Uniform Rotation of a Circular Cylinder. 343 



no alteration of its dimensions perpendicular to its median 

 plane, and i£ say the right side is to buckle so as to satisfy 

 the assumed principle o£ relativity, the left side will have 

 to take the shape shown in section in fig. 1, B, so that the 

 condition of the particles on the left side will not be 

 consistent with the principle. Again, the solution of the 

 problem is not to be found in the disk becoming strained, 

 for a strain would involve the alteration of the radius, and 

 the final state of the disk would be one inconsistent with the 

 conditions assigned above, which conditions are required by 

 the principle of relativity if this problem is one to which the 

 principle of relativity can be applied in the form which it 

 has been applied. 



The object of the present paper is to show that there is 

 no fundamental difficulty in the question as far as its 

 applications to ordinary matter is concerned, and in fact 

 that the apparent inconsistencies arise from neglect of 

 considering all the phenomena involved. 



In the first place we notice that though each point of the 

 circumference of the cylinder is moving with constant 

 velocity, the problem is not one of constant velocity in a 

 straight line : each particle has an acceleration towards the 

 centre. As a matter of fact, we know that if the disk were 

 set in rotation, it would not contract at all, it would expand 

 owing to centrifugal force, to an extent depending on the 

 elastic properties of the material. It would seem useless to 

 endeavour to limit the case to that of a rigid body, for the 

 very alterations of dimensions which we are discussing are 

 alterations which are necessary to secure equilibrium of the 

 internal forces and motions when the body is set in motion 

 as a whole, and the alteration in dimensions due to centrifugal 

 force is as necessary for the maintenance of internal equilibrium 

 as is the contraction of which ice are speaking. If we look 

 upon all internal forces, cohesion included, as being of 

 electromagnetic origin, a complete electromagnetic solution 

 of the problem, if it could be obtained for our rotating 

 cylinder, should show us that the cylinder actually does 

 expand, the centrifugal force phenomenon being in fact 

 involved in the electromagnetic scheme. It would be im- 

 possible, however, to obtain such a solution, unless we knew 

 the nature of the electronic distributions and motions in the 

 cylinder when at rest, because the solution would, as we 

 know from experience, involve the elastic properties of the 

 material, which on our view are totally determined by the 

 nature of the electronic distributions and motions. I think 

 the real solution of the apparent inconsistency is to be found 

 in the following. 



