286 THE PRINCIPLES OF SCIENCE. [CHAP. 



In a still greater number of cases, perhaps, we multiply 

 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, are sufficient instances of this procedure. 



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



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, 

 though slight, 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 oppo- 

 site one of diminution. Galileo found it difficult to measure 

 the velocity of a falling body, owing to the considerable 

 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. Wheatstone invented a beautiful method of gal- 

 vanometry for strong currents, which consists in drawing 

 off from the main current a certain determinate portion, 

 which is equated by the galvanometer to a standard 

 current. In short, he measures not 'the current itself but 

 a known fraction of it. 



In many electrical and other experiments, we wish to 

 measure the movements of a needle or other body, which 

 are not only very slight in themselves, but the manifes- 

 tations of exceedingly small forces. We cannot even 



