April 22, i8S6] 



NATURE 



595 



always increases from the surface of the ground up to 1800 

 feet above sea-level, and that the ratio of the increase steadily 

 diminishes up to that height. The only exception to the steady 

 decrease in the value of .r occurs in Group S> ^"^'^ 'his is evi- 

 dently due to the inclusion in that group of an abnormally large 

 value of X (o'576), corresponding to an equally abnormally small 

 velocity of 789 feet per minute, which is little more than a third 

 of the mean velocity of the stratum corresponding to that group. 

 The mean velocities of each group are also seen to increase with 

 some degree of regularity with the height, but this is, of course, 

 partly accidental. In estimating the value of the exponent x 

 for strata of the atmosphere at different heights above sea-level, 

 it must be remembered that the place of observation is 500 feet 

 above sea-level, and therefore that at a certain height above the 

 ground the motion of the air in all probability approximates to 

 what it would have at its real height above the sea. Where this 

 state of things actually occurs, we have no ready means of de- 

 termining, but at a height of 1000 feet above the ground we may 

 assume that the influence of the subjacent tableland is almost 

 obliterated, and the motion of the air approximates to what it 

 would have at its real sea-level height. On this assumption, if 

 we add the full 500 feet to each height in Group 6, we get the 

 following value for the exponent ; — 



Upper sea-level Lower sea-level Value of x 



height height 



Group 6 1595 1267 o'2S 



If more reasonably we add 400 feet only, we get x — o'26, or 

 almost identically the same value as o'2S, which I found agree 

 best on the average with Dr. Vettin's cloud observations at 

 Berlin, ranging from 1600 to 23,000 feet above sea-level (Nature, 

 January II, 1883). I think, therefore, that the results of the 

 present series of observations may be taken to add strong con- 

 firmation to the general agreement of the empirical formula 



- = ( - j , with the average motion of the air at heiglits 



over i6oo above sea-level. 



One great advantage which results from the representation of 

 the observations in the form of exponents is that we are thus 

 enabled to compare observations differing from one another, both 

 as to height and velocity, in a manner which would otherwise be 

 almost impossible. 



There are four principal variables which have been observed, 

 and which are likely to affect the value of these exponents, viz. 

 (i) the mean velocity at the upper and lower elevations ; (2) the 

 direction of the wind ; {3) the time of day ; and (4) the month 

 of the year. I have, so to speak, differentiated the exponents 

 with respect to each of these variables in turn, and have in each 

 case placed the corresponding values of the other variables 

 alongside, in order to see how much of the resulting variation 

 of the exponent is independent, or dependent on accidental 

 collocations of the other variables. The results I find most 

 curiously involved, owing to apparently accidental groupings of 

 some of the variables. 



One or two variations can, however, be shown to arise from 

 the influence of one factor alone, after that due to the co- 

 existence of others is allowed for. One of these is that due to 

 the change of mean velocity, and the other is the diurnal change 

 with the hour of the day. These are shown in the accompanying 

 Tables II. and III. respectively. 



In Table II. the exponent is found, on the whole, to increase 

 with an increase in the velocity in the two lowest groups 

 (i and 2), and to decrease in the four upper groups, the maxima 

 in each of these groups occurring at the lower velocities, and the 

 minima at the highest ones. 



This latter result is what might have been expected a priori, 

 and though the first two groups would appear at first sight to 

 present an anomaly, it mu'-t be remembered that in these groups 

 the lower instrument is hardly above the influence of surrounding 

 trees, so that in high winds, while the upper instrument might 

 be feeling the full force of the wind, the lower one might be 

 unduly sheltered from it by adjacent trees or buildings. 



In Table III. the diurnal variation in the value of the ex- 

 ponents, reaching its minimum from 2 to 3 or 3 to 4, and its 

 maximum between 6 and 8 (as far as the observations go), is 

 most clearly and regularly shown in each of the four upper 

 groups, .and as these last are well beyond the influence of local 

 obstructions, I regard the uniformity with which they exhibit 

 this variation as a strong proof in favour of its physical existence 

 independently of any similar variation caused by the parallel 

 march of other factors. Even if part of the variation in groups 3, 4, 



and 6 is due to the equally regular decrease in the mean velocity 

 from midday to evening, it can be shown from Table II. that 

 this only accounts for a portion of the observed variation. 



Thus, taking the ranges of the exponents in Table III., and 

 adding to or subtracting from them the proportional ranges of 

 the exponents for the corresponding opposite range of velocity 

 (deduced from the mean range of the exponents for 400 feet 

 range of velocity in Table II.), we get the following results : — • 



^i + -=73 + 'oSs + '^se -(- • 



that is to say, for Group 5 the variation is increased, and for the 

 rest not materially diminished. 



The opposite variation in the two lowest groups (i and 2) may 

 be capable of an explanation somewhat analogous to the similar 

 anomaly presented by these two groups in Table II., but in any 

 case it cannot be said either to sensibly corroborate or invalidate 

 the physical existence of the variation so statistically marked in 

 all the four upper groups. 



This diurnal change in the value of the ratio of the velocity 

 of the upper to the lower strata which is here shown to occur for 

 the afternoon hours, is confirmed by various other casual obser- 

 vation':, and is in complete accord with the results afforded by 

 anemometrical observations on Ben Nevis and other lofty 

 mountain observatories, as well as with Dr. Koppen's theory of 

 the diurnal period in the surface-wind alluded to in my former 

 paper. 



Since at stations near sea-level the diurnal wind-velocity 

 i-eaches its maximum at midday and its minimum at midnight, 

 while at lofty stations about 4000 feet above sea-level the critical 

 epochs are reversed, it is evident that somewhere between these 

 levels a neutral plane exists where the diurnal variation is nil. 

 The ratio of the upper velocity to the lower for a given difterence 

 of height would, however, continue to vary diurnally all the 

 way up (unless some unknown law intervene), reaching its 

 minimum value about midday and its maximum about midnight. 



Indications of other laws have been noticed in the value of 

 the exponents, such as a maximum for west winds and a mini- 

 mum for east winds in five out of six of the groups, and also a 

 maximum in the autumn, minimum in the winter, and maximum 

 again in the summer in all the gr'oups, but the observations are 

 too few and the factors too involved to establish these with any 

 certainty. I trust on a future occasion to be able to go into 

 these questions more in detail, and also to supply the morning 

 half of the diurnal variation, which I consider to be the most 

 certain and valuable result I have as yet obtained in addition to 

 the law of the general progressive decrease in the value of the 

 exponent up to 1800 feet above sea-level in the/?w atmosphere. 

 E. Douglas Archibald 



BASIC CINDER"- ' 

 'T'HE interest of this report centres principally around the 

 -*- question of the manurial value of undissolved phosphates 

 present in basic steel slag or cinder. The basic cinder is the 

 effete and broken up basic lining of the converters used in the 

 Thomas and Gilchrist process for dephosphorising iron, and is 

 made in very large quantities as a by-product of steel manu- 

 facture. It contains from 16 to 19 per cent, of phosphoric acid 

 in union with lime and other bases in combinations insoluble in 

 water. 



At the request of the North-Eastern Steel Company Prof. 

 Wrightson and Dr. Munro undertook field experiments in order 

 to test the manurial value of this substance. The«e experiments 

 were carried out last summer on the College farm at Downton, 

 and at East Howie, Ferry Hill, county of Durham, upon dis- 

 similar soils, and under different climatic conditions. The re- 

 sults as given in the very concise report before us are remarkable, 

 and certainly must be highly satisfactory to those who are inter- 

 ested in the future of basic cinder. The value of this substance 

 as a fertiliser for swedes and turnips, as well as for grass,^ is 

 placed beyond reasonable doubt by a most remarkable unanimity 

 of results obtained at both experimental stations. Each series 



' " Report on E.\periments made to test the Manurial Value of Basic 

 Cinder from the North.Eastern Steel Works." By Prof Wrightson and Dr. 

 Munro, of the College of Agriculture, Downton, Salisbury. Middles- 

 brough ; Daily Excliange Offices, 1886. 



