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difficult it was to obtain, on any terms, an actual examination.

About this time the theory of Dr. Halley was the chief subject of mathematical conversation; and though I could not but consider him as too much a rival to be appealed to as a judge, yet his reputation determined me to solicit his acquaintance and hazard his opinion. I was introduced to him by Mr. Lowthorp and Dr. Desaguliers, and put my tables into his hands; which, after having had them about twenty days under consideration, he returned in the presence of the learned Mr. Machin, and many other skilful men, with an entreaty that I would publish them speedily; for I should do infinite service to mankind.

It is one of the melancholy pleasures of an old man, to recollect the kindness of friends, whose kindness he shall experience no more. I have now none left to favour my studies; and, therefore, naturally turn my thoughts on those by whom I was favoured in better days: and I hope the vanity of age may be forgiven, when I declare that I can boast among my friends, almost every name of my time that is now remembered : and that, in that great period of mathematical competition, scarce any man failed to appear as my defender, who did not appear as my antagonist.

By these friends I was encouraged to exhibit to the Royal Society, an ocular proof of the reasonableness of my theory by a sphere of iron, on which a small compass moved in various directions, exhibiting no imperfect system of magnetical attraction. The experiment was shown by Mr. Hawkesbee, and the explanation, with which it was accompanied, was read by Dr. Mortimer. I received the thanks of the society; and was solicited to reposit my theory, properly sealed and attested, among their archives, for the information of posterity. I am informed, that this whole transaction is recorded in their minutes.

After this I withdrew from publick notice, and applied myself wholly to the continuation of my experiments, the confirmation of my system, and the completion of my tables, with no other companion than Mr. Gray, who shared all my studies and amusements, and used to repay my communications of magnetism, with his discoveries in electricity. Thus I proceeded with incessant diligence; and, perhaps, in the zeal of inquiry, did not sufficiently reflect on the silent encroachments of time, or remember, that no man is in more danger of doing little, than he who flatters himself with abilities to do all. When I was forced out of my retirement, I came loaded with the infirmities of age, to struggle with the difficulties of a narrow fortune; cut off by the blindness of my daughter from the only assistance which I ever had ; deprived by time of my patron and friends; a kind of stranger in a new world, where curiosity is now diverted to other objects, and where, having no means of ingratiating my labours, I stand the single votary of an obsolete science, the scoff of puny pupils of puny philosophers.

In this state of dereliction and depression, I have bequeathed to posterity the following table ; which, if time shall verify my conjectures, will show that the variation was once known; and that mankind had once within their reach an easy method of discovering the longitude.

I will not, however, engage to maintain, that all my numbers are theoretically and minutely exact: I have not endeavoured at such degrees of accuracy as only distract inquiry without benefiting practice. The quantity of the variation has been settled partly by instruments, and partly by computation : instruments must always partake of the imperfection of the eyes and hands of those that make, and of those that use them: and computation, till it has been rectified by experiment, is always in danger of some omission in the premises, or some errour in the deduction.

It must be observed, in the use of this table, that though I name particular cities, for the sake of exciting attention, yet the tables are adjusted only to longitude and latitude. Thus when I predict that, at Prague, the variation will in the year 1800 be 244 W. I intend to say, that it will be such, if Prague be, as I have placed it, after the best geographers in longitude, 14 30. E. latitude 50 40'. but that this is its true situation I cannot be certain. The latitude of many places is unknown, and the longitude is known of very few, and even those who are unacquainted with science will be convinced that it is not easily to be found, when they are told how many degrees Dr. Halley, and the French mathematicians, place the cape of Good Hope distant from each other.

Those who would pursue this inquiry with philosophical nicety, must, likewise, procure better needles than those commonly in use. The needle, which, after long experience, I recommend to mariners, must be of pure steel, the spines and the cap of one piece, the whole length three inches, each spine containing four grains and a half of steel, and the cap thirteen grains and a half.

The common needles are so ill formed, or so unskilfully suspended, that they are affected by many causes besides magnetism ; and, among other inconveniencies, have given occasion to the idle dream of a horary variation.

I doubt not but particular places may produce exceptions to my system. There may be, in many parts of the earth, bodies which obstruct or intercept the general influence of magnetism ; but those interruptions do not infringe the theory. It is allowed, that water will run down a declivity, though sometimes a strong wind may force it upwards. It is granted, that the sun gives light at noon, though, in certain conjunctions, it may suffer an eclipse.

Those causes, whatever they are, that interrupt the course of the magnetical powers, are least likely to be found in the great ocean, when the earth, with all its minerals, is secluded from the compass by the vast body of uniform water. So that this method of finding the longitude, with a happy coutrariety to all others, is most easy and practicable at sea.

This method, therefore, I recommend to the study and prosecution of the sailor and philosopher; and the appendant specimen I exhibit to the candid examination of the maritime nations, as a specimen of a general table, showing the variation at all times and places for the whole revolution of the magnetick poles, which I have long ago begun, and, with just encouragement, should have long ago completed.

CONSIDERATIONS ON THE

PLANS OFFERED FOR THE CONSTRUCTION

OF BLACKFRIARS BRIDGE.

In three letters, to the printer of the Gazetteer.

LETTER I.

SIR,

Dec. 1, 1759. The plans which have been offered by different architects, of different reputation and abilities, for the construction of the bridge intended to be built at Blackfriars, are, by the rejection of the greater part, now reduced to a small number ; in which small number, three are supposed to be much superiour to the rest ; so that only three architects are now properly competitors for the honour of this great employment; by two of whom are proposed semicircular, and by the other elliptical arches.

The question is, therefore, whether an elliptical or semicircular arch is to be preferred ?

The first excellence of a bridge, built for commerce, over a large river, is strength; for a bridge which cannot stand, however beautiful, will boast its beauty but a little while : the stronger arch is, therefore, to be preferred, and much more to be preferred, if, with greater strength, it has greater beauty.

Those who are acquainted with the mathematical principles of architecture, are not many; and yet fewer are they who will, upon any single occasion, endure any laborious stretch of thought, or harass their minds with un

accustomed investigations. We shall, therefore, attempt to show the weakness of the elliptical arch, by arguments which appeal simply to common reason, and which will yet stand the test of geometrical examination.

All arches have a certain degree of weakness. No hollow building can be equally strong with a solid mass, of which every upper part presses perpendicularly upon the lower. Any weight laid upon the top of an arch, has a tendency to force that top into the vacuity below; and the arch, thus loaded on the top, stands only because the stones that form it, being wider in the upper than in the lower parts, that part that fills a wider space cannot fall through a space less wide ; but the force which, laid upon a flat, would press directly downwards, is dispersed each way in a lateral direction, as the parts of a beam are pushed out to the right and left by a wedge driven between them. In proportion as the stones are wider at the top than at the bottom, they can less easily be forced downwards, and, as their lateral surfaces tend more from the centre to each side, to so much more is the pressure directed laterally towards the piers, and so much less perpendicularly towards the vacuity.

Upon this plain principle the semicircular arch may be demonstrated to excel in strength the elliptical arch, which, approaching nearer to a straight line, must be constructed with stones whose diminution downwards is very little, and of which the pressure is almost perpendicular.

It has yet been sometimes asserted by hardy ignorance, that the elliptical arch is stronger than the semicircular ; or in other terms, that any mass is more strongly supported the less it rests upon the supporters. If the elliptical arch be equally strong with the semicircular; that is, if an arch, by approaching to a straight line, loses none of its stability, it will follow, that all arcuation is useless, and that the bridge may at last, without any inconvenience, consist of stone laid in straight lines from pillar to pillar. But if a straight line will bear no weight, which is evident at the first view, it is plain, likewise, that an ellipsis will bear very

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