doubted, for I never yet knew the question proposed to a philosopher with out 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 female querist and her associates.

fire

CULINA. Question. Why have the rays of the sun a tendency to extinguish any 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, Yorkshire, and which is said to have been written by Dr. Lockyer, rector of Handsworth and dean of Peterborough.

Mathematical Repository.

SOLUTIONS TO THE QUERIES.

QUESTION 4. By Mr. W. Godward.

Ir 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 5-6 is a maximum, and 5x4x 6xx, whence x — §.

QUESTION 5. By Mr. Aaron Arch, York.

To construct the plane triangle there are given the base, the vertical an⚫ gle, 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 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 completed.

A

G FEC

DEMONSTRATION. Draw BE parallel to FD; then per sim. trian. GF FD GE EB; also 2GF: FĎ:: 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=

70.5

(7.5 X 7854

1)=3·4595 inches. The second section will cut the base, 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 or- r2-2; the versed sine or height of the segment=r+r2-2. Also, (Hutton's Mens. p. 104,) the area of the segment (2x + 3 √/2r2 +2\/r2 −x2) × ☆ (" +r-x); and (ib. p. 163),

2x3

=

3 +.(√r2−x2) × (2x + † √/2r2 + 2√\/r2 − x2) × fô (r + √r2 -x2

r + √r2 − x2

23.5

7.5

1.5294, and r Vr2 —x2 1.0771 inches

=

-; whence r of the segment of the base which belonged to the second man.

Original Poetry.

TRANSLATION OF THE LATIN LINES ON ROCHE ABBEY, which appeared in the Northern Star for March, p 235.

WHAT lovely charms this pleasing vale adorn
Which nature paints so fair at night and morn !
In former days within this green retreat
A tribe of monks had fix'd their lonely seat:
Then 'midst the shades of this sequester'd dell
Dark Superstition brooded in her cell.
Whilst her pale children, victims of her pow'r,
In pray'r and penance spent life's fleeting hour.
Ah! see what scenes, with every beauty bless'd,
Alluring scenes! the unhappy race possess'd.
Behold what lofty piles once grac'd the land
Which erring Faith had rais'd with labouring hand.
Now fall'n-how soon-beneath she stroke of Time
O'er their disjointed stones black Ruin smiles sublime!

Am I deceiv'd? or, in more happy hour,
Unwilling to usurp the rights of pow'r,

Has the good master of these rich domains
To social uses turn'd the cheerful plains?
His generous soul that look'd with noble scorn
On selfish joys and pride of ignorance born,
Not happy whilst himself alone possess'd

The beauteous charms with which this vale is bless'd,
Gave all its scenes of hill and dale and wood
To others' eyes--a great and public good:
These scenes adorn'd by arts that vainly try
The matchless charms of nature to outvie,
The muse of MASON, of mellifluous tongue,
In soft and polish'd verse has sweetly sung.
Here where in former times were only seen
Arcadian seats retir'd and meadows green,
Thro' which with pleasing murmur crept along
A small and humble stream, unknown to song,
Elysian fields we now surpris'd behold,

A river too whose waves are liquid gold,
With which not sweet Ilyssus can compare
Nor fam'd Callirhoe's stream, so bright and fair.

From these high rocks to that calm vale below
Which they protect from all the winds that blow,
And sep❜rate from the world, and so enclose
They seem to shut from thence all human woes,
How easy the descent! how smooth the way!
At brightly closing eve or op'ning day;
But from this peaceful vale our path t'explore,
And to the vain world turn our steps once more,
Ah! this is labour-this a task we find
That brings regret for scenes we've left behind,

Ah! how delightful on this peaceful plain
Life's ev'ning hours to spend, remote from pain!
How happy age, in this sequester'd vale,
Unmov'd by fortune's ever changeful gale,

Might wear out life, amidst calm scenes of peace "Till death, at length, the weary soul release.”

SONNET.

THERE are some periods in man's craving breast,
When satisfied with joy he asks no more,
Such as - when friendship bears its strongest test,
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:-
And there is sorrow in the heart so deep,
It resteth satisfied in its own sense,

It deigns not to complain, nor doth it weep,
But dwelleth in its loneliness intense.

3 C

It is a spirit bent, but not subdued,
The calm rebellion of a haughty mind,
That shuts out heaven from its stern solitude,
Living unbless'd and dying unresigned.

B. H.

SONNET.-TO LAURA.

CLING to my heart her image, whom I deem
Holy, as in remembrance is a dream

That rov'd the sphere of fancy hallowingly;
Like that, her smile my young affections crost;
Like' that, it had been early chas'd and lost;

But sweet like that,-could never, never fly. The form of her may perish-she may die !Flowers on her grave may spring:-yet then would I Gathering those flowers, her gentle name invoke, And for a moment, as death's spell was broke,

Hear her sweet speech again! then sigh and start,--
And place those flowers devote upon my breast,
And press them to the bosom she had blest;

-To wither where she liv'd-upon my heart.
May, 1818.

THE ROSE.

MORE glowing still its matchless hue,
Still sweeter with the morning dew,
The rose display'd its gayest bloom,
And fill'd the air with rich perfume;
Maria's bright, love-beaming eyes
Were fix'd upon the fragrant prize,
With ready hand young Henry prest
The flower, and plac'd it on her breast;
The gift with smiles the fair receiv'd
And blush'd; her snowy bosom heav'd
While Henry soft address'd the maid
And sighing press'd her hand, and said,
"Maria, mark the rose's fate,

How short how fleet its beauty's date;
How soon these peerless tints shall fly,
How soon these blooming leaves shall die!
Yet balmy still, these leaves dispense
Their odour to the gladden'd sense.
So when thy outward charms decay,
Thy cheeks soft roses fade away
Yet still thy virtue, sweet perfume—
Shall flourish in eternal bloom."

Richmond, May 4, 1818.

LEO.