Effects of Magnetism on Rods of I 



ron. ore. 



383 



21. Rigorously periodic motion of two planets. Given SVE 

 in line, the Sun and two planets at distances such as those of 

 Venus and the Earth : — it is required to project them with 

 such velocities that the subsequent motion is rigorously 

 periodic. A first solution is obtained by projecting them 

 perpendicularly to Y E with such velocities that their periods 

 of revolution round S are approximately equal ; and exactly 

 such that at the next time when Y E is again in line with S, 

 the motions are rigorously perpendicular to this line. The 

 velocities which must be given to fulfil this condition must be 

 such that the major axes of the ellipses approximately described 

 are approximately equal. This solution, however, belongs 

 rather to the Cometary than to the Planetary Theory. 



22. Project the planets perpendicularly to S Y E with 

 such velocities that after some given number of times of their 

 being in line with the Sun, their motions are, for the first time 

 again, perpendicular to SVE. The determinate velocities 

 which fulfil this condition must I think be such that the orbits 

 are approximately ellipses of eccentricities not differing much 

 from those required to make the major axes such that the 

 periods have the proper commensurability to render the line 

 of the three bodies at the second perpendicular crossing 

 approximately coincident with their line at the initial perpen- 

 dicular crossing. 



Madeira, Sept. 8, 1891. 



[To be continued.] 



XLIX. On some of the Effects of Magnetism on Rods of Iron, 

 Nickel, and other Metals which have received a permanent 

 Torsional Set ; and a new form of Chronograph Stylus. By 

 Frederick J. Smith, Millard Lecturer Mech. and Phys., 

 Trinity College, Oxford*. 



DURING the present year I have gone through rather a 

 long series of experiments with a view to discover some 

 form of chronograph stylus which would respond to rapid 

 vibrations and make a clear record of its vibrations on the 

 moving plate of a chronograph. I have succeeded in finding 

 a combination which appears to give satisfactory results. 

 During the research several facts of interest bearing on a 

 certain branch of magnetic induction presented themselves. 

 I beg respectfully to give a summary of some of them in the 



Coinmuuicated by the Author. 



