364 
LORD RAYLEIGH ON THE CONSTANT OF MAGNETIC 
doubly into the result, so that the whole error possible in determining the doable 
angle of rotation rises to 4e, and the use of the half-wave plate gives no advantage. 
One other point may be considered in conclusion. In determinations of rotation by 
magnetic force, the effect to be measured may be multiplied (as Faraday showed), by 
causing the light to be reflected backwards and forwards a,t the ends of the tube. 
Against this augmentation of the angle of rotation we must set the loss in the section 
of the beam, and the waste of light in reflection and by absorption. Putting out of 
sight for the moment the alteration in the section of the beam, we may easily deter¬ 
mine the most advantageous number of passages as dependent upon magnitude of 
rotation and intensity of light. If r be the factor by which the original intensity 
must be multiplied, in order to express the intensity after a single passage and reflec¬ 
tion, r 11 will express the intensity after n such passages and reflections. The accuracy 
of the determination will thus be proportional to nr ln , which is a maximum -when 
r=e~ Zhl . The values of r corresponding to n equal to 1, 3, 5, 7, ... , are '135, ’514, 
•670, '752, . . . , so that 3 or 5 passages wall usually give the best result. 
The argument in favour of a moderate use only of the principle of reflection is 
strengthened when we take into account the diminution in the section of the beam. 
The already contracted aperture is seen at a greater distance (proportional to n ), so 
that the apparent magnitude of the field of view is rapidly narrowed. Under these 
circumstances the comparisons cannot be made with the usual accuracy. If we have 
recourse to a telescope we can indeed restore the apparent magnitude, but (usually) 
only at expense of the illumination, since the aperture of the telescope is limited. 
If the available aperture do not exceed \ inch, any degree of magnification involves a 
loss of brightness. The importance of these considerations depends upon the length 
and diameter of the tube; but the tendency of the discussion is to show that more 
than five passages can rarely be desirable, and that in many cases three passages 
ought to be preferred to five. If there is any exception it will be when powerful 
white light (as from the sun) is available, or wdien it is possible by use of a larger 
number of passages to bring the whole rotation up to 90° or 180°, in which cases, as 
has already been noticed, the angle may be determined with peculiar advantage. 
Postscript. 
(October, 1885.) 
An important paper* has recently been communicated to the French Academy! by 
M. Becquerel, in which he abandons his former result (§ 4), obtained with the aid of 
terrestrial magnetic force, in favour of a number agreeing more nearly with that given 
by Gordon and myself. In the new experiments a long column of CS 3 was employed, 
encompassed by a spiral conveying a current, the effect of which is shown to depend 
upon the magnitude of the current and upon the number of turns, in approximate 
* Ann. d. Cbim., Oct., 1885. 
f C. R., June 2, 1885. 
