58 Firzcrratp— Quantity of Energy Transferred to Ether by a Variable Current. 
Now, as © = — — 9% in this case, and as 9% is parallel to %, inasmuch as 9{ = — ace | 
4a eae 
ive & | faite dy de = a [f) 92 dedy de 
Keon eee 
In order to calculate this we must calculate the value of 
cos — (t —/ Knr) 
[mae cosa0 } du dy dz. 
cos 5 (t — / Eur) : 
a cos ad0) 
r 
9 ey, Kyr dart | ID ET : 
— (cos ="t f BA jg ceria EE cos 0:0 ) 
Hh fl r ; vai 
Now as all we require is the average energy of the vibration, it evidently de- 
pends on the part independent of the time m a ze. on 
] cos 2 V Kpr : sin 5 n/p Kur , 
( — a6) + (e — COs aid) : 
/ 
Qar/ Ku 
If we call ii 
the values of 
Or : : 
wi =<. when } is the wave length, we require to calculate 
Las os 6d0. 
|= us cos 6d0, and of = 
In order to do this I shall assume a the radius of the current small, and take & 
the distance of the point from the centre of the current, and p its distance from the 
axis of 2; then 
a / ; 
r = (R? — 2ap cos 0+ a’)? =R (1 - Geos) 
R 
lap . 
therefore cos /y = cos lk + Re sn LR .cos 6; 
cos/k coslR ap : , 
and a = ph pe C08 O(cos /Rk + 1R sin LR). 
eee sindy sinlR | ap : 
Similarly, = ap + Be 098 6(sinlR — LR cos /R). 
therefore, |. al fr os 0d0 = 7. - (cos /R + JR sin 1h) 
I Su on 040 = a AE (sin IR — UR cos IR). 
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