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we must own that we cannot account for his giving us, so often, a chronological history of ihe times when the books in which they are contained were written and publiMed; namely, twice in the paper before us, and once in the Preface to his Meditationes Analyticæ If it he really the case, we think the Professor might have spoken more plainly without any breach of modelly or decorum.
MECHANIC A L. Art. XII. Tentamen continens Theoriam Machinæ fublicarum -
An Essay containing the Theory of the Machine for driving Piles. By Thomas Bugge, Aftronomer Royal, and Professor of Astronomy and Mathematics in the Academy of Copenhagen, and Member of the Societies of Sciences at Copenhagen and Drontheim. Communicated by Sir John Pringle, Bart.
Our Author sets out with observing, that among the numerous advantages which civil society have derived from the knowledge of mechanics, the art of driving piles, that is, large oblong beams, into the earth, by repeated blows, is not the lealt. This art was not unknown to the ancients, as may be proved from many passages in Vitruvius : for although this celebrated author does not describe the machine by which they did it, yet their knowledge, in this respect, is placed beyond all doubt, seeing that without it, it would have been impoffible for them to have built bridges, moles, dams, bulwarks, pyramids, columns, and other edifices, the fize, majesty, firmness and durability of which we admire, but can scarcely imitate; and all these things require the most firm and solid foundations. If the foundation of a building is to be laid in a marshy place, large piles must be driven, by means of engines of this kind, to great depths, and the spaces between them filled up with great stones, gravel, sand, and mortar, before the foundation of that building can be laid.
The exact form of the machine by which the ancient; drove these piles is not now fufficiently known. Several forts have been described by Leopold, Desaguliers, and Belidor. But amongii all those, that which was invented by Vauloie, described by Dejaguliers, and brought into use while the foundation of Westmintterbridge was laying, has greatly the pre-eminence over all others. Its peculiar advantages are, that the weight, usually called the Ram, may be raised with the least force ;-that when it is raised to a proper height, it readily disengages itself and falls with the utmoft freedom ;-that the forceps are lowered down spcedily, and instantly, of themselves, again lay hold of the Ram, and lift it up: on which account this machine will drive the greatest number of piles, in the least time, and with the sewelt -14. bourers.
Mr. Bugge next proceeds to fhew that Belidor has entirely mistaken the theory of this machine, and then goes on to lay down and explain the true theory of it; in doing which he delivers the following principles :
ift, If the refiftance of the ground, and the masses of the piles, he equal, the depths to which they will be driven with a fingle blov will be as the product of the weight of the Ram into the height through which it falls.
2d, If the malles of the Ram and heights through which it falls are both equal, the depths to which the piles will be driven will be in the inverse ratios of the masses of the piles into the fuperficies of that part of them which is already immersed in the earth.
30, If all these things be unequal, the depths will be in a ratio compounded of the direct ratio of the heights through which the Ram falls into its mass, and the inverle ratio of the mals of the pile into its immerfed fuperficies.
4th, If the weights of the Ram be equal, and also the weights of the piles; the depths to which they will be driven will be as the heights through which the Ram falls directly, and the immerfed fuperficies of the piles inversely. Or, because the immerfed fuperficies of the piles are as the depths which they are already driven into the earth, the depths they will be driven are fimply as the square roots of the heights through which the Ram falls.
From these principles, which are in a manner felf-evident, our ingenious Mechanician determines, that the distance which a pile will be driven by each fucceeding blow will be less and less, as the fuperficies of that part of the pile which is immersed in the ground increases; contrary to what had been afferted by M. Belidor : and, consequently, that there is a certain depth, beyond which a pile of a given mass and scantling cannot be driven; the mass of the Ram and the height through which it falls at first being assigned. He also refutes the notion which had been entertained by some, that the driving of piles is facilitated by loading them with weights : for the depth to which a pile can be driven by any single blow (all other things remaining the fame) being inversely as its mars, it is manifest that thus loading the pile, and thereby increafing its mars, will be so far from accelerating its descent, that it will absolutely retard it. He concludes his paper with some very useful practical hints, and observations, relative to proportioning the several parts of the machine to one another, the number of men which ought to be employed, examining the ground, and the part of it where the first pile ought to be driven, so that the others may drive with the greatest ease possible.
Art. XIII. Dedication to the collettive Body of the People of England,
in which the Source of our present political Diftrations are pointed out, and a Plan proposed for their Remedy and Redress. By the Earl of Abingdon. 8vo. 1 s. 6d. Almon, &c. 1780. IS Lordship opens this Epistle Dedicatory with an ex
planation of the reason why his Thoughts (see Monthly Rev. vol. lvii. p. 249) are dedicated to the collective body of the people of England at this period of their publication, and not at first.
The public good, fays he, was my object: but whether I had made use of the proper means to that end, or no, was not for me to determine. So far indeed as my intentions went of their rectitude I was conscious: but how far I had succeeded in ability relted upon the judgment of others.
• To the judgment of others I appealed, and I called upon the Pablic, if I was wrong to set me right. I declared that • Truth being my only ohject herein, I should as readily look for it in others as seek it in myself;' and I have waited impatiently for the event : but notwithttanding five editions of these Thoughts have been had, and much time has since elapsed, to this very hour, not the colour of objection, nor the Madow of argumene have been opposed to them.
•These then are the circuindances under which this Dedication now makes its appearance to you. What diffidence had before with-held, acquired confidence hath since produced ; and as, on the one hand, if truth be with me, my reward will be in its use to you ; so, on the other, if error, my consolacion is, that I have been ever ready to retract it.
• But having said, that not the colour of objection, nor the shadow of argument have been opposed to these Thoughts ; I feel myself obliged to offer a few words in answer to one writer, who has been pleased to honour me with his public correspondence. This writer is a Mr. Cartwright, and who, in a Letter addressed to me t, bas, fupposing me wrong in a pofition that I have laid down, called upon me, with great propriety, for my juftification. I rejoice to meet such inquiries. They are the avenues to truth. And I am no less pleased with the inquirer. He has written like a gentleman, and whatis more than this, like an honest man: for, unlike those anonymous writers, whose fears are left the infamy of their names thould increale the infamy of their writings, he has affixed his name to what he has written. It is therefore matter of concern to me to find myself mis. taken by this writer : but my hopes are, that to remove his mistake will be equally fatisfactory to him, as to me.'
His Lordship then enters upon his vindication, and, as we think, fully proves that the error has arisen merely from a milconception of his expression, and that, in fact, with respect to
+ Vid. A Letter to the Earl of Abingdon difcuffing a position relative to a fundamental right of the Constitusion, &c. By John Cartwright. See Review, vol. lviii. p. 237. Rev. May 1780
the matter in dispute he and Mr. Cartwright are both of the same opinion. He then proceeds to the discussion of another point; namely, the nature of allegiance; on the due solution of which, as his Lordship observes, the moft important conftitutional doctrine hangs. On this subject his Lordship reasons with fingular acuteness and ingenuity. In the course of his argument he examines the maxim that the King can do no wrong ; in illustration of which doctrine Sir William Blackstone lays it down, that the King is not only incapable of doing wrong, but even of thinking wrong: he can never mean to do an improper thing: in him is no folly or weakness.
. But let us see, says this spirited writer, how this Westminsterhall inference (for it is called a legal maxim) and its commenc agree with the Constitution, with nature, with reason, with common sense, with experience, with fact, with precedent, and with Sir William Blacknone bimself; and whether, by the application of these rules of evidence thereto, it will not be found, that (from the want of attention, as I have taken notice of before, to that important line of distincion which the Conftitution has drawn between the King of England, and the Crown of England) what was attributed to the monarchy has not been given to the monarch, what meant for the kingship conveyed to the King, what designed for the thing transferred to the person, what intended for theory applied to practice; and so in consequence that whilst the premisies of the perfection of the monarchy) be true, the conclusion (that the King can do no wrong) be not false
• And for in reference to the Constitution: to which if this matter be applied (meaning what it expresses, and if it do not it is unwosthy of notice) it is fubversive of a principle in the Constitution, upon which the preservation of the Constitution depends; I mean the principle of resistance: a principle which, whilst no man will now venture to gainsay, Sir William Blackstone himself admits, 'is juftifable 10 the person of the Prince when the being of the State is endan. gered, and the public voice proclaims such relittance necessary;" and thus, by such admillion, both disproves the maxim, and oversets bis own comment thereupon : for to say that “ the King can do no wrong,” and that “he is incapable even of thinking wrong," and then to admit that “ sesistance to his person is justifiable,” are such jarring contradictions in themselves, that until reconciled, the necesfity of argument is suspended t.
With respect then, in the next place, to the agreement of this maxim and is comment with nature, with reason, and with common sense, I should have thought myself sufficiently justified in appealing to every man's own reflection for decision, if I had not been made to understand that nature, season, and common sense had had nothing to do with either. Sir William Blackitone says, “ That though a philosophical mind will consider the royal person merely as one man How easily does the worship of the divinity deg
ate into a worthip of the idol?' Vid. Hume's Essays, p. 40. i Vid, Blackstone's Comm, . I. p. 251.
appointed by mutual consent to preside over others, and will pay him that reverence and duty which the principles of society demand, yet the mass of mankind will be apt to grow insolent and refractory if taught to confider their Prince as a man of no greater perfection than themselves ; and therefore the law ascribes to the King, in his high political character, certain attributes of a great and transcendent nature, by which the people are led to consider him in the light of a Juperior being, and to pay him that awful respect which may enable him with greater ease to carry on the business of Government.” So that, in order to govern with greater ease. (which by the bye is mere affertion without any proof) it is necessary to deceive the mass of mankind, by making them believe, not only what a philosophical mind cannot believe, but what it is impoflible for any mind to believe; and therefore in the investigation of this subject, according to Sir William, neither nature, reason, nor common sense can bave any concern.
• li remains to examine in how much this maxim and its comment agree with experience, with fact, with precedent, and with Sir William Blacktione himself, And here it is inatter of most curious speculation, to observe a maxim laid down, and which is intended for a rule of government, not only without a single case in support of it, but with a string of cases that may be carried back to Egbert the first monarch of England, in direct opposition to the doctrine. Who is the man, that reading the past history of this country, will thew us any King that has done no wrong? Who is the Reader that will not find, that all the wrongs and injuries which the free Constitution of this country has hitherto suffered, have been solely. derived from the arbitrary measures of our Kings ? And yet the mass of mankind are to look upon the King, as a superior being; and the maxim that “the King can do no wrong," is to remain as an article of belief. But without puthing this inquiry any further, let us see what encouragement Sir Williain Blackfone himself has given us, for our credulity. After itating the maxim, and presenting us with a most lively picture, “ of our sovereign Lord thus all perfect and immortal," what does he make this all-perfection and immortality in the end to come to *? His words are these : “ For when King Charles's deluded brother attempted to enslave the nation,” (no wrong this, 10 be jure) “ he found it was beyond his power: the people both COULD, and did relitt nim: and in consequence of such reliance obliged him, to quit his enterprize and his throne together t.”
The sum of all is this : that the Crown of England and the King of England are distinguishable, and not tynonimous terme: thác allegiance is due to the Crown, and through the Crown to the King : that the attributes of the Crown are sovereignty, perfection, and perpetuicy; but that it does not therefore follow, “ that she King can do no wrong.” It is indeed to be admitted, that in high respect for the Crown, high respect is also due to the wearer of that Crown; that is, to the King: but the Crown is to be preferred to the King,
* Vide Blackstone's Comm, v. 1. P. 290. | Id. v. 4. p. 433•