March 14, 1913] 



SCIENCE 



411 



tion, Dr. Arthur Hill Daniels, professor of 

 philosophy, was appointed acting dean. Dean 

 Daniels' appointment is to remain effective 

 until something definite shall be done in re- 

 gard to the proposed combination of the Col- 

 lege of Literature and Arts, and the College 

 of Science. 



Mr. C. Shearer, M.A., Clare College, Cam- 

 bridge, has been appointed university lecturer 

 in zoology. 



Dr. Constantin Caratheodory, of the 

 Technical Institute at Breslau, has been ap- 

 pointed professor of mathematics at Got- 

 tingen as successor to Professor Felix Klein. 



DISCUSSION AND COBBESPONDENCE 



RELATIVITY IN ELECTROMAGNETIC INDUCTION 



In Science of January 17, 1913, S. J. Bar- 

 nett adduces a certain experiment as consti- 

 tuting an experimentum crucis showing that 

 complete relativity does not exist in electro- 

 magnetic induction. The experiment is cer- 

 tainly an interesting one, but on closer exam- 

 ination does not seem to be so definitely in 

 contradiction to the principle of relativity as 

 may appear at first sight. 



For discussion let us consider the following 

 simple form of experiment which illustrates 

 the same principles. Take a cylindrical mag- 

 net magnetized longitudinally and symmet- 

 rically about its axis, and mount it in the 

 axis of a somewhat larger cylindrical metal 

 tube, with air or other dielectric between 

 insulating one from the other, and forming a 

 cylindrical condenser. Connect the two by a 

 metal brush or cross-connection reaching ra- 

 dially across from the tube to the middle of 

 the magnet. Now if the whole system con- 

 sidered as rigidly connected is spun around 

 its axis of figure there will of course be induc- 

 tion and a difference of potential established 

 between the magnet and the outer tube, and 

 if the brush connection be broken while the 

 system is in rotation, on bringing the whole 

 to rest the condenser, consisting of tube and 

 magnet, will be found charged. 



So also when the tube alone is rotated while 

 the magnet is kept at rest, a difference of 



potential is established, provided the metal 

 connecting brush rotates with the tube. Or 

 if the magnet is rotated and the tube kept at 

 rest experiment shows the inductive effect to 

 be the same if only the cross-connection ro- 

 tates with it. And finally if both magnet and 

 tube are kept at rest while the cross-connec- 

 tion alone is rotated about the axis of the sys- 

 tem the observed effect is the same. 



On the other hand, no inductive action is 

 observed when tube or magnet or both together 

 are rotated so long as the connecting brush 

 is at rest. 



The motion of the cross-connection is thus 

 the determining factor, but relative to what? 

 Must not any effect that we can ohserve be 

 due to motion relative to the apparatus and 

 connections ly which the inductive action is 

 tested. 



Of course the induction may be conceived 

 as due to motion relative to coordinates fixed 

 in the ether or in space, and the effect would 

 then depend on the direction of the axis of 

 the magnet relative to the earth's axis, and 

 the rotational velocity of the earth, and on 

 its translational velocity in space. But even 

 in that case the inductive action which also 

 takes place on the system by which the effect 

 is tested, in consequence of its motion in 

 space, may be expected to be such that no 

 inductive action could be observed except in 

 case of such relative motion as is specified 

 above. 



For so long as the cross-connection and the 

 testing apparatus by which the effect is to be 

 observed are at rest relative to each other no 

 change in the magnetic flux through the cir- 

 cuit will be produced by any rotation of the 

 whole system about the axis of the magnet. 



It appears therefore that if the testing ap- 

 paratus rotates about the axis of the magnetic 

 field at the same rate as the cross-connection 

 between magnet and tube, no charge will be 

 found, while if it rotates with an equal an- 

 gular velocity in the opposite direction the 

 charge found will be twice as great as if it 

 were at rest. 



If these statements are in accordance with 

 the experimental facts, as I believe them to be, 

 then such an experiment can afford no infor- 



