetic, or other sjrstem 

 of units is employed, is to insert these constants in their appropriate places ? 

 The mention of constants leads me to add that fi is certainly not always a 

 constant, i.e. independent of the field. It is difficult to find a suitable short 

 name in such cases ; what is meant is usually a non-dimensional factor, 



