3io 



NA TURE 



[July 31, 1884 



whence we see that this geometer " was familiar with the 

 generation of cylinders and cones, and had also clear 

 ideas on the interpretation of surfaces ; he had, moreover, 

 a correct conception of geometrical loci and of their appli- 

 cation to the determination of a point by means of their 

 intersection." Dr. Allman further maintains that in this 

 solution " the same conceptions are made use of, and the 

 same course of reasoning is pursued, which, in the hands 

 of his successor and contemporary Mencechmus, led to 

 the discovery of the three conic sections. Such know- 

 ledge and inventive power surely outweigh in importance 

 many special theorems." In arriving at these views he 

 has to combat (which he does in some detail and appa- 

 rently with success) the reasoning of Cantor, which is 

 " based on a misconception of the passage in which the 

 word Tojror occurs " Dr. Allman insists that tokos means 

 place and not U cits (as used by mathematicians). The 

 whole discussion is well worthy of the careful attention of 

 all interested in the history of geometry : we must forbear 

 to enter into the matter further. 



Eudoxus (born about 407 B a), a pupil of Archytas, 

 was an astronomer, geometer, physician, and lawgiver, 

 and hence a noteworthy man in more ways than one. 

 Here again Dr. Allman, one of whose great merits is his 

 independence and his thorough examination of the original 

 authorities, differs from Boeckh and Grote, but we cannot 

 give details. A full discussion of the additions to geo- 

 metry made by Eudoxus follows, and from it we learn 

 how great he was as a geometer ; his contributions to 

 astronomy must be sought for elsewhere, though they too 

 come under notice. " This eminent thinker — one of the 

 most illustrious men of his age, an age so fruitful in great 

 men, the precursor, too, of Archimedes and of Hipparchus 

 — after having been highly estimated in antiquity, was for 

 centuries unduly depreciated ; and it is only within recent 

 years that, owing to the labours of some conscientious 

 and learned men, justice has been done to his memory, 

 and his reputation restored to its original lustre." The 

 article under notice will considerably conduce to this right 

 placing of Eudoxus, amongst whose merits the least is 

 not that he was a true man of science. " Of all the 

 ancients, no one was more imbued with the true scientific 

 and positive spirit than was Eudoxus." Five reasons for 

 this statement follow, and the article closes. The whole 

 paper is a most interesting as well as valuable one ; 

 indeed the interest grows as the author approaches his 

 goal, and we venture to predict for Dr. Allman, when his 

 articles appear in a volume, a most cordial welcome from 

 all mathematicians. 



THE ROYAL GARDENS AT KE IV 

 THE Report of the Director on the Progress and Con- 

 - 1 dition of the Royal Gardens at Kew for the year 1882 

 was unavoidably delayed. It bears date only from 

 November 1, 1883, and was not published until well on in 

 1884. The date of the Report has, however, nothing to 

 say to its interest and merit, and there is always plenty of 

 both in these too short accounts of the great work carried 

 on at Kew. Passing over some details, noting that the 

 amount of damage which the collections have suffered 

 has been, notwithstanding the unprecedented number of 

 visitors, practically nil, and that the lecture-classes for 

 young gardeners continue to give satisfactory results, we 

 find an account of the formation of a Rock Garden at Kew. 

 The site selected lies between the wall bounding the 

 Herbaceous Ground on the east and the New Range on 

 the west. The general idea in laying out this space was 

 to imitate in some measure the rocky course of some 

 Pyrenean stream ; the dry bed is represented by the broad 

 walk (8 feet wide and 514 feet long), while on either side 

 are the rock-piled banks, in the interstices and pockets of 

 which grow the Alpine plants, and above all are thickets 

 <?f box and rhododendrons. Tree stumps have been 



somewhat freely used here and there. That some plants 

 grow well on them will be admitted ; that by their decay 

 they require renewal is their chief drawback. The col- 

 lection of 2630 plants bequeathed to the Gardens by Mr. 

 Joad formed a splendid commencement to the Rock Garden 

 series, and this section of the grounds has long since 

 proved not only a centre of attraction to the general 

 visitors, but has been a source of pleasure and profitable 

 study to many an amateur gardener. An apology is 

 made for not attempting some geographical arrangement 

 of the Alpines ; one was hardly needed. Where the plants 

 grow best there ought to be their (artificial) habitat, and 

 the practical gardener well knows what strange bed- 

 fellows plants often are, and how marvellously they vary in 

 their tastes. Within the last six weel;s we noted two 

 finely-grown plants of that popular Alpine cudweed, the 

 edelweiss ; one was flowering out of a crack in a dry 

 limestone wall, the other was on a deep clay bank. 



The elaboration of the natural family of the palms for 

 the " Genera Plantarum " of Bentham and Hooker led 

 the Director to make a critical study of the species of 

 palms in cultivation at Kew, the collection of which 

 proved to be of unexpected richness. In an appendix is a 

 classified list of 420 palms at present in cultivation at 

 Kew. This collection has now but two rivals — the mag- 

 nificent collection at Herrenhausen, Hanover, chiefly 

 made by Herr Wendland, and that of the unrivalled 

 tropical gardens at Buitenzorg in Java. 



The report about the Arboretum shows an enormous 

 amount of work accomplished. While the collection is 

 one of the richest in existence, its importance is gradually 

 more and more dawning upon those interested in planting, 

 and its national importance in this respect should not be 

 overlooked. 



The part of the Report giving extracts from the large 

 colonial correspondence that centres at Kew is full of 

 interest, none the less so that much of the information is 

 of a date often far on in 1 S83. The Argan tree seems likely 

 to be acclimatised at Natal from seeds sent from Kew. The 

 india-rubber (Ceara), introduced from Kew into Ceylon, 

 seems in a fair way of paying as well as Cinchona. Dr. 

 Trimen says it will grow anywhere up to almost 2500 feet, 

 and its commercial success is most satisfactory. " About 

 six months ago (October 24, 1883) some Ceara-rubber 

 seed was imported from Ceylon into Southern India. 

 The produce of these trees may now be seen flourishing 

 in a wonderful manner at the foot of the Neilgherry Hills. 

 The rapid growth of the trees is marvellous. Some which 

 were six months old from seed were fully eight feet high ; 

 and a cutting, said to have been planted scarcely six 

 months previously, was quite eight feet high, and was in 

 blossom. It seems to thrive on poor soil, requires shelter 

 but not shade, and very little rain. The demand for the 

 produce seems to be unlimited." Of the mahogany seeds 

 sent from Kew in 1S6S to Mauritius, nine of the trees 

 raised bore seeds in 1881, and numerous seedlings were 

 found self-sown. In a report from the Seychelles allusion 

 is made to " three different diseases which have seriously 

 affected the cocoa-nut palms," whereby large forests of 

 these valuable trees have been destroyed. No details are 

 given as to what these diseases are, though they " have 

 nearly stopped their depredations since 1882." In the 

 same report it is mentioned that the remains of the 

 clove plantations cover " about 250 acres " — surely a mis- 

 take. It is also stated that the Liberian coffee sent from 

 Kew in 18S0 has proved a success, and that about 100 

 acres of it have been recently planted. The report on 

 Cinchona robusta quotes with approval Dr. Trimen's 

 views on the hybrid forms of the Nilgiris — known under 

 the names pubcsccns and magnifolia — now settled to be 

 hybrids between C. succirubra and C. officinalis. 



Among the more important additions to the Herbarium 

 may be mentioned the collection of European and exotic 

 lichens made by the Rev. W. A. Leighton, the type speci- 



