4. The potential gradient near the ground varies with the season of the year and the hour of the day, and is largely dependent on the weather conditions. It is thus difficult to form even a rough estimate of the mean value at any place unless hourly readings exist, extending over the whole or the greater part of a year. It is even somewhat precipitate to assume that a mean value deduced from a single year is fairly representative of average conditions. At Potsdam, G. Lüdeling (9) found for the mean value for 1904 in volts per metre 242. At Karasjok in the extreme north of Norway G.C. Simpson (10) in 1903-1904 obtained 139. At Kremsmünster for 1902 P.B. Zölss(11) gives 98. At Kew (12) the mean for individual years from 1898 to1904 varied from 141 in 1900 to 179 in 1899, the mean from the seven years combined being 159. The large difference between the means obtained at Potsdam and Kremsmünster, as compared to the comparative similarity between the results for Kew and Karasjok, suggests that the mean value of the potential gradient may be much more dependent on local conditions than on difference of latitude.At any single station potential gradient has a wide range of values. The largest positive and negative values recorded are met with during disturbed weather. During thunderstorms the record from an electrograph shows large sudden excursions, the trace usually going off the sheet with every flash of lightning when the thunder is near. Exactly what the potential changes amount to under such circumstances it is impossible to say; what the trace shows depends largely on the type of electrometer. Large rapid changes are also met with in the absence of thunder during heavy rain or snow fall. In England the largest values of a sufficiently steady character to be shown correctly by an ordinary electrograph occur during winter fogs. At such times gradients of +400 or +500 volts per metre are by no means unusual at Kew, and voltages of 700 or 800 are occasionally met with.5. Annual Variation.—Table I. gives the annual variation of the potential gradient at a number of stations arranged according to latitude, the mean value for the whole year being taken in each case as 100. Karasjok as already mentioned is in the extreme north of Norway (69° 17′ N.); Sodankylä was the Finnish station of the international polar year 1882-1883. At Batavia, which is near the equator (6° 11′ S.) the annual variation seems somewhat irregular. Further, the results obtained with the water-dropper at two heights—viz. 2 and 7.8 metres—differ notably. At all the other stalions the difference between summer and winter months is conspicuous. From the European data one would be disposed to conclude that the variation throughout the year diminishes as one approaches the equator. It is decidedly less at Perpignan and Lisbon than at Potsdam, Kew and Greenwich, but nowhere is the seasonal difference more conspicuous than at Tokyo, which is south of Lisbon.TableII.—Diurnal Variation Potential Gradient.Station.Karasjok.Sodankylä.Kew(19,12).Greenwich.Florence.Perpignan.Lisbon.Tokyo.Batavia.CapeHorn(20).Period.1903-4.1882-83.1862-1864.1898-1904.1893-96.1883-85.1886-88.1884-86.1897-981900-1.1887-1890.1890-1895.1882-83.Days.All.All.Quiet.All.All.Fine.All.All.Dry.Dry.Pos.hl5.53.02.53.51.03.351.33.01.88.41.53.00.51.72.027.83.52.0Hour.183918793979278841011471258227385798889837280981411147336682748487777178971351098546384728386757281991281028156089718586747783121127101856689177939282929215413711795781979210310010010710116715814710688710010611210211211410514910411911899498107115100113111104117678211910101102100112101107100104874255123119998901019610096102703546123Noon.103102929497959910861304311511061059089969299111543042112210810791879490971144930439431081089288958999109533346894109108989397891051086141538851101081089910294113108766773846119110121108108113126111959110811071291021341151111211311161071201451078136111139118115129129114114137155123913911113811911713212010911914615511210133104128115117127109102120148147991112110811310811111497921191511438512102939999104100868511214713098TableIII.—Diurnal Variation Potential Gradient.Station.Karasjok.Sodankylä.Kew.Greenwich.BureauCentral (21).EiffelTower (21).Perpignan (21).Batavia.(2 m.)Period.1903-4.1882-83.1898-1904.1894 and ’96.1894-99.1896-98.1885-95.1887-90.Winter.Summer.Winter.Summer.Winter.Equinox.Summer.Winter.Summer.Winter.Summer.Summer.Winter.Summer.Winter.Summer.Hour.176104909991939687110791029072881451492669679848688908410171928367831391423578978908285857698708879668113713545583749981848477966984766783131127550797411182879078947594787292132123661838011486971018210183106878410713813677889861179510911394107981189710411416615388293951221041181209711111112010312210811892990939110911111911998102113106110126100746410104931061011141101101029811194109114934340111029298971079597103861088410798903536Noon.1199098100102868710794106771049995313011169411697998180107851127910796932933211897113979780761098211281110949028323119100121939982761117811178107958824414115991119610388801168111380105102923049512010610510610896871129312085106115986074613110411592111109981149812497109128110889471361101181021141201111179912412311313312211912281341131171061121241231131081161341101311271381359137125115901111231291111181041301091241251451471012513511290108118125110124971221051111171481481111412611310310310911610212090115101961081491521296111958596991059311683108948395148146At the temperate stations the maximum occurs near midwinter; in the Arctic it seems deferred towards spring.6.Diurnal Variation.—Table II. gives the mean diurnal variation for the whole year at a number of stations arranged in order of latitude, the mean from the 24 hourly values being taken as 100. The data are some from “all” days, some from “quiet,” “fine” or “dry” days. The height,h, and the distance from the wall,l, were the potential is measured are given in metres when known. In most cases two distinct maxima and minima occur in the 24 hours. The principal maximum is usually found in the evening between 8 and 10P.M., the principal minimum in the morning from 3 to 5A.M.At some stations the minimum in the afternoon is indistinctly shown, but at Tokyo and Batavia it is much more conspicuous than the morning minimum.7. In Table III. the diurnal inequality is shown for “winter” and “summer” respectively. In all cases the mean value for the 24 hours is taken as 100. By “summer” is meant April to September at Sodankylä, Greenwich and Batavia; May to August at Kew, Bureau Central (Paris), Eiffel Tower and Perpignan; and May to July at Karasjok. “Winter” includes October to March at Sodankylä, Greenwich and Batavia; November to February at Kew and Bureau Central; November to January at Karasjok, and December and January at Perpignan. Mean results from March, April, September and October at Kew are assigned to “Equinox.”At Batavia the difference between winter and summer is comparatively small. Elsewhere there is a tendency for the double period, usually so prominent in summer, to become less pronounced in winter, the afternoon minimum tending to disappear. Even in summer the double period is not prominent in the arctic climate of Karasjok or on the top of the Eiffel Tower. The diurnal variation in summer at the latter station is shown graphically in the top curve of fig. 1. It presents a remarkable resemblance to the adjacent curve, which gives the diurnal variation at mid-winter at the Bureau Central. The resemblance between these curves is much closer than that between the Bureau Central’s own winter and summer curves. All three Paris curves show three peaks, the first and third representing the ordinary forenoon and afternoon maxima. In summer at the Bureau Central the intermediate peak nearly disappears in the profound afternoon depression, but it is still recognizable. This three-peaked curve is not wholly peculiar to Paris, being seen, for instance, at Lisbon in summer. The December and June curves for Kew are good examples of the ordinary nature of the difference between midwinter and midsummer. The afternoon minimum at Kew gradually deepens as midsummer approaches. Simultaneously the forenoon maximum occurs earlier and the afternoon maximum later in the day. The two last curves in the diagram contrast the diurnal variation at Kew in potential gradient and in barometric pressure for the year as a whole. The somewhat remarkable resemblance between the diurnal variation for the two elements, first remarked on by J.D. Everett (19), is of interest in connexion with recent theoretical conclusions by J.P. Elster and H.F.K. Geitel and by H. Ebert.In the potential curves of the diagram the ordinates represent the hourly values expressed—as in Tables II. and III.—as percentages of the mean value for the day. If this be overlooked, a wrong impression may be derived as to the absolute amplitudes of the changes. The Kew curves, for instance, might suggest that the range (maximum less minimum hourly value) was larger in June than in December. In reality the December range was 82, the June only 57 volts; but the mean value of the potential was 243 in December as against 111 in June. So again, in the case of the Paris curves, the absolute value of the diurnal range in summer was much greater for the Eiffel Tower than for the Bureau Central, but the mean voltage was 2150 at the former station and only 134 at the latter.8.Fourier Coefficients.—Diurnal inequalities such as those of Tables II. and III. and intended to eliminate irregular changes, but they also to some extent eliminate regular changes if the hours of maxima and minima or the character of the diurnal variation alter throughout the year. The alteration that takes place in the regular diurnal inequality throughout the year is best seen by analysing it into a Fourier series of the typec1sin(t + a1) + c2sin(2t + a2) + c3sin(3t + a3) + c4sin(4t + a4) + ...where t denotes time counted from (local) midnight, c1, c2, c3, C4, ... are the amplitudes of the component harmonic waves of periods 24, 12, 8 and 6 hours; a1, a2, a3, a4, are the corresponding phase angles. One hour of time t is counted as 15°, and a delay of one hour in the time of maximum answers to a diminution of 15° in a1, of 30° in a2, and so on. If a1, say, varies much throughput the year, or if the ratios of c2, c3, c4, ... to c1, vary much, then a diurnal inequality derived from a whole year, or from a season composed of several months, represents a mean curve arising from the superposition of a number of curves, which differ in shape and in the positions of their maxima and minima. The result, if considered alone, inevitably leads to an underestimate of the average amplitude of the regular diurnal variation.It is also desirable to have an idea of the size of the irregular changes which vary from one day to the next. On stormy days, as already mentioned, the irregular changes hardly admit of satisfactory treatment. Even on the quietest days irregular changes are always numerous and often large.Table IV. aims at giving a summary of the several phenomena for a single station, Kew, on electrically quiet days. The first line gives the mean value of the potential gradient, the second the mean excess of the largest over the smallest hourly value on individual days. The hourly values are derived from smoothed curves, the object being to get the mean ordinate for a 60-minute period. If the actual crests of the excursions had been measured the figures in the second line would have been even larger. The third line gives the range of theregulardiurnal inequality, the next four lines the amplitudes of the first four Fourier waves into which the regular diurnal inequality has been analysed. These mean values, ranges and amplitudes are all measured in volts per metre (in the open). The last four lines of Table IV. give the phase angles of the first four Fourier waves.TableIV.—Absolute Potential Data at Kew(12).Jan.Feb.March.April.May.June.July.Aug.Sept.Oct.Nov.Dec.Mean Potential Gradient20122418013812311198114121153200243Mean of individual daily ranges203218210164143143117129141196186213Range in Diurnal inequality739483747157556054635282Amplitudes of Fourier wavesc12222171318966971430c2213334312223242623301721c37105531323657c4235641434323°°°°°°°°°°°°Phase angles of Fourier wavesa120620412372867948142154192202208a1170171186193188183185182199206212175a3119369610012512410716183836a1235225307314314277293313330288238249It will be noticed that the difference between the greatest and least hourly values is, in all but three winter months, actually larger than the mean value of the potential gradient for the day; it bears to the range of the regular diurnal inequality a ratio varying from 2.0 in May to 3.6 in November.At midwinter the 24-hour term is the largest, but near midsummer it is small compared to the 12-hour term. The 24-hour term is very variable both as regards its amplitude and its phase angle (and soits hour of maximum). The 12-hour term is much less variable, especially as regards its phase angle; its amplitude shows distinct maxima near the equinoxes. That the 8-hour and 6-hour waves, though small near midsummer, represent more than mere accidental irregularities, seems a safe inference from the regularity apparent in the annual variation of their phase angles.TableV.—Fourier Series Amplitudes and Phase Angles.Place.Period.Winter.Summer.c1.c2.a1.a2.c1.c2.a1.a2.°°°°Kew1862-640.2830.1601841930.1270.229111179”1898-1904.102.103206180.079.21387186Bureau Central1894-98.220.104223206.130.20095197Eiffel Tower1896-98.........133.085216171Sonnblick (22)1902-03.........208.120178145Karasjok1903-04.356.144189155.165.093141144Kremsmünster (23)1902.280.117224194.166.153241209Potsdam1904.269.101194185.096.1523431859. Table V. gives some data for the 24-hour and 12-hour Fourier coefficients, which will serve to illustrate the diversity between different stations. In this table, unlike Table IV., amplitudes are all expressed as decimals of the mean value of the potential gradient for the corresponding season. “Winter” means generally the four midwinter, and “summer” the four midsummer, months; but at Karasjok three, and at Kremsmünster six, months are included in each season. The results for the Sonnblick are derived from a comparatively small number of days in August and September. At Potsdam the data represent the arithmetic means derived from the Fourier analysis for the individual months comprising the season. The 1862-1864 data from Kew—due to J.D. Everett (19)—are based on “all” days; the others, except Karasjok to some extent, represent electrically quiet days. The cause of the large difference between the two sets of data for c1at Kew is uncertain. The potential gradient is in all cases lower in summer than winter, and thus the reduction in c1in summer would appear even larger than in Table V. if the results were expressed in absolute measure. At Karasjok and Kremsmünster the seasonal variation in a1seems comparatively small, but at Potsdam and the Bureau Central it is as large as at Kew. Also, whilst the winter values of a1are fairly similar at the several stations the summer values are widely different. Except at Karasjok, where the diurnal changes seem somewhat irregular, the relative amplitude of the 12-hour term is considerably greater in summer than in winter. The values of a2at the various stations differ comparatively little, and show but little seasonal change. Thus the 12-hour term has a much greater uniformity than the 24-hour term. This possesses significance in connexion with the view, supported by A.B. Chauveau (21), F. Exner (24) and others, that the 12-hour term is largely if not entirely a local phenomenon, due to the action of the lower atmospheric strata, and tending to disappear even in summer at high altitudes. Exner attributes the double daily maximum, which is largely a consequence of the 12-hour wave, to a thin layer near the ground, which in the early afternoon absorbs the solar radiation of shortest wave length. This layer he believes specially characteristic of arid dusty regions, while comparatively non-existent in moist climates or where foliage is luxuriant. In support of his theory Exner states that he has found but little trace of the double maximum and minimum in Ceylon and elsewhere. C. Nordmann (25) describes some similar results which he obtained in Algeria during August and September 1905. His station, Philippeville, is close to the shores of the Mediterranean, and sea breezes persisted during the day. The diurnal variation showed only a single maximum and minimum, between 5 and 6P.M.and 4 and 5A.M.respectively. So again, a few days’ observations on the top of Mont Blanc (4810 metres) by le Cadet (26) in August and September 1902, showed only a single period, with maximum between 3 and 4P.M., and minimum about 3A.M.Chauveau points to the reduction in the 12-hour term as compared to the 24-hour term on the Eiffel Tower, and infers the practical disappearance of the former at no great height. The close approach in the values for c1in Table V. from the Bureau Central and the Eiffel Tower, and the reduction of c2at the latter station, are unquestionably significant facts; but the summer value for c2at Karasjok—a low level station—is nearly as small as that at the Eiffel Tower, and notably smaller than that at the Sonnblick (3100 metres). Again, Kew is surrounded by a large park, not devoid of trees, and hardly the place where Exner’s theory would suggest a large value for c2, and yet the summer value of c2at Kew is the largest in Table V.10. Observations on mountain tops generally show high potentials near the ground. This only means that the equipotential surfaces are crowded together, just as they are near the ridge of a house. To ascertain how the increase in the voltage varies as the height in the free atmosphere increases, it is necessary to employ kites or balloons. At small heights Exner (27) has employed captive balloons, provided with a burning fuse, and carrying a wire connected with an electroscope on the ground. He found the gradient nearly uniform for heights up to 30 to 40 metres above the ground. At great heights free balloons seem necessary. The balloon carries two collectors a given vertical distance apart. The potential difference between the two is recorded, and the potential gradient is thus found. Some of the earliest balloon observations made the gradient increase with the height, but such a result is now regarded as abnormal. A balloon may leave the earth with a charge, or become charged through discharge of ballast. These possibilities may not have been sufficiently realized at first. Among the most important balloon observations are those by le Cadet (1) F. Linke (28) and H. Gerdien (29). The following are samples from a number of days’ results, given in le Cadet’s book. h is the height in metres, P the gradient in volts per metre.Aug. 9, 1893{h82483010601255129017451940208023102520P37434341423425211816Sep. 11, 1897{h114013781630191423727863136336439124085P43383325222119191413The ground value on the last occasion was 150. From observations during twelve balloon ascents, Linke concludes that below the 1500-metre level there are numerous sources of disturbance, the gradient at any given height varying much from day to day and hour to hour; but at greater heights there is much more uniformity. At heights from 1500 to 6000 metres his observations agreed well with the formuladV/dh = 34 − 0.006 h,V denoting the potential, h the height in metres. The formula makes the gradient diminish from 25 volts per metre at 1500 metres height to 10 volts per metre at 4000 metres. Linke’s mean value for dV/dh at the ground was 125. Accepting Linke’s formula, the potential at 4000 metres is 43,750 volts higher than at 1500 metres. If the mean of the gradients observed at the ground and at 1500 metres be taken as an approximation to the mean value of the gradient throughout the lowest 1500 metres of the atmosphere, we find for the potential at 1500 metres level 112,500 volts. Thus at 4000 metres the potential seems of the order of 150,000 volts. Bearing this in mind, one can readily imagine how close together the equipotential surfaces must lie near the summit of a high sharp mountain peak.11. At most stations a negative potential gradient is exceptional, unless during rain or thunder. During rain the potential is usually but not always negative, and frequent alternations of sign are not uncommon. In some localities, however, negative potential gradient is by no means uncommon, at least at some seasons, in the absence of rain. At Madras, Michie Smith (30) often observed negative potential during bright August and September days. The phenomenon was quite common between 9.30A.M.and noon during westerly winds, which at Madras are usually very dry and dusty. At Sodankylä, in 1882-1883, K.S. Lemström and F.C. Biese (31) found that out of 255 observed occurrences of negative potential, 106 took place in the absence of rain or snow. The proportion of occurrences of negative potential under a clear sky was much above its average in autumn. At Sodankylä rain or snowfall was often unaccompanied by change of sign in the potential. At the polar station Godthaab (32) in 1882-1883, negative potential seemed sometimes associated with aurora (seeAurora Polaris).Lenard, Elster and Geitel, and others have found the potential gradient negative near waterfalls, the influence sometimes extending to a considerable distance. Lenard (33) found that when pure water falls upon water the neighbouring air takes a negative charge. Kelvin, Maclean and Gait (34) found the effect greatest in the air near the level of impact. A sensible effect remained, however, after the influence of splashing was eliminated. Kelvin, Maclean and Galt regard this property of falling water as an objection to the use of a water-dropper indoors, though not of practical importance when it is used out of doors.12. Elster and Geitel (35) have measured the charge carried by raindrops falling into an insulated vessel. Owing to observational difficulties, the exact measure of success attained is a little difficult to gauge, but it seems fairly certain that raindrops usually carry a charge. Elster and Geitel found the sign of the charge often fluctuate repeatedly during a single rain storm, but it seemed more often than not opposite to that of the simultaneous potential gradient. Gerdien has more recently repeated the experiments, employing an apparatus devised by him for the purpose. It has been found by C.T.R. Wilson (36) that a vessel in which freshly fallen rain or snow has been evaporated to dryness shows radioactive properties lasting for a few hours. The results obtained from equal weights of rain and snow seem of the same order.13. W. Linss (6) found that an insulated conductor charged either positively or negatively lost its charge in the free atmosphere; the potential V after time t being connected with its initial value V0by a formula of the type V = V0e−atwhere a is constant. This was confirmed by Elster and Geitel (7), whose form of dissipation apparatus has been employed in most recent work. The percentage of thecharge which is dissipated per minute is usually denoted bya+ora−according to its sign. The mean ofa+anda−is usually denoted bya±or simply bya, whileqis employed for the ratioa−/a+. Some observers when giving mean values take Σ(a−/a+) as the mean value ofq, while others take Σ(a−)/Σ(a+). The Elster and Geitel apparatus is furnished with a cover, serving to protect the dissipator from the direct action of rain, wind or sunlight. It is usual to observe with this cover on, but some observers,e.g.A. Gockel, have made long series of observations without it. The loss of charge is due to more than one cause, and it is difficult to attribute an absolutely definite meaning even to results obtained with the cover on. Gockel (37) says that the results he obtained without the cover when divided by 3 are fairly comparable with those obtained under the usual conditions; but the appropriate divisor must vary to some extent with the climatic conditions. Thus results obtained fora+ora−without the cover are of doubtful value for purposes of comparison with those found elsewhere with it on. In the case ofqthe uncertainty is much less.TableVI.—Dissipation. Mean Values.Place.Period.Season.Observer orAuthority.a+qKarasjok1903-4YearSimpson (10)3.571.15WolfenbüttelYearElster and Geitel (39)1.331.05Potsdam1904YearLüdeling (40)1.131.33Kremsmüster1902YearZölss (42)1.321.18”1903YearZölss (41)1.351.14FreiburgYearGockel (43)..1.41Innsbruck1902Czermak (44)1.950.94”1905Jan. to JuneDefant (45)1.471.17Mattsee (Salzburg)1905July to Sept.von Schweidler (46)..0.99Seewalchen1904July to Sept.von Schweidler (38)..1.18Trieste1902-3YearMazelle (47)0.581.09Misdroy1902Lüdeling (40)1.091.58Swinemünde1904Aug. and Sept.Lüdeling (40)1.231.37Heligoland (sands)1903SummerElster and Geitel (40)1.141.71Heligoland plateau””Elster and Geitel (40)3.071.50Juist (Island)”Elster and Geitel (48)1.561.56Atlantic and German Ocean1904AugustBoltzmann (49)1.832.69Arosa (1800 m.)1903Feb. to AprilSaake (50)1.791.22Rothhorn (2300 m.)1903SeptemberGockel (43)..5.31Sonnblick (3100 m.)1903SeptemberConrad (22)..1.75Mont Blanc (4810 m.)1902Septemberle Cadet (43)..10.3Table VI. gives the mean values ofa±andqfound at various places. The observations were usually confined to a few hours of the day, very commonly between 11A.M.and 1P.M., and in absence of information as to the diurnal variation it is impossible to say how much this influences the results. The first eight stations lie inland; that at Seewalchen (38) was, however, adjacent to a large lake. The next five stations are on the coast or on islands. The final four are at high levels. In the cases where the observations were confined to a few months the representative nature of the results is more doubtful.On mountain summitsqtends to be large,i.e.a negative charge is lost much faster than a positive charge. Apparentlyqhas also a tendency to be large near the sea, but this phenomenon is not seen at Trieste. An exactly opposite phenomenon, it may be remarked, is seen near waterfalls,qbecoming very small. Only Innsbruck and Mattsee give a mean value ofqless than unity. Also, as later observations at Innsbruck give more normal values forq, some doubt may be felt as to the earlier observations there. The result for Mattsee seems less open to doubt, for the observer, von Schweidler, had obtained a normal value forqduring the previous year at Seewalchen. Whilst the averageqin at least the great majority of stations exceeds unity, individual observations makingqless than unity are not rare. Thus in 1902 (51) the percentage of cases in whichqfell short of 1 was 30 at Trieste, 33 at Vienna, and 35 at Kremsmünster; at Innsbruckqwas less than 1 on 58 days out of 98.In a long series of observations, individual values ofqshow usually a wide range. Thus during observations extending over more than a year,qvaried from 0.18 to 8.25 at Kremsmünster and from 0.11 to 3.00 at Trieste. The values ofa+,a−anda±also show large variations. Thus at Triestea+varied from 0.12 to 4.07, anda−from 0.11 to 3.87; at Viennaa+varied from 0.32 to 7.10, anda−from 0.78 to 5.42; at Kremsmünstera±varied from 0.14 to 5.83.14.Annual Variation.—When observations are made at irregular hours, or at only one or two fixed hours, it is doubtful how representative they are. Results obtained at noon, for example, probably differ more from the mean value for the 24 hours at one season than at another. Most dissipation results are exposed to considerable uncertainty on these grounds. Also it requires a long series of years to give thoroughly representative results for any element, and few stations possess more than a year or two’s dissipation data. Table VII. gives comparative results for winter (October to March) and summer at a few stations, the value for the season being the arithmetic mean from the individual months composing it. At Karasjok (10), Simpson observed thrice a day; the summer value there is nearly double the winter both fora+anda−. The Kremsmünster (42) figures show a smaller but still distinct excess in the summer values. At Trieste (47), Mazelle’s data from all days of the year show no decided seasonal change ina+ora−; but when days on which the wind was high are excluded the summer value is decidedly the higher. At Freiburg (43),qseems decidedly larger in winter than in summer; at Karasjok and Trieste the seasonal effect inqseems small and uncertain.TableVII.—Dissipation.PlaceWinterSummera+a−a±qa+a−a±qKarasjok 1903-19042.282.692.491.184.384.944.651.13Kremsmüster 19031.141.301.221.141.381.561.471.12Freiburg......1.57......1.26Trieste 1902-19030.560.590.581.070.550.610.581.13Trieste calm days....0.35......0.48..15.Diurnal Variation.—P.B. Zölss (41,42) has published diurnal variation data for Kremsmünster for more than one year, and independently for midsummer (May to August) and midwinter (December to February). His figures show a double daily period in botha+anda−, the principal maximum occurring about 1 or 2P.M.The two minima occur, the one from 5 to 7A.M., the other from 7 to 8P.M.; they are nearly equal. Taking the figures answering to the whole year, May 1903 to 1904,a+varied throughout the day from 0.82 to 1.35, anda−from 0.85 to 1.47. At midsummer the extreme hourly values were 0.91 and 1.45 fora+, 0.94 and 1.60 fora−. The corresponding figures at midwinter were 0.65 and 1.19 fora+, 0.61 and 1.43 fora−. Zölss’ data forqshow also a double daily period, but the apparent range is small, and the hourly variation is somewhat irregular. At Karasjok, Simpson founda+anda−both larger between noon and 1P.M.than between either 8 and 9A.M.or 6 and 7P.M.The 6 to 7P.M.values were in general the smallest, especially in the case ofa+; the evening value forqon the average exceeded the values from the two earlier hours by some 7%.Summer observations on mountains have shown diurnal variations very large and fairly regular, but widely different from those observed at lower levels. On the Rothhorn, Gockel (43) founda+particularly variable, the mean 7A.M.value being 4½ times that at 1P.M.q(taken as Σ(a−/a+) varied from 2.25 at 5A.M.and 2.52 at 9P.M.to 7.82 at 3P.M.and 8.35 at 7P.M.On the Sonnblick, in early September, V. Conrad (22) found somewhat similar results forq, the principal maximum occurring at 1P.M., with minima at 9P.M.and 6A.M.; the largest hourly value was, however, scarcely double the least. Conrad founda−largest at 4A.M.and least at 6P.M., the largest value being double the least;a+was largest at 5A.M.and least at 2P.M., the largest value being fully 2½ times the least. On Mont Blanc, le Cadet (43) foundqlargest from 1 to 3P.M., the value at either of these hours being more than double that at 11A.M.On the Patscherkofel, H. von Ficker and A. Defant (52), observing in December, foundqlargest from 1 to 2P.M.and least between 11A.M.and noon, but the largest value was only 1½ times the least. On mountains much seems to depend on whether there are rising or falling air currents, and results from a single season may not be fairly representative.16. Dissipation seems largely dependent on meteorological conditions, but the phenomena at different stations vary so much as to suggest that the connexion is largely indirect. At most stationsa+anda−both increase markedly as wind velocity rises. From the observations at Trieste in 1902-1903 E. Mazelle (47) deduced an increase of about 3% ina+for a rise of 1 km. per hour in wind velocity. The following are some of his figures, the velocityvbeing in kilometres per hour:—v0 to 4.20 to 24.40 to 49.60 to 69.a0.330.641.031.38q1.131.191.000.96For velocities from 0 to 24 km. per hourqexceeded unity in 74 cases out of 100; but for velocities over 50 km. per hourqexceeded unityin only 40 cases out of 100. Simpson got similar results at Karasjok; the rise ina+anda−with increased wind velocity seemed, however, larger in winter than in summer. Simpson observed a fall inqfor wind velocities exceeding 2 on Beaufort’s scale. On the top of the Sonnblick, Conrad observed aslightincrease ofa±as the wind velocity increased up to 20 km. per hour, but for greater velocities up to 80 km. per hour no further decided rise was observed.At Karasjok, treating summer and winter independently, Simpson (10) founda+anda−both increase in a nearly linear relation with temperature, from below −20° to +15° C. For example, when the temperature was below −20° mean values were 0.76 fora+and 0.91 fora−; for temperatures between -10° and -5° the corresponding means were 2.45 and 2.82; while for temperatures between +10° and +15° they were 4.68 and 5.23. Simpson found no certain temperature effect on the value ofq. At Trieste, from 470 days when the wind velocity did not exceed 20 km. per hour, Mazelle (47) found somewhat analogous results for temperatures from 0° to 30° C.;a−, however, increased faster thana+,i.e.qincreased with temperature. When he considered all days irrespective of wind velocity, Mazelle found the influence of temperature obliterated. On the Sonnblick, Conrad (22) founda±increase appreciably as temperature rose up to 4° or 5° C.; but at higher temperatures a decrease set in.Observations on the Sonnblick agree with those at low-level stations in showing a diminution of dissipation with increase of relative humidity. The decrease is most marked as saturation approaches. At Trieste, for example, for relative humidities between 90 and 100 the meana±was less than half that for relative humidities under 40. With certain dry winds, notably Föhn winds in Austria and Switzerland, dissipation becomes very high. Thus at Innsbruck Defant (45) found the mean dissipation on days of Föhn fully thrice that on days without Föhn. The increase was largest fora+, there being a fall of about 15% inq. In general,a+anda−both tend to be less on cloudy than on bright days. At Kiel (53) and Trieste the average value ofqis considerably less for wholly overcast days than for bright days. At several stations enjoying a wide prospect the dissipation has been observed to be specially high on days of great visibility when distant mountains can be recognized. It tends on the contrary to be low on days of fog or rain.The results obtained as to the relation between dissipation and barometric pressure are conflicting. At Kremsmünster, Zölss (42) found dissipation vary with the absolute height of the barometer,a±having a mean value of 1.36 when pressure was below the normal, as against 1.20 on days when pressure was above the normal. He also founda±on the average about 10% larger when pressure was falling than when it was rising. On the Sonnblick, Conrad (22) found dissipation increase decidedly as the absolute barometric pressure was larger, and he found no difference between days of rising and falling barometer. At Trieste, Mazelle (47) found no certain connexion with absolute barometric pressure. Dissipation was above the average when cyclonic conditions prevailed, but this seemed simply a consequence of the increased wind velocity. At Mattsee, E.R. von Schweidler (46) found no connexion between absolute barometric pressure and dissipation, also days of rising and falling pressure gave the same mean. At Kiel, K. Kaehler (53) founda+anda−both greater with rising than with falling barometer.V. Conrad and M. Topolansky (54) have found a marked connexion at Vienna between dissipation and ozone. Regular observations were made of both elements. Days were grouped according to the intensity of colouring of ozone papers, 0 representing no visible effect, and 14 the darkest colour reached. The mean values ofa+anda−answering to 12 and 13 on the ozone scale were both about double the corresponding values answering to 0 and 1 on that scale.
4. The potential gradient near the ground varies with the season of the year and the hour of the day, and is largely dependent on the weather conditions. It is thus difficult to form even a rough estimate of the mean value at any place unless hourly readings exist, extending over the whole or the greater part of a year. It is even somewhat precipitate to assume that a mean value deduced from a single year is fairly representative of average conditions. At Potsdam, G. Lüdeling (9) found for the mean value for 1904 in volts per metre 242. At Karasjok in the extreme north of Norway G.C. Simpson (10) in 1903-1904 obtained 139. At Kremsmünster for 1902 P.B. Zölss(11) gives 98. At Kew (12) the mean for individual years from 1898 to1904 varied from 141 in 1900 to 179 in 1899, the mean from the seven years combined being 159. The large difference between the means obtained at Potsdam and Kremsmünster, as compared to the comparative similarity between the results for Kew and Karasjok, suggests that the mean value of the potential gradient may be much more dependent on local conditions than on difference of latitude.
At any single station potential gradient has a wide range of values. The largest positive and negative values recorded are met with during disturbed weather. During thunderstorms the record from an electrograph shows large sudden excursions, the trace usually going off the sheet with every flash of lightning when the thunder is near. Exactly what the potential changes amount to under such circumstances it is impossible to say; what the trace shows depends largely on the type of electrometer. Large rapid changes are also met with in the absence of thunder during heavy rain or snow fall. In England the largest values of a sufficiently steady character to be shown correctly by an ordinary electrograph occur during winter fogs. At such times gradients of +400 or +500 volts per metre are by no means unusual at Kew, and voltages of 700 or 800 are occasionally met with.
5. Annual Variation.—Table I. gives the annual variation of the potential gradient at a number of stations arranged according to latitude, the mean value for the whole year being taken in each case as 100. Karasjok as already mentioned is in the extreme north of Norway (69° 17′ N.); Sodankylä was the Finnish station of the international polar year 1882-1883. At Batavia, which is near the equator (6° 11′ S.) the annual variation seems somewhat irregular. Further, the results obtained with the water-dropper at two heights—viz. 2 and 7.8 metres—differ notably. At all the other stalions the difference between summer and winter months is conspicuous. From the European data one would be disposed to conclude that the variation throughout the year diminishes as one approaches the equator. It is decidedly less at Perpignan and Lisbon than at Potsdam, Kew and Greenwich, but nowhere is the seasonal difference more conspicuous than at Tokyo, which is south of Lisbon.
TableII.—Diurnal Variation Potential Gradient.
TableIII.—Diurnal Variation Potential Gradient.
At the temperate stations the maximum occurs near midwinter; in the Arctic it seems deferred towards spring.
6.Diurnal Variation.—Table II. gives the mean diurnal variation for the whole year at a number of stations arranged in order of latitude, the mean from the 24 hourly values being taken as 100. The data are some from “all” days, some from “quiet,” “fine” or “dry” days. The height,h, and the distance from the wall,l, were the potential is measured are given in metres when known. In most cases two distinct maxima and minima occur in the 24 hours. The principal maximum is usually found in the evening between 8 and 10P.M., the principal minimum in the morning from 3 to 5A.M.At some stations the minimum in the afternoon is indistinctly shown, but at Tokyo and Batavia it is much more conspicuous than the morning minimum.
7. In Table III. the diurnal inequality is shown for “winter” and “summer” respectively. In all cases the mean value for the 24 hours is taken as 100. By “summer” is meant April to September at Sodankylä, Greenwich and Batavia; May to August at Kew, Bureau Central (Paris), Eiffel Tower and Perpignan; and May to July at Karasjok. “Winter” includes October to March at Sodankylä, Greenwich and Batavia; November to February at Kew and Bureau Central; November to January at Karasjok, and December and January at Perpignan. Mean results from March, April, September and October at Kew are assigned to “Equinox.”
At Batavia the difference between winter and summer is comparatively small. Elsewhere there is a tendency for the double period, usually so prominent in summer, to become less pronounced in winter, the afternoon minimum tending to disappear. Even in summer the double period is not prominent in the arctic climate of Karasjok or on the top of the Eiffel Tower. The diurnal variation in summer at the latter station is shown graphically in the top curve of fig. 1. It presents a remarkable resemblance to the adjacent curve, which gives the diurnal variation at mid-winter at the Bureau Central. The resemblance between these curves is much closer than that between the Bureau Central’s own winter and summer curves. All three Paris curves show three peaks, the first and third representing the ordinary forenoon and afternoon maxima. In summer at the Bureau Central the intermediate peak nearly disappears in the profound afternoon depression, but it is still recognizable. This three-peaked curve is not wholly peculiar to Paris, being seen, for instance, at Lisbon in summer. The December and June curves for Kew are good examples of the ordinary nature of the difference between midwinter and midsummer. The afternoon minimum at Kew gradually deepens as midsummer approaches. Simultaneously the forenoon maximum occurs earlier and the afternoon maximum later in the day. The two last curves in the diagram contrast the diurnal variation at Kew in potential gradient and in barometric pressure for the year as a whole. The somewhat remarkable resemblance between the diurnal variation for the two elements, first remarked on by J.D. Everett (19), is of interest in connexion with recent theoretical conclusions by J.P. Elster and H.F.K. Geitel and by H. Ebert.
In the potential curves of the diagram the ordinates represent the hourly values expressed—as in Tables II. and III.—as percentages of the mean value for the day. If this be overlooked, a wrong impression may be derived as to the absolute amplitudes of the changes. The Kew curves, for instance, might suggest that the range (maximum less minimum hourly value) was larger in June than in December. In reality the December range was 82, the June only 57 volts; but the mean value of the potential was 243 in December as against 111 in June. So again, in the case of the Paris curves, the absolute value of the diurnal range in summer was much greater for the Eiffel Tower than for the Bureau Central, but the mean voltage was 2150 at the former station and only 134 at the latter.
8.Fourier Coefficients.—Diurnal inequalities such as those of Tables II. and III. and intended to eliminate irregular changes, but they also to some extent eliminate regular changes if the hours of maxima and minima or the character of the diurnal variation alter throughout the year. The alteration that takes place in the regular diurnal inequality throughout the year is best seen by analysing it into a Fourier series of the type
c1sin(t + a1) + c2sin(2t + a2) + c3sin(3t + a3) + c4sin(4t + a4) + ...
where t denotes time counted from (local) midnight, c1, c2, c3, C4, ... are the amplitudes of the component harmonic waves of periods 24, 12, 8 and 6 hours; a1, a2, a3, a4, are the corresponding phase angles. One hour of time t is counted as 15°, and a delay of one hour in the time of maximum answers to a diminution of 15° in a1, of 30° in a2, and so on. If a1, say, varies much throughput the year, or if the ratios of c2, c3, c4, ... to c1, vary much, then a diurnal inequality derived from a whole year, or from a season composed of several months, represents a mean curve arising from the superposition of a number of curves, which differ in shape and in the positions of their maxima and minima. The result, if considered alone, inevitably leads to an underestimate of the average amplitude of the regular diurnal variation.
It is also desirable to have an idea of the size of the irregular changes which vary from one day to the next. On stormy days, as already mentioned, the irregular changes hardly admit of satisfactory treatment. Even on the quietest days irregular changes are always numerous and often large.
Table IV. aims at giving a summary of the several phenomena for a single station, Kew, on electrically quiet days. The first line gives the mean value of the potential gradient, the second the mean excess of the largest over the smallest hourly value on individual days. The hourly values are derived from smoothed curves, the object being to get the mean ordinate for a 60-minute period. If the actual crests of the excursions had been measured the figures in the second line would have been even larger. The third line gives the range of theregulardiurnal inequality, the next four lines the amplitudes of the first four Fourier waves into which the regular diurnal inequality has been analysed. These mean values, ranges and amplitudes are all measured in volts per metre (in the open). The last four lines of Table IV. give the phase angles of the first four Fourier waves.
TableIV.—Absolute Potential Data at Kew(12).
It will be noticed that the difference between the greatest and least hourly values is, in all but three winter months, actually larger than the mean value of the potential gradient for the day; it bears to the range of the regular diurnal inequality a ratio varying from 2.0 in May to 3.6 in November.
At midwinter the 24-hour term is the largest, but near midsummer it is small compared to the 12-hour term. The 24-hour term is very variable both as regards its amplitude and its phase angle (and soits hour of maximum). The 12-hour term is much less variable, especially as regards its phase angle; its amplitude shows distinct maxima near the equinoxes. That the 8-hour and 6-hour waves, though small near midsummer, represent more than mere accidental irregularities, seems a safe inference from the regularity apparent in the annual variation of their phase angles.
TableV.—Fourier Series Amplitudes and Phase Angles.
9. Table V. gives some data for the 24-hour and 12-hour Fourier coefficients, which will serve to illustrate the diversity between different stations. In this table, unlike Table IV., amplitudes are all expressed as decimals of the mean value of the potential gradient for the corresponding season. “Winter” means generally the four midwinter, and “summer” the four midsummer, months; but at Karasjok three, and at Kremsmünster six, months are included in each season. The results for the Sonnblick are derived from a comparatively small number of days in August and September. At Potsdam the data represent the arithmetic means derived from the Fourier analysis for the individual months comprising the season. The 1862-1864 data from Kew—due to J.D. Everett (19)—are based on “all” days; the others, except Karasjok to some extent, represent electrically quiet days. The cause of the large difference between the two sets of data for c1at Kew is uncertain. The potential gradient is in all cases lower in summer than winter, and thus the reduction in c1in summer would appear even larger than in Table V. if the results were expressed in absolute measure. At Karasjok and Kremsmünster the seasonal variation in a1seems comparatively small, but at Potsdam and the Bureau Central it is as large as at Kew. Also, whilst the winter values of a1are fairly similar at the several stations the summer values are widely different. Except at Karasjok, where the diurnal changes seem somewhat irregular, the relative amplitude of the 12-hour term is considerably greater in summer than in winter. The values of a2at the various stations differ comparatively little, and show but little seasonal change. Thus the 12-hour term has a much greater uniformity than the 24-hour term. This possesses significance in connexion with the view, supported by A.B. Chauveau (21), F. Exner (24) and others, that the 12-hour term is largely if not entirely a local phenomenon, due to the action of the lower atmospheric strata, and tending to disappear even in summer at high altitudes. Exner attributes the double daily maximum, which is largely a consequence of the 12-hour wave, to a thin layer near the ground, which in the early afternoon absorbs the solar radiation of shortest wave length. This layer he believes specially characteristic of arid dusty regions, while comparatively non-existent in moist climates or where foliage is luxuriant. In support of his theory Exner states that he has found but little trace of the double maximum and minimum in Ceylon and elsewhere. C. Nordmann (25) describes some similar results which he obtained in Algeria during August and September 1905. His station, Philippeville, is close to the shores of the Mediterranean, and sea breezes persisted during the day. The diurnal variation showed only a single maximum and minimum, between 5 and 6P.M.and 4 and 5A.M.respectively. So again, a few days’ observations on the top of Mont Blanc (4810 metres) by le Cadet (26) in August and September 1902, showed only a single period, with maximum between 3 and 4P.M., and minimum about 3A.M.Chauveau points to the reduction in the 12-hour term as compared to the 24-hour term on the Eiffel Tower, and infers the practical disappearance of the former at no great height. The close approach in the values for c1in Table V. from the Bureau Central and the Eiffel Tower, and the reduction of c2at the latter station, are unquestionably significant facts; but the summer value for c2at Karasjok—a low level station—is nearly as small as that at the Eiffel Tower, and notably smaller than that at the Sonnblick (3100 metres). Again, Kew is surrounded by a large park, not devoid of trees, and hardly the place where Exner’s theory would suggest a large value for c2, and yet the summer value of c2at Kew is the largest in Table V.
10. Observations on mountain tops generally show high potentials near the ground. This only means that the equipotential surfaces are crowded together, just as they are near the ridge of a house. To ascertain how the increase in the voltage varies as the height in the free atmosphere increases, it is necessary to employ kites or balloons. At small heights Exner (27) has employed captive balloons, provided with a burning fuse, and carrying a wire connected with an electroscope on the ground. He found the gradient nearly uniform for heights up to 30 to 40 metres above the ground. At great heights free balloons seem necessary. The balloon carries two collectors a given vertical distance apart. The potential difference between the two is recorded, and the potential gradient is thus found. Some of the earliest balloon observations made the gradient increase with the height, but such a result is now regarded as abnormal. A balloon may leave the earth with a charge, or become charged through discharge of ballast. These possibilities may not have been sufficiently realized at first. Among the most important balloon observations are those by le Cadet (1) F. Linke (28) and H. Gerdien (29). The following are samples from a number of days’ results, given in le Cadet’s book. h is the height in metres, P the gradient in volts per metre.
The ground value on the last occasion was 150. From observations during twelve balloon ascents, Linke concludes that below the 1500-metre level there are numerous sources of disturbance, the gradient at any given height varying much from day to day and hour to hour; but at greater heights there is much more uniformity. At heights from 1500 to 6000 metres his observations agreed well with the formula
dV/dh = 34 − 0.006 h,
V denoting the potential, h the height in metres. The formula makes the gradient diminish from 25 volts per metre at 1500 metres height to 10 volts per metre at 4000 metres. Linke’s mean value for dV/dh at the ground was 125. Accepting Linke’s formula, the potential at 4000 metres is 43,750 volts higher than at 1500 metres. If the mean of the gradients observed at the ground and at 1500 metres be taken as an approximation to the mean value of the gradient throughout the lowest 1500 metres of the atmosphere, we find for the potential at 1500 metres level 112,500 volts. Thus at 4000 metres the potential seems of the order of 150,000 volts. Bearing this in mind, one can readily imagine how close together the equipotential surfaces must lie near the summit of a high sharp mountain peak.
11. At most stations a negative potential gradient is exceptional, unless during rain or thunder. During rain the potential is usually but not always negative, and frequent alternations of sign are not uncommon. In some localities, however, negative potential gradient is by no means uncommon, at least at some seasons, in the absence of rain. At Madras, Michie Smith (30) often observed negative potential during bright August and September days. The phenomenon was quite common between 9.30A.M.and noon during westerly winds, which at Madras are usually very dry and dusty. At Sodankylä, in 1882-1883, K.S. Lemström and F.C. Biese (31) found that out of 255 observed occurrences of negative potential, 106 took place in the absence of rain or snow. The proportion of occurrences of negative potential under a clear sky was much above its average in autumn. At Sodankylä rain or snowfall was often unaccompanied by change of sign in the potential. At the polar station Godthaab (32) in 1882-1883, negative potential seemed sometimes associated with aurora (seeAurora Polaris).
Lenard, Elster and Geitel, and others have found the potential gradient negative near waterfalls, the influence sometimes extending to a considerable distance. Lenard (33) found that when pure water falls upon water the neighbouring air takes a negative charge. Kelvin, Maclean and Gait (34) found the effect greatest in the air near the level of impact. A sensible effect remained, however, after the influence of splashing was eliminated. Kelvin, Maclean and Galt regard this property of falling water as an objection to the use of a water-dropper indoors, though not of practical importance when it is used out of doors.
12. Elster and Geitel (35) have measured the charge carried by raindrops falling into an insulated vessel. Owing to observational difficulties, the exact measure of success attained is a little difficult to gauge, but it seems fairly certain that raindrops usually carry a charge. Elster and Geitel found the sign of the charge often fluctuate repeatedly during a single rain storm, but it seemed more often than not opposite to that of the simultaneous potential gradient. Gerdien has more recently repeated the experiments, employing an apparatus devised by him for the purpose. It has been found by C.T.R. Wilson (36) that a vessel in which freshly fallen rain or snow has been evaporated to dryness shows radioactive properties lasting for a few hours. The results obtained from equal weights of rain and snow seem of the same order.
13. W. Linss (6) found that an insulated conductor charged either positively or negatively lost its charge in the free atmosphere; the potential V after time t being connected with its initial value V0by a formula of the type V = V0e−atwhere a is constant. This was confirmed by Elster and Geitel (7), whose form of dissipation apparatus has been employed in most recent work. The percentage of thecharge which is dissipated per minute is usually denoted bya+ora−according to its sign. The mean ofa+anda−is usually denoted bya±or simply bya, whileqis employed for the ratioa−/a+. Some observers when giving mean values take Σ(a−/a+) as the mean value ofq, while others take Σ(a−)/Σ(a+). The Elster and Geitel apparatus is furnished with a cover, serving to protect the dissipator from the direct action of rain, wind or sunlight. It is usual to observe with this cover on, but some observers,e.g.A. Gockel, have made long series of observations without it. The loss of charge is due to more than one cause, and it is difficult to attribute an absolutely definite meaning even to results obtained with the cover on. Gockel (37) says that the results he obtained without the cover when divided by 3 are fairly comparable with those obtained under the usual conditions; but the appropriate divisor must vary to some extent with the climatic conditions. Thus results obtained fora+ora−without the cover are of doubtful value for purposes of comparison with those found elsewhere with it on. In the case ofqthe uncertainty is much less.
TableVI.—Dissipation. Mean Values.
Table VI. gives the mean values ofa±andqfound at various places. The observations were usually confined to a few hours of the day, very commonly between 11A.M.and 1P.M., and in absence of information as to the diurnal variation it is impossible to say how much this influences the results. The first eight stations lie inland; that at Seewalchen (38) was, however, adjacent to a large lake. The next five stations are on the coast or on islands. The final four are at high levels. In the cases where the observations were confined to a few months the representative nature of the results is more doubtful.
On mountain summitsqtends to be large,i.e.a negative charge is lost much faster than a positive charge. Apparentlyqhas also a tendency to be large near the sea, but this phenomenon is not seen at Trieste. An exactly opposite phenomenon, it may be remarked, is seen near waterfalls,qbecoming very small. Only Innsbruck and Mattsee give a mean value ofqless than unity. Also, as later observations at Innsbruck give more normal values forq, some doubt may be felt as to the earlier observations there. The result for Mattsee seems less open to doubt, for the observer, von Schweidler, had obtained a normal value forqduring the previous year at Seewalchen. Whilst the averageqin at least the great majority of stations exceeds unity, individual observations makingqless than unity are not rare. Thus in 1902 (51) the percentage of cases in whichqfell short of 1 was 30 at Trieste, 33 at Vienna, and 35 at Kremsmünster; at Innsbruckqwas less than 1 on 58 days out of 98.
In a long series of observations, individual values ofqshow usually a wide range. Thus during observations extending over more than a year,qvaried from 0.18 to 8.25 at Kremsmünster and from 0.11 to 3.00 at Trieste. The values ofa+,a−anda±also show large variations. Thus at Triestea+varied from 0.12 to 4.07, anda−from 0.11 to 3.87; at Viennaa+varied from 0.32 to 7.10, anda−from 0.78 to 5.42; at Kremsmünstera±varied from 0.14 to 5.83.
14.Annual Variation.—When observations are made at irregular hours, or at only one or two fixed hours, it is doubtful how representative they are. Results obtained at noon, for example, probably differ more from the mean value for the 24 hours at one season than at another. Most dissipation results are exposed to considerable uncertainty on these grounds. Also it requires a long series of years to give thoroughly representative results for any element, and few stations possess more than a year or two’s dissipation data. Table VII. gives comparative results for winter (October to March) and summer at a few stations, the value for the season being the arithmetic mean from the individual months composing it. At Karasjok (10), Simpson observed thrice a day; the summer value there is nearly double the winter both fora+anda−. The Kremsmünster (42) figures show a smaller but still distinct excess in the summer values. At Trieste (47), Mazelle’s data from all days of the year show no decided seasonal change ina+ora−; but when days on which the wind was high are excluded the summer value is decidedly the higher. At Freiburg (43),qseems decidedly larger in winter than in summer; at Karasjok and Trieste the seasonal effect inqseems small and uncertain.
TableVII.—Dissipation.
15.Diurnal Variation.—P.B. Zölss (41,42) has published diurnal variation data for Kremsmünster for more than one year, and independently for midsummer (May to August) and midwinter (December to February). His figures show a double daily period in botha+anda−, the principal maximum occurring about 1 or 2P.M.The two minima occur, the one from 5 to 7A.M., the other from 7 to 8P.M.; they are nearly equal. Taking the figures answering to the whole year, May 1903 to 1904,a+varied throughout the day from 0.82 to 1.35, anda−from 0.85 to 1.47. At midsummer the extreme hourly values were 0.91 and 1.45 fora+, 0.94 and 1.60 fora−. The corresponding figures at midwinter were 0.65 and 1.19 fora+, 0.61 and 1.43 fora−. Zölss’ data forqshow also a double daily period, but the apparent range is small, and the hourly variation is somewhat irregular. At Karasjok, Simpson founda+anda−both larger between noon and 1P.M.than between either 8 and 9A.M.or 6 and 7P.M.The 6 to 7P.M.values were in general the smallest, especially in the case ofa+; the evening value forqon the average exceeded the values from the two earlier hours by some 7%.
Summer observations on mountains have shown diurnal variations very large and fairly regular, but widely different from those observed at lower levels. On the Rothhorn, Gockel (43) founda+particularly variable, the mean 7A.M.value being 4½ times that at 1P.M.q(taken as Σ(a−/a+) varied from 2.25 at 5A.M.and 2.52 at 9P.M.to 7.82 at 3P.M.and 8.35 at 7P.M.On the Sonnblick, in early September, V. Conrad (22) found somewhat similar results forq, the principal maximum occurring at 1P.M., with minima at 9P.M.and 6A.M.; the largest hourly value was, however, scarcely double the least. Conrad founda−largest at 4A.M.and least at 6P.M., the largest value being double the least;a+was largest at 5A.M.and least at 2P.M., the largest value being fully 2½ times the least. On Mont Blanc, le Cadet (43) foundqlargest from 1 to 3P.M., the value at either of these hours being more than double that at 11A.M.On the Patscherkofel, H. von Ficker and A. Defant (52), observing in December, foundqlargest from 1 to 2P.M.and least between 11A.M.and noon, but the largest value was only 1½ times the least. On mountains much seems to depend on whether there are rising or falling air currents, and results from a single season may not be fairly representative.
16. Dissipation seems largely dependent on meteorological conditions, but the phenomena at different stations vary so much as to suggest that the connexion is largely indirect. At most stationsa+anda−both increase markedly as wind velocity rises. From the observations at Trieste in 1902-1903 E. Mazelle (47) deduced an increase of about 3% ina+for a rise of 1 km. per hour in wind velocity. The following are some of his figures, the velocityvbeing in kilometres per hour:—
For velocities from 0 to 24 km. per hourqexceeded unity in 74 cases out of 100; but for velocities over 50 km. per hourqexceeded unityin only 40 cases out of 100. Simpson got similar results at Karasjok; the rise ina+anda−with increased wind velocity seemed, however, larger in winter than in summer. Simpson observed a fall inqfor wind velocities exceeding 2 on Beaufort’s scale. On the top of the Sonnblick, Conrad observed aslightincrease ofa±as the wind velocity increased up to 20 km. per hour, but for greater velocities up to 80 km. per hour no further decided rise was observed.
At Karasjok, treating summer and winter independently, Simpson (10) founda+anda−both increase in a nearly linear relation with temperature, from below −20° to +15° C. For example, when the temperature was below −20° mean values were 0.76 fora+and 0.91 fora−; for temperatures between -10° and -5° the corresponding means were 2.45 and 2.82; while for temperatures between +10° and +15° they were 4.68 and 5.23. Simpson found no certain temperature effect on the value ofq. At Trieste, from 470 days when the wind velocity did not exceed 20 km. per hour, Mazelle (47) found somewhat analogous results for temperatures from 0° to 30° C.;a−, however, increased faster thana+,i.e.qincreased with temperature. When he considered all days irrespective of wind velocity, Mazelle found the influence of temperature obliterated. On the Sonnblick, Conrad (22) founda±increase appreciably as temperature rose up to 4° or 5° C.; but at higher temperatures a decrease set in.
Observations on the Sonnblick agree with those at low-level stations in showing a diminution of dissipation with increase of relative humidity. The decrease is most marked as saturation approaches. At Trieste, for example, for relative humidities between 90 and 100 the meana±was less than half that for relative humidities under 40. With certain dry winds, notably Föhn winds in Austria and Switzerland, dissipation becomes very high. Thus at Innsbruck Defant (45) found the mean dissipation on days of Föhn fully thrice that on days without Föhn. The increase was largest fora+, there being a fall of about 15% inq. In general,a+anda−both tend to be less on cloudy than on bright days. At Kiel (53) and Trieste the average value ofqis considerably less for wholly overcast days than for bright days. At several stations enjoying a wide prospect the dissipation has been observed to be specially high on days of great visibility when distant mountains can be recognized. It tends on the contrary to be low on days of fog or rain.
The results obtained as to the relation between dissipation and barometric pressure are conflicting. At Kremsmünster, Zölss (42) found dissipation vary with the absolute height of the barometer,a±having a mean value of 1.36 when pressure was below the normal, as against 1.20 on days when pressure was above the normal. He also founda±on the average about 10% larger when pressure was falling than when it was rising. On the Sonnblick, Conrad (22) found dissipation increase decidedly as the absolute barometric pressure was larger, and he found no difference between days of rising and falling barometer. At Trieste, Mazelle (47) found no certain connexion with absolute barometric pressure. Dissipation was above the average when cyclonic conditions prevailed, but this seemed simply a consequence of the increased wind velocity. At Mattsee, E.R. von Schweidler (46) found no connexion between absolute barometric pressure and dissipation, also days of rising and falling pressure gave the same mean. At Kiel, K. Kaehler (53) founda+anda−both greater with rising than with falling barometer.
V. Conrad and M. Topolansky (54) have found a marked connexion at Vienna between dissipation and ozone. Regular observations were made of both elements. Days were grouped according to the intensity of colouring of ozone papers, 0 representing no visible effect, and 14 the darkest colour reached. The mean values ofa+anda−answering to 12 and 13 on the ozone scale were both about double the corresponding values answering to 0 and 1 on that scale.