202 THE SCIENCE OF LOGIC 



229) only brought discredit on a procedure that is perfectly 

 legitimate within proper bounds. What these bounds are, a 

 glance at the nature of measurement, and its units and standards, 

 will immediately disclose. 



All measurement is observation and something more. As 

 observation, it is inseparably connected with interpretation of the 

 data offered to us ; and interpretation, being judgment, is subject 

 to error. But measurement is more than observation ; it is com 

 parison of the observed fact with some other fact taken as standard 

 or unit. And this comparison is not merely mental ; it implies 

 direct application of the unit or standard to the measurable magni 

 tude, and sense-observation of the result of such application. The 

 accuracy of measurement, therefore, ultimately depends on the 

 acuteness of our powers of sense-perception. But these powers 

 are trustworthy only within a certain range ; and even within this 

 range they are not infallible. There are, for all the senses, what 

 are called minima sensibilia : objects so small that our senses are not 

 sufficiently delicate to become aware of any smaller. No doubt, 

 our powers of observation have been increased by such mechani 

 cal devices as the telescope and the microscope ; and our powers 

 of measuring, i.e. counting the application of a unit to a quantity, 

 are aided by such delicate instruments as the micrometer screw, 

 the electrometer, the bolometer, 1 etc. But, even still, there is a 

 limit to the keenness of our sensibility ; so that every actual measure 

 ment is, normally speaking, only an approximation to the real state of 

 the facts. By accident, no doubt, a measurement may be just 

 accurate ; but, even when it is, we cannot be sure of this. So it 

 is no exaggeration to say, with Jevons, 2 that &quot; we may look upon 

 the existence of error in all measurements as the normal state of 

 things&quot;. 



To fix upon certain fundamental and derived units for measur 

 ing various physical magnitudes, units of spatial extension (dis 

 tance, area, volume), of time, of mass, of velocity or rate of 

 motion, of acceleration, of mechanical energy, of temperature, of 

 electromotive force, of strength of electric current, etc. ; to devise 

 means of applying these units with a greater approximation to 



1 &quot; Langley s bolometer can detect a change of temperature of one hundred- 

 millionth of a degree C.&quot; JOYCE, op. cit., p. 364. So, too, in measuring mass, 

 &quot; Metrology vouches for the hundredth of a milligramme in a kilogramme ; that is to 

 say, it estimates the hundred-millionth part of the magnitude studied &quot;. POINCARE, 

 op. cit., p. 33. 



8 Principles of Science, p. 357. 



