ment than the voltameter itself. To obtain the value of the contrary electromotive force, he compared two experiments in which the resistances remained the same, while the sum of the electromotive forces alone varied. It is obvious that, if there existed no contrary electromotive force, the measured effect in the two cases should be simply as the number of elements in the series employed. A battery of five single cells should have half the power of a battery of ten double cells; but instead of this, the effects measured by the voltameter were as 6: 20. The value of r in the formula, i. e., the resistance which the voltameter and connecting wires add to the circuit, will be ascertained in the following manner. The comparison was made with two batteries, one single and the other double, of ten cells each; the sum of the electromotive forces, therefore, remained the same, while the resistances only varied : Substituting the values thus found in the general formula he obtained the following results : Number of cells..... 3 4 5 10 15 20 15 17 cubic inches. 15 17 cubic inches. The existence of such a contrary electromotive force, and its great energy, are amply attested by connecting the platinum plates of a voltameter, which has been sometime in action, with a galvanometer; but I purpose to show the general agreement of the amended formula with the results of various and most trying combinations of different batteries, many of which were obtained without the slightest suspicion of the conclusions which might be derived from them. I say general agreement, for the extremely complicated nature of the actions to be measured, subjected as they were to the necessarily variable influence of circumstances affecting them, the large scale upon which the experiments were carried on, and the roughness and imperfection of the modes of measurement, would necessarily preclude the expectation of absolute accuracy. The remainder of the experiments, already published in my fifth letter, made with circuits which contained an equal number in series, but in which they were combined as double, treble, quadruple cells, &c., do not furnish results according with theory so well as might have been expected; they were therefore repeated with great care, and combined in various ways. The details of these experiments will presently appear. The first series was made with a constant battery composed of copper cylinders, six inches high, three and a half inches in diameter, charged in the usual way with dilute sulphuric acid and sulphate of copper. The first thing to be done, was to determine the value of e in these combinations in the modified formula, by comparing the results of two arrangements in which the sums of the electromotive forces might vary, while the resistance remained the same. therefore 5 E e: 10 E e + r Cubic Inches. = 11.25 by experiment; = 33.7 by experiment; Thus, e: 11.25 337, or e = 2.49 E. To determine the value of r in the formula, we might compare, in a similar manner, as pointed out by Professor Wheatstone, the results of two arrangements, in which the electromotive forces being equal, the resistances in the cells alone should vary. As, however, from the complicated nature of the arrangements, and the variability of different influential circumstances to which I have before alluded, I found it impossible to obtain two perfectly unexceptionable results for the comparison, I thought it allowable to take the mean of several; and from this I found that, with a voltameter whose platinum plates are three inches in length, by one inch in width, a quarter of an inch apart, and charged with the standard dilute sulphuric acid, (sp. gr. 1·126), r = 0·541 R in a constant battery of the dimensions just described. Now if a single cell of such a battery be taken and the circuits closed by a short thick wire, and the zinc rod forming the generating plate of the arrangement, be weighed at intervals of five minutes, it will be found to lose 11.26 grs. for every such interval. This is a measure of the effective force of the circuit; and its equivalent in mixed gases is twenty-five cubic inches. This will be taken as the unit of work in the Table that follows, i. e. and the calculated results for the different combinations will, in the third and fourth columns, be represented in fractions of this unit. It is evident, that the amount of zinc, dissolved in such a single circuit, furnishes a measure of the maximum work that any number of such cells, combined in a single series, would be capable of perE n E E = A, and can never be greater than n R+ r R' forming; for R however great the value of n may be, so long as r has a positive value. In other words, however great the number of cells in a series, it is impossible, so long as any external resistance is interposed, that the result should be greater than that of a single cell in which no exterior resistance is opposed; although when r is very small when compared with n R, the results may be virtually equal. If unity be taken to represent the maximum work that any single circuit can produce, then E will be represented by 1, and R also by 1, and It is evident that in an effective circuit R can never equal E, but for the convenience of calculation it may be assumed to be so; and as all the quantities in the numerator are compared with E, and all in the denominator with R, the relative proportions will be exact. Taking the formula nE e =A. If E1 and R = 1, then e 2·49, r = 0·541. Substituting different numerical values for n, we obtain for The agreement of the calculated and experimental results under such complicated circumstances, as shown in the last two columns of the preceding Table, must, I think, be deemed very satisfactory; and it is worthy of remark, that the result just named, of the independent experiment with the single cell, twenty-five cubic inches, is almost identical with that deduced from the experimental determination of five cells; taking 11.25 cubic inches to represent accurately the fraction 0.453 and indeed agree very closely with the calculated results of the above Table, whatever combination be taken as the foundation of the calculation. In the experiments already alluded to, which I performed in conjunction with Professor Wheatstone, the cells of the battery used were of the same character as the last, but with an efficient length of twenty inches, or 3.33 times greater. The duration of each experiment was in this case one minute. Upon making the calculations for these, E being = 1, R = 1, e was found = 2.85, by comparing the results of five single, with those of ten double cells; and r (by a mean of seven experiments) 1.757. Hence we find, These results again exhibit a general accordance with the calculation, but by no means so close as the preceding. I was therefore induced to repeat the experiments with great care. The following Table shows the results, which it will be seen closely correspond with those deduced by the formula. By a mean of fourteen experiments, r was again determined to be in this battery 1.725 R. =1, and e= 2.49, we obtain from Taking, as before, E = 1, R = |