THE EXACT MEASUREMENT OF PHENOMENA. 331 



The moving globe itself is the real standard clock, and the 

 transit instrument the finger of the clock, while the stars 

 are the hour, minute, and second marks, none the less 

 useful or accurate because they are disposed at unequal 

 intervals. The photometer is a simple instrument, by 

 which we compare the relative intensity of rays of light 

 falling upon a given spot. The galvanometer shows the 

 comparative intensity of electric currents passing through 

 a wire. The calorimeter guages the quantity of heat 

 passing from a given object. But no such instruments 

 furnish the standard unit in terms of which our results are 

 to be expressed. In one peculiar case alone does the same 

 instrument combine the unit of measurement and the 

 means of comparison. A theodolite, mural circle, sextant, 

 or other instrument for the measurement of angular mag- 

 nitudes has no need of an additional physical unit ; for 

 the very circle itself, or complete revolution, is the natural 

 unit to which all greater or lesser amounts of angular 

 magnitude are referred. 



The result of every measurement is to make known the 

 purely numerical ratio existing between the magnitude 

 to be measured, and a certain other magnitude, which 

 should, when possible, be a fixed unit or standard magni- 

 tude, or at least an intermediate unit of which the value 

 can be ascertained in terms of the ultimate standard. But 

 though a ratio is the required result, an equation is the 

 mode in which the ratio is determined and expressed. In 

 every measurement we equate some multiple or submul- 

 tiple of one quantity, with some multiple or submultiple 

 of another, and equality is always the fact which we 

 ascertain by the senses. By the eye, the ear, or the touch, 

 we judge whether there is a discrepancy or not between 

 two lights, two sounds, two intervals of time, two bars of 

 metal. Often indeed we substitute one sense for the other, 

 as when the efflux of time is judged by the marks upon 



