May 28, 190S] 



NA TURE 



79 



correspondence between things. A function or one-to-one 

 correspondence is a classification and cross-classification of 

 the things whicli correspond. For example, a division of 

 a number of models having different markings into two 

 classes by colour and a cross-classification by shape gives 

 a correspondence of the markings in one colour class to 

 the markings in the other. If each marking in one class 

 corresponds to the same marking in the other, we have 

 llie correspondence one. Similarly, various circular func- 

 tions may be illustrated by models, beginning with trans- 

 positions. If things which correspond are called operands, 

 and a correspondence of operands a function, then names 

 seem to be needed to mean a correspondence of functions, 

 and for the still higher correspondences which occur. In 

 the usual school course we practically begin with the corre- 

 spondences of functions, namely, of the numbers one, two, 

 three, &c. It would seem more natural to begin with the 

 ■rrespondence, first, of operands to operands, and then of 

 Derands to functions, and define words as power, product. 

 --im in reference to correspondences of operands illustrated 

 V models. For example, a set of things the correspond- 

 ■mce of whic?h to another set is under discussion may be 

 called a quantity. Two quantities W'hich correspond to the 

 same quantity correspond to each other ; and their corre- 

 spondence to each other is the product of the correspondence 

 of one to the intermediate quantity and of the intermediate 

 quantity to the other. In the case of vectors, since a 

 vector is a correspondence of points, this would require 

 the term product to be given to what is generally called 

 the sum. 



The properties of permutation, association, distribution 

 should be considered in reference to tables of operands 

 before considering tables of functions such as multiplica- 

 tion and addition tables. Space will not allow of discuss- 

 ing the illustration of addition, rule of signs, two-to-two 

 correspondence, &c. The study of irrational numbers and 

 continuous spaces should be postponed to a later stage. 

 Oundle. C. Elliott. 



An Emanation from Sodium. 



DuRI^•G the course of some experiments upon the contact 

 potential difference between the alkali metals and glass 

 I noticed that a freshly cut piece of sodium rapidly dis- 

 charged an electroscope. 



Further examination showed that this action occurred 

 only if the gold leaf was charged negatively. Little or 

 no effect was produced if it was positively electrified. The 

 action could be completely stopped by a membrane of 

 celluloid sufficiently thin to give interference colours, and 

 this fact alone points strongly to the discharging action 

 being due to a vapour. 



It was found, in fact, that a slight current of air directed 

 so as to carry the supposed gas away from the charged 

 plate of the electroscope enabled the leaf to retain its 

 cliarge. 



The effect is, however, unlike that met with in the case 

 III phosphorus, since the vapour from that substance dis- 

 charges both positive and negative electricity equally well. 

 It does not, therefore, appear due to the air becoming- 

 ionised by a change occurring at the surface of the sodium, 

 but more probably to the emission of an electrified gas. 

 Experiment has shown that the rapid oxidation of the 

 iLuface has little or nothing to do with the existence of 

 the emanation, and it is very significant that all action 

 ot-ases after prolonged heating (to melting point) of the 

 metal. .^fter some hours, however, the sodium shows 

 signs of recovering its power to discharge a negatively 

 electrified body. 



Since all portions 'of the same block of sodium do not 

 i-xhibit the action to the same extent, I am attempting 

 t.> concentrate those parts which show it most strongly 

 in order to determine whether some new radio-active bodv 

 1- present in the metal or whether there is a radio-active 

 I liinge occurring in the sodium itself. 



A slight indication that the emanation is capable of 

 Irpositing a radio-active layer of matter has been also 

 noticed. The other alkali metals are now being examined 

 ;ind the whole matter fully investigated. 



Charles E. S. Phillips. 



Castle House, Sliooters Hill, Kent. 



NO. 2013, VOL. 78] 



ITVA'D PRESSURE. 



'T^HE importance of a correct knowledge of the pres- 

 ■*■ sure e.xerted by the wind, as atiecting the 

 stability of modern structures, was brought pro- 

 minently before the public by the disaster to the Tay 

 Bridge on the night of December 28, 1879. At that 

 lime observatories at which wind pressure was directly 

 measured were rare, the usual observed characteristic 

 of the wind being its velocity as given bv the 

 Robinson cup anemometer. 



At some stations both the Robinson cup anemometer 

 and the Osier recording pressure plate were installed, 

 and it was for this reason that in the report of the 

 Royal Commission which was appointed in 1881 to 

 consider the question, an attempt was made to state 

 the relation between the probable maximum pressure 

 which would be recorded in a gale and the maximum 

 hourly run of the Robinson cups during that period. 

 Also from records of pressure plates which were con- 

 sidered by the Commission to be not due to instru- 

 mental error depending upon momentum, but which 

 represented real phenomena, it was decided that, for 

 structures in exposed situations in this countrv, a 

 maximum wind pressure of 56 lb. per square foot of 

 surface should be allowed for in the design. 



It was, however, felt by engineers at the time that 

 this value, assumed uniform over the whole surface of 

 a large structure, was very excessive, for, as the late 

 .Sir Benjamin Baker remarked at a discussion on wind 

 pressure at the Institution of Civil Engineers soon after 

 the report of the Commission was published, if such 

 pressure actually obtained there ought not to be a 

 bridge standing in the country. It was on this occa- 

 sion that -Sir Benjamin Baker stated his conclusions 

 as to the nature of the motion of the wind and the 

 pressures resulting from it, which theory was based, 

 not on elaborate experiments, but on close observation 

 ot the behaviour of natural objects in the wind. In 

 his words, 



" If leaves and other light objects floating in an appar- 

 ently steady current were watched it would be found that 

 certain leaves would shoot forward at an increased velocity 

 of 25 per cent, and upwards as compared with the mean 

 velocity. Over a width of 20 feet at the centre of a wide 

 and steady current the mean velocity might thus be 

 constant, whilst over some particular width of i foot it 

 might be momentarily fully 25 per cent, higher, and in 

 the case of wind pressure 25 per cent, increase of velocity 

 meant more than 50 per cent, increase of pressure. It 

 ivas quite possible, therefore, that the largo pressure 

 boards might register a notably less pressure than the small 

 boards, and might afford a clue to the reason why railway 

 carriages were not upset when traversing lofty and exposed 

 viaducts. " 



This appears to have been the first recognition of 

 what may be called the variable structure of the wind 

 as a factor of safetv in the stability of structures, and 

 it may be mentioned that the variation predicted by 

 Sir Benjamin Baker was found to exist at points 

 distant 11 feet apart in the experiments of Mr. Dines 

 in 1894. 



To test the truth of his conclusions Sir Benjamin 

 Baker erected some wind-pressure plates on the site 

 of the Forth Bridge, each provided with an arrange- 

 ment for measuring the maximum pressures experi- 

 enced. One of these gauges was 300 square feet in 

 area, and the others li square feet. Taking the mean 

 of the maximum daily readings for two years, the 

 sniall-gauge indications were found to be 50 per cent, 

 greater than the large-gauge indications, which was 

 the result anticipated. 



In experiments of this kind it is interesting to notice 

 that there is one particular case in which with the 



