1890.] Specific Resistance of Mercury in Absolute Measure. 435 



equal to the resistance of a column of mercury of 1 square mm. sectional 

 area and 106*307 cm. long, the probable error being +0*012. 



The author does not bring these numbers forward as the best deter- 

 mination possible by the method he has used. He is of opinion that 

 if the apparatus be constructed on a scale a little larger and with a 

 certain perfecting of detail, a single set of observations will give a 

 result accurate to one part in 10,000, and that as a mean of a number 

 of observations we may perhaps aim at the hundred-thousandth if 

 regard is paid to the maintenance of definite temperatures in all parts 

 of the apparatus, and if we can be said to know our length-standards 

 to this degree of accuracy. 



The observations were made by the method of Lorenz directly on 

 mercury. The chief variations in the method introduced in the 

 present investigation are as follows : 



(i) The elimination by a system of differential measurements of the 

 errors that have so far attended the use of a mercury column 

 as the measured resistance. 



Lorenz himself took for his measured resistance the resistance of a 

 mercury column contained in a glass tube, and the specific resistance 

 was calculated from the dimensions of the column. It is hardly possible, 

 however, that the latter calculation can have been, or is likely to be, 

 achieved with accuracy, however accurately the tube be calibrated. 

 For, on the one hand, if the wires from the disc (the terminal 

 portions of which may be called the electrodes) are led to the ends of 

 the tube, the equi-potential surfaces touched by them are not plane ; 

 and, on the other, if they are let into the tube at some distance 'from 

 the ends, it is difficult to see how the^distance between them is to be 

 measured with the requisite accuracy. 



These difficulties disappear if, instead of placing the mercury in a 

 tube, it is placed in a long trough, and if, instead of measuring the 

 distance between two electrodes, one electrode is kept fixed while 

 measurement is made of the distance moved through by the other 

 between two equilibrium positions corresponding to two different 

 rates of rotation of the disc. The latter measurement it is easy to 

 make with accuracy, for the movable electrode may be rigidly 

 attached to the movable headstock of a Whitworth measuring machine 

 or some other measuring bank placed parallel to the length of the 

 trough ; and the two equilibrium positions may be taken near the 

 middle of the trough so as to avoid danger of curvature in the equi- 

 potenlial surfaces passing through the electrode in its two positions. 



Let w l5 n 2 be the rates of rotation of the disc, and let I be the 

 distance between the corresponding equilibrium positions of the 

 movable electrode. 



2 K 2 



