CHAP. II.] ELECTRICITY AND MAGNETISM. 



109 



use for it the Greek letter IT. Hence the length of the circum- 

 ference of our circle, whose radius is one centimetre, will be 

 6-28318 . . . centimetres, or 2ir centimetres. We can then 

 reckon any angle by naming the length of arc that subtends it 

 on a circle one centimetre in radius. If we choose the angle 

 P C O, such that the curved arc O P shall be just one centimetre 

 long, this will be the angle one^ or unit of angular measure, or, 

 as it is sometimes called, the angle PCO will be one "radian" 



if nearly. All the 

 A right -angle will be 



360 



In degree-measure one radian = = 57 



2?r 



way round the circle will be 2ir radians. 

 ~ radians. 



131. Reckoning by Sines or Cosines. In trigonometry 

 other ways of reckoning angles are used, in which, however, the 

 angles themselves are not reckoned, but 

 certain "functions" of them called "sines," 

 "cosines," "tangents," etc. For readers 

 not accustomed to these we will briefly ex- 

 plain the geometrical nature of these 

 "functions." Suppose we draw (Fig. 61) 

 our circle as before round centre C, and 

 then drop down a plumb-line P M, on 

 to the line CO; we will, instead of reckon- 

 ing the angle by the curved arc, reckon it 

 by the length of the line P M. It is clear 



Fig. 61. 



that if the angle is small P M will be short ; but as the angle 

 opens out towards a right angle, P M will get longer and 

 longer (Fig. 62). The ratio between the length of this line and 

 the radius of the circle is called the "sine" 

 of the angle, and if the radius is I the 

 length of P M will be the value of the sine. 

 It can never be greater than I, though it 

 may have all values between I and - I. 

 The length of the line C M will also 

 depend upon the amount of the angle. If 

 the angle is small C M will be nearly as 



Fig. 62. 



long as CO; if the angle open out to nearly a right angle 

 C M will be very short. The length of C M (when the radius 

 is i) is called the "cosine" of the angle. If the angle be 

 called 0, then we may for shortness write these functions : 



132. Reckoning by Tangents. Suppose we draw our circle 



