398 USE OF THE GALVANOMETER 



in the thermometer-scale, this method can evidently be applicable 

 only to such slight differences of temperature and such feeble cur- 

 rents as the Italian physicist used in his experiments. 



Besides this, the assumption that the current which produces a 

 deflection of 24° must be 5. 1 stronger than one which produces a 

 deflection of 20°, because, when acting in opposition to the latter, it 

 caused a deflection of 5.1°, is only an approximation to the truth, 

 based on the tacit assumption of the proportionality between the 

 force of the current and the angle of deflection. If a, &, and b — a, 

 be the forces which produce, respectively, the deflections «, /9, y, 

 strictly taken, the ratio a : b = a : a -|- y can only exist when a : b=: 

 a : ft. This method, therefore, requires that the difference between 

 /? and a and the value of y should fall within the limits within which 

 this ratio is approximately true. 



From what has been said, it will be clearly seen that no perfect 

 method of determining the scale of intensity for the galvanometer has 

 hitherto been given. It may be said, indeed, that none is needed, 

 since the best galvanometer makes only a tolerable measuring instru- 

 ment, and for accurate investigations we have the mirror-apparatus 

 and the compass of sines. But these instruments are so costly as not 

 to be within the reach of every physicist. There are, moreover, 

 many experiments in which an accuracy of from one-half to a whole 

 degree in the deflection of the needle is quite sufficient. 



I therefore believe that the description of a mode of arranging the 

 galvanometer scale, which seems to me to satisfy all demands, will 

 be welcome to many experimenters. My method is convenient, cer- 

 tain, and susceptible of general application. It has also a decided 

 advantage over all hitherto described, in requiring but a single cur- 

 rent of uniform strength.* The principle of this method may be 

 expressed in a few words. The deflections, produced by currents of 

 different strength, passing through the coils of a multiplier lying in 

 the magnetic meridian, can be deduced from those produced by one 

 and the same current, passing through the same coils, at various 

 inclinations to the magnetic meridian. 



The possibility of this will be seen from the following geometric 

 considerations. The force with which the magnetism of the earth 

 tends to draw back a needle which has been deflected from the 



*Prof. Petrina,in Linz, lias recently described a method (v. Holger's Zeitschrift fur Physik, 

 Bd. I, s. 171) which has also this advantage, and is easily managed, but cannot be generally 

 recommended, because it gives only approximate results. Prof. P. lays the ends of the wires 

 of his galvanometer on the conducting wire of a constant battery, and then assumes that the 

 force of the branch current passing through this instrument will be exactly proportional to 

 the distance between the two points at which the conducting wire and the wires from the 

 galvanometer touch each other. But this is not true If we designate by r the resistance of 

 the portion of the conducting wire lying between the two points of contact, by r' the remain- 

 ing resistance of the battery, and by r" the resistance of the galvanometer wire, we shall 

 have for the force of the current passing through the latter, k being the electromotive force 

 of the battery, the expression — 



kr kr 



r r' -\- r r" -^ r' r" r' r" -\- (r' -\- r") r 



from which it is evident that the force of the current is approximately proportional to the 

 resistance r only so long as it is very small in comparison with r' and r". 



