DIURNAL VARIATIONS OF TERRESTRIAL MAGNETISM. 
15 
on these points, and examined their consequences in connection with the results, 
of his first memoir. 
It may be stated at the outset that the direct magnetic effect of the convective 
motion of masses of electrified air was examined and found to be negligible ( loc. cit., 
§ 10). Also it was shown (loc. cit., § 8) that the horizontal magnetic field of the earth, 
and the vertical atmospheric motions, might be neglected, so that the investigation 
was concerned with the determination of the electromagnetic effect of a horizontal 
oscillation of the atmosphere, acting on the known vertical component of the earth’s 
field. Initially the electrical conductivity of the upper atmosphere, where the 
currents flow, was supposed uniform and constant; afterwards examination was 
made of the modifications introduced into the theory by assuming the conductivity 
to be variable. 
It was first proved that the atmospheric oscillations necessary for the production 
of the diurnal and semi-diurnal* magnetic variations (the conductivity being 
uniform) are of types Qfi or Q3 1 and Q 2 2 or Q 4 2 respectively. These are the types 
of motion indicated by the diurnal and semi-diurnal barometric variations. The 
theory that the latter variations are closely connected with the daily magnetic 
variations had already been tentatively advanced in Schuster’s first paper; he now 
submitted it to a detailed numerical test. The main difficulty confronting the 
theory was that the ratio of the diurnal to the semi-diurnal term in the magnetic 
variation (C 2 1 /C 3 2 ) is very much greater than the corresponding ratio (cfi/c/) in the 
barometric variation. The former ratio was found in his first paper to be 9'6,f while 
the calculated ratio was only 2'6 ; the latter calculation assumed the atmospheric 
conductivity to be uniform. As regards phase, the calculated variations lagged 
behind the observed by about l|- hours (or from 2^ to 3 hours, on taking self 
induction info account). 
In the above, the effect of barometric terms of type Q., 1 and Q 4 2 was neglected, only 
Qfi and Q 2 2 being considered. The nature of the diurnal term in the barometric 
variation is not known very definitely, however, and it was pointed out that by 
representing it in part by an oscillation of type Qd the amplitude ratio 2'6 could be 
increased : also that such an oscillation may be present in the upper layers of the 
atmosphere, which do not greatly affect the barometer, even if it is not found in the 
surface variation. 
The term Q 3 X would be called on to a smaller extent if the atmospheric conductivity 
is not uniform, but varies with the zenith distance («) of the sun. In this case the 
12-hour oscillation Q 2 2 would contribute to the 24-hour magnetic variation Q/, and 
the 24-hour oscillation Qfi to the 12-hour magnetic variation Q 3 2 , but the effect would 
be much more marked in the former case than in the latter. It was shown, in fact, 
* Variations of higher frequency were not considered. 
t In equation (10) of the second memoir the coefficient of 4 3 2 should be 9 - 23 in place of ID 16 (this 
is the coefficient of y 2 2 as found in the first memoir, p. 486). 
