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Thus, for the first time, after having been an occasional object of research for more than 150 years, has the centre of oscillation of a compound pendulum been found by experiment alone, according to a inethod also of universal application, and admitting of mathematical precision. The ingenious author bas therefore the honour of giving the first solution of a problem, extremely curious and interesting in itself, independently of its immediate connexion with one of the greatest and most important questions in the natural history of the Earth.
The next thing to be done, was to measure the length of the pendulum, or the distance between the knife edges, which bad alternately served as the centres of suspension and oscillation, and from thence to deduce the length of the pendulum vibrating seconds in the latitude of London, which, at the spot (Mr. Browne's house in Portland Place) where the observations were made, is 51° 31' 8".4. It is sufficient here to state, that no expedient has been neglected that practical or theoretical science is at present in possession of, for giving precision to this measurement, and that it was in all respects such as to correspond to the accuracy of which we have just seen so striking an example. Including the effects of temperature, of the buoyancy of the atmosphere, of the shortening of the arcs of vibration from the beginning to the end of each trial, and reducing the actual vibrations to those in arcs infinitely small, the length of the seconds pendulum, from a mean of the 12 sets of experiments above mentioned, comes out 39.13829 inches, or 39.1386, reducing it to the level of the sea.a The greatest difference between this result and any one of the 12 of which it is a mean, is .00028 of an inch; that is, less than three of the ten thousandth parts. The mean difference among these results, adding the positive and negative together, as if they had all one sign, or were all on the same side, is little more than one ten thousandth of an inch; and as the above is obviously a supposition more unfavourable than ought
a The scale on which this pendulum is measured, is Sir George Shuckburgh's, the work of Troughton, and of the highest authority. It is described by Sir George in the Phil. Trans. for 1798. Gen. Roy's scale, which is very important, as being that from which are derived all the measurements in the trigonometric survey, was compared with the preceding by Captain KATER. So also was the yard on what is called the parliamentary standard, which was laid off by Bird, but it would seem not so carefully as might have been expected. The scales in the order in which they are now named, appear from these measures to be as the numbers 1 ;.99963464; 1.00000444.
In another communication from Captain Kater, in the same volume of the Phil. Trans. the length of the French metre is compared with the yard on Sir G. Shuckburgh's scale. He found the metre as marked by two very fine lines on a bar of platina 39.37076 inches on his scale; as marked by the ends of a metal rod in the usual way, the metre 39.37081. Supposing the two of equal authority, the mean length of the metre is 84.87074 inches. The temp. of the scale 62" of Fahr.
to be made, we think the probability is very great that the preceding result does not err so much as a unit in the last decimal place, or in that which denotes ten thousandths of an inch.
The determination given above is considerably different from that which had been received on the authority of the older experiments. The length given to the seconds pendulum, in the bill for the equalization of weights and measures, is 39.13047, differing from that just assigned by .00813; a considerable quantity, in a matter where it appears that a ten thousandth of an inch is a distinguishable magnitude.
To the paper which ends with the measures just given is added, in an Appendix, a letter from Dr. THOMAS YOUNG, containing a demonstration of a very remarkable property of the pendulum recently discovered by M. LAPLACE. The property is, that if the supports of a pendulum, inverted as above described, be two cylindric surfaces, the length of the pendulum is truly measured by the distance of those surfaces. This applies immediately to the experiments we have been considering; because the knife edges, supposing them somewhat blunted, may be regarded as cylindric surfaces of very great curvature, or of very small diameter; and in this way, as Dr. Young very justly remarks, is removed the only doubt that can reasonably be entertained of the extreme accuracy of the conclusions. The theory of experiments made with the inverted pendulum, is therefore much indebted to the calculus of the profound mathematician above named. We have not seen his analysis ; but a demonstration is sketched by Dr. Young, that seems sufficiently concise and simple, considering the recondite nature of the truth to be demonstrated.
Art. III. An Account of Experiments for determining the Variation
in the Length of the Penduluin vibrating Seconds at the principal Stations of the Trigonometrical Survey of Great Britain. By Captain H. KATER, F.R. S. From Pbil. Transactions. London, 1819. Part. III. (Review-Nov. 1820.]
We have now to direct the attention of our readers to a more extended investigation of the same careful observer, by which he has ascertained the length of a Seconds Pendulum, at the principal stations of the great survey of this Island.
It may be recollected, that this inquiry originated in a bill submitted to Parliament, for the general regulation of Weights and Measures, and fortunately thrown out in the House of Lords. We say fortunately,-because those who most readily admit the expediency of adopting some uniform system, will naturally be the first to reject a plan so crude and so ill calculated to attain that desirable object. One good, however, resulted from the discussion; an address was presented to the Crown, praying
416 Edinburgh Review on the Length of the Pendulum.
that instructions might be given for determining the length of a Seconds Pendulum in the latitude of London, as compared with the standard made for the House of Commons in 1758, known by the name of Bird's Parliamentary Standard—for ascertaining the variations in the length of the Pendulum at the different stations, and for comparing the standard measures with the ten millionth part of the quadrant of the meridian, the basis of linear measure in France. In order to carry this purpose into effect, a Committee was appointed by the Royal Society; and Captain Kater, a Member of it, was desired to conduct the inquiry. The choice has been amply justified by the success which has attended his labours.
[We regret that we have not room for the detail given of the experiments made at one of the Shetland Isles—the first station.]
On the 23d of July, 1818, he began to observe the coincidences of his two pendulums; and he found from two series of experiments, each of ten intervals, taken on each day, the mean number of vibrations in 24 hours, the temperature being corrected for 62°. The number of vibrations for each day of the intervals, was deduced from the rate of the clock, during the observed interval; results were obtained for seven different intervals, the greatest of which was from the 22d to the 28th of July—the least from the 26th to the 28th. Before employing those seven results to obtain a mean, he attended to the correction of errors.... The chief source of error arises from the position of the transit instrument with respect to the meridian mark : &c.... The next correction is the allowance for the height of the station above the level of the sea. This is readily obtained from the consideration that the force of gravity varies inversely as the squares of the distance from the Earth's centre; and this force is represented by the square of the number of vibrations of the pendulum. [Here a mistake of Capt. Kater is referred to, in drawing an erroneous conclusion from the statement of Dr. Young, in the Phil. Trans., relative to the effect produced by the attraction of the elevated part lying between the general surface and the place of observation.]....Another equation of error is for the buoyancy of the atmosphere.
The following Table exhibits the results of his observations at all the stations, the experiments being the same at each. They were concluded at the Isle of Wight, on the 16th of May, 1819.
Length of the Pendulum vibrating Seconds, in parts
of Sir G. Shuckburgh's scale. Unst
60° 45' 28".01 86096.90 39.17146 inches Portsoy
39.16159 Leith Fort
55 58 40 .80 86079.40 39,15554 Clifton
53 27 43.12 86068.90 39.14600 Arbury Hill
52 12 55 .32 86065.05 S9.14250 London
51 31 8.40 86061.52 39.13929 Shanklin Farm
Place of Observation.
57 40 58.65
50 87 23.94
Art. IV. Posthumous Works, in Prose and Verse, written in the
time of the Civil Wars, and Reign of K. Charles II. by MR. Samuel BUTLER, Author of Hudibras ; from original MSS. and scarce and valuable pieces formerly printed
: with a Key to Hudibras, by Sir Roger L'Estrange. In three Volumes. The
sixth Edition ; with Cuts. London, 1720. The Genuine Remains, in Prose and Verse, of MR. SAMUEL
BUTLER, Author of Hudibras. Published from the original MSS. formerly in the possession of W. Longueville, Esq. ; with Notes by R. Thyer, Keeper of the Public Library at Manchester. In two Volumes. London, 1759.
The Hudibras of Butler, like the fabled Arabian bird, is in itself a species : it had no precursor, and its imitators are forgotten. With all the disadvantages of a temporary subject, obsolete characters, and "a conclusion in which nothing is concluded,” it continues to be the delight of the few, and the text-book of the many: its couplets have passed into proverbs—the names of its heroes are “ faipiliar in our mouths as household words." With the exception of Shakspeare, there is, perhaps, no author whose expressions are so inextricably intertwined with our every day discourse, and whose writings afford such an inexhaustible variety of apothegms of universal and apposite application; yet there is no author, enjoying any considerable share of popularity, who is so imperfectly understood and appreciated. How many of the readers of Hudibras take it up with the same feelings with which they peruse the Scarronides, and the Homer Burlesqued? They find, it is true, the adventures ludicrous and the characters grotesque-but' then the speeches are long-winded, and, what is worse, they'require some attention to comprehend them. When, by dint of reconnoitring and skipping, they have reached the political canto, where the story gives them the slip, they lay down the book, and forget to take it up again. Of those who look more deeply into the work, and whose attention is not confined to the quaintness of the style, and the eccentricity of the rhymes, how many are contented to contemplate the brilliancy of Butler's wit, through the dusky medium of notes, or to found their admiration of it on “ men's opinion and the world's report.” The reader of Hudibras should not only be familiar with the history, the politics, and the religion, of the eventful period in which its author lived, but with its fashions, its feelings, its science, its follies, its literature, its superstitions. To enjoy it with a true and perfect relish, he should have sung catches in a tavern with a knot of jovial cavaliers-been compressed and stifled in a crowd of Vol II.
sturdy puritans, in a conventicle-deafened by the extempore eloquence of Dr. Burgess and Hugh Peters-been bewildered in the mazes of scholastic divinity with Aquinas and Duns Scotus -had his fortune told by Booker or Lilly-tried experiments with Sir Paul Neale-cross-examined the moon with the Royal Society—“ seen countries far and near” with “ Le Blanc the Traveller”-sympathized with Sir Kenelm Digby-yawned over the romantic tomes of Calprenede and Scuderi-been witty upon Gondibert—and deep in Cervantes and Coke upon Littleion.a
It is a common error among "the great vulgar and the small” to look upon Hudibras as extremely low-in fact, as a mere burlesque. It is as much above the common cry" of burlesque, as the novels of Fielding and the author of Waverley are above the ephemeral trash of the Minerva Press. It is a mighty and comprehensive satire—as powerful in argument-as just in sentiment—as rich in illustration, as any that united wit and learning have ever produced. All the weapons of controversial warfare-invective, irony, sarcasm, and ridicule--are alternately and successfully wielded. The most opposite and conflicting absurdities—the excrescences of learning and the bigotry of ignorance
—“time-honoured" prejudices and follies of recent growth or importation-are laid prostrate “at one fell swoop.” Butler makes none but “ palpable bits.” His sentences have the pithy brevity of a proverb, with the sting of an epigram. His subject was local and transitory—bis satire boundless and eternal. His greatest fault is profusion-he revels and runs riot in the prodigality of his imaginings-he bewilders himself and his readers amidsi" thick-coming fancies”—his poem is o'er-informed with wit, and dazzles and overpowers by an unremitting succession of brilliant corruscations. His narrative is, to its embellishments, but as “one poor half-pennyworth of bread to all this intolerable quantity of sack.” The adventures are meagre and unsatisfactory: we might
“Make suture times shake hands with latter,
And that which was before come after," without impairing or confusing the story. Like Bayes, in The Rehearsal, our author probably thought a plot was good for nothing but to bring in good things, and consequently troubled himself very little about its consistency or probability. His bero is the personification of contradictions—he is not the representative of a class, a sect, a party—but of all classes, sects, and par
a The difficulty of translating such a work as Hudibras, without letting the wit and spirit evaporate, is sufficiently obvious. This arduous task has been achieved, with extraordinary success, by Colonel Towneley, whose French version of Hudibras displays a singular union of spirit and fidelity, The German version of Soltau is also deserving of high praise.