AS A MEASURING INSTRUMENT. 399 



meridian, it is well known, is the product of three factors — the inten- 

 sity of the terrestrial magnetism, the magnetic force of the needle, and 

 the sine of the angle of deflection. This force ma}^ therefore, be 

 represented by a curve (31 N page 407) whose abscissas are the arcs, 

 and whose ordinates are the sines of the arcs, or the products pro- 

 portional to these sines. 



An analogous but inverted curve, i. e., increasing as the cosines of 

 of the arcs, would represent the force with which the electrical cur- 

 rent tends to deflect the needle, in traversing a straight or circular 

 wire lying in the magnetic meridian, at an infinite distance from the 

 needle or the diameter of its circle, when compared with the dimen- 

 sions of the needle. At the same time, the intersection of these two 

 curves, or rather the abscissa corresponding to it, would represent 

 the deflection of the needle under the influence of both these forces. 



With the galvanometer the latter curve is much more complex, 

 owing to the complicated form of the wire and its proximity to the 

 needle. Its course is not known, but it is evident that it must have 

 nearly the shape of a R in the figure. The problem is first to deter- 

 mine the shape of this curve, and as this is theoretically impracti- 

 cable, it must be done experimentally. 



This is done in the following way: Suppose a R to be the unknown 

 curve. Its form could evidently be determined by moving it to the 

 right and left along the axis of abscissas LR, and marking in each 

 position the co-ordinates of its point of intersection with the curve 

 M N, which ma}' be considered as given. Thus for the positions a R 

 and a' r', we should have the points of intersection c and c', the ordi- 

 nates c p and c' p 1 , and the abscissas M p and M p', and in order to 

 obtain the form of the curve, the distance iv M would have to be added 

 to, or subtracted from, the abscissas of the points of intersection in 

 every position but the original one. 



This simple geometrical supposition may be readily and exactly 

 carried out, if the coils of the galvanometer wire are movable in a 

 horizontal plane. These instruments generally have such an arrange- 

 ment, and it is then only necessary to fix an index near the coils, by 

 which the amount of rotation may be read off.* 



Set the galvanometer so that the index and the zero line of the 

 graduation shall be in the magnetic meridian, and the axis of rotation 

 of the needle exactly in the centre of the graduated circle. Then 

 pass a constant current through the coil so as to obtain a steady de- 

 flection of 35° to 40°. A thermo-electric current is best suited to 

 the purpose. 



This first angle of deflection represents the abscissa m p, and its 



* On my galvanometer the plate which carries the coil turns by means of a cogged wheel 

 and an endless screw, on a metallic axis, working on metallic bearings. Such an arrange- 

 ment is necessary in order to move it steadily. Strictly speaking, the support on which 

 the needle hangs should be fixed to the plate, so as to turn with the coil, and thus eliminate 

 the torsion of the thread; and secondly, the ends of the wire, which cannot turn, must be 

 twisted together so as to be without influence on the needle, and pass out through a hole 

 under the centre of the coil, as in the compass of sines. 



