24 Mr. H. Bauerman on an Experiment for showing the 



lie wholly in the primary plane ; and its actual section of the com- 

 plete cone at the limit is seen in fig. 2a. 



To sum the whole argument, Professor Cayley's solution is 

 based on, " what is true up to the limit will be true at the limit;" 

 but he has overlooked the condition, "provided there be no dis- 

 continuity at the limit." In the passage of an ellipse with po- 

 sitive radius vector through a parabola with vanishing latus 

 rectum to an ellipse with negative radius vector there is discon- 

 tinuity; yet it is thus that elliptic motion from positive trans- 

 verse initial motion passes to elliptic motion from negative trans- 

 verse initial motion. The difficulty arises from the discontinuity 

 in direction of the transverse initial motion in its passage through 

 zero. 



No remarks on (4) are needed, further than that it states one of 

 the mawyproblems of which rectilinear motion through an attract- 

 ing centre is the limit. I prefer it on account of the investigation 

 by means of the hodograph. An examination by that method 

 of the various proposed limit-problems and solutions will well 

 repay making it. 



d v LL 



Turning now to the equation —=— = ^, I find it uniformly 



az x 



applied to the above-discussed problem, even by those who accept 

 Laplace's views of the particle's motion. But here they are in- 

 consistent; for Professor Cayley's is not merely "an admissible 

 solution" of the equation, it is the only one. Negative values 

 of x cannot be expressed in actual [non-nil) values of t. Either 

 reject the equation or accept the solution. Here it is a case of 

 pure analysis ; and in such no man need attempt to glean after 

 Professor Cayley. The equation may be considered to express 

 the limiting case of, " A particle moves from rest under the action 

 of a spherical surface, all the parts of which at first attract the 

 particle with forces varying inversely as the square of the dis- 

 tance, but {each} passage of the particle through the centre of 

 the spherical surface converts the attraction into repulsion {or 

 vice versa}) find the law of the particle's motion." 

 Strathroy, Ontario, May 15, 18/5. 



V. An Experiment for showing the Electric Conductivity of various 

 forms of Carbon. By H. Bauekman, F.G.S.* 



THE following simple method of exhibiting the conducting- 

 power of carbon was brought to my notice by my friend 

 Mr. W. J. Ward, of the Metallurgical Laboratory of the Koyal 



* Read before the Physical Society, May 22, 1875. Communicated by 

 the Society. J 



