576 Mr. R. Beattie on a Possible Source of 



one. is likely to meet with in a not too feebly magnetized 

 needle. 



Mag nitride of Error when a Condenser is discharged through 

 the Galvanometer. — When a condenser charged to a difference 

 of potential E and containing a quantity Q is discharged 

 through a galvanometer of resistance R, the whole of the 

 energy, EQ/2, stored in the condenser is dissipated in the 

 galvanometer. We may therefore put 



j: 



ldt ~WV 



'0 



•so that the percentage error becomes 



5O«.^.0E . (2) 



For a very sensitive galvanometer wound with copper wire 

 the ratio G/R, expressed in C.G.S. lines per sq. cm. per 

 ampere per ohm, will probably not differ much from unity. 

 For such a galvanometer, therefore, with its needle dis- 

 placed 1° the error would be only 1 per cent, when 

 E = 600 volts. But in a less sensitive galvanometer wound 

 with thicker wire G/R may be far larger than unity * — may 

 be as much as 100 in fact; in which case a difference of po- 

 tential of 6 volts and a displacement of the needle of 1° would 

 suffice to produce an error of 1 per cent, in the thi'ow. A 

 galvanometer in which G/R is as large as 100 is not, it is true, 

 sufficiently sensitive to be well -adapted for conden s er w^ork ; 

 still, with a weak enough <con trolling field it will give a 

 readable throw 7 when a condenser of a few microfarads 

 -capacity chnrged to ]00 volts is discharged through it, and 

 then we might expect to find an error of perhaps Ifi per cent, 

 for every degree the needle happens to be displaced. 



The expression (2; may be given a different form if we 

 remember that the difference of potential to which a condenser 



* For an annular coil of rectangular cross-section (length of coil 2d cms., 

 inner radius «, cms., outer radius u cms.) wound with wire having a 

 resistance of p ohms per cm. the ratio GR is equal to 



C.G.S. lines per sq. cm. per ampere per ohm. Thus when d=l'5 cm?. ; 

 « L = -5 cm., rt., = 2 - 5 cms., G/R is only 7'2 if the coil is wound with 

 No. 40 S.W.G. copper wire, but increases to 500 if No. 19 S.W.G. wire 

 is used. 



