34 
dilate in a spherical conducting shell just outside the earth’s 
surface, and inquires what should be the intensity and 
direction of such currents in order that they should produce 
the diurnal variations of magnetic force observed on the 
earth’s surface. Following Clerk-Maxwell,^ he considers 
the particular case in which the whole spherical surface is 
divided b}^ successive stream-lines (for each of which the 
current-function is constant) into annuli, along which the 
currents flow, and which disappear at the two poles of the 
system of currents; and where no electricity enters or 
leaves the shell. And adopting Maxwell’s expressions for 
the values of the current-function and the magnetic poten- 
tial just within the shell, and again particularising by 
dealing only with the case in which the latter is a surface 
harmonic of degree i, he finds that the system of stream- 
lines is orthogonal to the system of lines of force. Then, 
remarking that “there seems for diurnal variation no term 
of the first order, and we may, therefore, take very 
approximately the currents to be at right angles to 
the magnetic force at any place,” he proceeds to 
calculate from the observed diurnal inequalities of 
magnetic force at Greenwich and at Bombay, the 
equivalent currents that should flow in the hypothetical 
conducting shell just above these places respectively. Here, 
to say nothing of the assumption that the potential of the 
magnetic variations is a surface harmonic of a single degree 
only, we have the same loose reasoning that pervades the 
previous investigation ; no reason is given why the stream- 
lines of the aerial currents should be regarded as dividing 
the earth’s surface into annuli, and until that is done we 
can have no assurance that their character is not such as to 
place them outside the class to which alone the formulae 
used apply. And in the absence of any application of the 
* “ Electricity and Magnetism,” First Edition, Vol. II., pp. 259 to 262 and 275 to 277. 
