May 7, 1885] 
NATURE 7 
most favourable estimate. In the first place, the image 
whose position is to be measured to within one-hundredth 
of a millimetre is the result of seventy-nine reflections 
from concave mirrors ! 
Secondly, one of these mirrors is to be 2 decimetres 
in diameter. Such a mirrorused in a reflecting telescope 
would show signs of distortion if not carefully mounted— 
even at rest. But this mirror is required to make fifty 
revolutions per second, and the distortion is multiplied 
by forty reflections from its surface ! 
Finally, notwithstanding the avowed purpose of di- 
minishing the path of the light (“saws augmenter le 
trajet de la lumiére”), the distance required is greater 
than in my own experiments in the proportion of 1600 to 
1200, and hence atmospheric disturbances would come 
into play in the same proportion—unless especial pre- 
cautions were taken to guard against them. 
And here, I am free to concede, is an important ad- 
vantage, but one which is by no means limited to M. 
Wolfs arrangement, but is universally applicable—for by 
repeated reflection by plane or by concave reflectors the 
whole path, either in Fizeau’s method or in Foucault’s, 
may be confined to a limited space. But I think the 
chief object of such an arrangement—namely, to control 
easily the homogeneity of the air-column— could be more 
advantageously effected by a long underground tunnel 
containing a pipe, surrounded, if necessary, by running 
water, or, better still, exhausted of air. 
At Prof. Newcomb’s request I have repeated, with some 
alterations, the experiments described in the paper re- 
ferred to, and occasionally the appearance of the image 
was better than in that work. On one occasion the width 
of the image was carefully measured, and found to be 
025 mm. Evidently there is nothing remarkable in 
measuring the position of the centre of an image of this 
width within a hundredth of a millimetre. 
Again, the “ probable error” of my final result, 5 kilo- 
metres, would seem to show a somewhat greater degree of 
consistency than would be possible had I only a “ ¢ache 
lumineuse” to bisect. 
I cannot forbear remarking that by astronomical 
methods—if M. Wolf entirely mistrusts the results ob- 
tained by Cornu, Newcomb, and myself—the velocity of 
light is known certainly within 1 per cent.. and that it 
would, therefore, denote rather an excess of caution to 
deduce a formula for the elimination of a possible un- 
certainty of from 5 to 1o per cent., as M. Wolf does in 
determining “/vrdre M de cette déviation.” 
In conclusion, I think M. Wolf is to be congratulated 
on the very happy combination he has devised for the 
solution of this most fascinating problem—a problem 
which, notwithstanding its difficulties, will ultimately 
yield a result correct not merely to one part in 3500, but, 
I firmly believe, one in 300,000—perhaps one in 1,000,000, 
ALBERT A. MICHELSON 
SELF-INDUCTION IN RELATION TO CERTAIN 
EXPERIMENTS OF MR. WILLOUGHBY 
SMITH, AND TO TAE DETERMINATION 
OF THE OHM 
Ee a lecture delivered by Mr. Willoughby Smith before 
the Royal Institution in June last (see Proceedings) 
some experiments are detailed, which are considered to 
afford an explanation of discrepancies in the results of 
various investigators relating to the ohm, or absolute unit 
of electrical resistance. As having given more attention 
than probably any one else in recent years to this subject, 
I should like to make a few remarks upon Mr. Willoughby 
Smith’s views, which naturally carry weight correspond- 
ing to the good service done by the author in this branch 
of science. 
In the first series of experiments a primary circuit is 
arranged in connection with a battery and interrupter, 
and a secondary circuit in connection with a galvanometer 
and commutator of such a character that the make and 
break induced currents pass in the same direction through 
the instrument. Under these circumstances it is found 
that at high speeds the insertion of a copper plate between 
the primary and secondary spirals entails a notable 
diminution in the galvanometer deflection, and this result 
is regarded as an indication that the molecules of copper 
need to be polarised by the lines of force—an operation 
for which there is not time at the higher speeds. The 
orthodox explanation of the experiment would be that 
currents are developed by induction in the copper sheet, 
which thus screens the secondary spiral from the action 
of the primary, and the result is exactly what might have 
been anticipated from known electrical principles. I have 
the less hesitation in saying this, because as a matter of 
fact I did anticipate from theory the action of a combina- 
tion very similar in character. The experiment is de- 
scribed in the Philosophical Magazine for May, 1882, 
and differs from Mr. W. Smith’s only in the substitution 
of a telephone for the galvanometer, and of a microphone 
for the interruptor, no reverser in the secondary circuit 
being required. By the interposition of a thick copper 
sheet the sound is greatly enfeebled. 
The second series of experiments were made with 
Faraday’s “new magneto-electric machine,” in which a 
copper disk rotates about its centre between the poles of 
a horse-shoe magnet. The currents developed are ex- 
amined with a galvanometer whose electrodes touch two 
points upon the disk—in Mr. W. Smith’s experiments, 
one at the centre, and the other at the circumference. 
At low speeds the distribution is symmetrical with respect 
to that diameter of the disk which is passing at any 
moment between the poles; but, as the speed is in- 
creased, a certain “drag” is observed, disturbing the 
symmetry. This drag, or lagging, was noticed by 
Nobili in a very similar arrangement as long ago as 
1833 (‘‘Wiedemann’s Electricity,” third edition, vol. iv., 
§ 374), and is no doubt to be attributed to the induction 
of the currents upon themselves. 
This question of self-induction is indeed a very im- 
portant one in respect of certain methods for determining 
the ohm; but it certainly cannot be said to have been 
neglected, as Mr. W. Smith seems to suggest. Both in 
the original experiments of the British Association Com- 
mittee with a coil revolving about a vertical axis, and 
in my own recent repetition of them, the self-induction 
of the coil is a most important feature, and may cause a 
displacement of the position of maximum current from 
the plane of the magnetic meridian through as much as 
20°. In my paper (Phil. Trans., 1882, p. 661) I thought 
I had discussed the question at almost tedious length. 
It is possible that Mr. W. Smith had in his mind rather 
| determinations by the method of Lorenz, in which 
Faraday’s disk is used. The arrangement here, however, 
differs in one very important respect from that of Mr. W. 
Smith’s experiments in that the lines of force are sym- 
metrically arranged in relation to the axis of rotation. 
The consequence is that, however great the speed of rota- 
tion, there are no currents circulating in the disk, and 
therefore no question arises as to the self-induction of 
such currents. What is observed is simply the difference 
of electrical potential between the centre and the circum- 
ference. It is impossible to discuss the matter fully here, 
but the reader will find all that is necessary by way of 
explanation in the paper published in the Phz/. Trans. 
(“Experiments by the Method of Lorenz for the further 
Determination of the Absolute Value of the British Asso- 
ciation Unit of Resistance,” &c.). My object in writing 
is to correct the inference, suggested by W. Smith’s 
remarks, that the question of self-induction has been 
neglected by workers upon this subject. 
RAYLEIGH 
