136 FUNDAMENTAL UNITS OF MEASURE. 



try. Of the latter little detail will l)e given, as the extensive and easily 

 accessible literatnre upon the subject renders it unnecessary. 



The measure of a magnitude is its numerical evaluation. In a direct 

 way this is accompli sIkhI by ascertaining how many times it contains 

 another magnitude of the same kind or nature which is adopted as a 

 unit. Thus a length is selected as a unit for the measurement of length, 

 a volume for the meaiuirement of volume, a time for time measurement, 

 and so on. At first it seems that this condition of sameness of the unit 

 and the thing measured is a necessity. A little reflection will show, 

 however, that it is oi)en to the objection that it naturally, although 

 perhaps not necessarily, leads to an almost indetinite multii)licatiou of 

 independent units. The discovery and development of inter-relations 

 among measurable magnitudes, which has gone on from the earliest 

 times, has tended towards a reduction in the number of units and, cou- 

 secpiently, to a great simplification of the whole subject of metrology. 

 So simple and evident a device as relating the unit of volume to the 

 unit of length has only been satisfactorily realized in comparatively 

 modern times; and, with a single exception, it maybe affirmed that 

 units of volume uow in use were originally in no way related to units 

 of length, most of them being of accidental and now unknown origin. 



That a legal bushel in the United States must contain 2150-42 cubic 

 inches is convincing evidence that the foot or the yard has no place iu 

 its ancestry, and although there is a plausible explanation of the fact 

 that a gallon contains 2;)1 cubic inches, it points only to a modified 

 volume and not a selected one. 



Many interesting illnstrations of the great advantage gained by 

 neglecting the princii»le that " like measures like" might be given, and 

 one or two will, perhaps, be found instructive. In observing that prop- 

 erty of matter known as "conductivity," either as to heat or electricity, 

 qualitative or relative conclusions were for a long time all that was 

 re(|uired. It was at first sufficient to say and to know that one sub- 

 stance conducted heat or electricity better or worse than another, but 

 with the advance of knowledge of physics it became desirable, and 

 often necessary, to give numerical expression to these relations. In 

 such cases as this the practice has usually been to select some partic- 

 ular substance which possesses the property in question iu a higher or 

 in a lower degree than any other and adopt it as a standai'd. Thus 

 barely a (juarter of a century ago conductivities of difl'erent bodies for 

 heat or electricity were expressed in terms of cop])eror silver; a lamp- 

 black surface was the stancbird for radiation or absorption, and in most 

 instances the standard was arbitrarily rated at 100. The literature of 

 science contains many examples of elaborate and otherwise valuable 

 investigations which are rendered quite worthless by the uncertain and 

 unscientific units of measure employed. An example of the persistent 

 use of this piinciple is to be found in the still common mode of express- 

 ing the density of matter by referring it to the density of a certain 



