84 Prof. G. Kirchhoffon the Measuring 



It' the resistance p can be theoretically expressed by the 

 conductivity and the dimensions of the conductor in question, 

 if these dimensions have been measured, and if P and the 

 ratio of the resistances id — w and W'—W are known, that 

 conductivity can be calculated. 



An essential basis of the above-instituted considerations was 

 the assumption that the electrode surfaces are surfaces of equal 

 potential. An electrode surface having this property can be 

 found if electricity be brought to the conductor through a sur- 

 face of which the dimensions are infinitesimal compared with 

 all the dimensions of the conductor. If, namely, around a 

 point in this surface we describe a sphere with a radius inde- 

 finitely large compared with its dimensions, but indefinitely 

 small compared with the dimensions of the conductor, the 

 part of this sphere which is within the conductor is a surface 

 of equal potential ; and hence, if it be reckoned as part of the 

 boundary of the conductor considered, it is an electrode sur- 

 face of the sort supposed. Such a surface can be found in 

 another way, if the conductor, entirely or in part, consists of 

 a cylinder of any form we please of cross section, the length 

 of which considerably exceeds the dimensions of the cross sec- 

 tion, and if the electricity flows in at its end. A cross section 

 distant a moderate multiple of the longest chord of the cross 

 section from this end can then be regarded as a surface of 

 equal potential, and therefore also as an electrode surface of 

 the kind in question, if it be considered as belonging to the 

 boundary of the conductor. 



An arrangement which can, accordingly, be employed when 

 the conductivity of a substance is to be measured which is 

 present in the form of a cylinder of moderate length, is the 

 following: — The current of the battery is conducted into and 

 out of the rod through its ends ; the ends of one of the wires 

 of the galvanometer are in conducting connexion with spikes 

 which are pressed against its enveloping surface in two points 

 whose distances from the nearest end amount to a moderate 

 multiple of the longest diameter of the cross section. Two 

 cross sections of the rod can then be regarded as electrode 

 surfaces 1 and 4, and two segments of spherical surface de- 

 scribed with infinitesimal radii about the two spikes as electrode 

 surfaces 2 and 3. The resistance p is then equal to the dis- 

 tance of the cross sections passing through the two spikes, 

 divided by their surface and the conductivity. 



It may, however, be desirable to make use of the whole 

 length of the given rod, in order to make the resistance to be 

 measured as large as possible. If the rod has the shape of a 

 rectangular parallelepipedon, then the arrangement can be 



