solving certain simple Electrical Problems, 371 



cat tables. This construction requires to be slightly modified 

 according to whether the instrument used is a tangent-gal- 

 vanometer or a sine-galvanometer. It is as follows : — 



1. For a tangent-galvanometer . — The battery is connected in 

 simple circuit with a tangent-galvanometer, and the deflection a 

 of the galvanometer is observed ; then a known resistance r 1 is 

 added to the circuit and the deflection is observed again. Let 

 the second deflection be denoted by «'. The following con- 

 struction then gives the electromotive force of the battery { = e) 

 and the permanent resistance of the circuit ( = r). 



From any point A in the straight line A (fig. 3) draw A P, 

 making the angle OAP = a; produce A to A', making A A' 

 proportional to the added resistance r 1 , and from A' draw A' V $ 

 making the angle A' P' = «' and on the same side of A as 

 A P. Since a' is less than a, the straight lines A P and A' P' 

 will intersect. From the point of intersection Q draw Q 

 perpendicular to A. Then A represents the permanent 

 resistance of the circuit, and Q represents the electromotive 

 force, in terms of that electromotive force taken as unity which, 

 if it acted in a circuit of unit resistance, would generate a 

 current capable of causing a deflection of 45° on the particular 

 galvanometer employed. 



2. For a sine-galvanometer. — Let /3 be the deflection observed 

 when there is no extra resistance, and /3' the deflection when an 

 additional resistance r' has been inserted in the circuit. Make 

 B B' (fig. 4) proportional to r 1 , make the angles B P and 

 B' P', on the same side of B B', equal respectively to /3 and/3', 

 and let B P and B' P' intersect at the point Q. Draw Q to 

 bisect the external angle B Q P', and cutting B' B produced in 

 O ; then B represents the permanent resistance of the circuit, 

 while the radius of a circle drawn with the point as centre so 

 as to touch the straight lines B P and B' P' measures the elec- 

 tromotive force, the unit of measurement for the latter being 

 the electromotive force which, in a circuit of unit resistance, 

 would give a current strong enough to deflect the galvanometer 

 used through 90°*. 



If the constructions indicated above are carried out for several 

 different values of the external resistance, it is clear that, with a 

 strictly constant battery, lines drawn according to the same rule 



* It may be worth while to point out that any galvanometer may be 

 used as a sine-galvanometer, even though it is not provided with a gradu- 

 ation to show the angle through which it has been turned. It is only 

 needful, after setting the instrument so that the zero of the scale is exactly 

 below the needle while the current is passing, to interrupt the current ; 

 the needle then swings away from the zero-mark,, returning to the magnetic 

 meridian; and the angle now indicated by it is the angle through which 

 the galvanometer has been turned from the meridian. 



