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"teens" and are fond of reading. "The peculiarity in this selection is the plan of introducing every poem with an appropriate piece of prose. To a considerable number of the poems there are questions subjoined, principally with the view of directing the attention of the student to the more difficult passages." There is also a useful vocabulary at the end, containing words of Saxon and classic derivation. Upon the whole we think the work a valuable addition to our school series, and well adapted to the purposes of education.
ANSWERS TO THE MATHEMATICAL QUESTIONS.
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 14 time the work of B?
Answered by Prismoid, Mr. Morris, Mr. O'Sullivan, Mr. Scott, Mr. Dyer, Mr. Sothern, Mr. Salter, and J. P.
Part done by A and B per day = 14.
But A does & times the work of B, therefore if we suppose their work divided into 9 equal portions, A would do 5 of them, and B 4 of them :
.. Part done by A per day
~ 116 = 88% ;
.. Part done by A and C per day
126 + 638 = 6.
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?
Now we have
Answered by Mr. Brookes, Mr. Sheppard, Mr. Hill, Mr. Levy, Mr. Herbert, and Mr. Righton.
Here Radius of the large circle
If the centres of the four inscribed circles be joined, the lines will form a square, the diagonal of which will pass through the centre of the large circle. Let a the radius of each inscribed circle; then
the side of the square .. the diagonal of the square
2 x √2. Diam. large circle = 2 radii small circle + diagonal sq.; .. 56.4189 x 2
2x + 2 x √2,
= 2x, 18202
.. x =
= 23.369 chains.
= 56·4189 (√2 — 1)
.. Area small circle
.. Each daughter's share
which is each son's share.
Now the central portion, or the widow's share, will be equal to the area of the square, formed by joining the centres of the four circles, less by the area of one of these circles, that is,
2 x 23.369)2
LIST OF MATHEMATICAL ANSWERS.
T. Laurie, Oundel, ans. 105, 106; T. Wilson, Sebergham, ans. 105, 106; E. Carthew, Roehampton, ans. 105; Prismoid, ans. 105, 106; C. Watson, Preston, ans. 105; J. Bolton, Old Malton, ans. 105, 106; C. Linton, Burton on Trent, ans. 105; W. Cowper, ans. 105; G. Morris, Gosport, ans. 105, 106; G. Barnacle, Empingham, ans. 105, 106; J. Sheppard, Gillingham, ans. 105, 106; D. O'Sullivan, Preston, ans. 105, 106; J. B. Bayley, Uttoxeter, ans. 105; S. Dyer, Wanstead, ans. 105, 106; J. Scott, Low Moor, ans. 105, 106; T. Sothern, Burton Wood, ans. 105, 106; W. L. Brown, Ightham, ans. 105; W. Davies, Coniston Cold, ans. 105, 106; J. Rowlatt, Evercreech, ans. 105; H. Hill, Mortlake, ans. 105, 106; J. Brokes, Manchester, ans. 105, 106; J. O. Clazey, Durham, ans. 105, 106; P.T, ans. 105, 106; C. Smith, Billericay, ans. 105, 106; W. H. Levy, Shalbourne, ans. 105, 106; John Reed, Brendon Week, ans. 105, 106; A. M. ans. 105, 106; J. Salter, Durham, ans. 105, 106; J. Herbart, Woolton, ans. 105, 106; W. Righton, ans. 105, 106.
(1000 46.879-4 × 171·572) × ‡
= 66.708 acres.
TO BE ANSWERED IN OUR NUMBER FOR OCTOBER, 1851.
33x to find x.
QUES. 108.-Proposed by Prismoid, Tewkesbury.
Six equal circles are described within a given circle, in contact with one another and the given circle; required the area of each.
QUES. 109.-Proposed by Mr. Herbert.
At what time between 11 and 12 o'clock, are the hands of a clock approaching the 12 with the same velocity?
QUES. 110.-Proposed by Mr. Righton.
Determine the segment of a sphere so that the ratio of its solidity to its convex surface may be a maximum.
J. N. We cannot give you the information you ask for.
ON THE GENITIVE CASE. [The following remarks on the Genitive Case are taken from an Essay on English
Orthography, by Archdeacon Hare, published iu the “ Philological Museum," in 1832. They are referred to in an article in our June number, and are now printed
here by permission.] Op our Anglosaxon cases we kept but one, the genitive, and that only in particular constructions; for this genitive must always precede the noun it depends on. Thus, becoming unused to inflexions, we lost the perception of their meaning and nature; and the precursors of Horne Tooke in the sixteenth century fancied that the s of the genitive stood for his. Under this notion his was often written at length, especially where the noun ended in s. At what period this errour was first broacht, and how it crept into vogue, my own very limited acquaintance with our ancient writers does not enable me to determine. I believe it is not found in Chaucer or Maundeville, and probably not in the other writers of the same age. The earliest instances I have noticed belong to the latter half of the sixteenth century. In the Palace of Pleasure (1575) we find Christe his secretes, Vol. 1. p. 44 (ed. Hazlewood), Rinaldo his servaunt p. 115, Landolpho his barque p. 125, Andreuccio his parentes p. 130, without any knowledge of the prince his beiny there p. 169, Didaco his sword, p. 220, sir Stricca his garden p. 322. So in the Mirrour for Magistrates: by Mars his furce, King Albanact 10, to Hercules his pillars, 35, and so on. In Gerarde's Herbal this corruption occurs perpetually. The title of Silvester's translation is Dubartas his Divine Weekes; that of Purchas, Purchas his Pilgrimes. Even Spenser, though one is loth to detect errour in a writer 10 whom the language owes so much, has Pegasus his kynd. I, 9. 21, Mars his bed, 11. 6. 24, Satyrane his chaunce, ul. 9. 27, Satyrane his steed, iv. 4. 40, Brute Silvius his sonne, 111. 9. 48. This led our grammarians long ago to protest against the blunder. Charles Butler, one of the earliest of them, in his English Grammar publishit in 1634, says: “The Teutonik termination of the genitive some refined wit hath turned to his, perswading himself that s is but a corrupt abbreviation of his, which hee thought necessary to restore : and therefore hee wil not write my masters son is a child, but my master his son is a child ; which is just as good as if in Latin hee would say, not heri filius, but herus ejus filius, est infans.” Ben Jonson too, in his Grammar, which did not come out till 1640, after his death, says: “Nouns ending in x, s, sh, 9, and ch, in the declining take to the genitive singular i, and to the plural e ; as rose, bush, age, breach; which distinctions not observed brought in first the nionstrous syntax of the pronoun his joining with a noun betokening a possessor. Yet in spite of these protests it has been so much the fashion for Englishmen to know nothing about their own tongue, that instances of this “monstrous syntax” are to be found in many even of our best and purest writers. Milton indeed, like Jonson, seems to have kept clear of.it; but Randolph, Jonson's adopted son, forgot his father's precept concerning it: Clarendon talks of Mr. Hobbes his friends, Mr. Hobbes his Leviathan : in Dryden's letters, in printing which Malone has rightly followed the poet's own way of spelling, the same corruption occurs repeatedly : Otway, Pope, Congreve,
VOL. IX.-NO, X.
Farquhar use it: the argument of Hudibras begins with Sir Hudibras his passing worth ; and shortly after, 1. 1. 439, we come to
" As Cæsar's horse would kneel and stoop,
(Some write) to take his rider up;
Would often do to set him down." Nay, Addison in the Spectator, No. 135, asserts that "the single letter s on many occasions does the office of a whole word, and represents the his and her of our forefathers :" though, as Lowth observes, his own words carry their confutation along with them; and a little reflexion would show that s can hardly have usurpt the place of her. In a Grammar indeed by Joseph Aickin, publisht in 1693, an attempt is made to get over this difficulty. “The casual preposition of (he says) is sometimes changed into an adjective possessive; as, the King's son, for of the King, where s is put for his; Jane's daughter, where s is put for hers: hell's darkness, where s is put for its. It never struck him to ask what his and hers and its were; or that they were originally only the genitives of he, her, it. This erroneous persuasion had become so inveterate, that the republisher of Ben Jonson in 1692, taking upon him to correct his author, audaciously and tacitly put in the room of the passage before cited : “To the genitive cases of all nouns denoting a possessor is added 's with an apostrophe, thereby to avoid the gross syntax of the pronoun his joining with a noun; as the Emperor's court; not the Emperor his court. Thus foisting in his own conviction that s stands for his, and yet retaining the expression " the gross syntax,” which is directly opposed to it, he has made old Ben write sheer nonsense, in a chapter which even in the old edition is far from correct.
In Wallises Grammar one is startled at first by the assertion that noun substantives in English have no distinction of gender or case : which in a true English spirit he boasts of as an advantage, because it saves us a world of trouble : as if the same might not be said of ignorance ; or as if anything good were to be got at without trouble. But does Wallis then entirely pass over our genitive case? He speaks of it indeed, but under another name, and calls it a positive adjective: “ which may be formed from any substantive, whether singular or plural, by adding s, or if needful for the sake of the sound, es. Its meaning is the same as that of the preposition of, when it answers to the Latin genitive : as mans nature, the nature of man, natura humana vel hominis ; mens nature, the nature of men, nutura humana vel homi
Here in the first place it strikes one that there is nothing in the nature of our adjectives analagous to this needless variation between the two so-called possessives, mans and mens. But how is a mans nature to be reconciled with the character of our adjectives ? and what is a thousand mens swords ? is it mille humani enses? The assumption is altogether arbitrary and groundless; and taken up merely for the sake of supporting the paradox, that we have no cases. Had Wallis been acquainted with our old language, a knowledge which our grammarians and lexicographers have strangely thought it not worth their while to acquire, he would have found that we had just as good, or as troublesome, cases as the Latin or Greek. But in comparing the disorder of
our own with the regularity and symmetry of the ancient languages, one is evermore reminded how to him that hath is given, and he hath more abundance; while from him that hath not is taken away even that he hath.
That the final s stands for his however, Wallis positively denies : “ for (he says) it is joined to feminine nouns, and to plurals, where his would be a solecism; and it is found in the possessive ours, yours, theirs, hers, where nobody can dream that his is contained : and indeed his itself, as well as whose, are only hee's, who's, his being written for hees as bin is for been." Yet to such a pitch was the confusion on this point carried, that the compiler of the index to Stow's Survey of London in the edition of 1633 writes St. James's his Parke, though Stow in the text wrote St. James Purke. In our Liturgy too, as every one koows, we read Christ his sake : for though the ancient spelling of our prayerbooks has been modernized, and some slight changes made, such inatters, from our recklessness about grammar, are left to the ignorant, and this gross blunder is still allowed to keep its place. Its introduction in the Prayer for all sorts and Conditions of Men, contrary to the analogy of the Collects for Quinquagesima, and for the fourth and twenty-fourth Sundays after Trinity, is to be accounted for from the prayers being one of the additions made on the accession of Charles JI. : the same blunder occurs repeatedly in the Forms of Prayer framed at the same time for Charles the Martyr, and for the Restoration. The passages in our Bible on the other hand where the same errour is pointed ont by Lowth.-Asa his heart, 1 Kings xv. 14; Mordecai his matters, Esther 111. 4,-have since been altered : here again, though the corruption is found in all the old editions of the versions made under James I. most of the earlier translations are without it: in Cranmer's Bible of 1549 we read Asaes harte : in Tyndales of 1549, A sus : in Barkers of 1582 and 1616, Asas and Mordecais : and such is the old and right way of writing our genitives. For it was this very mistake about the origin of the final S,
gave rise to that useless and unmeaning practice, with which all our modern books are disfigured, of prefixing a mark of elision to it. There is no better ground for placing such an ugly mark over the genitive than over the nominal plural : where the vowel which used to precede the s has been omitted in the one case, it has also been omitted in the other; and that no confusion or ambiguity of the slightest moment is obviated by the use of such a mark, anybody may satisfy himself by reading our old authors in the original editions, or in the reprints where the old orthography has been retained. For in our old books the genitive is written without any mark of the sort. In Hearne's edition of Robert of Gloucester indeed one finds it : but no doubt it owes its introduction to a piece of carelessness on the part of the editor, who in other respects rightly follows the orthography of his author's age. Even so late as at the publication of Paradise Lost, the apostrophe was only introduced in a few peculiar cases. In the early editions of Milton wê read “Of Mans First Disobedience;"
“ Yet to their Generals Voyce they soon obeyd
Innumerable, as when the potent Rod