Measurement of Mechanical and Electrical Forces. 91 



of the two currents — that is, to the energy being expended; 

 but if the wires are allowed to more, the force will depend 

 also on the position. The question then is, how can the wires 

 be so arranged that the force exerted may be used to incline 

 the tan gent- wheels and yet be independent of their motion. 

 The arrangement of solenoids shown in section in fig. 12 is 

 a complete and perfect answer. Si and S 2 are two fixed sole- 

 noids concentric with one another ; and the main current is 

 made to pass through each in the same direction. S 3 is a 

 solenoid made of a very great length of fine wire, preferably 

 of aluminium silver, as suggested by Mr. Imray; and the 

 upper half is wound in one direction and the lower half in the 

 opposite direction ; and the derived current is made to pass 

 through it so as to pass in the upper half in the same direction 

 as the main current passes in the fixed solenoids, and in the 

 lower half in the opposite direction. This solenoid is hung in 

 the annular space between the fixed ones by a band passing 

 over the arc of the beam B. The tubes within and without 

 the fixed solenoids and the rings above and below them, all of 

 which are shown dark in the figure, are made of iron, and 

 may or may not be used according as the currents employed 

 are in general weak or strong. But whether the tubes are 

 or are not retained, the use of the rings has certain advan- 

 tages, which I now proceed to explain. Fig. 13 is a diagram 

 taken by iron filings, which shows the distribution of the lines 

 of force due to the fixed solenoids alone, without the tubes or 

 rings. Here the lines of force cut the walls of the solenoid at 

 an oblique angle, so that the force, which is at right angles 

 both to the wires and the lines of force, tends to stretch the 

 movable coil, and only a portion of it is effective in drag- 

 ging down the solenoid : moreover the lines of force are very 

 widely distributed over the solenoid, so that, unless it is of 

 very great length, the upper part will leave by its motion 

 many lines. It is true that on the lower end the movable 

 solenoid will, when at its central position, enter as many lines 

 in an element of motion as it leaves at its upper end ; but 

 after any considerable movement the upper end will leave 

 many more than the lower end enters ; and the force, as it is 

 proportional to the number of lines enclosed, will become less 

 as the solenoid moves from its central position. This will be 

 referred to again later. jSTow the iron rings act as traps, so to 

 speak, and catch nearly all the lines of force which without 

 them stray over so great a space. Fig. 14 shows the field pro- 

 duced when the iron is present. It will be seen at once that 

 nearly the whole of the induction takes place across a very 

 narrow band of the solenoid, and that the lines of force, 



