under the Operation of Feeble Magnetic Forces. 229 



When the resistance was altered to 11,000 ohms, the com- 

 pensating-coil of course remaining undisturbed, contact ( — ) 

 produced no visible motion, showing that the same compen- 

 sation is suitable for the much smaller force. But at this 

 point we require to be assured that the absence of disturbance 

 is not due merely to want of sensitiveness. The necessary 

 information is afforded at once by making reversed contact 

 ( + ), which (with 11,000 ohms) gave a swing of 57 divisions. 



To diminish the magnetizing force still further, a shunting 

 arrangement was adopted. The current from the Daniell was 

 led through 10,000 ohms and then through a box capable 

 of providing resistances from 1 to 1000. The circuit of the 

 apparatus included another coil of 10,000 ohms, and its ter- 

 minals were connected to those of the box. The battery- 

 current was thus about *0001 ampere, or 10~ 5 C.G.S. If a 

 be the (unplugged) resistance in the box, the E.M.F. at the 

 terminals of the apparatus- circuit is axlO -4 volts; and the 

 current C through the magnetizing helix and compensating- 

 coil is a x 10" 9 C.G.S. 



When a = 1000 ohms, ( — ) gave no visible deflection, while 

 ( + ) caused a swing of 5 divisions. 



At this stage recourse was had to the " method of multipli- 

 cation " in order to increase the sensitiveness*. A pendulum 

 was adjusted until its swings were synchronous with those of 

 the suspended needle. It was then easy to make and break 

 contact in such a way as to augment the swing due to any 

 outstanding force. Thus, when a = 1000, the swing was in- 

 creased by the use of the timed contacts and ruptures ( -f ) 



* The advantage of the method of multiplication seems to be hardly 

 sufficiently appreciated. It is not merely that the effect is presented to 

 the eye in a magnified form. That object can be attained by optical 

 appliances, and by diminishing the directive force upon the suspended 

 parts, whether by using a nearly astatic system of needles, or by com- 

 pensating the held. For the most part these devices augment the un- 

 avoidable disturbances (which exhibit themselves by a shifting zero) in 

 the same proportion as the effect to be measured, or at any rate rendered 

 apparent. The real ultimate impediment to accuracy of measurement is 

 almost always the difficulty of distinguishing the effect under examination 

 from accidental disturbances, and it is to overcome this that our efforts 

 should be directed. The method of multiplication is here of great service. 

 The desired effects are largely magnified, while the disturbances, which 

 are not isoperiodic with the vibrations of the needle, remain unmagnified, 

 and therefore fall into the background. 



It is obvious that, in order to secure this advantage, the vibrations 

 must not be strongly damped. No doubt a highly damped galvanometer- 

 needle is often convenient, and sometimes indispensable. But it seems to 

 be a mistake to use it where a null method is applicable, and when the 

 utmost delicacy is required. In such a case the inertia of the needle, and 

 the forces both of restitution and of damping, should all be made small. 



