508 PROF. JACOBI ON THE APPLICATION OF ELECTRO-MAGNETISM 



at the same distance, and that the branches themselves be exactly cylindri- 

 cal. Filing them into shape will perhaps have the disadvantage of hard- 

 ening too much the surface of the iron, and of rendering it less apt to 

 receive and to part with the magnetism. The form proposed offers a 

 further inconvenience, in the application of the copper wire helices, 

 which have to be previously bent on another cylinder of the same di- 

 mension. These helices ought very nearly to touch the bars, which 

 should be covered with silk on account of the insulation which is neces- 

 sary. In future an arrangement similar to the one in fig. 2 will be pre- 

 ferred, in which y are the fixed bars, and m the bars moveable around the 

 axis a. We shall have the advantage of being able to employ cylindrical 

 bars of soft iron, such as may be had of all dimensions in the shops. It 

 will only be necessary to cut them into equal pieces, and the helices may 

 be strongly wound round the bars by means of the lathe. 



5. 

 As the magnetic attraction decreases rapidly as the distance increases, 



the integral C Mds will always be such a function of the amplitude 



a, that its value will not greatly differ from a constant, a being rather 

 considerable. Admitting, for an instant, that the magnetic attraction 

 is in an inverse ratio to the squares of the distances, we shall have 



/Mds = f •' = -y arc tg — , d being the distance of the mag- 



netic centres when the bars are placed the nearest possible ; thus d being 



vervsmallwithrespecttoa, / Mds=-i-^ or = -^!^, n represent- 

 ■' i/ o 4a 4a 



ing the number of bars. We shall then have for the action of the mo- 

 tor, during one entire revolution, the expression —^^' The radius of 



the circle upon which the bars are arranged does not enter into this 

 expression ; and for a stronger reason it will not enter into any of 

 the other expressions, if the attraction still decreases more rapidly than 

 the inverse ratio to the square of the distance. Thus the size of the 

 circle for the same number of bars scarcely adds anything to the action 

 of the motor. 



I conceived that the system of bars, which in my apparatus are fixed, 

 might also be rendered moveable. Therotation of the two systems will 

 then be in a contrary direction and have the same velocity, the masses 

 being equal. These two motions might be combined by means of conical 

 wheels, in order to produce the motion of a second axis of rotation in- 

 tended for the work. The action of the motor, during the amplitude a, 

 that is to say from one meeting of the poles to the other, would be as 



above ^^^^j but the poles meeting each other 2h times in one revolu- 



