PROBLEMS. 479 



so that an observer can read, say, to -yL of an ampere anywhere 

 on the scale, (a) Find the percentage error due to the error of 

 reading when the reading is I ampere ; (//) find ditto when the 

 reading is 10 amperes. Ans. (a) 10 per cent.; (fr) i percent. 



130. An electrodynamometer-ammeter (a Siemens instrument) 

 has a scale of equal parts. The position of the pointer can be 

 read to, say, ^ of a division anywhere on the scale, (a) Find 

 how many times as great the error in amperes, due to the given 

 error in the reading, is when the reading of the pointer is 25 

 divisions than when the reading of the pointer is 250 divisions; 

 (b) find the percentage error in each case and the ratio of these 

 percentage errors. Ans. (a) 3.16 ; (&) i per cent, y 1 ^ per cent. ; 

 ratio i o : i . 



131. Given a direct-reading ammeter (or voltmeter) of the alter- 

 nating current type of which the actual length of any scale division 

 under the pointer is proportional to the reading of the pointer ; a 

 scale division being supposed to correspond to, say, o. i ampere 

 over the entire scale. The position of the pointer can be read to 

 a certain fraction of a degree of angle, so that the error in am- 

 peres due to an error of reading is inversely proportional to the 

 length of the scale division under the pointer, that is, inversely 

 proportional to the reading of the pointer, (a) Find how many 

 times as great the error in amperes due to an error in reading is 

 when the instrument reads i ampere than when the instrument 

 indicates 10 amperes, (b) Find how many times as great the per- 

 centage error is in the first case than in the second case. Ans. 

 (a) 10 times as great; (b) 100 times as great. 



NOTE. Ammeters and voltmeters which are suitable for direct-current circuits 

 only, always give a deflection which is approximately proportional to the current or 

 voltage. Therefore the scales of direct-reading instruments of this type are scales of 

 approximately equal parts. 



Ammeters and voltmeters which are suitable for both alternating and direct-cur- 

 rent circuits always give a deflection which is nearly proportional to the square of the 

 current or voltage. Let y be the deflection of such an instrument read on a scale of 

 equal parts or, say in degrees, let dy be one of the divisions of this scale, and let x be 

 the current or voltage corresponding to the deflection y. Then 

 y kx z and dy = zkxdx 



