THE EXACT MEASUREMENT OF PHENOMENA. 329 



to different results. We may sometimes overcome this 

 difficulty to a certain extent, by observations repeated in 

 a special manner, as -we shall afterwards see ; but when 

 possible, we should choose opportunities for measure- 

 ment when precise definition is easy. The moment of 

 occultation of a star by the moon can be observed with 

 great accuracy, because the star disappears with perfect 

 suddenness ; but there are many other astronomical con- 

 junctions, eclipses, transits, &c., which occupy a certain 

 length of time in happening, and thus open the way to 

 differences of opinion. It would be impossible to observe 

 with precision the movements of a body possessing no 

 definite points of reference. The spots on the sun, for 

 instance, furnish the only direct criterion of its rotation, 

 and the possibility that these spots have a tendency to 

 move in one direction throws a doubt upon all deter- 

 minations of the sun's axial movement. 



The colours of the complete spectrum shade with perfect 

 continuity into each other, so that their separation is 

 entirely an arbitrary matter. Exact determinations of 

 refractive indices would have been impossible, had we not 

 the fixed dark lines of the solar spectrum as precise points 

 for measurement, or, what comes to the same thing, various 

 kinds of homogeneous light, such as that of sodium, pos- 

 sessing a nearly uniform length of vibration. 



In the second place, we cannot measure accurately 

 unless we have the means either of multiplying or dividing 

 a quantity without considerable error, so that we may 

 correctly equate one magnitude with the multiple or sub- 

 multiple of the other. In some cases we operate upon the 

 quantity to be measured, and bring it into accurate coin- 

 cidence with the actual standard, as when in photometry 

 we vary the distance of our luminous body, until its 

 illuminating power at a certain point is equal to that of a 

 standard lamp. In other cases we repeat the unit until it 



