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The scale of the Royal Astronomical Society. The two 3-foot bars of the Ordnance Survey.

Recent Publications.

It was resolved (provisionally) that the parliamentary standard of length be a measure à traits, [subsequently confirmed; that the material be gun-metal (including any variations in the proportion of tin, &c.) or steel, as Mr. Baily should think best; that the standard be about an inch square; that its ends be notched away to half its thickness, and that the marks defining the standard length be made upon pins (if necessary) inserted in the surface parallel to the length of the bar thus exposed; that the marks be adjusted to represent the length of one yard at the temperature of 61° or 62°, as nearly as possible; and that the bar be supported by a series of supports distributed over many points through its whole length, so as to destroy the effect of gravity in bending the bar as completely as possible.

Mr. Baily proceeded to make experiments on different materials, with the view of ascertaining the substance most suitable for the construction of standard bars. In accordance with the Astronomer Royal he entertained the opinion that if a bell-metal or gun-metal mixture could be found possessing the properties most essential to the present use of a standard bar, it would be greatly preferable to iron or steel for the construction of a standard intended to last through many ages, by reason of its almost perfect immunity from rust.

The results of Mr. Baily's experiments were communicated to the committee by the Astronomer Royal on the 30th of November, 1844. The gun-metal, No. 4, was adopted in all the standard bars subsequently made (except where a difference is specially mentioned), and appears to the author to be an admirable alloy for all similar purposes. Its exact composition is,

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Mr. Baily, having concluded his experiments on the suitableness of metals for standard bars, proceeded to make a series of experiments on the influence produced by small inequalities of the surface supporting a bar. About the same time experiments on thermometric expansion were made by Mr. Simms at 138 Fleet Street, under the general instruction of Mr. Baily, and with some suggestions from the Astronomer Royal.

Mr. Baily finally proceeded to make comparisons of the standards of superior construction which were known to have been compared with the Imperial Standard, with the view of ascertaining how far they might prove available for the restoration of the standard yard. The results were of a negative character. It was shown that in no instance did there exist a trustworthy representative of the Imperial Standard. Mr. Baily died on the 30th of August, 1844. The state in which the problem was left to his successor is thus enounced by the Astronomer Royal:

"The formation of a new standard must be an operation de novo; the length must be confined within certain limits (wide in the scientific, narrow in the commercial sense), but within these it might have any definite value; and when that definite value was fixed, it must be in no way referred again to the old standards or scales, whether original or intermediary. The principal object now was to ensure constancy and definiteness to the new standard and its copies, and means of reducing without sensible error the comparisons which might be made with them. As far as depended on the standard itself, it was hoped that the construction adopted gave sufficient security. As regarded the means of making comparisons, a far firmer apparatus than had been hitherto used was requisite. As regarded the effects of temperature, it was necessary to create an entirely new system of thermometers, founded upon the natural

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constants, to be determined by appropriate physical experiments, and to use them in new determinations of thermometric expansion."

Section IV. Proceedings of the Committee and of Mr. Sheepshanks to 1847, June; Construction of new Thermometers and erecting of Comparing Apparatus; Description of the Apparatus and of Mr. Sheepshanks' method of Comparing.

The committee at their meeting on the 30th of November, 1844, received with pleasure and thankfully accepted Mr. Sheepshanks' offer to continue the work commenced by Mr. Baily. A request to that effect was in consequence addressed by the Lords Commissioners of the Treasury to Mr. Sheepshanks, which was acceded to by the latter, who, like Mr. Baily, declined to accept any pecuniary remuneration for his services. On the 6th of June, 1845, Mr. Sheepshanks communicated a Report to the Committee in which he further explained his proposed plan of operations.

"Mr. Sheepshanks," says the author, "now turned his attention energetically to the practical preparation of the various apparatus to which his Report alludes. Of the details of the incessant labour of the next two years, few traces remain except in Mr. Sheepshanks' correspondence with myself. But to these labours there was little interruption. Old apparatus was to be tested, and new to be planned and carried into execution; instrument-makers, much occupied with other business, were to be kept closely to the work; manipulations of various kinds were to be learned; and all was done under the disadvantage of Mr. Sheepshanks' domestic residence being at Reading, while the work of every kind was executed in London. The most tedious of the operations actually carried on appears to have been the preparation of original thermometers (or rather the acquisition of the experience necessary for their preparation, for I do not think that a thermometer was really finished before the end of 1847). It would seem that at this time there was no workman in London who could be trusted without the closest superintendence even in the minutest points, to make a thermometer."

Mr. Sheepshanks' experiments were conducted at the Apartments of the Royal Astronomical Society, Somerset House, in one of the cellars two storeys below the ground-floor. Upon a solid platform of masonry were erected two stone pillars, upon which rested a horizontal slab, carrying two cross-stones or transoms, to which the micrometer-microscopes were attached. Upon a movable platform was placed a large trough of castiron nearly filled with water, for adjustment of temperature, and within this trough was a drop-box, into which the bars intended for comparison were put. During the comparison of a bar it was made to float very nearly in quicksilver. For this purpose a quicksilver box was inserted in the drop-box. The bars, before being placed in the quicksilver, were all covered with gold-beater's skin. The defining points of the bars were illuminated by means of two lamps, whose light passed through perforations in the horizontal slab towards the reflectors of the microscopes. In all the bars ultimately constructed by Mr. Sheepshanks, the defining mark is a fine line, transversal to the bar; accompanied by two lines parallel to it, one on each side at the distance of th of an inch, which were intended to give the means of ascertaining the value of the divisions of the micrometer. For further details we must refer to the paper. The views of Mr. Sheepshanks met with the cordial approval of the Committee.

Section V. Proceedings of Mr. Sheepshanks to the middle of 1850; Preparation of Thermometers, &c.-This section contains an account of the measures made by Mr. Sheepshanks with the various apparatus described in the preceding section. Various bars were compared in succession with the best primary representatives of the lost Imperial Standard. In the course of these observations he was finally induced to

adopt a bar denominated "Bronze 28," as the type of his subsequent measures. He remarked that the length of this bar was as nearly as possible that of the Imperial Standard, that the bar floated evenly in the quicksilver, and that it was nicely divided. Bronze 12, which had also engaged his attention for the same purpose, was not nicely divided and did not float evenly; and one of its gold dots was tarnished while the other was quite bright; and the tarnished dot was much disfigured by a mercurial stain; it was, moreover, found to be peculiarly liable to personal equation.

Section VI. Operations of important character to the end of 1853; Comparisons of a small number of Bars with Bronze 28; Investigation of Personal Equation, &c.-This section contains results for determining the influence of personal equation. The persons who assisted Mr. Sheepshanks in these experiments were, Mr. Henderson and Mr. Dunkin, of the Royal Observatory; Mr. Simms, Mr. W. Simms, jun., and Mr. Warren De La Rue. Five bars were compared with the bar denominated Bronze 28, and two other bars were similarly compared together. The author has rigorously treated the aggregate observations by the principles of the theory of probabilities. The following are the results of a comparison of Bronze 10 with Bronze 28. The letter d indicates a division of the micrometer screw or a hundredth part of a revolution, or oin-0000358:

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The foregoing numbers, as well as those relative to the other bars, indicate the existence of a personal equation of considerable magnitude. The final results for each case are obtained by taking the simple arithmetical mean of the results of the different observers. This section also contains experiments for ascertaining the relative expansions of bars of several metals.

Section VII. Comparisons of numerous Bars, from 1851 to 1855: Suspicion of Change in Bronze 28; Removal of the Suspicion; Close of the Operations for determining the Yard by Line Measure.—In addition to a large number of bronze bars Mr. Sheepshanks made experiments upon bars of brass, copper, iron, and steel. The present section contains the results of accurate comparisons of bars of all these different metals. Bronze 28 is employed as the standard of reference. The list contains comparisons of between forty and fifty bronze bars, and of about thirty bars of other metals. In April, 1855, an unexpected anomaly presented itself to Mr. Sheepshanks. The difference between the standard-bar denominated "Bronze 28" and a bar of cast steel, when determined by the intermediation of comparisons with four iron bars, was found to be different from the result obtained by direct comparison of the two bars with each other. Finding it impossible to account for the whole of the discordance he was reluctantly led to suspect that Bronze 28 had sensibly shortened. And so deeply and so painfully And so deeply and so painfully was this impression fixed on his mind that he actually contemplated the rejection of all the results which had cost so many years of labour, and the commencing of the work de novo. Further experiments, however, showed that his suspicion was unfounded, and established beyond doubt the general trustworthiness of the results already obtained by him.

'I have now,” says the author, "to give the melancholy

termination of this part of the work. To 1855, July 14 inclusive, the whole of Mr. Sheepshanks' observations, so far as I can discover, are transferred from the memorandum-book to the reduction-papers, and the means are taken. The final series of observations are the last two sets of comparisons of Bronze 17 with Bronze 28. After the observations of July 14, the following note is placed in the memorandum-book:

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1855, July 25. I went to Reading on the 14th, and felt my head so deranged that I stayed there till Friday 20th, when I came up to arrange my apparatus. I did only a little in the latter affair, but I left pretty full instructions for W. S. [William Simms, junr.], who has, I believe, carried them out with his usual skill. I told him that the microscopes had not the same scale, and that D would require to be set a trifle lower. He preferred taking a bit off A, and so get them nearer to the same length, and to have the focus of distinct vision in the same horizontal line; but it will alter the scale of A.' "Then follow a few observations (one page only, with a few subtractions on the next page) which I am not able to interpret with certainty. They are not dated.

"Mr. Sheepshanks had returned to London on some day in the week commencing with Monday, July 23, and had, as I conceive, made some trials of the apparatus, which were registered (for the moment only) in the unintelligible entries to which I have alluded. I understand that he was engaged on the apparatus on Saturday, July 28; but several persons had remarked that he was evidently in great distress. On the afternoon of that day he went to his residence at Reading, carrying with him a large travelling-bag full of papers relating to the Standards. In the afternoon of Sunday, July 29, while sitting in family society, he fell speechless from his chair, struck with apoplexy, and expired on August 4.

"Thus died-almost in the scene of his labours, and with his thoughts still intent on them- a man, whose equal in talent and perseverance, in disinterestedness, in love of justice and truth, I have scarcely known. He had, however, brought to a satisfactory termination the great division of the Standardwork which best suited his taste, having well overcome the last of the difficulties which had presented themselves, and leaving the work in such a state that not a single additional comparison of line measures was required."

Section VIII. Formation of End-measure Bars.-The form given to the end-bars depended in some degree upon the process adopted for comparing end-measure bars with line-measure bars, which originated in a suggestion of the author's. Suppose that we have two end-bars, each nearly equal in length (as measured between its extreme ends) to the length of the line-bars (as measured from line to line). Suppose, also, that each of the end-bars has a well sunk to the middle of its depth, with a transverse line cut upon a pin (as in the line-measures); the line being not necessarily at the middle of the length of the bar, though it is essential that its distance from the centre of the bar's length be nearly the same in both end-bars. As, generally, one segment of the bar, from the transverse line to the end, will be longer than the other segment, let the longer segment be denoted by +, and the shorter by And suppose that the two bars are placed end to end, the end of one being opposed to the end of the other. The distance between their transverse lines will evidently be the sum of the + segment of the first bar and the segment of the second bar; and the conditions stated, as to the similar division of the lengths of the two bars, will make that sum so nearly equal to the length of the line-measure, that the difference may be measured by the micrometer-apparatus. Then interchanging the positions. of the end-bars, so that their other ends shall be in contact, the distance under observation will be the sum of the seg◄ ment of the first bar and the + segment of the second bar. Adding together the two measured distances, we have a com

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parison of the sum of the two end-bars with double the length comparison of other bars, or for other scientific purposes in of the line-bar.

In order to make this determination available, it is necessary further to determine the difference between the whole lengths of the two end-bars. A felicitous suggestion by Mr. W. Simms, jun. gave the means of doing this. Mr. W. Simms's proposal was, to apply the process above described to three end-bars, determining the measure of the sum of each pair of end-bars in reference to double the length of the line-bar; then there are given three equations to find three unknown quantities. The length of each of the three end-bars is thus found without difficulty.

Mr. Sheepshanks had commenced the preparation of some end-bars, but no efficient progress was made in their completion up to the time of his decease. The Astronomer Royal, on then revising the condition of the work, requested Mr. Simms to undertake the whole operation of testing and adjusting the bars in his own workshops, and, finally, of making the definitive comparisons with Bronze 28 on Mr. Sheepshanks' apparatus at Somerset House.

Section IX. Closing Proceedings of Official Character; Extracts from the Final Report of the Commission; Extracts from the Act of Parliament legalising the new Standard; Standard Temperatures for the Compared Bars; Disposal of the Bars. -The final Report of the Committee, addressed to the Lords Commissioners of Her Majesty's Treasury, was signed on the 28th of March, 1854. We can only afford room for the following extracts:

"20. The expansions of these bars corresponding to a given change of temperature had been sufficiently determined in the course of the experiments; and it was then judged expedient, instead of stating the difference in the length of the selected bars at the same temperature, to infer the difference of temperature which would cause all to represent the same length, by the application of which it would be possible to assign the specific temperature at which each bar represents precisely the length of one yard. Thus it was found that the length of one yard, as given by the lost Imperial Standard, is represented with no sensible uncertainty, except in the measures of the Imperial Standard itself, by the following bars, at the temperatures placed opposite to them:

Bronze 19, or No. 1, at 62°00 Fahrenheit.
Bronze 20, or No. 2, at 61.94 Fahrenheit.
Bronze 2, or No. 3, at 62.10 Fahrenheit.

Bronze 7, or No. 4, at 61.98 Fahrenheit.
Bronze 10, or No. 5, at 62.16 Fahrenheit.

Bronze 28, or No. 6, at 62:00 Fahrenheit.

"21. The degrees of temperature for the use of these standards are defined as proportional to the corresponding apparent increase of volume of quicksilver in the thermometertube; the degree 32° representing the freezing-point of water; and the degree 212° representing the temperature of steam under Laplace's standard atmospheric pressure, or the atmospheric pressure corresponding to the following number of inches in the barometric reading reduced to 32° Fahrenheit:29*9218+00766 × cosine (2. latitude) +0'00000179 × height in feet above the sea;

and the degree 62° denoting the temperature which produces in the quicksilver an apparent expansion equal to 30% of the expansion between 32° and 212°; and so in proportion for other degrees.

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which reference to the Standard may soon be required. We will advert shortly to the proposed places of deposit of the Standards Nos. 1, 2, 3, 4, 5.*

"33. Remarking this probable intention of the Legislature in the year 1760, and remarking also the evident propriety of placing the National Standards under the care of the Executive, we recommend that the Parliamentary Standards of one yard and one pound be deposited in the office of the Exchequer, there to be preserved under such regulations as the Parliament may affirm fitting.

"34. In selecting places for the preservation of the authentic copies of the Parliamentary Standards, we have been guided by a consideration of the general fitness of the offices named; by an appreciation of the careful and accurate habits of the persons employed in them; by the limited accessibility to standards preserved in such offices, which it may be presumed will be made available for their legitimate purposes only; and by the occasional utility of accurate standards in verification of the operations to which these offices are devoted. . . . We adhere to the recommendation in Article 6 of the Report of 1841, that one set of copies should be imbedded in the masonry of a public building. In the distribution of the different copies, we have been guided by trifling peculiarities in the copies themselves.

...

"35. After careful consideration, we recommend,— "That the copy of Length Standard No. 2, and the copy of Weight Standard, PC, No. 1, be deposited in the Royal Mint. "That the copy of Length Standard, No. 3, and the copy of Weight Standard, PC, No. 2, be transferred to the Royal Society.

"That the copy of Length Standard, No. 5, and the copy of Weight Standard, PC, No. 3, be deposited in the Royal Observatory of Greenwich.

"That the copy of Length Standard, No. 4, and the copy of Weight Standard, PC, No. 4, be immured in the cill of the recess on the east side of the Lower Waiting Hall in the New Palace at Westminster."

On the question of referring the values of the measure and weight represented by the standards to natural elements.

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40. After due consideration of this question, referring to the reasons explained in Chapter II. of the Report of 1841, December 21, we adhere to the recommendation contained in that chapter, and embodied in articles 1 and 2 of the same Report, that no reference be made to natural elements for the values represented by the standards.

"41. We consider the ascertaining of the earth's dimensions and of the length of the seconds pendulum in terms of the standard of length, and of the weight of a certain volume of water in terms of the standard of weight, as philosophical determinations of the highest importance, to the prosecution of which we trust that Her Majesty's Government will always give their most liberal assistance; but we do not urge them on the Government at present as connected with the conservation of standards."

The Act of Parliament for legalising the Standards of Weight and Measure received the Royal Assent on the 30th of July, 1855, the day succeeding that on which Mr. Sheepshanks was attacked by the illness of which he died.

The Astronomer Royal closes his paper with the new nomenclature of the bars, and the temperatures at which they represent the British yard. He has also given a statement of their distribution. Bar, No. 6, has been retained at the Royal Observatory, as accessible representative of the National Standard.

*Reference is here made to a Bill which was introduced into Parliament in 1760, containing provisions for the safe custody of the standards of weight and measure.

A Treatise on Navigation and Nautical Astronomy. By John Riddle, F.R.A.S., Head Master of the Nautical School, Royal Hospital, Greenwich. 8vo. Seventh Edition. London, 1859.

This excellent standard work, in which theory and practice

are so judiciously blended together, is too well known to require any detailed statement of its contents. The present edition is the result of a careful revision, by which the work is adapted to the best modern practice of the art of navigation.

VOL. XIX.

June 10, 1859.

No. 8.

Rev. R. MAIN, President, in the Chair.

Rev. Dr. Booth, Incumbent of Stone, Bucks; Christopher George, Esq., 5 Barnes Street, Limehouse; F. H. Elliott, Esq., 56 Strand;

Thomas Cooke, Esq., York;

Rev. Francis Redford, Silloth by Carlisle; and
J. E. Richard, Esq., West Hill, Wandsworth,

were balloted for and duly elected Fellows of the Society.

Occultation of Saturn by the Moon on May 8, as observed at the Cambridge Observatory. By Professor Challis.

The observations were taken by myself and my senior assistant, Mr. Bowden. I employed the Northumberland telescope, with a magnifying power of 215, the junior assistant, Mr. Christy, counting the seconds from a sidereal clock; and Mr. Bowden observed with the telescope of the 5-feet equatoreal, using a magnifying power of 120. The atmospheric circumstances were favourable. The following are the Greenwich mean times of observation, the letters C and B denoting the observers.

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(a.) The occultation occurring earlier than was expected, the first contacts of the planet and ring were lost. The time noted by C is that of coincidence of the moon's limb with that point of Saturn's limb which was judged to be on the axis major of the ring. (b) and (c.) These times were considered to be "good."

(d.) This time is very doubtful. The limb of the ring was partially obscured at emergence by the micrometer wires set to indicate where to look for it, and had evidently projected a few

seconds of arc from the moon's limb when the time was noted. (e) and (f) C's times were considered "pretty certain :" those of B were "extremely unsatisfactory." (g.) The limb of the ring appeared to C to separate suddenly from the moon's limb, and the recorded time was thought to be late: B considered his observation of no value, the edge of the moon being badly defined, from an effect of the telescope, it was supposed, and not from atmospheric causes.

The time of disappearance taking me by surprise, I had scarcely an opportunity of making physical observations in addition to notes of time. I remarked, however, that the moon's limb, where it crossed the middle of Saturn and his rings, appeared to be unusually curved, and that both the ball and the ring were reduced before disappearance to a very narrow strip of light. The disappearance seemed to linger. I noted also that the moon's limb was fringed by a darkish border; but I have reason to say that this was merely an effect of the Ramsden eyepiece that was used, the planet, in the hurry, not being placed in the middle of the field. Mr. Bowden remarked as follows: "I did not perceive the slightest change in the appearance of Saturn, except just before the total disappearance, when the edge of the ring lost its sharpness of definition, and I thought I saw it wave to and fro. I also thought that just before the total disappearance the edge seemed to hang on the moon's limb, and that the final disappearance was retarded."

The circumstances of the reappearance were very favourable for observing physical phenomena. The moon's limb, as seen in the Northumberland telescope, was steady, and the irregularities were sharply defined. I looked particularly to see whether Saturn's disk was crossed by a dark band like that noticed at the occultation of Jupiter on Jan. 2, 1857. Nothing of the kind was visible. At the place of reappearance the moon's limb was neither depressed nor elevated, but accorded with the general contour. When the planet was a little separated from the moon's limb, a regular increase of its brightness from the parts nearest the limb to the parts more remote was very observable, and was probably the effect of the dispersed light, which in a telescope is usually seen near the moon's bright limb. The colour of the planet, which very much resembled that exhibited by Jupiter at the occultation above mentioned, was in remarkable contrast with the whiteness of the moon's light. Mr. Bowden described it as "a dull earthy colour."

From calculations of the occultation made according to the formulæ given in the appendix to the Nautical Almanac for 1854, I have obtained results as follows. Let x and y be the corrections of the tabular R.A. (in arc) and tabular N.P.D. of the moon's centre; e and f the like quantities for Saturn's centre; Sx (I + 0·001 n) the moon's true apparent semidiameter; c the distance of Saturn's centre from the moon's limb; D the distance between the centres. Then the tabular

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The President, on the Controversy respecting the Amount of Acceleration of the Moon's Mean Motion. 268, 269

quantities being calculated from the Nautical Almanac for the Greenwich mean time, 8h 18m 35.09 +t, and the latitude and longitude of the observatory, and the moon's parallax being assumed to require no correction, the following equation of condition was obtained,

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The values of c for the contacts of Saturn were calculated from the equatoreal diameter adopted in the Nautical Almanac, and an assumed ellipticity of; and the value for the contact of the ring was calculated from the data in p. 510 of the Nautical Almanac for 1859. The three values were found to be +472, -8"-30, and 12" 24. Hence the numerical value of the left-hand side of the above equation as given by C's three observations is 2"04, +0′′·61, and +1"58; and as given by B's two observations, -o"90 and +1"13.

The analogous equation of condition for the reappearance, calculated for the Greenwich mean time 9h 16" 38.3+ is the following,

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-311, +286.

These results are not all entitled to the same weight. For instance, C's first time, from the nature of the observation, was liable to error; and B's time for the complete immersion of Saturn is plainly too early, probably by an error in recording. Omitting these, the mean result for the other three times is +111. Again, the first of C's times of reappearance, and the last of B's, may be rejected, as being considered at the time of no weight; and the remainder will then give the mean result 159. Thus the two equations of condition become,

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On the Present State of the Controversy respecting the Amount of the Acceleration of the Moon's Mean Motion. By the Rev. R. Main, President.

There is probably no astronomical subject in which the advance or improvement within the last twenty-five years has been so great as in the lunar theory, and in the means taken for increasing the number of observations necessary for bringing the theory to perfection. To begin with observations: during the whole of this period the moon has been observed at Greenwich on the meridian with inflexible rigour, and with an amount of precision which was never previously attempted; and during a portion of it, that is, since the year 1847, a series of observations have been made by an instrument especially designed for the purpose, by which the gaps in the meridian observations, necessarily occurring for about three hours before and three hours after each conjunction, have been in a great measure filled up. These results of observation are, of course,

independent of those obtained at other great observatories, which are, on the whole, not inconsiderable, though of very inferior importance.

But, however remarkable be the quantity of materials for the correction of the lunar orbit during the latter portion of the present century, the use which has been made of them is still more so. The gigantic work undertaken by the Astronomer Royal, of reducing, on a uniform plan and with the best modern elements, the whole of the lunar observations made by his predecessors, for a period of eighty years, namely, from 1750 to 1830, comes first in order, as more nearly related to the observations, and is, perhaps, absolutely first in order of importance. The first result from the publication of these observations was the discovery, by Professor Hansen, of the long inequality produced by Venus, and the second has been the completion of his invaluable Tables. It is too early to predict that the errors of these tables in all parts of the orbit are so small that all future improvements may be considered to belong to speculative rather than practical science; but this is known already, that, in a rigorous comparison of the Greenwich Observations for the year 1852, the errors rarely exceed those which might be due in a great measure to faulty observations; and the scientific public will look with great interest and anxiety for the results of the completion of Mr. Hind's laborious and self-imposed task of comparing all the Greenwich Observations from the year 1847 to the present time with the Tables.

observation has a very great share; but there is one developIn all the improvements of the lunar theory yet mentioned, ment of a purely theoretical character of great importance in itself, but of still greater interest on account of the controversy to which the conflicting results arrived at by most eminent analysts have given rise. This inequality is the secular acceleration of the moon's mean motion, of which the fact has been known for nearly two centuries, but concerning the amount of which there is even at the present time a doubt of so interesting a character, whether it be regarded practically or theoretically, that a statement of the leading features of the state of the controversy seems to be not only desirable, but absolutely necessary.

"If any

Dr. Halley appears to have been the first astronomer who was acquainted with the fact of the acceleration of the moon's mean motion, though it is not likely that he could, from the elements of the lunar orbit which had been obtained from observation in his day, give any guess as to its probable amount. His note on this occurs in a paper containing "Some Account of the Ancient State of the City of Palmyra, &c. &c." (Phil. Trans. for 1695, No. 218.) curious traveller," he says, "or merchant residing there, would please to observe, with due care, the phases of the moon's eclipses at Bagdat, Aleppo, and Alexandria, thereby to determine their magnitudes, they would do the science of astronomy a greater service; for in and near these places were made all the observations whereby the middle motions of the sun and moon are limited; and I could then pronounce in what proportion the moon's motion does accelerate, and shall (God willing) one day make it appear to the public."

The next paper of importance, as proving the fact, and with tolerable approximation determining the amount of the acceleration, is that of the Rev. Richard Dunthorne, given in the Phil. Trans. for 1749.

Comparisons of the Tables with four well-known eclipses observed by Albategnius gave no certain result, on account of the want of a knowledge of the position of the place of observation; but there are, fortunately, observations of two ancient eclipses which are very favourable for the determination: these are, first, the eclipse of the moon said by Hipparchus to have been observed at Babylon in the 366th year of Nabonassar, or

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