AS A MEASURING INSTRUMENT. 401 



ratio to the force of the current. Knowing, therefore, the form of 

 the curve for a current of one intensity, we can obtain its form for 

 any other intensity by lengthening or shortening all the ordinates in 

 proportion to the force of the second current. Thus, if a R (page 407) 

 be the curve for the intensity one, A R will be the curve for the in- 

 tensity one and a half, all the ordinates of the latter being one-half 

 longer than those of the former. 



If we suppose the curves for all intensities of the current which 

 can be measured by the galvanometer to be delineated in this way, 

 the main problem is still to be solved: to deduce the values of these 

 intensities, or their ratio to the force assumed as unity, from the points 

 of intersection of the curves with magnetic curve 31 iV, the co-ordi- 

 nates of these points being given only by observation. 



The mode of doing this may be exemplified by the two curves a R 

 and A R in the figure. According to what has been said, the forces 

 of the currents which they represent will be to each other as P h : P C, 

 or, what is the same, as p c : p k. It is now required to deduce this 

 ratio from M p, p c, and 31 P, P C, the co-ordinates of the points of 

 intersection c and C. 



Two cases must be distinguished: either the greater or the less 

 intensity of current may be given, i. e., the upper or the lower curve 

 may be known. Let us consider the first case. 



In this case we have to determine P h in the ratio P h : P C. If 

 we imagine the curve a R, which is known, to be moved toward the 

 left parallel to the axis of abscissas, its intersection with the 

 magnetic curve will evidently fall lower down, and there will be a 

 position a' r' in which its ordinate p' c' will be equal to P h. But dp' 

 is the sine of M p\ i. e., the sine of a value of a for which the cor- 

 responding values of m and n have been determined by the process 

 already described. Moreover, P G is the sine of 31 P; but 31 P is 

 equal to wp\ which is the value of n, corresponding to the given 

 value of a. 



Therefore, the currents whose effects are represented by the curves 

 a R and A R, and which produce the deflections 31 p and 31 P, when the 

 coils lie in the meridian, are to each other as one of the values of sin 

 a to one of the values of sin n of the table before given; i. e., if 

 n, and m t be the special value of n and m, corresponding to the position 

 a' r' of the lower curve, the ratio will be sin n' — ml : sin n'. 



In the same manner the value of p k may be determined, if the 

 upper curve A R be that for which the table before given was made. 

 We have onlv to imagine A R to be moved to the right, to a position 

 A' R', in which C P' =p h. Then p k = O P' = sin 31 P' = sin (n -f m) 

 and pc=z sin 31 p =. sin W P' = sin n. Now if ml and n' be the special 

 values of m and n, corresponding to the position A' R' of the upper 

 curve, we shall have for the ratio of the currents p c : p k z=z sin 

 n' : sin (nf -j- m'). 



From this it is evident that, according as the force of the current 

 to be measured is greater or less than that assumed as unity, the 

 curve representing the latter must be moved to the right or left, 



26 



