io8 ELEMENTARY LESSONS ON [CHAP. n. 



but is liable to be disturbed in its distribution by the 

 near presence of other magnet poles, for no steel is so 

 hard as not to be temporarily affected by magnetic 

 induction. The law of inverse squares is only true when 

 the distance between the poles is so great that the dis- 

 placements of their magnetism due to mutual induction 

 is so small that it may be neglected. 



NOTE ON WAYS OF RECKONING ANGLES AND 

 SOLID-ANGLES. 



129. Reckoning in Degrees. When two straight lines cross 

 one another they form an angle between them ; and this angle 

 may be defined as the amount of rotation which one of the lines 

 has performed round a fixed point in the other line. Thus we 



may suppose the line C P in Fig. 60 to 

 have originally lain along C O, and then 

 turned round to its present position. The 

 amount by which it has been rotated is 



T j^ , clearly a certain fraction of the whole way 



tv round ; and the amount of rotation round 

 C we call "the angle which P C makes 

 s. / with O C," or more simply "the angle 



^^J^.-^ PCO." But there are a number of 

 270 different ways of reckoning this angle. 



Fig. 60. The common way is to reckon the angle 



by "degrees" of arc. Thus, suppose a circle to be drawn 

 round C, if the circumference of the circle were divided into 

 360 parts each part would be called "one degree" (l), and 

 the angle would be reckoned by naming the number of such 

 degrees along the curved arc O P. In the figure the arc is 



about 57 J, or ~ of the whole way round, no matter what size 



the circle is drawn. 



130. Reckoning in Radians. A more sensible but less 

 usual way to express an angle is to reckon it by the ratio between 

 the length of the curved arc that "subtends" the angle and the 

 length of the radius of the circle. Suppose we have drawn 

 round the centre C a circle whose radius is one centimetre, 

 the diameter will be two centimetres. The length of the 

 circumference all round is known to be about 3^ times the 



length of the diameter, or more exactly 3*14159 



This number is so awkward that, for convenience, we always 



