At Wolfenbüttel, a year’s observations by Elster and Geitel (56) made A vary from 4 to 64, the mean being 20. In the island of Juist, off the Friesland coast, from three weeks’ observations they obtained only 5·2 as the mean. On the other hand, at Altjoch, an Alpine station, from nine days’ observations in July 1903 they obtained a mean of 137, the maximum being 224, and the minimum 92. At Freiburg, from 150 days’ observations near noon in 1903–1904, Gockel (57) obtained a mean of 84, his extreme values being 10 and 420. At Karasjok, observing several times throughout the day for a good many months, Simpson (10) obtained a mean of 93 and a maximum of 432. The same observer from four weeks’ observations at Hammerfest got the considerably lower mean value 58, with a maximum of 252. At this station much lower values were found for A with sea breezes than with land breezes. Observing on the pier at Swinemünde in August and September 1904, Lüdeling (40) obtained a mean value of 34.
Elster and Geitel (58), having found air drawn from the soil highly radioactive, regard ground air as the source of the emanation in the atmosphere, and in this way account for the low values they obtained for A when observing on or near the sea. At Freiburg in winter Gockel (55) found A notably reduced when snow was on the ground, I+ being also reduced. When the ground was covered by snow the mean value of A was only 42, as compared with 81 when there was no snow.
J. C. McLennan (59) observing near the foot of Niagara found A only about one-sixth as large as at Toronto. Similarly at Altjoch, Elster and Geitel (56) found A at the foot of a waterfall only about one-third of its normal value at a distance from the fall.
21. Annual and Diurnal Variations.—At Wolfenbüttel, Elster and Geitel found A vary but little with the season. At Karasjok, on the contrary, Simpson found A much larger at midwinter—notwithstanding the presence of snow—than at midsummer. His mean value for November and December was 129, while his mean for May and June was only 47. He also found a marked diurnal variation, A being considerably greater between 3 and 5 a.m. or 8·30 to 10·30 p.m. than between 10 a.m. and noon, or between 3 and 5 p.m.
At all seasons of the year Simpson found A rise notably with increase of relative humidity. Also, whilst the mere absolute height of the barometer seemed of little, if any, importance, he obtained larger values of A with a falling than with a rising barometer. This last result of course is favourable to Elster and Geitel’s views as to the source of the emanation.
22. For a wire exposed under the conditions observed by Elster and Geitel the emanation seems to be almost entirely derived from radium. Some part, however, seems to be derived from thorium, and H. A. Bumstead (60) finds that with longer exposure of the wire the relative importance of the thorium emanation increases. With three hours’ exposure he found the thorium emanation only from 3 to 5% of the whole, but with 12 hours’ exposure the percentage of thorium emanation rose to about 15. These figures refer to the state of the wire immediately after the exposure; the rate of decay is much more rapid for the radium than for the thorium emanation.
23. The different elements—potential gradient, dissipation, ionization and radioactivity—are clearly not independent of one another. The loss of a charge is naturally largely dependent on the richness of the surrounding air in ions. This is clearly shown by the following results obtained by Simpson (10) at Karasjok for the mean values of a± corresponding to certain groups of values of I±. To eliminate the disturbing influence of wind, different wind strengths are treated separately.
Table VIII.—Mean Values of a±.
| Wind Strength. |
I±0 to 0·1. | 0·1 to 0·2 | 0·2 to 0·3 | 0·3 to 0·4 | 0·4 to 0·5 |
| 0 to 1 1 to 2 2 to 3 |
0·45 0·65 .. |
0·60 1·08 .. |
1·26 1·85 2·70 |
2·04 2·92 3·88 |
3·03 3·83 5·33 |
Simspon concluded that for a given wind velocity dissipation is practically a linear function of ionization.
24. Table IX. will give a general idea of the relations of potential gradient to dissipation and ionization.
Table IX.—Potential, Dissipation, Ionization.
| Potential gradients volts per metre. |
q | Karasjok (Simpson (10)). | ||||||
| Kremsmünster (41). | Freiburg (43). | Rothhorn (43). | a+ | a− | I+ | I− | Q | |
| 0 to 50 50 to 100 100 to 150 150 to 200 200 to 300 300 to 400 400 to 500 500 to 700 |
.. 1·14 1·24 1·48 .. .. .. .. |
1·12 1·31 1·69 1·84 .. .. .. .. |
.. .. .. .. 3·21 4·33 5·46 8·75 |
.. 4·29 3·38 1·85 1·37 0·60 .. .. |
.. 4·67 3·93 2·58 1·58 0·85 .. .. |
.. 0·43 0·37 0·36 0·26 .. .. .. |
.. 0·39 0·32 0·28 0·19 .. .. .. |
.. 1·11 1·15 1·28 1·42 .. .. .. |
If we regard the potential gradient near the ground as representing a negative charge on the earth, then if the source of supply of that charge is unaffected the gradient will rise and become high when the operations by which discharge is promoted slacken their activity. A diminution in the number of positive ions would thus naturally be accompanied by a rise in potential gradient. Table IX. associates with rise in potential gradient a reduced number of both positive and negative ions and a diminished rate of dissipation whether of a negative or a positive charge. The rise in q and Q indicates that the diminished rate of dissipation is most marked for positive charges, and that negative ions are even more reduced then positive.
At Kremsmünster Zölss (41) finds a considerable similarity between the diurnal variations in q and in the potential gradient, the hours of the forenoon and afternoon maxima being nearly the same in the two cases.
No distinct relationship has yet been established between potential gradient and radioactivity. At Karasjok Simpson (10) found fairly similar mean values of A for two groups of observations, one confined to cases when the potential gradient exceeded +400 volts, the other confined to cases of negative gradient.
At Freiburg Gockel (55, 57) found that when observations were grouped according to the value of A there appeared a distinct rise in both a− and I+ with increasing A. For instance, when A lay between 100 and 150 the mean value of a- was 1·27 times greater than when A lay between 0 and 50; while when A lay between 120 and 150 the mean value of I+ was 1·53 times larger than when A lay between 0 and 30. These apparent relationships refer to mean values. In individual cases widely different values of a− or I+ are associated with the same value of A.
25. If V be the potential, ρ the density of free electricity at a point in the atmosphere, at a distance r from the earth’s centre, then assuming statical conditions and neglecting variation of V in horizontal directions, we have
r −2(d/dr)(r 2 dV/dr) + 4πρ＝0.
For practical purposes we may treat r 2 as constant, and replace d/dr by d/dh, where h is height in centimetres above the ground.
We thus find
ρ＝−(1/4π) d2V/dh2.
If we take a tube of force 1 sq. cm. in section, and suppose it cut by equipotential surfaces at heights h1 and h2 above the ground, we have for the total charge M included in the specified portion of the tube
4πM＝(dV/dh)h1 − (dV/dh)h2.
Taking Linke’s (28) figures as given in § 10, and supposing h1＝0, h2＝15 × 104, we find for the charge in the unit tube between the ground and 1500 metres level, remembering that the centimetre is now the unit of length, M＝(1/4π) (125 − 25)/100. Taking 1 volt equal 1⁄300 of an electrostatic unit, we find M＝0·000265. Between 1500 and 4000 metres the charge inside the unit tube is much less, only 0·000040. The charge on the earth itself has its surface density given by σ＝−(1/4π) × 125 volts per metre,＝0·000331 in e ectrostatic units. Thus, on the view now generally current, in the circumstances answering to Linke’s experiments we have on the ground a charge of −331 × 10−6 C.G.S. units per sq. cm. Of the corresponding positive charge, 265 × 10−6 lies below the 1500 metres level, 40 × 10−6 between this and the 4000 metres level, and only 26 × 10−6 above 4000 metres.
There is a difficulty in reconciling observed values of the ionization with the results obtained from balloon ascents as to the variation of the potential with altitude. According to H. Gerdien (61), near the ground a mean value for d2V/dh2 is −(1⁄10) volt/(metre)2. From this we deduce for the charge ρ per cubic centimetre (1/4π) × 10−5 (volt/cm2), or 2·7 × 10−9 electrostatic units. But taking, for example, Simpson’s mean values at Karasjok, we have observed
ρ ≡ I+ − I1＝0·05 × (cm./metre)3＝5 × 10−8,
and thus (calculated ρ)/(observed ρ)＝0·05 approximately. Gerdien himself makes I+ − I− considerably larger than Simpson, and concludes that the observed value of ρ is from 30 to 50 times that calculated. The presumption is either that d2V/dh2 near the ground is much larger numerically than Gerdien supposes, or else that the ordinary instruments for measuring ionization fail to catch some species of ion whose charge is preponderatingly negative.
26. Gerdien (61) has made some calculations as to the probable average value of the vertical electric current in the atmosphere in fine weather. This will be composed of a conduction and a convection current, the latter due to rising or falling air currents carrying ions. He supposes the field near the earth to be 100 volts per metre, or 1⁄300 electrostatic units. For simplicity, he assumes I+ and I− each equal 0·25 × 10−6 electrostatic units. The specific velocities of the ions—i.e. the velocities in unit field—he takes to be 1·3 × 300 for the positive, and 1·6 × 300 for the negative. The positive and
