484 REPORT — 1867. 



to the following experiments. Tlie capacity of any condenser can be directly 

 measured in absolute measure by the following formula applying to the effect 

 of a single discharge from the condenser through a galvanometer : — 



g__o^ sin|i 



(vide Eeport, 1863, Appendix C, p. 144), where R^ is the resistance of a 

 circuit in which the electromotive force used to charge the condenser would 

 produce the unit deflection, whUe i is the angle to which the needle is ob- 

 served to swing from a position of rest, and is half the period or time of a 

 complete oscillation of the needle of the galvanometer under the influence of 

 terrestrial magnetism alone. 



This formula, which is analogous to that for any ballistic pendulum acted 

 upon by a known impulse, supposes that the whole impulse is given in a time 

 very short as compared with t, and it also supposes that the deflection i is 

 unimpeded by friction. 



I employed a Thomson's astatic reflecting galvanometer with double coils 

 of German-silver wire. The oscillations, with the usual mirror and magnet, 

 subside so rapidly that t cannot be measured with accuracy, and i is very 

 sensibly affected by the resistance of the aii" ; to obviate this I attached a 

 brass ball to the lower magnet of the galvanometer, weighing 55 grains*. 



A single floss-silk fibi'e can just support this weight, under which it con- 

 tinues to stretch sensibly for about three days. In order tliat the discharge 

 from the condenser, electrified by from 20 to 30 cells, should have force to move 

 this heavy ball through a sensible angle, the galvanometer was made highly 

 astatic, and then I found that with even a single cocoon fibre the needle did 

 not return to zero within three or four divisions of the scale for some 

 minutes, exhibiting a kind of viscosity. The floss-silk fibre, though much 

 weaker, gave a very constant zero. The value of t with the weighted 

 needle seldom differed much from 20 seconds, and the times could be observed 

 for 10 or 11 minutes, during which time t was found to remain sensibly 

 constant. As there was no difiiculty in observing the tiuaes of oscillation 

 within one second, it may be said that the observed value of t was correct 

 within one part in 500. Greater accuracy was not required, as the possible 

 error from other sources considerably exceeds this. Twenty Daniell's cells 

 were used to charge the condenser, and the discharge observed was about 

 180 divisions ; but the observations were recorded within a quarter of a 

 division : as this is done by estimating the position of the reflected sjjot 

 stationary between the two black lines of the scale for an almost insensible 

 time, it would not be right to assume that the deflection i is observed with 

 greater accuracy than one part in 400. When the spot of light returned 

 after making one complete oscillation, the diminution in the deflection was 

 from 10 to 12 divisions ; one quarter of this amount was therefore added as 

 correction in each case to the deflection observed. The resistance of the 

 whole circuit was composed of the batteiy resistance, that of German-silver 

 resistance-coUs, and of the German-silver coils in the galvanometer ; no 

 considerable variation could therefore occur except in the battery, which 

 formed only a small portion of the total resistance. The coils (adjusted by 

 Mr. Hockin) are probably correct within one part in a thousand, and the 

 measurement of the galvanometer-coils is equally well known. 



From what has been said, it might be expected that the capacity of any 

 condenser could be obtained with an accuracy of one part in 400 or 500 at 



* The ball, two mngnets, mirror, and connecting bar, forming the whole suspended 

 system, weighed STj gr;iins. 



