THE EXACT MEASUREMENT OF PHENOMENA. 333 



the standard unit until we get a magnitude equal to that 

 to be measured. Ordinary measurement by a foot rule, 

 a surveyor's chain, or the excessively careful measurements 

 of the base line of a trigonometrical survey by standard 

 bars form a sufficient instance of this case. 



In the second case, where p~ = q, we multiply or divide 



v 



a magnitude until we get what is equal to the unit, or to 

 some magnitude easily comparable with it. As a general 

 rule the quantities which we desire to measure in 

 physical science are too small rather than too great for 

 easy determination, and the problem consists in multiply- 

 ing them without introducing error. Thus the expansion 

 of a metallic bar when heated from o C to 100 may be 

 multiplied by a train of levers or cog wheels. . In the 

 common thermometer the expansion of the mercury is 

 rendered very apparent, and easily measurable by the 

 fineness of the tube, and many other cases might be 

 quoted. There are some phenomena, on the contrary, 

 which are too great or rapid to come within the easy 

 range of our senses, and our task is then the opposite 

 one of diminution. Galileo found it difficult to measure 

 the velocity of a falling body, owing to the very consider- 

 able velocity acquired in a single second. He adopted 

 the elegant device, therefore, of lessening the rapidity 

 by letting the body roll down an inclined plane, which 

 enables us to reduce the accelerating force in any required 

 ratio. The same purpose is effected in the well known 

 experiments performed on Attwood's machine, and the 

 measurement of gravity by the pendulum really depends 

 on the same principle applied in a far more advantageous 

 manner. Sir Charles Wheatstone has invented a beauti- 

 ful method of galvanometry for strong currents, which 

 consists in drawing off from the main current a certain 

 determinate portion, which is equated by the galvano- 



