i6 



NATU'RE 



[September 6, 191 7 



student of science are, of course, only side-issues, 

 and do not touch the main problem of evoking, on 

 the part of the pure mathematician, an interest in 

 the applications. The pure mathematician has not 

 the leisure necessary for familiarity with the history 

 and essentials of a proposed problem, but he could 

 assist by turning the thoughts of his better students 

 into such a direction. When he does become interested 

 in an application, he usually studies only the mathe- 

 matical methods tried more crudely by others. His 

 interest, in fact, lies more in the logic of the matter 

 than in any co-ordination of new phenomena which 

 may be obtained. Yet at the same time he must not 

 be blamed, for the physicist and engineer rarely pre- 

 sent their problems in such a form that the mathe- 

 matician can even begin to seek a solution. He does 

 not know what approximations he may make and vet 

 retain a solution of value. The proper function of a 

 treatise on applied mathematics is to give strict 

 formulations of problems and an account also of the 

 principles which underlie good physical approxima- 

 tions. The applied mathematician who can fulfil 

 this function, and intervene between the mathe- 

 matician and the experimenter, is now lamentably 

 rare. The temptation to go to one of the extremes 

 is too strong under the present system, though Prof. 

 Brown suggests various ways in which such men 

 could be encouraged to steer the middle course. 



The fundamental subjects which, from the present 

 point of view, demand systematic examination, and, 

 more especially, simple exposition from the mathe- 

 matician, are : the numerical solution of classes of 

 differential equations, symbolic forms adapted for 

 rapid numerical calculation, reduction of a series of 

 numbers to the best formula, and Fourier and other 

 representations of periodic phenomena. Under this 

 last heading a considerable contribution is made by 

 Sir Joseph Larmor's address, which cannot in this 

 respect be noticed at all adequately in our present 

 space. But it is readily accessible, and this fact some- 

 what precludes the necessity. In so far as it is general 

 the views expressed are essentially similar to those 

 outlined above, and it includes, moreover, an instruc- 

 tive account of the history and present state of the 

 society, with suggestions towards its future adaptation 

 to changing conditions. 



In his critical analysis of the Fourier harmonic 

 method Sir Joseph sketches the history of its 

 development, and afterwards points to an insistent 

 question : What is to be done with the accumulated 

 observational data such as are being piled up by 

 meteorologists and statisticians, and to what extent 

 should they be continued? Such questions are of the 

 essence of pure mathematics and not strictly of its 

 technical application. It is a curious fact that pro- 

 gress in such directions was practically stopped by 

 difficulties in running the Kelvin integrating machine. 

 Sir Joseph Larmor makes a powerful appeal to the 

 pure mathematician to revive his former interest in 

 such problems, and cites the work of Schuster as a 

 striking illustration of the success which could be 

 obtained by an organised attack. We may cite, as 

 another illustration. Sir Joseph's own discussion of 

 some^ of the problems of radiation, which forms the 

 remainder of his address, for it presents many sides 

 of the question which have been only too imperfectly 

 considered by those who work with any aspect of the 

 Fourier analysis. 



We can only repeat that it is a fortunate event, 

 and perhaps a sign of the times, that the presidents 

 of the two leading mathematical societies in the 

 English-speaking world should have chosen the same 

 ground so closely, and independentlv expressed con- 

 cordant opinions even in points of detail. This fact 

 must surely stimulate workers to an interest in these 

 NO. 2497, VOL. 100] 



questions, the elucidation of which, even if only 

 partial, would be a fundamental gain to the whole 

 range of work in the province of natural science. 



J. W. Nicholson. 



'PRECISE LEVELLING IN THE WEST 



OF ENGLAND.'^ 

 HTHIS recently published Professional Paper of the 

 •*■ Ordnance Survey gives an interesting account 

 of the revision of a line of precise levelling which had 

 been carried out under the direction of a committee 

 of the British Association in the years 1837 and 1838. 

 The line was run from Axmouth, on the coast of the 

 English Channel, to three points on the southern coast 

 of the Bristol Channel, and the terminal points were 

 marked with metal bolts "to afford a basis for a com- 

 parison with the position of the lines then determined, 

 at present, and at any future period." When the re- 

 vision of the primary levelling network of Great 

 Britain was undertaken the revision of this particular 

 line was included in order to see whether there was 

 any indication of earth movement, and in the course 

 of the last three years it has been found practicable to 

 carry out this work by the reserve levelling staff which 

 has to be maintained at Southampton. The earlier 

 levelling was carried out by Mr, T. G. Bunt, and full 

 details are given by Dr. W. Whewell and him in the 

 report of the British Association for 1838. 



He used a level by Simms which had a telescope 

 14 in. in length and a magnification of 26. The bubble 

 is said to have been affected by a movement of 

 1/100,000 in. of either end. The staff used was at 

 first of brass, but this being found unsatisfactory, it 

 was replaced by one of seasoned oak 9 ft. long and 

 having scales on both sides. Nothing is stated about 

 the verification of the staff divisions. The staff was 

 read with the aid of a vane or target, of which the 

 position was read by a vernier to 1/500 ft., and it is 

 stated that the average error of a single reading was 

 1/250 in. Lines were levelled in both directions from 

 beginning to end, then from end to beginning, and the 

 discrepancies found are recorded. Mr. Bunt mentions 

 a systematic error which he experienced, viz. that 

 " the heights of all points came out less by the levels 

 returning than by the levels going," and from Portis- 

 head to Axmouth, a distance of seventy-four miles, 

 the discrepancy between forward and backward level- 

 ling was I 029 ft. The old levelling books are not now 

 to be found, so that the comparison with modern work 

 could only be made over the distances between Ax- 

 mouth, Axmouth Church, Stolford, and Perry Farm, 

 where the old marks are still existing. 



The discrepancy between the older and the new 

 levelling from Axmouth to Perry Farm, a distance of 

 fifty-seven miles, is but 0-92 in., though at Stolford, 

 fifty-five miles, it reached 2-11 in. The amount of the 

 accidental and systematic errors of Bunt's levelling 

 computed by the formulae adopted by the International 

 Geodetic Commission is 10 mm. and 09 mm. per 

 kilometre respectively, against the limits of i mm. and 

 0-2 mm. per kilometre, as laid down by international 

 agreement for precise levelling. 



The conclusion arrived at is that there is no evidence 

 of any change in the relative levels of the marks near 

 the shores of the English Channel and the Bristol 

 Channel. 



The Ordnance Sur\ey levelling was executed with 

 a Zeiss No. 3 pattern 14-in. level with a parallel plate 

 object-glass micrometer, and invar levelling staves. 

 The operation is one of much interest as affording a 

 comparison between the best class of levelling work 

 in this country at the two periods. H. G. L. 



1 Report on the Re-levelling in i9i5-i7of a Line from the English Channel 

 to the Bristol Channel. Ordnance Survey Professional Papers. New 

 Series, No. 4, 1917. Price 6ei. 



