1879.] the number of primes between limits. 309 



completion of the printing of the fifth and sixth milHons will 

 enable them to be extended to 9,000,000. In the case of Legendre's 

 formula however and Gauss's remarks upon the value of the 

 constant, which were founded upon enumerations of the first 

 three millions, the existing data were sufficient to permit of a 

 fairly complete discussion of the question ; however, when the two 

 millions which are wanting are published, I propose to extend the 

 tables in this paper from 4,000,000 to 9,000,000. 



In conclusion I may mention that Tchebycheff states that the 

 difference between Legendre's formula and his own, viz. 



du 



log a; -1-08866 U logw 



has a minimum value for x — 1,247,646, but continually increases 

 for greater values of x, so that it is important that comparisons 

 between these formulae should extend beyond 4,000,000. 



(2) Mr W. N. Shaw, M.A., On experiments with mercury 

 electrodes. 



In the Philosophical Magazine of 1874 (l7. series, vol. 47) is a 

 paper by Lippmann, translated from Poggendorf's Annalen, in 

 which the author announces as the result of experiments on the 

 electrical effects of the motion of a mercury electrode in a 

 capillary tube, that if the circuit be closed a current is produced 

 through the dilute sulphuric acid from the electrode with increas- 

 ing surface to the other, that the quantity of electricity dis- 

 engaged is proportional to the increase of surface and independent 

 of the form, and that these effects are due to the polarization of 

 the increasing surface by hydrogen. 



These results are criticized somewhat adversely by Quincke 

 (Pogg. Ann. CLiii., p. 184), who, while he refuses to admit the pro- 

 portionality of the electricity disengaged to the increase of surface, 

 attributes some considerable part of the action caused by the 

 motion of the electrode to the state of the fluid in contact with 

 the mercury. Quincke's experiments also shewed a current from 

 an increasing electrode through the fluid to the other. 



Some of Lippmann's results, as remarked by the editor of the 

 Philosophical Magazine, in a foot-note, were anticipated by Varley 

 in a paper in the Phil. Trans., 1871 (p. 129). Varley there 

 describes an apparatus in which two funnels of mercury act as 

 electrodes in dilute sulphuric acid. One of these electrodes was 

 polarized by hydrogen, and the two connected through a galvano- 

 meter. After the polarization current had disappeared the rock- 

 ing of the apparatus caused the mercury to flow higher in one 

 funnel and lower in the other. This gave rise, according to 

 Varley, to a current, " the diminishing surface acting as the zinc 



