Sept. 20, 1883J 



NA TV RE 



491 



surface, or at about high-water mark, the coins having 

 been apparently lost by the Romans scrambling over the 

 soft slippery mud. This discovery proves the thick peat 

 beds to be of older date than the Romans ; this is also 

 bome out by the very remarkable sections along the north 

 coast of Wirral, especially near Leasowe, which have 

 afforded the fine collection of antiquities preserved in the 

 Liverpool Free Museum ; the silty beds over the peat 

 yield Roman coins of Nero, Antoninus Pius, and Marcus 

 Aurelius, while in the peat beds beneath occur flint im- 

 plements of the Neolithic type. When the peat beds of 

 Western Lancashire are followed into the valleys of the 

 large rivers that traverse the country, they are found to 

 pass insensibly into a peaty seam occurring at the base of 

 the alluvium of the lowest plain of these rivers. This is 

 well seen in the valley of the Ribble at Preston ; it is 

 more than a mile in width, and 180 feet in depth ; it is 

 excavated entirely in the Glacial deposits, down to the 

 rocky floor, which lies somewhat below high-water mark, 

 and nearer the sea slopes down considerably beneath it. 

 On the slopes of the valley lie terraces of old alluvium, 

 marking successive stages in the process of denudation, 

 commenced since the deposition of the Upper Boulder 

 Clay, as the bottom of the valley is the ordinary alluvial 

 plain, made of silt, resting on a peaty bed, with trunks of 

 trees lying on rough river gravel, the latter marking a 

 period of great fluviatile denudation, when the land was 

 at least as high, if not higher, above the sea as it is at 

 present. To this era belong the marine beds lying beneath 

 the peat I have called the Prcsall shingle, occurring east 

 of Fleetwood, and the Skirdley Hill sands near Southport, 

 which mark the position of old sea-beaches and old sand 

 dunes respectively. 



From these facts it appears that the excavation of the 

 Western Lancashire river valleys was entirely carried out 

 since the Glacial episode, that they had reached their 

 present depth when Neolithic mm inhabited the north- 

 west of England, and that since that era much land has 

 been destroyed, now covered by the Irish Sea, but since 

 Roman times there has been but little change. 



C. E. de Rance 



THE BRITISH ASSOCIATION 



T'HE Southport meeting promises to be one of the 

 -*■ most successful since the Association met in Liver- 

 pool twelve years ago. According to the latest statistics 

 it is expected that in attendance it may even rival the 

 York meeting, when over 2500 people gathered to cele- 

 brate the jubilee of the Association. From the informa- 

 tion we have already published it will have been seen 

 that Southport has shown the greatest zeal in preparing 

 to give a generous reception to the representatives of 

 British science ; and if only the weather be propitious, 

 there can be little doubt that the meeting will be a suc- 

 cess. Both the papers to be read and the reports to be 

 presented are expected this year to suggest some specially 

 interesting subjects for discussion. 



Last night Sir C. W. Siemens resigned the presidential 

 chair to Prof. Cayley, who then delivered the opening 

 address. 



Inaugural Address by Arthur Cayley, M.A., D.C.L., 

 LL.D., F.R.S., Sadlerian Professor of Pure Mathe- 

 matics in the University of Cambridge, President. 



Since our last meeting we have been deprived of three of 

 our most distinguished members. The loss by the death of 

 Prof. Henry John Stephen Smith is a very grievous one to those 

 who knew and admired and loved him, to his Univer-ity, and 

 to mathematical science, which he cultivated with such ardour 

 and success. I need hardly recall that the branch of mathe- 

 matics to which he had specially devoted himself was that most 

 interesting and difficult one, the Theory of Numbers. The im- 

 mense range of this subject, connected with and ramifying into 

 so many others, is nowhere so well seen as in the series of re- 



ports on the progress thereof, brought up unfortunately only to 

 the year 1865, contributed by him to the Reports of the Associa- 

 tion ; but it will still better appear when to these are united (as 

 will be done in the collected works in course of publication by 

 the Clarendon Press) his other mathematical writings, many of 

 them containing his own further developments of theories 

 referred to in the reports. There have been recently or are 

 being published many such collected editions — Abel, Cauchy, 

 Clifford, Gauss, Green, Jacobi, Lagrange, Maxwell, Riemann, 

 Steiner. Among these the works of Henry Smith will occupy 

 a worthy position. 



More recently, General Sir Edward Sabine, K. C.B. , for 

 twenty-one years general secretary of the Association, and a 

 trustee, president of the meeting at Belfast in the year 1852, and 

 for many years treasurer and afterwards president of the Koyal 

 Society, has been taken from us at an age exceeding the ordinary 

 age of man. Born October, 1788, he entered the Royal Artil- 

 lery in 1803, and commanded batteries at the siege of Fort Erie 

 in 1S14 ; made magnetic and other observations in Ross and 

 Parry's North Pi Jar exploration in 1818-19, and in a series of 

 other voyages. He contributed to the Association reports on 

 Magnetic Forces in 1836-78, and about forty papers to the 

 Philosophical Transactions ; originated the system of Magnetic 

 Observatories, and otherwise signally promoted the science of 

 Terrestrial Magnetism. 



There is yet a very great loss : another late president and 

 trustee of the Association, one who has done for it so much, and 

 has so often attended the meetings, whose presence among us at 

 this meeting we might have hoped for — the president of the 

 Royal Society, William Spottiswoode. It is unnecessary to say 

 anything of his various merits : the place of his burial, the 

 crowd of sorrowing friends who were present in the Abbey, 

 bear witness to the esteem in which he was held. 



I take the opportunity of mentioning the completion of a work 

 promoted by the Association : the determination by Mr. James 

 Glaisher of the least factors of the missing three out of the first 

 nine million numbers : the volume containing the sixth million 

 is now published. 



I wish to speak to you to-night upon Mathematics. I am quite 

 aware of the difficulty arising from the abstract nature of my 

 subject ; and if, as I fear, many or some of you, recalling the 

 Presidential Addresses at former meetings — for instance, the 

 resume and survey which we had at York of the progress, during 

 the half century of the lifetime of the Association, of a whole 

 circle of sciences — Biology, Palaeontology, Geology, Astronomy, 

 Chemistry — so much more familiar to you, and in which there 

 was so much to tell of the fairy-tales of science ; or at South- 

 ampton, the discourse of my friend who has in such kind terms 

 introduced me to you, on the wondrous practical applications of 

 science to electric lighting, telegraphy, the St. Gothard Tunnel, 

 and the Suez Canal, gun-cotton, and a host of other purposes, 

 and with the grand concluding speculation on the conservation 

 of solar energy : if, I say, recalling these or any earlier ad- 

 dresses, you should wish that you were now about to have, from 

 a different president, a discourse on a different subject, I can very 

 well sympathise with you in the feeling. 



But, be this as it may, I think it is more respectful to you that 

 I should speak to you upon and do my best to interest you in the 

 subject which has occupied me, and in which I am myself most 

 interested. And in another point of view, I think it is right 

 that the Address of a President should be on his own subject, 

 and that different subjects should be thus brought in turn before 

 the meetings. So much the worse, it may be, for a particular 

 meeting ; but the meeting is the individual, which on evolution 

 principles must be sacrificed for the development of the race. 



Mathematics connect themselves on the one side with common 

 life and the physical sciences ; on the other side with philosophy, 

 in regard to our notions of space and time; and in the questions 

 which have arisen as to the universality and necessity of the 

 truths of mathematics, and the foundation of our knowledge of 

 them. I would remark here that the connection (if it exists) of 

 arithmetic and algebra with the notion of time is far less obvious 

 than that of geometry with the notion of space. 



As to the former side, I am not making before you a defence 

 of mathematics, but if I were I should desire to do it — in such 

 manner as in the "Republic" Socrates was required to defend 

 justice, quite irrespectively of the worldly advantages which 

 may accompany a life of virtue and justice, and to show that, 

 independently of all these, justice was a thing desirable in itself 

 and for its own sake— not by speaking to you of the utility of 

 mathematics in any of the questions of common life or of physi- 



