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DR. LARDNER'S LECTURES ON MECHANICS.

269 but it is not the object of this science will be = f if 2=1, &c. This is the to investigate that cause-it is suffi

general law of gravity; and it is by cient for the knowledge of mechanics this law that the planets are kept that the effect is produced. Conse in their course round the sun. It quently, by “ attraction” is to be un

may be asked, what is the difference derstood that one body moves towards between this kind of attraction and another, and by repulsion that one any other species ? The difference is, body moves from or is repelled by the that the former is an universal proother; the language of effects and

perty, which the others a re not. not of causation being used.

The last rule applied only to Attraction is reduced into several

equal masses, but let us now suppose classes, each having peculiar or spe them to be unequal. Let A be one cific properties, as magnetic attrac

Fig. 2. tion, electric attraction, &c. all of

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OB 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.

mass, and B and C be two others, If two equal masses of matter be

each equal to A. Now they each placed near each other, and no force

exert the same degree of attraction as exerted to keep them in their places, A; but if they be incorporated, their they will move towards each other

effect is not changed, but the single and along a straight line supposed to

mass will then possess double the atjoin them, and they will meet at a

traction that is possessed by A: thus point equidistant between them.

the attractive power is increased in Thus let A and B be the two masses

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 in

versely as the square of the distance beyond the influence of all other between them. bodies; they will move along the It may be asked, why is not every straight line A B, and will meet at a thing attracted ? In fact, such is the point C, midway between the two. And this effect will ensue,

case, but in so small a de ree, as to be whatever

only perceptible to philosophical tests. the quality of the masses may be. To explain this, let A, B, and C be three But in what proportion will these

Fig. 3. consequences ensue? The force with which the two masses are found to

B 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 de bodies: now, if they be equal, they will crease in the same proportion as (or, all meet in the central point D. But what is the same thing, will be in the suppose one of these bodies, c, be inverse proportion to the square of

Fig. 4. the distance between them: therefore, as 1:2:: (42) 16 : }, which will be the force of attraction In the sam manner, if the distance be 3, the force

Fig. 1.

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

larger than the others, then the point

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270

DR. LARDNER'S LECTURES ON MECHANICS. D, at which they meet, is nearer that accurately known by astronomical body than the others. Again, let

means. Lastly, let EČ represent part Fig. 5.

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 D

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 \D

other side 0, and the distance found between a point m and the same star

But these two distances, when c

added together, were found to be DEF be an arch, representing the greater than an arch, MN, of the surface of the earth, of which the same number of degrees as the base, centre of attraction is C, and let A OF, of the mountain: the half of the and B be two bodies situated near the surplus then gives the variation from surface, it is evident that, from the the perpendicular, on account of the point at which they will meet (D) attraction of the mountain, which, in being so near the centre C, the two the above experiment, was found to 'bodies will have but little sensible be 9 seconds. motion towards each other.

There are some instances, however, There are some phenomena of this in which the earth seems to possess property which are, however, mani- properties exactly opposite to the last; fest. For instance, a weight being viz. it seems to repel some bodies, or suspended near a mountain from a to drive them away from its surface. fixed point, was found to be attracted A balloon, for instance, when filled by the mountain, and consequently with gas is found to rise, instead of to deviate from the perpendicular. being attracted towards the earth: This experiment was made on a this ascent is precisely analogous to mountain called Chimborazo, and that of a cork in water, and is, on acwas done in the following ingenious count of its being bulk for bulk, lighter Fig. 6.

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 reLet A OF B represent

sistance of the air, the velocity dethe surface of the earth, of which C

pending on the horizontal surface of is the centre, and of the base of a

the body, which may be proved thus mountain ODF.* Let e represent

-If a piece of metal be let drop from the position of a star in the arch of

any place at the same time, with a the heavens, the place of which is

feather or other light body, it is well

known that the metal will reach the The mountain is here drawn in a

ground considerably sooner than the much larger proportion to the earth

feather will; but if the experiment than it really is, but it shows the effect

be made in the exhausted receiver of in a greater degree.

an air-pump, they will both reach the

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ON DOME-VAULTING,

271 bottom at the same time: thereby in the two cases are of a nature toclearly proving that it is the resist tally different; yet many persons ance of the air which causes the reasoned from one case to the other, bodies to descend with different velo as though they were both alike. cities.

Residing in the country, as I do, it (To be continued.)

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 ON DOME-VAULTING, AND THE CON

the kind of inquiries occur to me, DOMÈ THE

which at other times I am anxious to ST. PAUL's.

make. My acquaintance with this crowning part of the structure is, therefore, incomplete. And, as I

meet with many persons who know 10

even less of it than I do, I have hoped that it would not be difficult to obtain more extensive and correct informa

tion both for them and myself through ki,

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 frustuni 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 augle 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 b

two bricks thick, and it has several chains or girdlings, some said to be of

iron, some of brick, and one of stone, Sir,—Although I am not an archi at uniform distances in its slant tect, as this letter will probably show, height. yet I have long taken a deep interest From the top of the larger conic in all that is connected with the frustum and the bottom of the brick theory and practice of architecture. frustum springs the inner cupola, I cannot but suspect that the theory which is open at top; the eye (as it is of the equilibrium of domes is very called) being surrounded with animperfectly understood, even by archi other gallery, which is at about twotects themselves (except a few who fifths of the vertical distance between are men of real science); and I was the stone-gallery, and that above the greatly strengthened in this suspicion exterior cupola usually denominated by the crude comparisons which were the golden-gallery. made some time ago, in many of our But how is this immense and cuperiodicals, between the walls of the riously-adjusted mass supported ? Brunswick Theatre and the brick By eight very massy pillars, which cone which supports the cupola of are not so arranged as to occupy the St. Paul's. The thrusts and pressures angles of an equilateral octagon, but

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272

ON DOME-V.SULTING, those of an octagon of four longer and 8. What are the dimensions of the four shorter sides: this octangular exterior cupola ? Is it a hemisphearrangement being in a certain sense roid, a conoid, or is its contour conhidden by the contrivance of throw stituted of portions of circular arches? ing the eight angles into the four sides 9. What are the principal excel(E. W. N. S.) of the central quad lencies in this central structure of rangle; while, however, it is easily St. Paul's ? detected by the semicircular tops of the 10. What are its chief defects ? eight vaults which pierce the cylinder Which of them were original misin which the octagon is inscribed. takes of Sir Christopher Wren; and

The preceding brief description which of them resulted from the inmay, perhaps, be rendered more in terference of the Commissioners, who, telligible by the aid of the prefixed as it is generally understood, sadly" outline sketch, which, though it has annoyed this great man in the prono pretension to accuracy, may serve gress of his splendid undertaking? for illustration.

Hoping that your Magazine will For the sake of more thoroughly soon be the vehicle of some instruccomprehending this interesting struc tive replies to the questions which I ture, I beg to propose the following have thus ventured to propose, questions to such of your readers as I am, Sir, yours, &c. 0.C. F. :are able, and will be so obliging as, to furnish the requisite information. CONDUCT OF THE NEW POLICE IN CASES 1. What is the diameter, bb, of the

OF FIRE. circle which bounds the octagon, and Sir,--Notwithstanding the numerous intima what are the sides of the octagon ?

tions of the impropriety of breaking open doors,

&c. to the lower parts of houses discovered to 2. Does the foundation of the dome

be on fire, our new watchmen appear not to merely occupy the bases of the eight have had any instructions on that subject ; for

in several recent instances we are informed, the piers or pillars ? Or, does it occupy first steps of the police-men was to "break open the entire ring in which those bases the doors."

Allow me here to mention a circumstance are placed ? Or, does it comprehend

which appears to hare escaped the notice of the the area of the whole circle bb?

gentleman who has spoken so much in praise of 3. What are the dimensions of a the cast-iron brestsuminers, recently introduced

in the Strand. In the event of fire, although horizontal section of each pier or pil these girders will not burn, yet they will become lar, and what is its height, bt, from heated, and the water beiug thrown upon there

in that state will cause them to crack ; in which the foundation to the springing of the

case there is no more security for the brick work, semicircular arches?

than if it had been supported by a wooden-beam. 4. What is the estimated weight of

I am, Sir, yours, &c.

J. S. Si the whole structure above tt? How much of that is supposed borne by

INTERIM NOTICES, each pier? And what is the average

We feel obliged to W. H. B. for the trouble

he has taken; but there are too many matters pressure in tons sustained by each of living interest claiming our attention, to square foot of horizontal section of a leave us at liberty to spare room for the torbs

either of Greek Emperors or Irish Kings. pier?

“One who has recently become a Subscriber" 5. What are the dimensions of the will obtain what he inquires about in Giltspur.

street, interior conic frustum, mnrq? What

The impression of the lithographic Engraving is the thickness, rp, gs? And what of the Steam Carriages given in our last nuinber. the angle of inclination, sng, with

having been exhausted, another edition has beep

published, executed also on stone, but in the the vertical plane ?

chalk manner, and on large paper. It will suit 6. Is the interior cupola, pov, he well for framing or portfolios. 'Price 18.

Communications received from D. Y, R. mispherical or not? What are its

A. W.-Mr. Murdoch-Mr. Cookes-Mr. Otty. dimensions ? And of what material will-Mr. Hayter---Mr. Horwood (3) - Mr. is it built?

Russel-J. R.-James C-A Constant Reader

-S. P. W.-Novice-J. O. B.-C. B7. What are the dimensions of the

Jn-s-Mr. Russel-Juvenis-Y.-Investigator brick conic frustum, Pguy? How -A Sincere Friend-Mr. Taylor-Mr. Badde

ley-Mr, Jopling. many bricks is it in thickness? How many girdlings or chains surround it?:

LONDON: Published for the Proprietor, by Are any of them mere iron chains ?

M. SALMON, at the Mechanics Magazine Are any of them of free-stone ? Where Ofice, No. 115, Fleet Street; where Coin mu and how are they placed, and what is

nications for the Editor (post paid) are re.

quested to be addressed. their precise use ?

M. SALMON, Printer, Fleet-street.

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