TBAX8ACTION8 OF THE SECTIONS. 
39 
bi A isabaolntely impossible to conceive of the currents which he ^^scnbca round 
lie molecules of matter as having a physical existence, fhe idea of an 
utiitnaturallv presents itself, when we endeavour to imagine a possibly lexical 
ttorvofterresirial magnetism; and the question which nowocc^s *1“ 
phsnomena at the earth’s surface and above JSace be 
Bfail distribution of closed galvanic currents, occupying a certain limited spacye- 
Iwtte surface? The answer is, that whattn,-cr be the form and magnetic 
d&tartb, the same force as that whicJi it exerts uison “y 
niiully be produced by means of a distribution of closed eicctnc curr^ta on 
abce! 1 have arrived at this result with the aid of Ampere s theoiy of 
c«it. by mBaoB of the theorem of Green already meotionod, and by an 
imm of which a physical demonstration may be given by f 
vail floid motion, lie steps in the analytical process of determining the required 
teiktion of closed currents are as follows:— 
la V be the magnetic potential, according to Green s definition, at any 'xtemr 
pmt p; do- an element of the surface; A the distance from d<r to I f, m, n tne 
btetioD cosines of the normal at dv. 
I. Find j, so that 
II. Find U, BO that for internal points, and 
nr" ay* dz* 
dx^ 
d\J 
,dU , 
'd;+"dj 
iZlT .. 
-j.n^^-=g at the surface, or ■^=e- 
U<6 
in. Construct on the surface a “ map of the values of U.’ anffipicntlv 
, If wires be laid along the lines round the surface 
'•«»: ciiuidiffercnt values of U, as indicated by this map, and if c 
■“taisitybe made to circulate through them (each being a closed curve), the eiec 
Bo-magnitic force that wiU result, upon external imints, will he the same as the lore 
SwSrStioTof this problem is very easy, when the refer! 
M is actually the case, to a sufficient degree of approximation, with reier 
to the earth. 
Tbus. if the potential at tlic surface be given by the equation 
V=Y,+Ya+Y8+^®*- 
Yj. &c. may be calculated, for any latitude, by means of the Gaussian 
“ostantB, we readily find 
U=l{2V-h(Y,+yY,+-^Y3+&c.)} 
1 electro-magnetw uiv^v^v. > 
can be expressed in a map constructed 
^ttawe have the means of constructing an electro-magnetic 
wo Would exhibit all the iieculiarities that t 
*l»ii Gauss’s theoiy. 
an extraordinary .ViVooe witnessed at Birkenhead 
By D. 1>. Thomsons M.B.. of Wrmbury, Uwshire, ^ 
''Y’ 2rSrabouf3 P*M^. an erict 
Zoological Gardens at Liverpool, on Sept. 27, i > ^ggj. 
^,of Edinburgh, depicted on the clouds over ’Tnlmitcs 
m the Great Park at Birkenhead, for a period of forty minutes. 
A Map of the Coast Sumj of the United States. 
By Prof. A. Baciie, LLM^ ^c. 
