A TREATISE 



ON 



ELECTRICITY AND MAGNETISM. 



PART I. 

 METHODS OF 



CHAPTER I. 

 MEASUREMENT OF ANGLES. 



656. PRINCIPAL KINDS OF MEASUREMENTS. The various 

 magnitudes which are met with in physical measurements may all 

 be referred to the three fundamental mechanical units the units 

 of length, of mass or weight, and of time. 



We need not dwell here on the measurement of rectilinear 

 lengths, nor on that of weight ; these are the most frequent physical 

 operations, and they present no particular difficulty when we do 

 not attempt to reach the ultimate limits of accuracy. We shall 

 restrict ourselves to mentioning some of the corrections which they 

 necessitate. 



The scale used for measuring lengths is ordinarily divided in 

 millimetres. Whatever may be the value of the divisions, frac- 

 tions of divisions are estimated either by a vernier or by a 

 micrometric telescope. It is clear that the accuracy of any par- 

 ticular mode of subdivision cannot exceed the accuracy with which 

 the scale has been graduated. 



If we denote by e the value of a division of the scale at the 

 temperature 0, then if A is the coefficient of linear expansion of 

 the scale, this length at the temperature / will be equal to e (i + A/). 



If a length A measured on the scale at the temperature /, is 

 represented by n divisions, its true length is 



VOL. II. 



