Mar. 21, 1872] 



NATURE 



401 



For the last two years he has been engaged in carrying 

 through the press, for the Indian Government, a photo- 

 hthographic edition of the " Mahabhashya," of which 300 

 pages still remain to be done. By his decease, what may 

 be called the "traditional" school of Vedic criticism, 

 which gives to the interpretations of native tradition the 

 preference over those derived from comparative philology, 

 ceases to have a European representative. His manu- 

 script of a Sanskrit grammar has long been finished, and 

 it is hoped that this work, which is likely to revolutionise 

 the teaching of Sanskrit in many respects, may be allowed 

 to see the light. The great psychological value as an 

 educational instrument which he attached to the Sanskrit 

 language, if properly taught, was well known to his 

 ] friends ; and it w;5s through his advocacy that a commit- 

 j tee of the professors of University College, London, was 

 I appointed to report on the desirableness of making Sans- 

 j krit an integral part of all the degree examinations in the 

 I University of London. 



Of the philosophical literature of India, the '''Mimansa," 



I from its close connection with grammatical researches, 



I engaged his chief attention ; some fruit of his labours in 



this field is a nearly finished edition, prepared for the 



Sanskrit Society, of Madhava's " Jaiminiya-nyaya-mala- 



I vistara" (1865). 



It was however GoldstUcker's thorough familiarity with 

 the legal and ceremonial literature of the Hindus which 

 ! rendered his advice of so much value to the Indian 

 Government. A paper recently published by him " On 

 the Deficiencies in the Present Administration of Hindu 

 i Law" (Triibner, 1S71), contains an exposure of the frequent 

 failures of justice arising from the misunderstandings of 

 native codes, which disgrace our Indian administration. 



Besides some papers in the Keader and the Atlicna-um, 



Goldstiicker contributed an excellent essay on the "Maha- 



; \AAxdii.2i" \.o\^e. Westminster Revieiv m April 186S ; and 



i among his papers will be found a copy of the great Eastern 



epic collated with the best European MSS. His library 



is, we are glad to hear, to be kept together. 



■ Dr. Goldstiicker was Professor of banskrit in LIniversity 



College, London, President of the Philological Society, a 



member of the Council of the Asiatic Society and of the 



Association of the Friends of India. 



REPORT OF THE ASSOCIATION FOR 

 THE IMPROVEMENT OF GEOMETRICAL 

 TEACHING 



A T the Second Annual Meeting of this Association, 

 -^~^ held at University College, London, on January 12, 

 Dr. Hirst, the president of the association, delivered the 

 following address : — ■ 



In opening the proceedings of this, the Second Annual 

 Meeting of the Association for the Improvement of Geo- 

 metrical Teaching, I ain glad to be able to congratulate 

 you on the decided progress which has been made during 

 the past year towards the realisation of >our views. The 

 discussions recorded in English journals, and the recep- 

 tion given to recendy published text-books on geometry, 

 unquestionably indicate that public opinion is far more 

 inclined now than it was a few years ago to entertain the 

 notion of an improved exposition of the elements of geo- 

 metry. We are no longer warned that to touch that edi- 

 tion of Euclid to which, for more than a century, we have 

 paid such literal homage, would be to ruin the teaching 

 of geometry. On the contrary, it is now generally ad- 

 mitted that, without departing from the admirable e.xacti- 

 tude and geometrical purity of Euclid's elements, we 

 ought to be able, by judicious revision and extension, to 

 bring them more into harmony with the scientilic methods 

 and the habits of thought of our own day. I alluded last 

 year to the retrograde step that had been taken in Italy 



on this question of the teaching of geometry. The an- 

 nouncement excited much interest in England, though 

 the true purport of the Italian movement was, I fear, 

 slightly misunderstood. I have, therefore, thought it my 

 duty to procure original documents, to make inquiries 

 into the success of the Italian movement of 1867, and also 

 to ascertain the present aspect of geometrical instruction 

 in that country. 1 hold in my hand the historically in- 

 teresting document which was issued by the Italian 

 Government in 1S71. It contains instructions and pro- 

 grammes relative to the teaching of mathematics in their 

 Ginnasi and Licei* Before quoting it I may observe 

 that the Ginnasio is essentially a classical school, mathe- 

 matics being studied only in its fifth or highest class, and 

 then only for five hours a week ; and that in the Liieo the 

 instruction is still to a great extent classical, though less 

 exclusively so. Here, as the pupil advances through its 

 three classes, mathematics, physics, natural history, and 

 philosophy become more and more prominent as subjects 

 of study. The instructions, as already observed, relate 

 solely to the teaching of mathematics in these classical 

 schools ; nevertheless, the following introductory remarks 

 on the objects of mathematical study are, I venture to 

 think, applicable to all schools in which the foundation 

 of a truly liberal education is to be secured : " Mathe- 

 matics should not be looked upon as a mere collection 

 of intrinsically useful propositions or theorems of which 

 boys ought to acquire a knowledge in order to be able to 

 apply them subsequently to the practical purposes of life. 

 The study should be regarded principally as a means of 

 intellectual culture, directed towards the development of 

 the faculty of reasoning, and to the strengthening of that 

 just and healthy judgment which serves as the light 

 whereby we distinguish truth from that which has but the 

 semblance thereof." 



Afcer describing the course of instruction in arithmetic 

 and algebra best suited to the end in view, the document 

 before me proceeds thus :— " In order to give to the in- 

 stiuction in geometry its maximum intellectual efficacy, 

 and at the same time to bring the subject-matter within 

 reasonable limits, it will suffice to follow, in our schools, 

 the example of English ones by returning to the elements 

 of Euclid, universally admitted to be the most perfect 

 model of geometrical rigour." It would be a grave error 

 to suppose that it was the good results on geometrical 

 teaching of our adherence to the elements of Euclid that 

 induced the Italians to return to them. Although England 

 is made, in some measure, responsible for the step taken, 

 we know from sources alluded to in my address last year 

 that the main object in taking it was to purge from Italian 

 schools the many worthless books which private enter- 

 prise had succeeded in introducing, and by no other means 

 than the one adopted could the Italian Government, in 

 the opinion of their advisers, have achieved this end with 

 sufficient promptitude and impartiality. 



The real motive of the order issued in 1867 is a little 

 more apparent in the following passage from the In- 

 structions, wherein allusion is made to the practice, then 

 prevalent, of striving after a deceptive facility of treatment 

 by the introduction of algebraical processes in place of 

 geometrical reasoning : " The instruction in geometry is 

 to extend to the first six, and to the eleventh and twelfth, 

 books of Euclid, and to be followed by lessons on the 

 most essential propositions of Archimedes relating to the 

 measure of the circle, of the cylinder, of the cone, and of 

 the sphere. Taught by the method of the ancients, 

 geometry is easier and more attractive than the abstract 

 science of number ; hence,instead of postponing geometry 

 to algebra, one part of the subject (the first book) is 

 assigned to the fifth class in the Ginnasio, and another 

 (the second and third book) to the first class of the Licco. 

 The teacher is recommended to adhere to the method of 



* Instruzione e Programmi, per I'lnsegnamenlo dclU Malcmatici nei 

 Ginnasi e nei Licei, approvali con R. Dccreto, 10 Ottobre, 1867. 



