Galvanometers of High Sensibility. 259 



material could be neglected, Paschen showed that if two 

 systems were made with magnets of the same cross section but 



of lengths I and respectively, then the second should give a 



deflection n* times as large as the first system, for if 



the magnetic moment of the first system = M. 1 

 and the moment of inertia " " " = K. 



then 



the magnetic moment of the second system == 



and the mom. of inertia " " " = 



The deflection of first system is proportional to 



n 

 K, 



n 



Mi 



M / 



and " " " second " proportional to — 1 /-g- 



"/ 



n 



i. e., the deflection of the second system is ?i 2 times that of 

 the first system. The assumption (that M oc / for given cross 

 section) on which the deduction is based is not even approxi- 

 mately true for short magnets, as the preceding experiments 

 show, but it does at least indicate an advantage in favor of 

 short magnets. This deduction is supported by experiment. 

 Thus Paschen found by testing three similar systems having 

 magnets 4 mm , 2 mm , and l-3 mm long respectively, made from 

 the same fine hair-spring, that the second gave three times the 

 deflection and the third six times the deflection of the first 

 system. 



From curve 1 it will be seen that, if the moment of inertia 

 of the non-magnetic parts of the system can be neglected in 

 comparison with that of the magnetic (a condition which can 

 perhaps be realized even with systems as light as 2 mg. total 

 weight) the sensibilities of two systems having magnets 2 mm 

 and l mm long respectively, of the same matcr'al and cross 

 section, would be proportional to 



M x 5*2 ' . ' 



— i- = lor system 1 



K, (2)' •> 



M 2 1-38 , , 



K7 = -Jrr fors y stera2 



i. e. the second system would be about twice as sensitive as the 

 first, instead of four times as deduced by Paschen on the 

 assumption that M ex I for given cross section. 



If it were always possible to use enough magnets, so that the 

 non-magnetic moment of inertia could be neglected, then the 



