326 REPORT— 1886. 



value of the chemical equivalent of copper can be assigned with greater accuracy than 

 appears at present to be practicable. AVe may, however, notice that the value 3-4086 

 is that which would be obtained with comparatively very small current-densities, 

 and occupies a place in the middle of a continuous series, and there seems to be no 

 reason in the electrolytic behaviour of the cells for accepting that value as indicat- 

 ing a limiting result. We may therefore fairly approach tlie question the other 

 way, and, using the observations to calculate the chemical equivalent of copper by 

 Faraday's law, consider the results which follow. If we assume, as we seem fairly 

 entitled to do, that the differences of the weights for different current-densities are 

 due to the solution of the deposited copper, it follows (assuming Faraday's law) 

 that we must get a nearer approximation to the true amount of copper equi\alent 

 to the amount of silver deposited the greater the current-density. The value would 

 be affected by the correction discussed above ; but it has been already stated that it 

 is unsafe to apply the correction, or, at any rate, to assign to the value that of k' 

 assigned above. But the consideration of that correction serves us to this extent, 

 viz., to show that for current-densities above -02 its value must be very small in- 

 deed, reaching, as a matter of fact, with the value of k = -00002, to less than one 

 milligramme per gramme. But in determining by Faraday's law as accurately as 

 possible the chemical equivalent of copper from that of silver, the correction cannot 

 be disregarded without sufficient reasons. Some reasons for that course have been 

 given, but in order to test further whether or not the correction should be applied 

 I have plotted the observations on sectional paper, taking as ordinates the ratios of 

 copper to silver, and as abscissae the reciprocals of current-densities. If the cor- 

 rection should be applied throughout, the grouping of the observations should show 

 a straight line inclined to the axis of current-densities. I have adopted this 

 method of combining the observations belonging to different experiments for this 

 purpose, in preference to the arithmetical one of taking means, because the latter 

 is liable to be seriously affected by a set of observations, each one of which is far 

 from the mean in the same direction, but which does not extend throughout the 

 whole range. In the estimation by eye of a mean result of plotted observations 

 allowance can be made for the effect such observations produce, wliereas they may 

 give a false appearance of general law to a set of arithmetical means. 



The observations included in the Table II. when plotted do not give any in- 

 dication of the divergence of the mean ordinates from a straight line parallel to the 

 axis of reciprocals of current-densities until the current-density is less than -02, 

 and the straight line passing through the ' centre of gravity ' of the group of ob- 

 servations for highest current-densities, and inclined to the axis with the angle 

 given by the value k' = -000025, would leave all the rest of the observations except 

 three on one side of it : but a very fair result is obtained if the value of k' be some- 

 what reduced, and the line be drawn at the corresponding less inclination through 

 the point corresponding to the ' centre of gravity ' of observations about the current- 

 density -02. If we must take a straight line inclined to the axis as representing 

 the results, the one which must be selected has an inclination to the axis of about 

 one-half that given by k' = -000025, and even that leaves on one side of it nearly 

 the whole group of observations whose current-densities have reciprocals between 

 60 and 30. Further, the values of the ratios obtained from the observations for 

 current-densities above -02 are remarkably close, except in two instances; in one 

 the ratio is very high, with a high current-density, and differs widely from other 

 obsei-vations at about the same current-density ; the other is very low, and belongs 

 to an experiment which gives a series of very low values ; this has been rejected 

 because the wire which gave it was marked in the note-book as ' discoloured,' i.e. 

 oxidised, at the time of weighing. 



_ In order, therefore, to obtain the value of the chemical equivalent by 

 this method, I have taken all the values obtained for current-densities greater 

 than -025 ampere per square centimetre. They are included in the following 

 table : — 



