370 Prof. Ayrton and Mr. Mather on Galvanometers. 



ment gave a result about ^ of the published value, or about 

 two-thirds of the calculated maximum. 



In treating the subject mathematically the following as- 

 sumptions are made : — 



(1) Clearance between coil and end of magnets 1 millimetre. 



(2) Mirror and stem of negligible inertia compared with 



that of magnets. 



(3) Perfect astaticism of needle. (Thickness negligible.) 



(4) Coil unlimited in size and of best shape as voltmeter. 



(5) Thickness of insulation on wire negligible. 



(6) Control of suspension negligible. 



(7) Deflecting field equal to field at centre of coil. 



Note. — All the assumptions except (7), and perhaps (1), 

 will give too high a value for the calculated sensitiveness. 



Let 21 = length of magnets. 



A sb area of cross-section of magnets. 



B = induction density in the steel. 



A = density of steel. 



m = strength of pole. 



a = specific magnetism of needles. 



t = time of vibration (complete). 



Then, 



Magnetic moment = 2 ml, 



= M (say), 



••• «-*£-'; (8) 



Mass = 2AIA, 

 Moment of inertia I = § Al 3 A • (9) 



Specific magnetism= j— -r ; (10) 



B 



(7 SB 



r=2'V : 



5£ approximately. 

 For an astatic pair we have 



MHi-MHs 



where H x and H 2 are the controlling fields acting on the two 

 magnets respectively ; 



-S3 <») 



from (8), (9), and (10). 



