July 12, 1907] 



SCIENCE 



55 



taking the observations given below, the mag- 

 netizing current and the current in the con- 

 ductor were measured with two Weston port- 

 able ammeters. 



Observations were first taken te show that 

 when the field is constant, the force on a given 

 conductor is proportional to the current flow- 

 ing through it. In taking the observations 

 given in Table I., a wire extending through 

 the slot, then bent straight back and clamped 

 in the binding posts was used. The con- 

 ductor was therefore not in a uniform field. 

 The table gives the first set of observations 

 taken. 



TABLE I. 



Steady current in magnetizing coil, 0.798 amperes. 



In taking the next set of observations, Table 

 II., the length of the conductor, as well as the 

 current in it, was varied. To obtain these 

 results, wires of the form shown in Fig. 1 were 

 used. The length of the horizontal part of 

 the wire lying in the slot and measured from 

 center to center of the turned-up ends, was 

 used as the length of the conductor. That 

 this is the " effective " length of the con- 

 ductor, if Ampere's law is true, may be shown 

 below. 



If the force acting on a straight conductor 

 is ilf, then the force acting on an element of 

 the conductor, of length dx, at the bend of the 

 conductor will be equal to the product of four 

 factors, the area of the section of the con- 

 ductor to the right of dx, the current per unit 

 area, the intensity of the field, and the length 

 dx. Assuming that the current is uniformly, 

 distributed throughout the conductor before 

 it reaches the turn and that it becomes uni- 

 formly distributed after it passes the turn 

 and before it leaves the air gap, we obtain as 

 the expression for the vertical force acting 



Steady current in magnetizing coil, 0.800 amperes. 



on that part of the conductor to the right of 

 the section AB, Fig. 2, 



if 



X2r /^x 



(TTr'— j 2ydx)(ix, 



where r is the radius of the conductor. In- 

 tegration of this expression gives ifr as the 



B 



Fig. 2. 



force acting on that part of the conductor to 

 the right of AB, or r as the length to be added 

 to the straight part of the conductor. 



The third factor in the expression for the 

 force on the conductor is f, the intensity of 

 the magnetic field. This apparatus can be 

 used conveniently for showing the relation be- 

 tween the force and f if a curve is plotted 

 showing the relation between f and the cur- 



