Nov. II, iS86] 



NA TURE 



27 



a cat. The two nerves were divided about the middle, 

 and the distal end of tlie median was united to the 

 proximal end of the ulnar, and vice versA. Union 

 occurred : sensation and motion returned in six weeks. 

 The cat regained complete use of the limb, and did 

 not appear to suffer any inconvenience. It would be 

 of great interest to repeat the experiment by attaching 

 the proximal end of the median to the distal end of the 

 ulnar, but to prevent the other ends from uniting. Would 

 the result bean unimpaired function of the median nerve, 

 transmitted from the portions of the brain and cord 

 formerly associated with the function of the ulnar? 



The classification of the cysts and neoplasms of the 

 animal kingdom are illustrated by many typical ex- 

 amples. The teratomata are fully discussed, and it is 

 shown that they almost invariably occur only in spots 

 where the epi-, meso-, and hypo-blastic layers have been 

 temporarily but directly in continuity with each other. 

 Thus prassacral tumours are associated with the obso- 

 lete neurenteric canal ; pituitary tumours with the canalis 

 craniopharyngeus (a canal through the floor of the basi- 

 sphenoid), lingual dermoid cysts with the ductus thyreo- 

 glossus(a canal running from the basihyoidto the foramen 

 ctecum of the tongue), and ovarian dermoid cysts with 

 the obsolete Miillerian and Wolffian ducts. The predis- 

 position of obsolete ducts to disease has for some time 

 been recognised, but the close relationships of teratomata 

 to such ducts is a more recent piece of work. 



The novel illustrations of the leading pathological pro- 

 cesses make the work one of extreme interest, and we 

 heartily congratulate the author on the good use to which 

 he has turned his exceptional opportunities. 



PLANE GEOMETRY 

 The Elements of Plane Geometry. Part II. (correspond- 

 ing to Euclid, Books III., IV., V., VI.). (London: 

 Swan Sonnenschein, iSS5.) 

 T^ HIS book contains a revised edition of Books III., 

 IV., v., of the " Syllabus of Plane Geometry" drawn 

 up by the Association for the Improvement of Geometrical 

 Teaching, with demonstrations of the propositions, and 

 an excellent, though limited, collection of suitable exer- 

 cises. If nothing else than these two parts had been the 

 outcome of the movement first set on foot in our columns^ 

 the Association would have amply justified its formation. 

 Much difference of opinion has prevailed as to the desira- 

 bility or expediency of the Association producing such a 

 work as this. The late Mr. Merrifield for some years 

 strenuously opposed any such proceeding, but at the 

 annual meeting of 1881 he expressed himself as "now 

 satisfied from the experience which he had had in dealing 

 with the examining bodies that they would not get their 

 work really adopted by the public until they had a text- 

 book. Everywhere he was met with the impossibility of 

 wading through a dry Syllabus. Nobody who was not 

 thoroughly versed in mathematics could judge whether 

 there was any real possibility of teaching from the Syllabus 

 at all." Circumstances appear to have compelled the 

 Association at last to take the field with demonstrations 

 put forward by a selected committee of its members : a 

 principal reason being that the Association was bound to 

 help teachers. The plan of teaching the Syllabus without 



giving written proofs was found to succeed so long as the 

 teaching was confined to the earlier parts of the subject, 

 but when the later books were reached it was found 

 necessary to give formal written proofs for subsequent 

 reference (Report, 1881, p. 30). 



Some teachers who wish for the more copious intro- 

 duction of modern ideas and methods into the very 

 elements may not consider the work of the Association 

 as satisfactory as could be wished, and may think there 

 is very little of the influence of the aforesaid modern 

 ideas in the Syllabus, yet even such admit, and express 

 satisfaction in making the admission, that "the use of the 

 Syllabus has spread pretty widely, and it is to be hoped 

 that it will continue to do so" (Prof. Henrici, British 

 Association address, NATURE, vol. xxviii. p. 500). It is 

 to be borne in mind that the Professor hardly gave the 

 Syllabus a fair trial, though he says that when it appeared 

 " I resolved to give it a thorough trial, and took the best 

 means in my power to form an opinion on its merits by 

 introducing it into one of my classes. The fact that it 

 did not quite satisfy me, and that I gave up its use again, 

 does not of course prove that it fails also for use in 

 schools, for which it was originally intended." 



These students had, we assume, to take down in writing 

 the Professor's proofs, and it is not as agreeable work to 

 " grind up " manuscript as it is to read a printed 

 page ; then there would be by-gone remains of the old 

 text- book haunting the students' brains, want of fami- 

 liarity with the Syllabus possibly on the teacher's part, 

 and finally shortness of time over which the trial ex- 

 tended. At this point we may cite some remarks by the 

 late Dr. Todhunter, which make as much for Syllabus 

 upholders as for Euclidians. " It will be hard to secure 

 that pupils shall be selected of equal power, and be trained 

 with equal assiduity ; and then if our teacher is to try 

 various methods he is liable, since he knows that a con- 

 troversy is now existing as to the result, to deviate from 

 impartiality in his treatment of the rival methods. More- 

 over, there may naturally arise some disagreement as to 

 the means to be used for testing the value of the results, 

 and as to the accurate application of the principle which 

 may be finally adopted for this end " (" Conflict of 

 Studies," &c., p. 156). A fair trial would be to take two 

 classes of students of as nearly as possible equal 

 mental calibre, and with equal want of acquaintance 

 with geometry, and to take each through the re- 

 spectiv'e courses for the same time, and to take care that 

 each teacher should be equally skilled and acquainted 

 with his author and equally enthusiastic, for, as our 

 essayist just cited writes, "if the teacher is only languid 

 without being positively hostile, his real sentiments are 

 soon discovered : hypocrisy has but a slender chance of 

 deceiving school-boys" (p. 164). But such a fancy is 

 Utopian ; the hope of the Association at first lies in such 

 far-away parts as the Cape and India, where its work is 

 being taken up by enthusiastic and able teachers. 



We have read the proofs, and believe them to be 

 thoroughly accurate ; there is also a careful avoidance 

 of all looseness of language. Dr. Todhunter's " deliberate 

 judgment " was that " our ordinary students would suffer 

 very considerably if instead of the well-reasoned system 

 of Euclid any of the more popular but less rigid manuals 

 were allowed to be taken as a substitute " (p. 16S). So 



