on Magnetic Rotatory Polarization in Gases. 405 



corresponding variations in the plane of polarization of the 

 different images ; and if a sudden displacement occurred 

 during the progress of a measurement, the latter would be 

 erroneous. In order to guard against these variations, a 

 large number of consecutive measurements were made by 

 alternating the direction of the electric current in the coils. 



During the greater part of the time it was easy to see, by 

 the constancy of the direction of the planes of polarization 

 reflected in one direction or the other, that the luminous 

 point was fixed. From time to time a gradual displacement 

 of the planes of polarization was apparent ; but as the devia- 

 tions in one direction or the other were measured alternately, 

 this cause of error could be eliminated by taking the average 

 of the deviations in one direction and the average of the de- 

 viations in the other. All the numbers obtained were exa- 

 mined with great care from this point of view, and the 

 averages calculated in two ways: — the first, by taking the 

 averages of the double rotations directly observed ; the 

 second, by deducing the rotation from the difference between 

 the average positions of the planes of polarization deflected in 

 one direction or the other. 



When the two calculations did not give exactly the same 

 result, the average of the two numbers was taken. The differ- 

 ence, however, did not generally amount to more than a few 

 tenths of a minute of arc. 



Finally, I may add that all the phenomena which might be 

 due to dilatation, even of the copper tube, must be considered 

 as introducing no appreciable perturbation into the measure- 

 ments. 



Accuracy of the Measurements. 



The magnetic rotations obtained for the gases are some- 

 times so feeble that it is very important to take the most 

 exact account possible of the degree of accuracy of the obser- 

 vations. As will be seen, this determination presents great 

 difficulties ; and I shall confine myself to indicating the supe- 

 rior limits of the errors to be feared. 



The causes which may vitiate the measurements are the 

 following : — 



1st. The greater or less precision in the determination of 

 the position of the planes of polarization, in consequence of 

 the imperfection with which the eye appreciates the equality 

 of tint in the two halves of the image from the polariscope. 



2nd. The precision with which the electromagnetic inten- 

 sity is measured. 



3rd. The uncertainty as to the true wave-length of the 

 light studied. 



