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DR. LARDNER'S LECTURES ON MECHANICS.

but it is not the object of this science to investigate that cause-it is sufficient for the knowledge of mechanics that the effect is produced. Consequently, by "attraction" is to be understood that one body moves towards another, and by repulsion that one body moves from or is repelled by the other; the language of effects and not of causation being used.

Attraction is reduced into several classes, each having peculiar or specific properties, as magnetic attraction, electric attraction, &c. all of which form the foundations of distinct sciences; but the only one now to be considered, is the attraction of gravitation, which is found to exist in every thing, whether solid, liquid, or gas.

The first thing to be considered, with regard to gravity, is its law; viz.

If two equal masses of matter be placed near each other, and no force exerted to keep them in their places, they will move towards each other and along a straight line supposed to join them, and they will meet at a point equidistant between them. Thus let A and B be the two masses Fig. 1. C

B

beyond the influence of all other bodies; they will move along the straight line A B, and will meet at a point C, midway between the two. And this effect will ensue, whatever the quality of the masses may be. But in what proportion will these consequences ensue? The force with which the two masses are found to attract each other, decreases in the same proportion* as the square of the distance between them. Let the distance be equal to 1, and let the force be equal to 2. Now, if the distance be increased to 4, the force will decrease in the same proportion as (or, what is the same thing, will be in the inverse proportion to) the square of the distance between them: therefore, as 1:2:: (42) 16, which will be the force of attraction. In the same manner, if the distance be 3, the force

* This proportion is the same both in magnetic and electric attraction.

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It

will be if 2=, &c. This is the
general law of gravity; and it is by
this law that the planets are kept
in their course round the sun.
may be asked, what is the difference
between this kind of attraction and
any other species? The difference is,
that the former is an universal pro-
perty, which the others are not.

The last rule applied only to
equal masses, but let us now suppose
them to be unequal. Let A be one
Fig. 2.
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AQ

mass, and B and C be two others, each equal to A. Now they each exert the same degree of attraction as A; but if they be incorporated, their effect is not changed, but the single mass will then possess double the attraction that is possessed by A: thus the attractive power is increased in the same proportion as the size.

The general rule is, therefore, that the force of gravity varies directly as the quantity of the masses, and inversely as the square of the distance between them.

It may be asked, why is not every thing attracted? In fact, such is the case, but in so small a de ree, as to be only perceptible to philosophical tests. To explain this, let A, B, and C be three Fig. 3.

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270

DR. LARDNER'S LECTURES ON MECHANICS.

D, at which they meet, is nearer that body than the others.

D

Fig. 5.

E

Again, let

F

DEF be an arch, representing the surface of the earth, of which the centre of attraction is C, and let A and B be two bodies situated near the surface, it is evident that, from the point at which they will meet (D) being so near the centre C, the two bodies will have but little sensible motion towards each other.

There are some phenomena of this property which are, however, manifest. For instance, a weight being suspended near a mountain from a fixed point, was found to be attracted by the mountain, and consequently to deviate from the perpendicular. This experiment was made on a mountain called Chimborazo, and was done in the following ingenious Fig. 6.

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accurately known by astronomical means. Lastly, let EC represent part of the equator, and P be the North Pole. The first experiment was made on the side F of the mountain, and the distance was found from the star e to n a place at which a line continued in the direction of the string by which the weight was suspended, would reach the arch MeN. The experiment was then repeated on the other side O, and the distance found between a point m and the same star

e.

But these two distances, when added together, were found to be greater than an arch, MN, of the same number of degrees as the base, OF, of the mountain: the half of the surplus then gives the variation from the perpendicular, on account of the attraction of the mountain, which, in the above experiment, was found to be 9 seconds.

There are some instances, however, in which the earth seems to possess properties exactly opposite to the last; viz. it seems to repel some bodies, or to drive them away from its surface. A balloon, for instance, when filled with gas is found to rise, instead of being attracted towards the earth: this ascent is precisely analogous to that of a cork in water, and is, on account of its being bulk for bulk, lighter than common air, as the latter is in the same way lighter than water. The attraction in gas may be proved by weighing it, as may also that of common air.

Gravity subsists not only in every mass, but also in every particle of a body. Let there be one particle of matter imagined which is attracted in a certain degree, now a second particle would receive an action independent of the first, and they would fall together. A heavy body falls with a greater velocity than one that is lighter: for, on account of the resistance of the air, the velocity depending on the horizontal surface of the body, which may be proved thus -If a piece of metal be let drop from any place at the same time, with a feather or other light body, it is well known that the metal will reach the ground considerably sooner than the feather will; but if the experiment be made in the exhausted receiver of an air-pump, they will both reach the

ON DOME-VAULTING,

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Sir,-Although I am not an architect, as this letter will probably show, yet I have long taken a deep interest in all that is connected with the theory and practice of architecture. I cannot but suspect that the theory of the equilibrium of domes is very imperfectly understood, even by architects themselves (except a few who are men of real science); and I was greatly strengthened in this suspicion by the crude comparisons which were made some time ago, in many of our periodicals, between the walls of the Brunswick Theatre and the brick cone which supports the cupola of St. Paul's. The thrusts and pressures

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in the two cases are of a nature totally different; yet many persons reasoned from one case to the other, as though they were both alike.

Residing in the country, as I do, it is only now and then that I can get a peep at the noble metropolitan church; and when I can, it is not always that the kind of inquiries occur to me, which at other times I am anxious to make. My acquaintance with this crowning part of the structure is, therefore, incomplete. And, as I meet with many persons who know even less of it than I do, I have hoped that it would not be difficult to obtain more extensive and correct information both for them and myself through the medium of your valuable Magazine.

The exterior dome rests, by means of a framing of wood-work, upon a brick conic frustum, which also carries upon its top an immense stone lantern, globe, and cross. This brick conic frustum does not, as is usually imagined, rest upon a cylinder, of 110 or 112 feet diameter, but upon a structure of columns and windows, or elegant open-work masonry, of which the exterior perimeter is cylindrical, and the interior peristyle is another conic frustum, making a less angle with the vertical cylinder than the superposed brick frustum, and extending nearly from the base of the whispering-gallery to that of the stone-gallery.

The brick frustum is, I believe, of two bricks thick, and it has several chains or girdlings, some said to be of iron, some of brick, and one of stone, at uniform distances in its slant height.

From the top of the larger conic frustum and the bottom of the brick frustum springs the inner cupola, which is open at top; the eye (as it is called) being surrounded with another gallery, which is at about twofifths of the vertical distance between the stone-gallery, and that above the exterior cupola usually denominated the golden-gallery.

But how is this immense and curiously-adjusted mass supported?

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By eight very massy pillars, which are not so arranged as to occupy the angles of an equilateral octagon, but

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those of an octagon of four longer and four shorter sides: this octangular arrangement being in a certain sense hidden by the contrivance of throw ing the eight angles into the four sides (E. W. N. S.) of the central quadrangle; while, however, it is easily detected by the semicircular tops of the eight vaults which pierce the cylinder in which the octagon is inscribed.

The preceding brief description may, perhaps, be rendered more intelligible by the aid of the prefixed outline sketch, which, though it has no pretension to accuracy, may serve for illustration.

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For the sake of more thoroughly comprehending this interesting structure, I beg to propose the following questions to such of your readers as are able, and will be so obliging as, to furnish the requisite information. $1. What is the diameter, bb, of the circle which bounds the octagon, and what are the sides of the octagon ?

2. Does the foundation of the dome merely occupy the bases of the eight piers or pillars? Or, does it occupy the entire ring in which those bases are placed? Or, does it comprehend the area of the whole circle bb?

3. What are the dimensions of a horizontal section of each pier or pillar, and what is its height, bt, from the foundation to the springing of the semicircular arches?

4. What is the estimated weight of the whole structure above tt? How much of that is supposed borne by each pier? And what is the average pressure in tons sustained by each foot of horizontal section of a

square pier?

5. What are the dimensions of the interior conic frustum, mnrq? What is the thickness, rp, gs? And what the angle of inclination, sng, with the vertical plane?

6. Is the interior cupola, pqv, hemispherical or not? What are its dimensions? And of what material is it built?

7. What are the dimensions of the brick conic frustum, pquy? How many bricks is it in thickness? How many girdlings or chains surround it? Are any of them mere iron chains? Are any of them of free-stone? Where and how are they placed, and what is their precise use?

8. What are the dimensions of the exterior cupola? Is it a hemispheroid, a conoid, or is its contour constituted of portions of circular arches?

9. What are the principal excellencies in this central structure of St. Paul's?

10. What are its chief defects? Which of them were original mistakes of Sir Christopher Wren; and which of them resulted from the interference of the Commissioners, who, as it is generally understood, sadly annoyed this great man in the progress of his splendid undertaking?

Hoping that your Magazine will soon be the vehicle of some instruc-" tive replies to the questions which I have thus ventured to propose,

I am, Sir, yours, &c. O. C. F.

CONDUCT OF THE NEW POLICE IN CASES

of FIRE.

Sir,-Notwithstanding the numerous intima tions of the impropriety of breaking open doors &c. to the lower parts of houses discovered to be on fire, our new watchmen appear not to have had any instructions on that subject; for in several recent instances we are informed, the first steps of the police-men was to "break open the doors."

Allow me here to mention a circumstance which appears to have escaped the notice of the gentleman who has spoken so much in praise of the cast-iron brestsuminers, recently introduced in the Strand. In the event of fire, although these girders will not burn, yet they will become heated, and the water being thrown upon then, in that state will cause them to crack; in which case there is no more security for the brickwork. than if it had been supported by a wooden-beam. I am, Sir, yours, &c. J. S. S.

INTERIM NOTICES.

We feel obliged to W. H. B. for the trouble he has taken; but there are too many matters of living interest claiming our attention, to leave us at liberty to spare room for the tombs either of Greek Emperors or Irish Kings.

"One who has recently become a Subscriber" will obtain what he inquires about in Giltspur. street.

The impression of the lithographic Engraving of the Steam Carriages given in our last number having been exhausted, another edition has been published, executed also on stone, but in the chalk manner, and on large paper. It will suit well for framing or portfolios. Price 18.

Communications received from D. Y. R.A. W.-Mr. Murdoch-Mr. Cookes-Mr. Otty. will-Mr. Hayter-Mr. Hopwood (3)-Mr. Russel-J. R.-James C-A Constant Reader -S. P. W.-Novice-J. O. B.-C. BJn-y-Mr. Russel-Juvenis-Y.-Investigator A Sincere Friend-Mr. Taylor-Mr. Baddeley-Mr. Jopling.

LONDON: Published for the Proprietor, by M. SALMON, at the Mechanics Magazine -* Office, No. 115, Fleet Street; where Commu nications for the Editor (post paid) are requested to be addressed.

M. SALMON, Printer, Fleet-street.

Mechanics' Magazine,

MUSEUM, REGISTER, JOURNAL, AND GAZETTE,

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