Page:Proceedings of the Royal Society of London Vol 60.djvu/387

360 Hence* when the small condenser is tinder the surface of liquid oxygen its capacity C', as a whole,, is Kc+0-05c,

and the whole quantity of electricity, Q, given up to the reservoir condenser after n charges of the small one, charged to potential Y, have been put into it, is Q = Vc (K + 0'05) (l— = Y c ( K + o-05)M,

where m = --— -- - — and M = —3 L -(l—mw). C + (K + 0*05)c 1—rav Again, when the small condenser is lifted out of the liquid oxygen into the gaseous oxygen lying on the surface, its capacity becomes c+0'05c = l ‘05c, and the whole quantity Q' stored up in the reservoir condenser, after n charges at a potential Y, is Q'= Yc(l-05) (1 -m '«) 1—m = V c(ro 5 )M /, pi t where m'— —— - and = ——— ( l—m'n). C + r05c 1—m

If in each case the reservoir condenser is discharged through a ballistic galvanometer, the “ throw ” or elongation of which is proportional to the quantity of electricity sent through it, and if and O' are the throws produced by the quantities Q and Q', we have 0_ Q _ K+0-05 M W ~Q '— 1-05 M' ‘

The ratio 0)0' is given from the observations. To solve this equation completely and determine K would be difficult, since the quantity M is a somewhat complicated function of K.

We know, however, that the ratio of M/M' cannot be very far from unity. A rough experiment h ad. shown that K was a number in the neighbourhood of 1*5, and a calculation shows that when ten discharges of the small condenser are made in' each case into the large condenser, and if the large condenser has a capacity of 0‘5 microfarad, and the small one a capacity of nearly 0001 microfarad, that the ratio M/M' = 1030/1019 nearly. Hence M/M' comes in as a correcting factor of about 1 per cent, in value.

Before relying on the above method, it was necessary to prove that the loss of charge of the small condenser was negligible during the time elapsing between the end pf the charge and the end of the discharge of the small condenser.