84 Dr. Matthiessen on the Electric Conducting Power of 



nature before specified is formed, ayIiosc angular points are c and 

 c', the point of contact of the copper shield, and the quicksilver 

 cup h. By altering, therefore, the position of the commutator, 

 the relative position of the silver wire and the wire whose resist- 

 ance we want is exchanged. In the scale on the wood the zero- 

 point is equally distant from c andc'; each division is 6*75 mil- 

 lims. ; the length of the wire from the zero-point to c or c' is 

 170'5 such divisions. 



Let / represent this number, Lj the number indicated by the 

 scale at the point of contact by the copper shield for the position 

 of the commutator numbered 1, and Lg for the position 2 of the 

 commutator ; then we have the ratio of the resistances of that 

 branch containing the silver wire to that containing tlie wire in 

 the trough 



Z+L. /— L. 



:= =■ OV = ■ —. 



l-L,'""^ Z+L2 



Let 71 represent the resistance of the silver wire, w that of the 

 wire under observation, a that of the wires making up the first- 

 mentioned branch with the silver wire, and b that of those com- 

 pleting the second branch ; then 



w + b _l+Jjj ^ _l—^ci 

 71 + a / — Lj' l + liq 



In order from this formula to calculate iv for the observed 

 values of Lj and Lg, on the supposition that n is known, it was 

 only necessary to determine a and b by preliminary experiments. 

 This was done as follows: — In the place of wires of potassium, 

 sodium, &c., under the same circumstances, silver wires from the 

 same piece as the normal wire were fastened ; let w' and w" be 

 the resistances of two such wires, and L\ and L"j the correspond- 

 ing values of Lj ; then 



iv' + b_l+L>, w" + b_ l+L'\ 



— "5 — tT~ ancl — "5 -|- II • 



n + a I — Lj n + a l—L\ 



Taking the unit of electrical resistance to be that of 1 millim. of 

 the normal silver wire, we then call the values of n, 10', w" the 

 lengths expressed in millimetres of the wires whose resistances 

 they represent, and from the two equations we can calculate tbe 

 values of a and b. For the experiments with potassium, sodium 

 and lithium, these values were 



«= 500-9, «;' = 492-4, z(;" = 594-2. 



These numbers express in millimetres the lengths of these 

 three wires, from each of which 4 millims. having been subtracted 

 to allow in the first case for the soldering on, for the others for 



