Let the triangle ABC be drawn, and suppose, for instance, we divide the side BC into two equal parts in the point D, then is BD equal CD; now draw DE parallel to AB, then, if we mechanically measure AE, we shall find it correspond to EC, or that AC is also divided into two equal parts in the point E.

Or, more geometrically, from B draw BF parallel to AC, and CF parallel to AB; then, if through D we draw DGH parallel to AC, we shall have the two triangles, CDH and BDE, identical, as the angle CHD is equal to the angle BGD, and the opposite sides are equal by construction; and also the angle CHD is equal to the angle BGD; and, of course, the third angle at C and B equal, they will correspond in all respects, or the remaining side will also be equal; hence GD equals GH, but DH equals HC, because of the parallels HD and CH to the lines EC and ED, and GD equals AE, for the same reason; hence AE equals EC; but BD equals DC, or the lines AB and BC are divided in

the same proportion, and this will hold good, whatever proportion the lines CD and DB bear to each other; for if we draw IK parallel to ED, so that CK equals, for instance, the quarter of CB, IC will be equal a quarter of CA, for CE equals half CD; and we have shown, that when CB is divided into two equal parts, CA is divided also into two equal parts; hence CI equals half CE, and, of course, equals a quarter of CA; that is, as CK: CB:: CI : CA; that is, the lines CB and CA are divided by the line IK in the same proportion, viz. as 1 to 4, which was to be shown.

COR. 1.-Hence, if we draw two or more lines parallel to the base of a triangle, it will divide the other two sides in the same proportion.

COR. 2.-Hence, also, any line drawn in a triangle parallel to the base, cuts off another triangle from the vertex, similar to the original triangle, for all the angles in the one are equal to all the corresponding angles of the other, and their sides proportional (by Def. 21, Part

1.); for the triangle ABC is similar to the triangle EDC or IKC, because the angles are all equal, and the sides have (by this proposition) been shown to be proportional.

COR. 3.-Hence, likewise, we see, that in similar triangles the sides that are opposite the angles that are equal to each other, are proportional to each other; that is, the side AC, in the triangle ABC, is to the side EC, in the triangle EDC, in the same proportion as the side BC, in the triangle ABC, is to the side CD, in the triangle EDC; that is, as AC; EC:: BC: CD.

(To be continued.)

G. A. S.

RISE OF QUICKSILVER IN THE
TORRICELLIAN TUBE.

SIR,-I will be much obliged to some of your numerous Correspondents to inform me, through the medium of the Mechanics' Magazine, if it be the fact, which I have met recorded in some scientific work, the name of which, and particulars of the case, I have now no recollection of, that quicksilver stands supported, in a Torricellian Tube, at times, as high as seventy inches. It is said to be only accidentally so, but the phenomenon cannot happen without a cause; and when it is recollected, that the barometer never ascends, from atmospheric pressure, to thirty-five inches (which one would suppose is the cause in both instances), I confess it puts my faith

in the recital to no small trial. Se

venty inches of quicksilver, giving seventy feet ascent of water, is what no pump-sinker ever obtained yet. Being anxious to investigate the subject, I have searched many philosophical works lately, but could meet nothing of the case; yet being strongly persuaded it is mentioned as having taken place, and, of course, is worthy investigation, I beg to solicit your publishing this my request, to be informed whether it is the fact, and on what principles it takes place,

AS MY LAST HOPE.

HEATING ROOMS.

349

SIR,-I have for some time been at great expense and inconvenience, from not being able to accomplish the heating a room with warm air (impartially) to a sufficient degree, and should feel greatly obliged if you would allow my inquiry a place in your useful Journal.

What is the best means of attaining one hundred degrees of Fahrenheit in a room of 12 feet square ?— I have tried the design given in your 49th Number, but find it insufficient to my purpose.

I should also be indebted, if Mr. Vallance would favour me with a more explicit explanation of his principle upon that subject. The system proposed in Number 35 does not procure the heat required. I am, Sir, Your obliged servant,

Brighton.

INQUIRIES.

D. C.

NO. 140.-GILDING OLD PICTURE

FRAMES.

SIR,-It would very greatly oblige me if any of your intelligent.readers would inform me of the mode of gilding old picture frames in oil gold-whether there is any method of varnishing them with gold varnish, so as to look well and stand? The great expense of frames in this rich of the pleasure of ornamenting country deprives those who are not their rooms with their own paintings or drawings, and consigns many a good old family picture to the garret, from the shabbiness of its frame. It has occurred to me that some of your ingenious Correspondents at Birmingham might make frames of metal, lackered as they do ornaments for chairs, tables, &c.: they would be durable, light, and cheap. Mouldings might be made of any convenient length, and various breadths and patterns, so as to be cut and jointed to any size wanted. Mould

NO. 142.

NOVACULA.

QUESTION IN TRIGONOMETRY.

SIR,-Standing on a plane with a Theodolite, required a method to determine the distance and elevation of a tower, or any similar perpendicular object, from one station, the horizontal distance of the object not exceeding five or six hundred feet.

I am, Sir,
Yours respectfully,
THOMAS HENRY BELL.

Alnwick.

NO. 143.-MACHINE FOR PRESSING STRAW BONNETS.

SIR,-Permit me, through the medium of your valuable Publication, to request one of your numerous and ingenious Correspondents to dedicate a small portion of time

to the service of a numerous class of the fair sex, in forming a cheap and useful machine for the purpose of pressing Straw Bonnets, which are at present done by a common iron

ing-box, by leaning with their whole weight upon their side, which is at all times a very hard and laborious employment, and often causes violent pains of the side, and sometimes produces more serious consequences. If some simple machine were invented, and a sketch inserted in your excellent Magazine, it would confer a lasting obligation upon a large portion of the fair, and ensure their eternal gratitude. I am, Sir,

Your humble servant,

M-ld-n.

W. C-R.

NO. 144.-MAKING LENSES.

SIR, A description is wanted of the best method of making Lens Glasses, the most simple and easiest plan of grinding them, together with the ingredients and instruments used in the whole process of forming a good magnifier.

I am, Sir, yours, &c.

D. J.

NO. 145.-WIND-LATHE. SIR,-Having a workshop in the. centre of a town, and in which I have a Lathe, which I wish to work by sails, on the principle of a windmill, but which must have the sails in a horizontal position, I wish to know how this would act; and will thank any of the contributors and Correspondents to your Magazine to favour me, through its medium, with a plan or description of this sort of wind-engine. I should wish the description to state how many arms there should be, and whether every other arm should dip or not, to catch the wind better. Any other information on the subject, either derived from personal experience, or from books, or otherwise, will be very acceptable, as I never saw a movement of this description.

I remain, Sir,
Your very obedient servant,
E. B.
Cabinet-maker.

Skipton, near Craven.

NO. 146.-BORING FOR COAL. SIR-The present very high price of fuel is severely felt by manufacturers consuming quantities of Coal for the purpose of steam-engines, and the extra demand, arising from the manufacture of gas, makes it probable, that unless some means are used to increase the quantity brought to market, there will still be a further increase upon the price of that important material.

In order to effect this desirable object, would it not be a study worthy some practical men, to endeavour to adopt some means of ascertaining where coal may be found?

The present plan of boring appears to have received very little of that attention so evident in other pursuits, although its vast importance so much requires it.

With the exception of a plan proposed in your valuable Miscellany, a few weeks ago, for procuring water, I do not recollect seeing any thing noticed upon the subject. Could there not be an instrument invented, of the form of a tube, with teeth on the bottomedge, and springs inside, that would secure the core when charged with it, and show the strata through which it has per

forated?

If something of the kind he found that would operate to the depth of 130 yards, I know a person who would at once have an experiment tried to prove an estate, where there is very little doubt of coal; but, from the old expensive and ineffectual method of boring, has been deterred from the attempt.

An answer from any of your Correspondents who can accomplish the object, would oblige,

A constant reader,

Z.

P.S. There is a shaft, 30 yards deep, before the water is found, on the estate.

351

ANSWERS TO INQUIRIES,

NO. 134. STUCCO IMAGES.

SIR, I intended to have replied to Aurum's first inquiry, but forgot the circumstance until reminded of ber. If he will wash the figures it by his letter in a late Numin a strong solution of alum, 1 think his expectations will be fully answered. I had the information

from a friend (a modeller) who always makes use of it for that its effects were but little known. purpose, and I also understood that The figures, when dry, appeared to have acquired considerable hardness on the surface, and seemed capable (when rubbed) of taking a pretty good polish. I should conceive, therefore, that a varnish might afterwards be applied, without sinking, in the manner described by Aurum. I remain, Sir, Your obedient servant, X. M. N. R.

Old Change, August 23, 1825. P.S. Your readers might probably wish to know how far it answers his wishes.

made use of alum for the purpose A friend informs us, that he has with great success, but in a manner somewhat different from that suggested in the preceding letter. He immersed the images in a strong solution of alum, which he put on the fire for four hours, and then set to cool. On taking out the images, they had acquired all the appearance, and, in some degree, the consistency of alabaster. The images must not, however, be hollow, like those usually sold by the Italian boys; but either cast entire or filled up, in the manner, perhaps, suggested in the following communication.-EDIT.

SIR,-Permit me to inform Aurum, that my plumber has had for the last five years a figure of Neptune, and others, in his shop,which

I always took for leaden figures; but, one day, the base of one of them having a bit broken off, and it leaving a white mark behind, on inquiry, I found they were plaster figures painted, and once a week thoroughly cleaned with a black lead brush, which gave them this leaden appearance. To prevent their breaking, I would advise Aurum, as soon as he buys a figure, to get some chalk or plaster, and make a thick mess of it; then place the figure on its head, fill it with the mess, and let it stand so till it dries up in the figure.

I am, Sir, with due respect,
CLIO.

SIR, I am happy to have it in my power to supply the "further explanation desired," on the Varnish for Plaster of Paris Figures. The proportions are as follow:Of white soap and white wax each half an ounce, of water two pints; boil them together for a short time in a clear vessel. The varnish is to be applied, when cold, by means of a soft brush-an old shavingbrush will answer the purpose very well. I have not tried the prócesses recommended in your last by W. Tatner, but I am inclined to think that, besides the additional trouble and expense, neither of them is as likely to answer as that which I have supplied.

I cannot withhold from expressing the great satisfaction which I have experienced in witnessing the success which attends your work; and I am particularly gratified with the increasing and combined efforts of all classes to promote the improvement of the labouring population.

I am, Sir,

Your faithful coadjutor,

WM. JOHNS, M.D. F.L.S.

CORRESPONDENCE.

In the 4th Number of the Mechanics' Magazine, there is a description of a Double Door Spring, invented by "Mr.

James White, of Laystall-street." A Correspondent says, that, up to this time, he has not been able to find ont where the article is to be met with. About last September, a friend, whom he requested to procure one, traversed Laystall-street from end to end, without being able to find such a person as Mr. White, or any place where such an article was to be sold. He farther inquired of a carpenter, who was at work in the street, and who said it was not the first time he had been asked the same question, which he could not satisfactorily answer. He therefore requests to know where Mr. White's door-springs are to be procured?

P. M. O. would feel obliged to G. Brown, if he will say where the BugDestroying Machine (described in Number 92, p. 123) is to be purchased, or who made his for him? He has shown the drawing to a tinman in his neighbourhood, but he will not make it for twice the sum G. B. says he paid for his.

We shall endeavour shortly to gratify Mr. K. and friends, by a description of the Machine alluded to. An account of Mr. K.'s new Picking Machine will be acceptable.

J. N. says, he "cannot resist an inclination to trouble our readers with some ideas on the neglect of Cosmogony." We are sorry we cannot give him leave so to trespass on their attention.

Sir Sydney Smith's Six-wheeled Carriage in our next.

Communications received from-An Old Sailor-R. S. S.-H. M.-D. W.G. M. E.-Amicus-A Learner-Tyro— J. G. C.-William Grant-An Original Subscriber-Thomas Martin--M. M. (Wilts)-M. M. (Edinburgh)—" A Few Inquirers at Leeds"-U. T.—L, S.

T. M. B. will find a letter for him at our publishers on Monday.

Advertisements for the Covers of the Monthly Parts must be sent to the Publishers before the 20th of each Month.

Communications (post paid) to be addressed to the Editor, at the Publishers', KNIGHT and LACEY, 55, Paternoster-row, London. Printed by Mills, Jowett, and Mills (late Bensley), Bolt-court, Fleet-street.