The Possibility of separating Isotopes. 523 



for we have disregarded the effect of the inertia of the 

 shaft, i. e. we have neglected the effect of wave motion along 

 the shaft. The effect of this mav be gauged by the following 

 considerations : — 



The velocity propagation of a simple wave of tension or 

 compression is V(E/p). where p is the density of the material 

 of the shaft. The time for such a wave to pass along a 

 length L of shaft will accordingly be Lv / (E//>). For the 

 calculations given in this paper to hold then, this time must 

 be quite small compared with the time of vibration of the 

 shaft as given by (xxv.). It will be readily seen that this is 

 not always the case, particularly when the shaft is running 

 at very high speeds. 



§ 12. The general conclusions to be drawn from the paper 

 are as follows : — 



The presence of the excentric load does not alter the 

 fundamental character ot: the vibrations (natural) of the 

 shaft. The periods obtained are the same as those ^ith 

 the symmetrical load. At the same time, there is a state of 

 steady deflexion, given by (xyii.), about which the natural 

 vibrations take place. This steady state of deflexion becomes 

 impossible when the whirling speed is attained ; such 

 whirling speed being given by (xviii.). Tt may also be noted 

 that fxvii.) and a corresponding result for 6, will enable one 

 to assign an inferior limit to the stresses due to the bending 

 that takes place at any speed. 



In addition, the effect. -of yielding at the bearing will cause 

 the critical speed to become lower. The practical effect of 

 this it is difficult to gauge. A calculation is given, depending 

 on unknown constants. 



XLVIII. The Possibility of separating Isotopes. 

 By F. A. Lindemann, Ph.D., and Y . W. Aston, M.A., D.Se* 



AS the existence of elements of different atomic weights 

 which occupy the same position in the periodic table 

 but appear to be inseparable by chemical means seems now 

 to be generally accepted, it is of interest to consider the 

 various methods by which there may be some hope of sepa- 

 rating them. These appear to fall into four main groups: — 

 Distillation, to which chemical separation is closely allied 

 thermodynamically, Diffusion, Density, and Positive Rays. 



* Communicated bv the Authors. 



