230 PROCEEDINGS OF THE AMERICAN ACADEMY 



then wound two outer coils, each of 800 ohms' resistance, which were 

 as large as it was convenient to fit on to the dynamometer. 



For maximum sensitiveness, the resistance of the outer coils should 

 he equal to one fourth of the resistance in circuit. The sensitiveness 

 falls off much more rapidly with decrease of resistance below this 

 point, than it does by increase of resistance above this point. The 

 law is represented by the equation 



T= X 



(. + W 1 



in which T is a measure of the sensitiveness ; X, the resistance per 

 foot of the wire in terms of the resistance per foot of the wire of the 

 standard coil ; /?, the total resistance of the standard coil ; and a, all 

 other resistance in circuit, about 1,100 ohms. (3 X' 2 is the resistance 

 of the outer coil, the resistance of a fixed weight of wire being di- 

 rectly as the square of its resistance per foot. T is a maximum when 

 a = 3/?X 2 . 



It will be seen from the above equation, that, if the outer coils are 

 used in series, the resistance, 1,600 ohms, is much too large ; if they 

 are used in parallel, the resistance, 400 ohms, is also large ; and the 

 instrument is 64 per cent more sensitive with the parallel arrange- 

 ment. For best effect, the wire of the outer coils should have had a 

 section 91 per cent larger, and the coils should have been used in 

 series, or a section 4 per cent larger, and have been used in parallel. 

 However, we found that if the outer coils were used in parallel, the 

 dynamometer was sufficiently sensitive. 



For a suspension, we finally used a platinum wire, 0.004" in diame- 

 ter, all lighter ones breaking because of the weight of the coil. The 

 length of the wire was about twenty inches. The inner coil carried 

 a vane, swinging in dilute sulphuric acid, by which one connection 

 was made, the other being made by means of the suspending wire. 

 Mercury was not used, as its surface tension would not allow free 

 enough motion of the contact wire. The deflection of the inner coil 

 was read by a telescope and scale, a mirror being fixed to the coil. 



As the currents to be measured were alternating, it was necessary 

 to calibrate the electro-dynamometer for alternating currents ; for in 

 rapidly alternating currents the inner coil is acted on by the outer 

 coils only, while in direct currents the magnetism of the earth is felt 

 also. Mr. Hopkins in his experiments had inserted a current alter- 

 nator between the battery and his dynamometer, but found a great 

 deal of trouble from leakage across the insulation. We therefore 



