QUES. 104.-Proposed by Tom Tomkins. Required an expression for the side of an equilateral triangle inscribed in a given parabola. Answered by Mr. Sheppard, Mr. Righton, and Mr. D. Now a will be an abscissa, and y an ordinate of the parabola; hence we have from the equation to the parabola, and by substitution, y2 = 4 ax, y24 a x y √3, y=4 a√3. . LIST OF MATHEMATICAL ANSWERS. J. Sheppard, ans. 102, 103, 104; J. Reed, Brendon, Cornwall, ans. 102,103; D. O'Sullivan, Fox-street Preston, ans. 102, 103, 104; Thomas Sothern, Burton-wood, ans. 102, 103; W. H. Levy, Shelbourne, ans. 192, 103, 104; J. Salter, Durham, ans. 102, 103, 104; J. Herbert, Woolton, aus. 102, 103; W. Righton, ans. 102, 103, 104; A. M., ans. 102, 103, 104; J. Bolton, Old Malton, ans. 102, 103; G. Turner, Queen's Head, ans. 102, 103; G. Barnacle, Empingham, ans. 102, 103; J. Scott, Low Moor, ans. 102, 103; E. Carther, Roehampton, ans. 102, 103; W. Davies, Coniston Cold, ans. 102, 103; T. Horsman, Chelsea, ans. 102; A Buglass, S. Shields, ans. 102; Kerslake, ans. 102, 104; J. Rowlatt, ans. 102, 103; J. B. Bayley, Uttoxeter, ans. 102, 103; J. Fox, Burton-on-Trent, ans. 102, 103; W. E., ans. 102, 103; J. R. Prowse, Yeovil, ans. 102, 103; S. Dyer, aus. 102, 103, 104; W. Bower, Bridgenorth, ans. 102, 103; J. Lowres, ans. 102; G. Morris, Gosport, ans. 102, 103; E. Napier, Yeovil, ans. 102; W. Wakely, Marlborough, ans. 102, 103; C. H. Kennion, Farmouth, ans. 102, 103; Regulus, Bradford, ans. 102; T. Dungate, Ightham, ans. 102. NEW QUESTIONS, TO BE ANSWERED IN OUR NUMBER FOR SEPTEMBER, 1851. A and B can do a piece of work in 14 days, and B and C in 15 days: in what time can A and C do it, allowing that A can do 11 time the work of B? QUES. 106.-Proposed by Mr. J. Reed. A gentleman dying, left a circular estate of 1000 acres, to be divided among his four sons, four daughters, and widow, in the following manner-The four sons were to have as much as should be contained in four equal circles as large as could be described (without cutting each other) within the largest circle; the four daughters were to have the four equal pieces remaining between the smaller circles and the larger, and the widow the centre part between the four sons. Required the number of acres each son, each daughter, and widow possessed? NOTICE TO CORRESPONDENTS.-We should be glad if our correspondents would favour us with a greater choice of new questions. Entelligence. EDUCATION IN NEW ZEALAND. -The Lord Bishop of New Zealand and the Bishop Designate of Lyttelton, in concert with the other resident clergy, were most anxiously engaged during his lordship's stay at the settlement, in consulting for the future well-being of the new diocese, considered especially in its relation to the rest of the province of Australasia. It was impossible to do more at present than to make temporary provision for the due supply of religious ordinances to the inhabitants of the Canterbury settlement, and for such educational institutions as the pecuniary means at present at the disposal of the agent of the Canterbury Association would admit. It was determined to commence an elementary and commercial school at Christchurch as soon as possible, for both boys and girls. The want of such an institution begins to be greatly felt on the plains. It will probably be felt as a disappointment by some persons, that the senior department of the college cannot at once be commenced at Christchurch, or at some place in the neighbourhood of the future capital. This was found to be impossible; first, for want for want of the necessary accommodation (a want which is temporarily supplied at Lyttelton, by the simple adaptation of a portion of the Emigration Barracks); and secondly, because there are no funds available for the erection of proper buildings. As soon as the Bishop Designate reaches England, his best and persevering efforts will be applied to the collection of funds for this great purpose. Meanwhile, Mr. Cridland has prepared a series of designs, embodying the economical principles and arrangements for discipline, which were contemplated in the drawings brought by the Bishop Designate from London. Mr. Cridland's designs are, in other respects, adapted to the building materials available in the colony. The Bishop Designate entertains, we believe, the confident hope that he will be able to send from England, by monthly instalments, a sum sufficient to erect all the parts of the college necessary for the full and efficient working of its discipline and scheme of general instruction, should the funds of the Canterbury Association derived from land sales be found insufficient for that object, after providing for liabilities already incurred. Meanwhile, the upper department opens at Lyttelton with four pupils, and with the immediate prospect of several additions from the other settlements of New Zealand. Assuming that the college buildings are commenced out of the first funds derived from the above sources, and are ready for occupation by the time the Bishop Designate returns to the colony; and that the estates attached to the scholarships, for which he has already procured funds in England, are at that time sufficiently productive, he proposes to hold examinations in the Greek and Latin languages, and in mathematics; at which, as we are informed, any person being a member of the Church of England, and whose age does not exceed twentyone years, may compete. The successful candidate will immediately enter upon the enjoyment of any emoluments which may be derived from the foundations referred to. The following are the foundations at present:-1. The Somes Scholarship. In the examination for this scholarship a preference will be given to the next-of-kin of the founder, Mrs. Maria Somes. It is endowed with fifty acres of rural land, and one quarter of an acre section in the Port town of Lyttelton. 2. The Rowley Scholarship, of fifty rural acres, and one town section at Christchurch. 3. The Charles Buller Scholarship; endowed with one hundred acres of rural land, and two town sections at Christchurch. 4. The Hulsean Chichele Professorship of History, at present vacant. There is reason to hope that a gentleman in England distinguished for his talents and learning may be persuaded to accept it. Meanwhile, the Bishop Designate, acting upon the expressed wishes of the munificent founder (Edward Hulse, Esq. M. A., Fellow of All Souls College, Oxford), that the attention of the Professor should be called, in the terms of the trust deed, to the Reformation, and the period immediately preceding it, proposes to present a prize of books, to the value of not less than five guineas, to the author of an English Historical Essay, founded on the following passage, selected from the Colloquies of Erasmus: "Exulat Christianus Danorum rex, pius Evangelii fautor: Franciscus Galliarum rex hospes est Hispaniarum, nescio quam ex ipsius animi sententia, vir certe dignus meliore fortuna: Carolus molitur monarchiæ proferre pomoeria: Ferdinandus rerum suarum satagit in Germania: balimia pecuniarum urget aulas omnes: periculosos motus coercitant agricolæ, nec tot stragibus ab instituto deterrentur; populus meditatur anarchiam; periculosis factionibus collabitur ecclesiæ domus: hinc atque hinc distrahitur illa Jesu tunica inconsulitis."-Erasmi Colloquia. The Bishop Designate also offers to the students of the college, two prizes of books, to the value of five guineas each, for the best two poems, one in English and one in Latin, on the voyage of the five ships, containing founders of the Canterbury settlement, and on the foundation of the colony itself; these poems to be recited at the opening of the college. -Lyttelton Guardian. INDUSTRIAL TRAINING INSTITUTION. The foundation stone of a new Industrial Training Institution, for the counties of Essex and Hertford, has just been laid at Hockerhill, The object of the founders of these schools is, the more effectual training of young women for the offices of teachers and housewives. The amount of money required to give practical efficiency to the institution is estimated at £9000, towards which sum £7500 have been already collected-including £300 from Government, and £600 from the National Society. BATTERSEA TRAINING INSTITUTION.-The Rev. Robert Graves, for some years Mathematical Tutor of St. Mark's College, has been promoted to the office of Vice-principal of the Battersea Training Institution. C. F. Eastburn, Esq., B. A., sixth wrangler of St. John's College, is appointed to the office vacated by the Rev. R. Graves. To Correspondents. A SCHOOLMASTER is informed that the Selections he alludes to were not continued. Several communications received too late for insertion this month will appear in our next, ON LATIN ETYMOLOGY. No. XIII. WHEN two changes in the form of a root happen to coincide, there is a fair excuse for those who fail to recognise the substantial identity of the two varieties. Thus it would not be an easy problem to find out the Latin word that represents the Greek xwv-vv. The base of this word we should prefer to write xov- rather than χων. The presence of the w we believe to signify that the first of the two liquids was not pronounced. It was no uncommon thing in both Greek and Latin to suppress an n after a vowel o. Thus convention- was softened into covention- before it was compressed into contion- (n. contio) “an assembly." So the Roman words consul, and Constantinus were pronounced with a long o and the n altogether silent. Hence the Romans abbreviated the former by the letters cos., and the Greeks wrote the other Κωνσταντινος οι Κωσταντινος, just as they also wrote Κηνσωρ οι Κησωρ for censor. It was in this way probably that the Romans wrote the Greek names Eevoowv, Zrpaßwy without a final v, Xenopho, Strabo. That they was not pronounced with much care in the base of χωννυμι is proved by the derivatives χοος χωσις χωμα. In discussing the question under what form xor may be expected to appear in the Latin vocabulary, we must first deal with the aspirated guttural. Now we have had not a few examples of pairs of words in which to a Greek aspirate corresponds a Latin medial, as ovv and unguis, oupaλoc and umbilicus, vepos vepeλn, and nubes, λexos, 'a bed,' and lingere, "to lay or spread out," whence the compound pollingere. Thus we are invited to look out for some word beginning with a g, and perhaps ending in an r, as the representative of the base χον of χωννυμι. Again, as a Latin short vowel before an r commonly takes the form of an e, we arrive at a hypothetical base ger-. Now the Latin actually possesses this verb with the very sense we should desire, but it happens to be found only in compounds; and must carefully be distinguished from that other verb gero, which signified, as we have already said, "to carry habitually," "to wear," and in fact corresponds in sense to the Greek φορεω. It is true that all our lexicons deduce from this verb gerere, "to carry," the compounds ingerere, congerere, egerere, suggerere, regerere, and are most unduly biassed in their translation of these compounded verbs by the erroneous origin they give to them. Thus even Forcellini for the first meaning makes ingero= intro gero, and Mr. Riddle "to carry into." So egero is said to be = extra gero, "to carry out ;" and regero = retro gero, "bear or carry back." Now we believe that the notion of shovelling or moving in successive masses is the only notion to be found in every one of these compounds. Thus egerere means nothing but "shovel out," "shovel up," or if speaking of water, "bale out," 99 66 empty out in buckets," as egere fluctus (e navi) Ov. Ingerere likewise is used of emptying buckets, &c. of water into a vessel, and indeed the very passage first quoted by Forcellini in justification of his alleged equivalent phrases intro gero, infero, importo, has the sense we speak of: viz. VOL. IX.-NO. IX. I Plaut. Pseud. i. 2. 24, "Tu qui urnam habes, aquam ingere, face plenum ahenum sit cito." More commonly ingerere is "to heap upon," especially in the sense of "heaping abuse upon a person,' e. convicia. This metaphor no doubt arose from the practical proceeding of "heaping dirt or dirty water upon a person," and thus we are prepared for the return in kind, the retort, expressed in regerere convicia. But if Forcellini has made mistakes in dealing with these compounds, these mistakes are as nothing compared to the mass of error accumulated by Lünemann under regero, and with all care reproduced in Mr. Riddle's book. We have room for but two specimens. Under the first division, and third subsection, for there is no little pretension to accuracy and completeness, we find: "to let boil away (verkochen lassen) Varr." The passage referred to is in the De Re Rust., i. 64, a passage corrupt in many ways. Gesner first proposes to alter duas partes quoad regerunt into ad duas partes quoad redegerunt; but subsequently defends the existing text, and attributes to regerunt a sense which it can in no wise bear; viz. igne expellunt. For this unwarrantable supposition he refers us to a note of Scaliger's on R. R. ii., 2, 18, where that learned critic has the courage to invent a compound regere from re and agere, on the model of degere. The present of Scaliger's imaginary verb would of course be rēgo, and this forsooth is a justification for assigning to regero the sense of "to let boil away." We have thought it right to give this detail because it is a fair specimen of the authority upon which not a few strange meanings are foisted into our lexicons. The other extraordinary translation stands in the second division, first sub-section-" Fig. to enter, in commentarios, Quint."-The passage is quoted at length in Forcellini, from lib. ii. c. 11, where Quintilian is talking of youngsters who shovel into the recesses of their note books for future use whole passages of declamatory rubbish that they hear applauded. But we return to our view that gerere, as seen in the compounds egerere, &c., means always to shovel, heap, pour in large and successive quantities;" and that it has no connection whatever with the verb 61 gerere, to wear." We believe also that it is the equivalent in form of χον the base of xwvvvμi, &c., but whether this connection be true or not, the importance of the doctrine as to the meaning of egerere, &c., is not diminished.* But perhaps the best evidence of the real power of the compounds of ger- may be found in an examination of the passages quoted by Forcellini himself, in spite of the bias in his mind arising from the belief that ger-, carry,' is the parent of the whole family. The two ideas of "shovelling," or, as we say, "shooting (earth, rubbish, &c.)" and baling out (water)," stand out in the most marked manner in the quotations of that writer. Thus, under agger- we find examples with the following accusatives: luta et limum, Cic.; tellurem, Virg.; terram, * We have not included in our paper the word carmen, which prima facie seems to be a modification of canimen, from can- "sing." This word is thought, and not without some show of reason, to be formed from an obsolete verb car-, " make,” whence, probably, creare and crescere. The Sanscrit has the verb kri "make." The derivation of Tоτns from яolew, would justify this derivation of carmen, so far as regards meaning. |
