Sept. 19, 1889] 



NATURE 



509 



press mathematical conceptions that we are sometimes left in 

 iiicertainty as to our author's meaning. When Prof. Bohm- 

 werk remarks that there is something special in the labour- 

 irket, in that the buyer will vary his arrangements according 

 i ' the price of the article, the rate of interest (" Kapital," p. 

 407), does he specify the property which Messrs. Auspitz and 

 I.ieben have stated as general — that the utility function [our \//, 

 note {e) above] is discontinuous, being different for large and 

 ^mall values of the variable under consideration ? 



These deficiencies are more conspicuous in other writings of 

 the Austrian school. A glance at Fig. 10, an intuition of the 

 corresponding algebraic formulae, will show that the notion of an 

 i}:'erage imported into the doctrine of value by Dr. Emil Sax 

 ( " Staatswirthschaft ") is not quite appropriate. As an instance in 

 wliich great abridgment would be effected by mathematical ex- 

 inession, we might notice the last three chapters of Dr. Zucker- 

 kandl's ",Theorie der Preise." Again the difficulty of conveying 

 technical propositions without the proper phraseology may be 

 illustrated by Prof. Wieser's "Der natiirliche Werth," when he 

 speaks of value and final utility having place in a Communistic 

 Socialistic State (p. 26, note, o^nA passim). May his meaning 

 IS be formulated ? In an economical regime distribution and 

 ^ ^change are regulated by the condition that the final utility 

 of all concerned should be zero, the total utility a minimum, 

 subject to the law that thei-e should be only one rate of exchange in 

 a market. In a communistic or utilitarian regime the limitation 

 which the last italicized clause expresses is removed. In terms 

 employed in our note (<?) the economical adjustment is determined 

 by the equations (o), (j8), and (7) ; the utilitarian adjustment is 

 determined by (S) and (7) only — in short, the distinction between 

 the points r and ti in our Fig. 9 referring to note {e). 



In offering these too brief criticisms I regret that my limits 

 impose a curtness which is hardly consistent with courtesy. 



SFXTION G. 



MECHANICAL SCIENCE. 



Opening Address by William Anderson, M.Inst. C.E., 

 President of the Section. 



I have had considerable difficulty in selecting a subject which 

 should form the main feature of my address. This meeting being 

 held in Newcastle, it seemed almost imperative that I should 

 dwell upon two industries which may be said to have had their 

 genesis here : that I should direct your attention to the extra- 

 ordinary development of the system of transmitting power by 

 hydraulic agency, and the use of the same agency for lifting 

 enormous weights and exerting mighty pressures ; and that I 

 should not neglect to notice a manufacture of specially national 

 importance — that of heavy artillery, and of ships of war sent 

 forth fully equipped and ready to take their places in our first 

 line of defence. 



The desire which I felt of treating of these subjects was 

 heightened by the opportunity which it would have afforded of 

 jMiying a tribute of respect and admiration to the distinguished 

 citizen of this town, who, by his genius and perseverance, created 

 the Elswick Works, raised the character of British engineering, 

 and rendered his country services so eminent that Her Majesty 

 has seen fit to recognize them by bestowing honours higher than 

 any which an engineer has hitherto been able to achieve. 



But I felt that the themes mentioned, important as they are, 

 have been frequently treated of by able men, and that I would 

 perhaps render more service to "Mechanical Science if I drew your 

 attention to a subject which appears to me to be bearing with 

 daily augmenting force on the practical manipulation of the 

 materials used in construction. I allude to the molecular struc- 

 ture of matter. This branch of science has, up to the present 

 time, been left very much in the hands of the chemist and the 

 physicist, and I dare say that many engineers may think that it 

 is by no means desirable to change the arrangement ; but I hope 

 to show that the progress of engineering, the more exact methods 

 of dealing with the properties of materials, the increased demands 

 on their powers of endurance, render it imperatively necessary 

 that mechanics should interest themselves more deeply in their 

 internal structures and the true meaning of the laws by which 

 their properties are defined. 



Five years ago, at Montreal, in his address to the Mathematical 

 Section, Sir William Thoaiso.i took for his subject the ultimate 



constitution of matter, and discussed, in a most suggestive- 

 manner, the very structure of the ultimate atoms or molecules. 

 He passed in review the theories extant on the subject, and 

 pointed out the progress which had been made in recent years 

 by the labours of Clausius, of Clerk Maxwell, of Tait, and of 

 others, among whom his own name, I may add, stands in 

 unrivalled prominence. 



I will not presume to enter into the field of scientific thought 

 and speculation traversed by Sir William Thomson, because I 

 am only too conscious that both my mathematical knowledge and 

 my acquaintance with the natural sciences is too limited to entitle 

 the views which I may have formed to any respect ; I propose to- 

 draw attention only to some general considerations, and to point 

 out to what extent they practically interest the members of this 

 Section. 



In a lecture delivered at the Royal Institution last May, 

 Prof. Mendeleeff attempted to show that there existed an analogy 

 between the constitution of the stellar universe and that of matter 

 as we know it on the surface of the earth, and that from the 

 motions of the heavenly bodies down to the minutest interatomic 

 movements in chemical reactions the third law of Newton held 

 good, and that the application of that law afforded a means of 

 explaining those chemical substitutions and isomerisms which are 

 so characteristic, especially of organic chemistry. 



Examined from a sufficient distance, the planetary system 

 would appear as a concrete whole, endowed with invisible internal 

 motions, travelling to a distant goal. Taken in detail, each 

 member of the system may be involved in movements connected 

 with its satellites, and again each planet and satellite is instinct 

 with motions which, there is good reason to believe, extend to 

 the ultimate atoms, and may even exist, as Sir W. Thomson has 

 suggested, in the atoms themselves. The total result is complete 

 equilibrium, and, in many cases, a seeming absence of all motion, 

 which is, in reality, the consequence of dynamic equilibrium,, 

 and not the repose of immobility or inertness. 



The movements of the members of the stellar universe are, 

 many of them, visible to the eye, and their existence needs no 

 demonstration ; but the extension of the generalization just 

 mentioned to substances lying, to all appearances, inert on the 

 earth's surface is not so apparent. In the case of gase^, indeed,, 

 it is almost self-evident that they are composed of particles, 

 so minute as to be invisible, in a condition of great indi- 

 vidual freedom. The rapid penetration of odours to great 

 distances, the ready absorption of vapour and of other 

 gases, and the phenomena connected with diffusion, compres- 

 sion, and expansion seem to demonstrate this. One gas 

 will rapidly penetrate another and blend evenly with it, even 

 if the specific gravities be very different. The particles of 

 gases are, as compared with their own diameters, separated 

 widely from each other ; there is plenty of room for additional 

 particles ; hence any gas which would, by virtue of its molecular 

 motion, soon diffuse itself uniformly through a vacuum will 

 also diffuse itself through one or more other gases, and once so 

 diffused, it will never separate again. A notable example of ' 

 this is the permanence of the constitution of the atmosphere, 

 which is a mere mixture of gases. The oxygen and the nitrogen, 

 as determined by the examination of samples collected all over 

 the world, maintain sensibly the same relative proportions, and 

 even the carbonic acid, though liable to slight local accumula- 

 tions, preserves, on the whole, a constant ratio ; and yet the 

 densities of these gases differ very greatly. 



Liquids, though to a much less degree than gases, are also 

 composed of particles separated to a considerable relative distance 

 from each other, and capable of unlimited motion where no- 

 opposing force, .'^uch as gravity, interferes; for under such 

 circumstances their energy of motion is not sufficient to overcome 

 the downward attraction of the earth ; hence they are constrained 

 to maintain a level surface. 



The occlusion of gases without sensible comparative increase 

 of volume shows that the component particles are widely 

 separated. Water, for example, at the freezing-point occludes 

 above one and three-quarter times its own volume of carbonic 

 oxide, and about 480 times its volume of hydrochloric acid, with 

 an increase of volume, in the latter case, of only one- third ; and 

 sulphuric acid absorbs as much as 6co times its bulk of methylic 

 ether. The quantity of gas occluded increases directly as the 

 pressure, which seems to indicate that the particles of the 

 occluded gas are as free in their movements among the particles 

 of the liquid as they would be in an otherwi.se empty containing, 

 vessel. 



