n. ELECTRICAL RHEOMETRY. 51 



vanish, and the results are as assigned by the celebrated mathematician, so that 

 this problem is but a particular case of our own, and may be resolved by the same 

 formula, making due modifications for the different circumstances. 



"We must now discuss some circumstances which have not yet been taken into 

 consideration, and upon which most probably depends the difference between 

 observation and calculation. 



§ 12. Remarks on some Anomalies presented by Observation. 



The comparison of calculation with observation is sufficiently satisfactory, as we 

 have seen ; there is, however, a little difference between both and among the expe- 

 riments themselves, when the needle is at /jths of the radias, which we can by no 

 means ])e induced to attribute to errors of observation alone. Beginning with the 

 considerations suggested by the diffei-ences of the observations, we observe that 

 combining several series together, the results are almost identical when the total 

 resistance at the centre is very nearly the same, but differ considerably when this 

 varies. I thought in the beginning that this was due to the lesser deviation of the 

 needle, and this engaged me in the long calculations already presented. This has 

 certainly some influence, as appears from the above results of several series of 

 experiments, in which to the deviations 



G0°; 30°; 25°; 17° 36'; 0°, 

 correspond the values 



2.196; 3.419; 3.584; 3.823; 4.738. 



A small increment in the ratio is therefore given by calculation in the case of a 

 small deviation, but not so great as it should be. A little variation also in the 

 position of the needle has a great influence ; thus if we reckon the distances from 

 the inside layer of wires in the globe at Aths, we obtain by experiment the ratio 

 = 2.849, but reckoning from the most outside layer we have it = 3.537; the mean 

 of these is 3.243, not very far from what we found directly. It seems, thei'efore, 

 that we must inquire for another cause. Comparing several results obtained with 

 the globe, I perceived that using long constant resistances when the needle was at 

 the centre, the ratio of forces became very great, and also for the globe sometimes 

 reached the number 4.001 ; but I attributed it to some irregularity in the battery, 

 and rejected those observations, as having been made with a Daniell's battery 

 almost exhausted. On repeating them, however, the last time, I found the same 

 difference, and being now sure of the good order of the battery, I cannot reject the 

 results as erroneous. If this be the case, it is evident that making two series of 

 experiments on the same deviation, but with different central resistances, we must 

 have different results. For this purpose the series 2 and 5 (§ 9) were made where 

 the difference of half a degree in the deviation can scarcely have any influence on 

 the result : now the central resistance in the series 5th being 87.25 turns of the 

 rheostat, the ratio of forces at youths is 4.103 ; on the contrary, in the series 2d, 

 the central resistance being 101.53, the ratio is 4.522. 



As far, therefore, as we can judge from this induction, the cause of discordance 



