unpleasant situation. This, combined with other considerations, induced him to undertake the mastership of the boys' charity in Sheffield, which was then vacant. How well he fulfilled the duties of that situation, the worthy trustees of that institution can testify. About three years ago, on account of Mrs. Youle's very serious indisposition totally incapacitating her for the domestic part of the business of the institution, he resigned the situation, and took the academy in West-Street, the irksome duties of which he faithfully discharged till within a few days of his sudden dissolution. The intensity of the heat the 3rd of this month had induced him to keep the windows of his school-room open during the whole day, by which he took a violent cold, that terminated in the jaundice and pleurisy. He died the 10th inst., aged 62 years.

As a mathematician Mr. Youle was extensively learned; and he gave proofs of his knowledge in the solutions to the questions in a variety of periodical publications, and particularly the Gentleman's Diary, for upwards of thirty years. He frequently contributed to different works under fictitious signatures. Many ingenious papers in different branches of Mathematical and Philosophical science were published by him in this manner. His "Arithmetic," which was sent into the world while he was at the charityschool, bears evident marks of a scientific mind. It was his object to apply science to useful purposes, and I dare venture to assert that whoever compares that work with any other which we have, will find in it excellences exclusively its own. The tract on magic squares is perhaps the best ever published on this curious, but neglected subject; and had his life been pro tracted a little longer we should have been favoured with it in a separate and more improved form.

As a man, he was virtuous; as a christian, pious; and as a teach er, luminous and impressive. His conversational talents were great, when the mathematics and philosophy were the subjects. He thought well on every subject, and his remarks were in general characteristic of a more than ordinary degree of intellectual energy. His proficiency in most branches of science rendered him an intelligent companion, and his accurate and spirited illustrations could not fail to make learning appear with advantage under every circumstance of life.

S.S.S.

Mathematical Repository.

SOLUTIONS TO THE QUERIES.

QUESTION 7. By Lysis.

Find an arc, such that the nth power of its sine multiplied into its cosine, shall be the greatest possible.

Solution, by Mr. J. Harker.

Put a sine, and/2=cosine; theo, per question, a' × √1:

Thus, also, it was answered by Messrs. Davies, Godward, and Wallace.

QUESTION 8. By Mr. J. C. Wallace, Sheffield.

A pole, six feet long, casts a shadow from a lamp on an horizontal plane: the height of the lamp is twelve feet, and the distance of its base from that of the pole is six feet; what angle does the pole make with the plane, its shadow being a maximum?

Solution, by Mr. T. S. Davies, Sheffield.

Under the conditions given in the question, the lamp-post will become a tangent to the circle whose radius is the length of the pole: now it is obvious that the shadow will be greatest when the rays from the lamp make a right angle with the extremity of the pole, or, which is the same thing, when they run in the direction of a tangent to the circle. It is farther well known that this tangent will be equal to the lamp-post, or tang. 63° 26′; and 180° 126° 52′ 53° 8' the angle required.

Other solutions were given by Messrs. Harker, Godward, and Wallace.

QUESTION 9. By Mr. J. C. Wallace, Sheffield.

In a plane inclined to the horizon at a given angle, to determine geometrically a point such that two straight lines being drawn from this point to two other points situated above the plane, and given in position, the times of descent down these lines may be equal.

Solution, by the Proposer.

Let AB be the given inclined plane, C, D the given points, join C,D which bisect by the perpendicular EF meeting the plane in F, and join EF. In EF, take any point G, from which draw GH perpendicular to the horizon meeting the plane in H; from centre G with radius GH describe a circular arc, cutting CF in K, then join GK, parallel to which draw CL, and let LM be demitted perpendicular to the horizon, and meeting the plane in quired.

A

E

K

M, which is the point re

Demonstration.-By similar triangles, CL GKLF: GF:: LM: GH, but KG = GH by construction; therefore CL LM. Hence a circle described from centre L with radius LM will pass through C and D, and the diameter at M is perpendicular to the horizon. Then, per Mechanics, bodies will fall down CM and DM in the same time.

It was also answered by Messrs. Davies and Harker.

Original Poetry.

TRANSLATIONS FROM PETRARCH.

SONNETTO CCXXIX.

ROTTA è l'alta colonna, e 'l verde lauro
Che facean ombra ál mio stánco pensiero :
Perdut' ho quel che ritrovar non spero

Dal Borea all' Austro, o dal mar Indo al Mauro.
Tolto m' hai, Morte, il mio doppio tesauro;

Che mi fea viver lieto, e gir altiero ;

E ristorar nol può terra, nè impero,
Ne gemme oriental, nè forza d' auro.
Ma se consentimento é di destino ;
Che poss' io più, se no aver l' alma trista,
Umidi gli occhi sempre, e 'l viso chino ?

O nostra vita, ch' é sì bella in vista,
Com' perde agevolmente in un mattino
Quel che 'n molt'anni a gràn pena s'acquista?

The lofty column and the laŭrel green,

Beneath whose shade, when tired, I oft reclined,

Are broken down-O melancholy scene!—

And will no more support or soothe my mind.
Death, thou hast robb'd me of that double store
That made me happy and that made me bold:
Ah! nothing can, what I have lost, restore,

Not earth nor empire, eastern gems por gold.
Since such my hapless fate, what can my soul

But weep her destiny for evermore?

My flowing tears will ever, ever roll

And from my gushing eyes the torrents pour.

How bright in prospect human life appears

And yet an hour destroys the fruit of anxious years !

SONNETTO CCXXXVIII.

Se lamentar uccelli, ó verdi fronde
Muover soavemente all' aura estiva,
Oroco mormorør di lucid' onde
'S' ode d' una fiorita e fresca riva :

Là ov'io seggia d'amor pensoso, è scriva ;
Lei che 'l Chiel ne mostro, terra n' àsconde,
Veggio, ed odo, ed intendo: ch' ancor viva
Di sì lontano a' sospir miei risponde.

Alta Colonna refers to Signior Stefano Colonna, a young friend of Petrarch, whom he had the mis fortune to lose a short time after the death of Laura, who is in this Sonnet beautifully denominated

'I Verde Lauro.

Deh perchè innanzi tempo ti consume ; Mi dice con pietate: a che pur versi Degli occhi tristi un doloroso fiume ?

Di me non pianger tu, che miei di fersi, Morendo, eterni; e nell' eterno lume, Quando mostrai di chiuder gli occhi, apersì.

Where the sweet birds indulge their plaintive song,
And the leaves whisper to the summer-breeze,
Where the bright waves flow murmuring along,
Upon a flow'ry bank, beneath the shady trees,
Pensive I sit, and pour my mournful strain.

There her whom now the earth hides from our eyes, I hear, I see, I know, from far, again,

Where living thus she answers to my sighs:
Ah! why with grief too soon thy life consume?
Why from thine eyes do ceaseless torrents pour?
Thy former smiles, thy look, thy voice resume,
Nor ever thus my destiny deplore:

My eyes, which seem'd to close in death's dark night,
Then open'd joyful in eternal light."