Yet upon this secret property of magnetism I ventured to build my hopes of ascertaining the longitude at sea. I found it undeniably certain that the needle varies its direction in a course eastward or westward between any assignable parallels of latitude: and, supposing nature to be in this, as in all other operations, uniform and consistent, I doubted not but the variation proceeded in some established method, though, perhaps, too abstruse and complicated for human comprehension.
This difficulty, however, was to be encountered; and by close and steady perseverance of attention I at last subdued, or thought myself to have subdued it: having formed a regular system in which all the phenomena seemed to be reconciled; and, being able, from the variation in places where it is known, to trace it to those where it is unknown; or from the past to predict the future; and, consequently, knowing the latitude and variation, to assign the true longitude of any place.
With this system I came to London, where, having laid my proposals before a number of ingenious gentlemen, it was agreed that during the time required to the completion of my experiments, I should be supported by a joint subscription to be repaid out of the reward, to which they concluded me entitled. Among the subscribers, was Mr. Rowley, the memorable constructor of the orrery; and among my favourers was the lord Piesley, a title not unknown among magnetical philosophers. I frequently showed, upon a globe of brass, experiments by which my system was confirmed, at the house of Mr. Rowley, where the learned and curious of that time generally assembled.
At this time great expectations were raised by Mr. Whiston, of ascertaining the longitude by the inclination of the needle, which he supposed to increase or diminish regularly. With this learned man I had many conferences, in which I endeavoured to evince what he has at last confessed in the narrative of his life, the uncertainty and inefficacy of his method.
About the year 1729, my subscribers explained my pretensions to the lords of the Admiralty, and the lord Torrington declared my claim just to the reward assigned, in the last clause of the act, to those who should make discoveries conducive to the perfection of the art of sailing. This he pressed with so much warmth, that the commissioners agreed to lay my tables before Sir Isaac Newton, who excused himself, by reason of his age, from a regular examination: but when he was informed that I held the variation at London to be still increasing; which he and the other philosophers, his pupils, thought to be then stationary, and on the point of regression, he declared that he believed my system visionary. I did not much murmur to be for a time overborne by that mighty name, even when I believed that the name only was against me: and I have lived till I am able to produce, in my favour, the testimony of time, the inflexible enemy of false hypotheses; the only testimony which it becomes human understanding to oppose to the authority of Newton.
My notions have, indeed, been since treated with equal superciliousness by those who have not the same title to confidence of decision; men who, though, perhaps, very learned in their own studies, have had little acquaintance with mine. Yet even this may be borne far better than the petulance of boys, whom I have seen shoot up into philosophers by experiments which I have long since made and neglected, and by improvements which I have so long transferred into my ordinary practice, that I cannot remember when I was without them.
When Sir Isaac Newton had declined the office assigned him, it was given to Mr. Molineux, one of the commissioners of the Admiralty, who engaged in it with no great inclination to favour me; but, however, thought one of the instruments, which, to confirm my own opinion, and to confute Mr. Whiston’s, I had exhibited to the Admiralty, so curious or useful, that he surreptitiously copied it on paper, and clandestinely endeavoured to have it imitated by a workman for his own use.
This treatment naturally produced remonstrances and altercations, which, indeed, did not continue long, for Mr. Molineux died soon afterwards; and my proposals were for a time forgotten.
I will not, however, accuse him of designing to condemn me, without a trial; for he demanded a portion of my tables to be tried in a voyage to America, which I then thought I had reason to refuse him, not yet knowing how 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 24-1/4 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 i
s 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 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, 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 unaccustomed 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 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, perhaps, without any claim to such superiority, either by greatness of birth, dignity of employment, extent of knowledge, or largeness of fortune.
LETTER II.
SIR, Dec. 8, 1759.
In questions of general concern, there is no law of government, or rule of decency, that forbids open examination and publick discussion. I shall, therefore, not betray, by a mean apology, that right which no man has power, and, I suppose, no wise man has desire to refuse me; but shall consider the letter published by you last Friday, in defence of Mr. M — — ‘s design for a new bridge.
Mr. M —— proposes elliptical arches. It has been objected, that elliptical arches are weak; and, therefore, improper for a bridge of commerce, in a country where greater weights are ordinarily carried by land, than, perhaps, in any other part of the world. That there is an elliptical bridge at Florence is allowed, but the objectors maintain, that its stability is so much doubted, that carts are not permitted to pass over it.
To this no answer is made, but that it was built for coaches; and if it had been built for carts, it would have been made stronger: thus all the controvertists agree, that the bridge is too weak for carts; and it is of little importance, whether carts are prohibited, because the bridge is weak, or whether the architect, knowing t
hat carts were prohibited, voluntarily constructed a weak bridge. The instability of the elliptical arch has been sufficiently proved by argument, and Ammanuti’s attempt has proved it by example.
The iron rail, whether gilt or varnished, appears to me unworthy of debate. I suppose every judicious eye will discern it to be minute and trifling, equally unfit to make a part of a great design, whatever be its colour. I shall only observe how little the writer understands his own positions, when he recommends it to be cast in whole pieces from pier to pier. That iron forged is stronger than iron cast, every smith can inform him; and if it be cast in large pieces, the fracture of a single bar must be repaired by a new piece.
The abrupt rise, which is feared from firm circular arches, may be easily prevented, by a little extension of the abutment at each end, which will take away the objection, and add almost nothing to the expense.
The whole of the argument in favour of Mr. M —— , is only, that there is an elliptical bridge at Florence, and an iron balustrade at Rome; the bridge is owned to be weak, and the iron balustrade we consider as mean, and are loath that our own country should unite two follies in a publick work.
The architrave of Perrault, which has been pompously produced, bears nothing but its entablature; and is so far from owing its support to the artful section of the stone, that it is held together by cramps of iron; to which I am afraid Mr. M —— must have recourse, if he persists in his ellipsis, or, to use the words of his vindicator, forms his arch of four segments of circles drawn from four different centres.
That Mr. M —— obtained the prize of the architecture at Rome, a few months ago, is willingly confessed; nor do his opponents doubt that he obtained it by deserving it. May he continue to obtain whatever he deserves; but let it not be presumed that a prize granted at Rome, implies an irresistible degree of skill. The competition is only between boys, and the prize, given to excite laudable industry, not to reward consummate excellence. Nor will the suffrage of the Romans much advance any name among those who know, what no man of science will deny, that architecture has, for some time, degenerated at Rome to the lowest state, and that the pantheon is now deformed by petty decorations.
Complete Works of Samuel Johnson Page 329