124> DISCOURSE ON THE STUDY 



evident that every step of our enquiry must be per- 

 fectly free from the slightest degree of looseness 

 and indecision, and carry with it the full force of 

 strict numerical announcement ; and that, therefore, 

 the observations themselves on which all laws ulti- 

 mately rest ought to have the same property. None 

 of our senses, however, gives us direct information 

 for the exact comparison of quantity. Number, 

 indeed, that is to say, integer number, is an object 

 of sense, because we can count ; but we can 

 neither weigh, measure, nor form any precise esti- 

 mate of fractional parts by the unassisted senses. 

 Scarcely any man could tell the difference between 

 twenty pounds and the same weight increased or 

 diminished by a few ounces ; still less could he judge 

 of the proportion between an ounce of gold and a 

 hundred grains of cotton by balancing them in his 

 hands. To take another instance : the eye is no 

 judge of the proportion of different degrees of illu- 

 mination, even when seen side by side ; and if an 

 interval elapses, and circumstances change, nothing 

 can be more vague than its judgments. When we 

 gaze with admiration at the gorgeous spectacle of 

 the golden clouds at sunset, which seem drenched 

 in light and glowing like flames of real fire, it is 

 hardly by any effort we can persuade ourselves 

 to regard them as the very same objects which at 

 noonday pass unnoticed as mere white clouds basking 

 in the sun, only participating, from their great hori- 

 zontal distance, in the ruddy tint which luminaries 

 acquire by shining through a great extent of the 

 vapours of the atmosphere, and thereby even losing 

 something of their light. So it is with our esti- 



