282 THE PRINCIPLES OF SCIENCE. [CHAP. 



the needle ; daily and yearly periodic changes have also 

 been detected, and all the elements are found to be subject 

 to occasional storms or abnormal perturbations, in which 

 the eleven year period, now known to be common to many 

 planetary relations, is apparent. The complete solution 

 of these motions of the compass needle involves nothing 

 less than a determination of its position and oscillations in 

 every part of the world at any epoch, the like determina- 

 tion for another epoch, and so on, time after time, until 

 the periods of all changes are ascertained. This one sub- 

 ject offers to men of science an almost inexhaustible field 

 for interesting quantitative research, in which we shall 

 doubtless at some future time discover the operation of 

 causes now most mysterious and unaccountable. 



The Methods of Accurate Measurement. 



In studying the modes by which physicists have ac- 

 complished very exact measurements, we find that they 

 are very various, but that they may perhaps be reduced 

 under the following three classes : 



1. The increase or decrease, in some determinate ratio, 

 of the quantity to be measured, so as to bring it within 

 the scope of our senses, and to equate it with the standard 

 unit, or some determinate multiple or sub-multiple of this 

 unit. 



2. The discovery of some natural conjunction of events 

 which will enable us to compare directly the multiples of 

 the quantity with those of the unit, or a quantity related 

 in a definite ratio to that unit. 



3. Indirect measurement, which gives us not the quan- 

 tity itself, but some other quantity connected with it by 

 known mathematical relations. 



Conditions of Accurate Measurement. 



Several conditions are requisite in order that a mea- 

 surement may be made with great accuracy, and that 

 the results may be closely accordant when several inde- 

 pendent measurements are made. 



In the first place the magnitude must be exactly defined 

 by sharp terminations, or precise marks of inconsiderable 



