48 REPORT — 1876. 



it is excessively small : suppose we call it —20 for convenience of calculation ; 

 this corresponds to the fraction ^^^^=^^ of 30 ohms. 



But the whole deviation is probably introduced by some slight defect in 

 the apparatus, and part at least can be accounted for ; for it occurred to me, 

 in looking over the results quoted above, that a defect in the insulation at 

 the divided cup would partly account for such a deviation. Suppose that 

 the divided cup offered a very large, but not infinite, resistance / to the 

 passage of the current, then the single coil in multiple-arc experiments would 



111 



be replaced by a multiple arc of resistance E', where i7l=5r) + :^' 



^"^'" 11^ = 30-^'. 



Now let us find what / inust be to give a decrease of 20 in our observed 

 value of u — Kft + y + o + e): 



30^_ 20 

 / lOOOO'^'^ 

 7=6,000,000 



that is,/=6 megohms. Curiously enough, when I proceeded to measiu'c the 

 insulation resistance of the divided cup it came out very nearly 6 megohms ; 

 but the insulation resistance between any two of the remaining cups was 

 found to be about 12 megohms, which reduces the correction somewhat. The 

 complete solution of the problem would be complicated ; but we may approxi- 

 mate by considering each of the coils in the multiple arc replaced by a 

 multiple arc whose arms are 30 ohms and 12 meghoms respectively ; this 

 requires that /3, y, 2, e should each be reduced by 10. Hence the whole reduc- 

 tion in a—^Q3+y + d + e) would be on this supposition 10. It would really 

 be somewhat less ; however, this would almost bring the deviation between 

 observation and calculation within the limits of experimental error. Any 

 remaining ditference is probably duo to a defect in some mercury-cup in the 

 multiple arc, for there being more there than on the other side of the balance 

 the chance of a defect is greater. 



It ought to be mentioned that the insulation of the quintuple coil was 

 tested, and found in every case to be of a higher order of magnitude than a 

 megohm. 



Some time after the series of experiments just described, I dismounted the 

 mercury-cups from the stand, which had meantime been carefully dried on 

 the hot-water pipes in the laboratory. Each cup was remounted with a 

 piece of gutta percha between it and the board ; and the divided cup, which 

 was found radically defective, was replaced by two mercury- cups on separate 

 'pieces of insulating material. The insulation between every pair of cups was 

 then tested afresh and found in every case of a higher order than a megohm. 



The experiments were then repeated with the altered stand. The sensi- 

 bility of the arrangement was about the same as before, although a less 

 electromotive force was used (10 cells). The results were much the same 

 as before, except that the sum of the values of a — K/S+y-f^-l-e), &c. was 

 now much smaller, two experiments giving —-31 and —34. Dividing this 

 by 5, we get — G for the average deviation, which is very small. The fact 

 that we still get a result in the same direction shows that this is not an 

 accidental error ; but it might very well be accounted for by some of the 

 suppositions mentioned already. It might also arise from over-correction for 

 symmetry. -^ 



