264 Experiments in Explanation of Hall's Phenomenon. 



acted upon by a force equal to a hundredth or a thousandth 

 part of that which acted upon the whole. Then it becomes 

 evident that each individual stratum, including the bottom 

 one, will be affected in precisely the same manner as the sum 

 of them w r hich constitutes the thick plate. Of course, if the 

 film of metal is so exceedingly thin that its physical properties 

 of cohesion and elasticity are impaired, we should expect 

 the effects of extension and compression to be diminished. 

 This is, in fact, the case with thin gold-leaf, not so much on 

 account of its mere thinness as of the inequalities and irregu- 

 larities necessarily existing in it; and accordingly we find it 

 noted by Mr. Hall (Phil. Mag. November 1880, p. 312) that 

 the transverse effect in gold-leaf appears to be relatively much 

 smaller than the effect in strips of sensible thickness*. C ceteris 

 paribus, the galvanometer-deflection is, of course, greater with 

 a thin sheet than with a thick one, because the difference of 

 potential at any two points in a thick sheet must always be 

 comparatively small. 



If it is objected that, since the plate is firmly cemented to 

 glass, the distortion actually produced must be very small, it 

 may be replied that the consequent effect is also very small, 

 and that a distortion far too insignificant to be visible to the 

 eye would be sufficient to produce it. The warmth commu- 

 nicated to the plate by lightly touching opposite corners of it 

 with the fingers is capable of causing galvanometer-deflec- 

 tions many times as great as those produced by Peltier effects 

 requiring three or four amperes of current for their pro- 

 duction. 



Lastly, it may be urged that the force available for pro- 

 ducing the required strain is a very small one. This is 

 undoubtedly true. But, apart from the fact that a very small 

 force would be sufficient to cause a sensible strain in a very 

 thin sheet of metal, it must be remembered that the force 

 with which we are dealing acts in an exceedingly advan- 

 tageous manner. It does not, like an external push or pull, 

 act upon a single point or group of points in the sheet, but it 

 exerts a perfectly independent action upon every individual 

 molecule of the metal which is within the magnetic field, 

 most powerfully in the middle, gradually falling off towards 

 the ends. It acts, in short, in the most effective manner 

 possible for the production of the strain. 



Though it may not impossibly turn out, on further investi- 



* Mr. Hall thinks that the apparent difference may be accounted for 

 by the existence of a multitude of small holes in the thin leaf, by impu- 

 rities in the gold, and by the difficulty of securing good contact with the 

 electrodes. 



