April 3, 1902] 



NA TURE 



511 



Consider the case of an able schoolboy who makes mathe- 

 matics liis chief study between the ages, say, of fifteen and 

 nineteen ; this period should suffice to give him a working 

 knowledge of three-dimensional analysis, integral calculus and 

 differential equations with their applications to the mechanics of 

 solids, in addition to the subjects now required by the colleges, 

 were it not for certain side issues which have arisen from the 

 latter and assumed stupendous proportions. Foremost among 

 these stands the excessive measure of attention given to the 

 analysis of curves of the second degree. These form naturally 

 a small section in a treatise on analytical geometry ; yet while 

 the far-reaching principles of the latter are lightly passed over, 

 there is .scarcely a method so abstruse or an artifice so petty that 

 it may not give rise to a question in an entrance scholarship 

 paper if its bearing be upon conic sections ; so that no less than 

 a third of a schoolboy's mathematical hours are frequently 

 sacrificed to these curves. Their real interest is due, firstly, to 

 their appearance in astronomy (the properties there required 

 are few, and might be treated in the appendix of a text-book on 

 dynamics), and, secondly, to their adaptability to treatment by 

 pure geometry, the direct methods of which lend them an interest 

 which is alien to every other branch of mathematics, and supply 

 a mental discipline which is elsewhere unattainable. On this 

 alone rests their title to rank as a separate subject. 



But this, though the most aggravated, is not the only instance 

 of the kind. The time spent on advanced trigonometry is out 

 of all proportion to its practical or educational value ; the subject 

 contains an introduction to the use of the complex quantity which 

 properly forms part of the theory of functions, and includes a 

 number of highly specialised problems which have no place in a 

 syllabus so elementary as to exclude the integral calculus. A 

 similar waste is caused by several large classes of questions, 

 especially some on series, the ability to solve which implies 

 nothing but an effort of memory, and by other fragments of 

 high subjects which are thrust upon boys at an early stage and 

 made artificially difficult by isolation from their proper context. 



The above criticisms are not made in any spirit of hostility to 

 examiners, who in framing their papers are trying to obviate 

 the shortcomings of a system which is out of date and in need 

 of radical reform. Five decades ago it was doubtless advisable, 

 in view of the then state of school mathematics, to limit the 

 entrance scholarship course to a few subjects, but under new 

 and improved conditions is not an extension of syllabus prefer- 

 able to the interweaving with these of a quantity of matter 

 which, valuable as it may be to the problem setter, is for the 

 student little else than a barrier to his progress? 



But if the examinations in mathematics and science are to be 

 brought into harmony, it is not only in the former that a new 

 regime is needed. Under present conditions a boy could learn 

 at school nearly the whole of the mathematics necessary for an 

 advanced physical course. But to do this would jeopardise his 

 chance of obtaining a first class in the science tripos unless the 

 authorities recognised the value of his mathematical training by 

 a substantial equivalent of marks, so that he might make a 

 mathematical entrance scholarship the preliminary to a science 

 course. For those who have not a taste for theory it would 

 still be possible to adopt an experimental regime from the 

 outset, though it is questionable whether they could in the long 

 run bear comparison with men who had cultivated a faculty 

 which it is no exaggeration to call a sixth sense. The glory of 

 Cambridge and her highest traditions are centred in the names 

 of her mathematical physicists. But the environment which 

 surrounded Maxwell and Kelvin no longer exists. And to-day 

 the growth of subjects and the consequent tendency to special- 

 isation have gone far to materialise the phantom barrier which 

 separates the practical from the theoretical, and have laid on 

 the authorities the burden of creating a new system w'hich shall 

 be capable of reproducing the giants of the past. 



Dulwich College, March 13. C. A. Rumsey. 



The Morphology of Pleuronectidae. 



In the Memoir on the Plaice by Messrs. Cole and Johnstone, 

 reviewed in Nature of March 20 (p. 459), there is a reference 

 to Steenstrup's work on the metamorphosis of Pleuronectidae 

 which I think the reviewer would have done well to correct. 

 The statement to which I refer is the following : — " This 

 supposition (that the left eye passed through the substance of 

 the head to reach the ocular side), absurd as it may seem to us 

 now, was in fact believed by such an observer as Steenstrup." 



NO. 1692, VOL. 65] 



The truth of the matter is that Steenstrup did not believe any 

 supposition, absurd or otherwise, on the subject, but stated from 

 actual observation that in certain larval Pleuronectida; the eye 

 of one side passed through the tissues of the head and emerged 

 on the other side. The form in question was long known as 

 Plagusia, and is now known to be the larva of Rhamboidichthys. 

 The truth of Steenstrup's observations was fully confirmed by 

 Alexander Agassiz at Newport, R.I. 



On the other hand, in the " Story of Life in the Seas," by 

 Prof. S. J. Hickson, it is stated that in the young of the soles 

 the eye of one side passes through the head to the other side. 

 This is equally incorrect. 



Messrs. Cole and Johnstone also state that the Gadidse are 

 the nearest relatives of the Pleuronectidii?, and promise to show 

 that the morphological differences between the cod and the 

 plaice, apart from the question of symmetry, are comparatively 

 few and unimportant. I cannot find in the Memoir that they 

 have redeemed this promise, and the morphological similarity 

 of the two forms is contradicted by the authors themselves on p. 

 1S5 of the Memoir. I believe it could be shown by proper 

 investigation that the morphological differences between these 

 two fish are numerous and profound. 



I think some explanation was due from the reviewer concern- 

 ing Dr. Woodward's "startling discovery" that in Cretaceous 

 times Teleostei of the Clupeoid type had already translocated 

 the pelvic fin into the jugular position. I have not yet had the 

 pleasure of seeing Dr. Woodward's latest volume, but a Clu- 

 peoid with jugular fins seems to me indeed a startling discovery. 



Penzance, March 22. J. T. Cunningham. 



When writing I was well aware that the sentence Mr. 

 Cunningham quotes was not happily construed, but seeing that 

 comment (like that of Mr. Cunningham himself) would needs 

 be hypercritical, I allowed the matter to pass, in consideration 

 of the context and of the desire to keep my review within 

 bounds. 



Concerning the Cretaceous teleostean described by Dr. 

 .Smith Woodward, I can only express my surprise that Mr. 

 Cunningham should be so neglectful of the current literature of 

 his subjects as to be unaware of its occurrence. With the rest 

 of his letter I have no concern. 



The Writer of the Review. 



Sun Pillars. 



I HAVE been deeply interested in the correspondence in 

 Nature bearing on the appearance of sun pillars, and particu- 

 larly so in the communication of Prof. Johnstone Stoney (p. 465). 



The display of March 6 mentioned by the Rev. Guy Bridges 

 and Mr. W. A. Knight was not visible here ; but a very note- 

 worthy occurrence of the phenomenon took place here on 

 December 3 last and another on January 7 last, and there was 

 one feature common to both of these events which has not been 

 mentioned as occurring in relation to those recorded by other 

 observers, so far as I am aware, but which seems to me to be a 

 prime factor in the causation of the phenomenon under con- 

 sideration, and it is this : — -Before, and after, the actual time of 

 the setting of the sun, during my own observations, there was a 

 strong display of cirrus cloud in the "true cirrus" form of 

 parallel bars, which appeared to run at right angles to the track 

 of the setting sun, and roughly parallel, of course, to the horizon. 

 ,\s the setting sun neared the horizon, these bands of cloud 

 became magnificently iridescent, displaying the spectrum colours 

 of the rainbow, with the red nearest the horizon. As the sun 

 set further the colours faded, beginning first at the red and 

 following on in succession to the violet until this colour alone 

 remained visible. Then ascended a beautiful pillar of a violet 

 colour in exquisite shades, ascending gradually to a height of 

 somewhere about twenty degrees above the horizon and then 

 fading away slowly. 



It seemed to me that the occurrence depended on (a) the 

 presence of cirrus cloud (ice spiculx) ; (b) these clouds must be 

 in a banded or striated form ; (c) they must lie at right angles 

 to the track of the sun ; and (il) these clouds must, of course, 

 be present in the immediate neighbourhood of the setting sun. 

 There are, besides, certain atmospheric conditions which seem 

 to be desiderated in order to favour opacity, as dryness of the 

 air, with calmness in its movements, and, I believe, a com- 

 paratively high barometric pressure. At the time of ray 



