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 241 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 enquiry 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 inconveniences 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 contrariety 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, shewing the variation at all times and places for the whole revolution of the magnetic 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 BLACK-FRIARS BRIDGE.

IN THREE LETTERS, TO THE PRINTER OF THE GAZETTEER.

SIR,

LETTER I.

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 Black-Friars, 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 unaccustomed investigations. We shall therefore attempt to shew 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 low

er.

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 little; and that as the arch is more curved, its strength is increased.

Having thus evinced the superiour strength of the semicircular arch, we have sufficiently proved, that it ought to be preferred; but to leave no objection unprevented, we think it proper likewise to observe, that the elliptical arch must always appear to want elevation and dignity; and that if beauty be to be determined by suffrages, the elliptical arch will have little to boast, since the only bridge of that kind has now stood two hundred years without imitation.

If in opposition to these arguments, and in defiance at once of right reason and general authority, the elliptical arch should at last be chosen, what will the world believe, than that some other motive than reason influenced the determination? And some degree of partiality cannot but be suspected by him, who has been told that one of the judges appointed to decide this question, is Mr. M―ll—r, who having by ignorance, or thoughtlessness, already preferred the elliptical arch, will probably think himself obliged to maintain his own judgment, though his opinion will avail but little with the publick, when it is known that Mr. S-ps-n declares it to be false.

He that in the list of the committee chosen for the superintendency of the bridge, reads many of the most illustrious names of this great city, will hope that the greater number will have more reverence for the opinion of posterity, than to disgrace themselves, and the metropolis of the kingdom, in compliance with any man, who, instead of voting, aspires to dictate,