( 2fi3 ) 



distance has been reduced to 0.68 7n» ^^^fter 15 seconds to 0.25 7o 

 of the total deflection. 



Now putting in formuhx (51) Tj ^ 2.5, / i= J2.7 and 7/?^?/' as mini- 

 mum = 1.394 X 10"^ <'ie minimum of H works out al 940 (C.G.S.) 

 By formula (50) we calculate from this the maximum of sensitiveness 

 Cs = 434 mm per microvolt. 



Let us now consider the shortening of /. If a limit was soon found 

 where diminution of H ceased (o he useful, (his is not the case 

 Avith the shortening of /, which ma}' be })ushed as far as we like 

 as long as no practical difficulties are met with. By making /shorter 

 e.g. a times, as well the mass as the ohmic resistance are each 

 reduced a times. The \alue of m^in thus becomes a"^ times less, so 

 that Tj remains unaltered (formula 51) and the sensitiveness c., (for- 

 mula 50) becomes a times greater. 



A last remark may follow about the two formulae (50) and (51). 

 We first assume that they are both valid, and that tlie values of 

 m^w, I and H have been so chosen that T^ = 2.5. We next assume 

 that the mass w.^ is changed, Avhile all the rest of the instrument, 

 including tn, remains constant, and ask how the movement of the 

 wire is altered by this. When ???i is increased, the motion of the 

 wire becomes oscillatory. When m^ is diminished the motion remains 

 aperio(Hc but transgresses the limit of aperiodicity. The duration of 

 the deflection is lengthened while the sensitiveness remains the same. 



This latter case agrees with the actual conditions in the string 

 gah'anometer used b}' myself. The mass of the quartz thread is in 

 reality very small. If it were ^= the duration of the deflection 

 would be exactly twice as great as when w^ possessed the desired 

 value. Hence there is under these circumstances an advantage in 

 increasing the mass of the wire to a certain value. ^) 



String n". 18 has a mass and an air-dainping which were not 

 accurately measured, but which will not differ much from the cor- 

 responding values of string n". 10. Its ohmic resistance is about 

 2 times smaller, liowever, and amounts to 5100 ohms. With a time 

 of deflection of about \'^ minute the sensitiveness is e,, = 20 mm. 

 per micro^■o]t. If I could increase the mass of this string in a prac- 

 ticable manner, I should with unaltered .sensitiveness bring the 



1) The time constant is doubled when m = 0. See Fleemfng 1. c. 



It may be superfluous to remark that for the measurement of insulating resis- 

 tances increase of »?i will offer the same advantages as were mentioned above 

 for the measm^ement of thermo-currents. 



