1867.] 



On the Maintenance of Electric Currents, 



397 



an upright position, and at a given angle of inclination 0^, let and be 

 those radii respectively ; then make 



This will be the radius of the required circle ; and its positive or negative 

 sign will show whether it is to be laid off downwards or upwards from the 

 metacentre. For any given angle of inclination the radius of curvature of 

 the metacentric involute will be given by equation (1), which may also be put 

 in the following form : 



P=Po + (p-P«)^y (3) 



Let S be the depth of the ship's centre of gravity below her metacentre, 

 and ja the perpendicular let fall from that centre of gravity upon the radius 

 of curvature of the metacentric involute at any given angle of inclination 6 ; 

 then 



p = (a-r)sinO + r0; (4) 



and the moment of stability is 



20 X displacement (5) 



It is obvious that the condition of isochronous rolling is that ^— ?'=0 ; 

 that is to say, that the centre of the circle which is the evolute of the meta- 

 centric evolute shall coincide with the ship's centre of gravity ; a proposi- 

 tion already demonstrated by me in a paper read to the Institution of Kaval 

 Architects in 18G4, and published in their Transactions, vol. v. p. 35. 



^Postscript. — Received March 11, 1867.] 

 Since the above was written, I have been informed by Mr. Merrifield, to 

 whom I had communicated my proposed modification of his method, that 

 it has been tried at the lloyal School of N?cval x\rchitecture and found to 

 answer v/ell. 



II. On the Theory of the Maintenance of Electric Currents by 

 Mechanical Work without the use of Permanent Magnets.-" By 

 J. Clerk Maxwell, F.R.S. Received February 28, 1887. 



The machines lately brought before the Royal Society by Mr. Siemens 

 and Professor Wheatstone consist essentially of a fixed and a m.oveable 

 electromagnet, the coils of which are put in connexion by means of a com- 

 mutator. 



The electromagnets in the actual machines have cores of soft iron, which 

 greatly increase the magnetic efJ^ects due to the coils ; but, in order to 

 simplify the expression of the theory as much as possible, I shall begin by 



