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Editor, and your correspondents, recommending your female readers, before they are too seriously enamoured of their polite gallants to analyse their composition; to consider how little many of them are indebted to nature, and how much to art for the splendour of their attractions.
I am, Sir, Yours, &c.
REMARKABLE INSTANCE OF THE SORTES VIRGILIANÆ.
DURING the residence of Charles I. at Oxford, in the time of the civil wars, he went one day into the public library accompanied by Lord Falkland, who, recollecting that the ancients pretended to discover fortunes hy dipping into Virgil and taking the lines which first presented themselves, suggested to his Majesty for an amusement that he should read his destiny in this oracular poet. The king opening the book inet with the following remarkable, and as events proved, prophetical lines.
“ At bello audacis populi vexatus et armis,
Finibus extorris, complexu avolsus lüli,
Æneid iv. 615.-20.
His peaceful entrance with dire arms oppose :
QUERY, BY CULINA.
To the Editors of the Northern Star. I AM sorry that the short question which I transmitted for insertion did not procnre a place in your Magazine. I was not at all surprised at the intimation, contained among the Notices to Correspondents, that the fact was doubted, for I never yet knew the question proposed to a philosopher without a similar plea being advanced. You will, gentlemen, I should suppose, readily acknowledge that the members of that useful class of society to which I have the honour to belong, have multitudinous opportunities of ascertaining it, and I will risk the credit of our profession on the truth of the following statement. Any of your cooks shall, in the height of summer, when the noon-day sun is most powerful, put down to roast two joints of meat, which shall each require two hours and a half to be enough done. Let them have equal advantages of fire, turning, basting, &c. only let them be in different rooms, and therays of the sun fall direct upon the fire before which one of the joints is placed; your patience will, you may depend upon it, be exercised if you be hungry, by finding that the sun has a tendency to put out the fire, and that the joint of meat thus situated will require almost half an hour longer than the one in the other room.
There are few things which cause more grumbling than this circumstance, when husbands come to dinner and wish to hasten back to their warehouse ; or more lamentation, when children complain that they get beaten for being late to school. Excuse me trespassing upon your patience, while I request you will insert the annexed question, which I hope some of your readers will be kind enough to answer, if it be only out of compliment to your
fe male querist and her associates.
CULINA. Question.-- Why have the rays of the sun a tendency to extinguish any fire upon which they may chance to fall ?
To the Editors of the Northern Star. I SHOULD esteem myself greatly indebted to the politeness of any such of your intelligent readers as would condescend to favour me, through the medium of your Magazine, with a literal translation of the following epitaph, which was put over a dog by Lord Molesworth, in Edlington Wood, York. shire, and which is said to have been written by Dr. Lockyer, rector of Handsworth and dean of Peterborough.
Siste, Viator, nec mirare
adhæsit assiduus comes sociusque tori.
Istis pro meritas
SOLUTIONS TO THE QUERIES.
QUESTION 4. By Mr. W. Godward. It is required to find that number whose 6th power being taken from its 5th, shall have the greatest remainder possible ?
Solution, by the Proposer. Let x denote the number, then by the question i5-36 is a maximum, and 5042 = 6x5t, whence x = 6
QUESTION 5. By Mr. Aaron Arch, York. To construct the plane triangle there are given the base, the vertical angle, and the ratio of a line from the vertex intersecting the base in a given angle to the difference between the segments of the base made by the intersecting line.
Solution, by Mr. T. S. Davies, Sheffield.
CONSTRUCTION.-Draw AC the given base, and ABC a segment to contain the given vertical angle; bisect AC
B in G, and from any point F draw FD, making the assigned angle with FC; then take FD : FG :: line bisecting the base : half the difference of the segments of the base made thereby, and through D draw GB cuting the circle in B; describe AB, BC, and the triangle is com
G FEC DEMONSTRATION.Draw BE parallel to FD; then per sim. trian. GF: FD :: GE : EB; also 2GF: FD :: 2GE : EB but BC is the line from the vertical angle making the assigned angle with the base, and 2GE the difference of the segments of the base made thereby, which have therefore the given ratio. Q.E.D.
QUESTION 6. By the same. Three men agree to drink a quart of ale out of the same tankard : it is required to determine the divisions of the vessel made by the surfaces of the liquor at the time each man ceased to drink, supposing the height 71 inches.
Most of our correspondents have remarked that this question is not properly limited, as it is not stated whether the tankard is a cylinder or a frustrum of a cone, the latter being its true shape, in which case the ratio of its ends, or some data from which it may be determined, is necessary. We have
received correct solutions wherein this has been assumed. The following is the Proposer's Solution, who considers it as a cylinder.
The first section will be the diagonal of a cylinder of the same base, and two-thirds of the altitude of the given one. The diameter of the base =
) 3.4595 inches.' The second section will cut the base, 7.5 X 7854 but the circular segment which remains covered will evidently be greater than a semicircle. Let r=1•7297; x = sine of half the arc which bounds the greater segment; then will cosine be negative -1p2 --2; the versed sine or height of the segment=rt r2- x2. Also, (Hutton's Mens.p. 104,) the area of the segment (2x + $ 1/2r2 + 2Vp2 –22) X $ (" + Vr2--22); and (ib. p. 163),
rtvrz - x2 23.5 -; whence x 1.5294, and
rp2---2 = 1.0771 inches = height of the segment of the base which belonged to the second man.
TRANSLATION OF THE LATIN LINES ON ROCHE ABBEY, ' which appeared in the Northern Star for March, p 235.
Am I deceiv'd? or, in more happy hour,
Has the good master of these rich domains
From these high rocks to that calm vale below
Ab! how delightful on this peaceful plain
When satisfied with joy he asks no more,
When love's bright eye with kindness runneth o'er, Or, when his first born to his bosom prest
Lispeth the father's name, its sum of infant lore:
It resteth satisfied in its own gense,