324 



REPORT — 1886. 



■would make the observations fairly comparalile. This may fairly be applied, since 



the disturbing causes I have mentioned depend upon the current-density. 



In order to put this to the test, I have assumed in the first place that the 



action upon the deposit may be represented by an expression of the same form as 



■would be required to represent the action of the solvent upon a ■wire immersed in 



the solution without any current. This we may take to be, for the comparatively 



short times of the experiments, a case of solution going on at a constant rate, 



and proportional to the area exposed. Thus if d be the actual loss of copper in an 



experiment "when the area exposed is A, and the time t, we shall take 



8 = kM, 



and shall investigate whether a constant value of k can be taken to bring the observa- 



S k' 

 tions into agreement. It is easily seen that this is equivalent to - = ^ ■where e 



c a 



is the total amount of copper deposited during the experiment, and d the current- 

 density ; and ■where k is also constant, but numerically different from k. In words 

 ■we may express this by saying that the fractional correction is inversely pro- 

 portional to the current-density. 



Law of Variation of the Deposit ■with CtrKRENX-DENsiTT. 



It is difficult to settle what value to assume for k'. If k' he a true constant, 

 its value can of course be calculated from any pair of observed results ; but the 

 magnitude of possible experimental errors, in comparison with that of the quantity 

 under consideration, makes it highly improbable that the results would be at all 

 concordant. It will at any rate be well, in order to avoid a possible error in the 

 weighing of the silver, to use observations belonging to the same experiment for 

 determining the value of k'. I have determined the values of k' for several pairs 

 of observations, taken somewhat at random, with the follo^wing results : — 



Table III. 



The values of k' thus obtained are not very concordant. It must, however, be 

 remembered that it is difficult to assign with confidence a numerical value to the 

 current^density, since the effective area of the copper surface may be practically 

 very different from that of the platinum on which the copper is deposited. In the 

 expectation that the action of the solution upon the copper when no current is 

 flo^wing might help to decide which value of k to take, the * one wire ' and ' six- 

 teen wires ' of October 20 were replaced in the solution, after the weighing was 

 completed, and remained there for the time of duration of the experiment, viz., 

 five hours. The 'one wire' lost -0008 gm., and the 'sixteen wires,' "OllO gm. 

 This gives a loss of •0007 gm. per wire, and corresponds to a value of k' = "000025. 

 On November 27, a loose copper wire was left in each of the cells during the ex- 

 periment ; and the mean loss of each of the wires during the time was '0003 gm., 

 which con-esponds to approximately the same value. It will therefore be well to 

 see what effect the correction of the weighings on the hypothesis that A '="000025 

 would have upon the tabulated results. The correction may be introduced by 

 adding •00014 gm. to the weight of each wire immersed for each hour during which 



