240 Intelligence and Miscellaneous Articles. 



A mathematical analysis, which cannot be given in this abstract, 

 shows that, from these laws, to the differential equations of the motion 

 of a system of plane waves normal to the axis of z in a medium sub- 

 mitted to magnetic influence'^there cannot be assigned the form 



d 2 £ , d 2 £ : d^ d V 



^=A ^+A 1 ^+...-fm— 



. d'rj . d* v dl 



df~"°dz 



which M. Charles Neumann deduced from a particular hypothesis 

 on the cause of these phenomena, and which Mr. Airy had proposed 

 seventeen years ago, a few months after the publication of Mr. Fara- 

 day's discoveries. On the contrary, these laws agree equally either 

 with the equations 



d^_ d 2 l d*Z d 3 r, 



df- A o~d? +A iaY + '" + m dz T dt 



dS_, «[V A A, d*Z 



df - A °dz 2 + Al <&> + " ' ' ~ m dz 2 to' 



which Mr. Maxwell has deduced from an hypothesis quite different 

 from that of M. Charles Neumann, or with the equations 



d%_ d*Z d^ d^ 



dt 2 ~ A °dz 2 +A idz i + '~ +m d?' 



dt 2 ~ A °dz 2 +Al dz* + '"- m dt 3 ' 



The precision of the experiments, moreover, leaves no room for 

 choice between the two systems*. 



In conclusion, experiments on the magnetic rotations of dissolved 

 tartaric acid have shown that the proportionality imagined by 

 M. Wiedemann between the magnetic rotations and the special 

 rotations of an active substance do not in reality exist. In fact I 

 obtained for the two kinds of phenomena the following series of 

 results : — 



C. D. F. G. 



Magnetic rotations . . 0*79 1-00 1*52 2*01 



Natural rotations 0-85 1*00 101 0*89 



The exact law of the square of the wave-length would have required 

 C. D. F. G. 



0-80 1-00 1-48 1-88 



— Comptes Rendus, April 6, 1863. 



* It is immaterial to these conclusions whether we admit, with Cauchy, 

 that the coefficients A , A ls A 2 . . . form a rapidly decreasing series, or, with 

 M.Christoffeljthat the coefficients A and Ai are of the same order of mag- 

 nitude, all the others being negligible. 



