At the meeting of the Academy of Sciences of February 1857, the author described a new system of telescopes, the speculum of which was made of glass silvered by Mr. Drayton's process. Mirrors, so constructed, upon their removal from the bath of silver, already possess the necessary brilliancy for being used in the telescope; but the brilliancy may be still further increased by spreading, with a piece of chamois leather, the pulverulent and non-adhering layer which partly hides the polishing of the silver-coating.

Objections have been advanced against telescopes of this construction, on the ground of the fragility of the metallic layer, but experience has proved them to be unfounded. In the outset of his labours it occurred to the author that he could not do better than apply all his attention to the obtaining of spherical surfaces, the only ones which are produced regularly by mechanical means. In endeavouring to ascertain and to correct all the defects which subsist in such surfaces, he succeeded in executing at pleasure all the ellipsoidal surfaces which establish the transition between the sphere itself and the paraboloid of revolution. As a preliminary to such labours he made himself acquainted with the various processes employed in the working of glass by practical experience in the workshop of M. Secretan, the well-known optician of Paris.

As soon as a piece of glass which was being worked out began to reflect the light to a focus it was submitted to a course of optical experiments, by means of which it was possible to find the real shape of the surface. In the course of these experiments the author became convinced that surfaces as formed by opticians acquire their real value only at the final period of the polishing. They further served to establish this unexpected result, that the mechanical processes actually used in arts and industrial pursuits do not realise the spherical surface with such a degree of approximation as to withstand optical test. This circumstance suggested to him the idea of retouching polished surfaces with the hand in those instances wherein there existed defects, and of modifying them by means of local corrections, until light showed them to be irreproachable.

"This operation, which is repugnant to practical men, answered better than one could have hoped. When attempted for the first time on a speculum of 36 centimètres (14 inches) in diameter, which exhibited a central eminence very prejudicial to the formation of images, it brought the surface back in a few hours to a figure which was sensibly spherical. Afterwards, by dint of several successive tests to which the surface was submitted, I established beyond doubt the fact that it is possible by such means to arrive at a true spherical surface. I then conceived the idea of realising the parabolic surface with the degree of approximation necessary for the application I had in view.

"The method employed in effecting this transformation of the surface of the sphere is founded on the direction which the aberrations follow in the different positions of the conjugate foci of a concave speculum.

"If the speculum be exactly spherical, a luminous point placed at the centre of curvature produces at that centre an image which is free from aberration. But when the luminous point approaches the principal focus, the image recedes and is surrounded by an image of aberration which increases with the distance.

"First, let us conceive that the luminous point undergoes only a very slight displacement, in order that the image formed in its vicinity exhibits only a slight aberration, or the first indications of such. The speculum may then be corrected by means of a polisher of a suitable form until the aberration disappears; and as the mirror was spherical it becomes now ellipsoidal by the duplication of the primitive centre in two corresponding foci at the places occupied by the luminous point and its image.

"This correction being made for a first distance of the two foci it would be easy to find the value of that distance. Upon bringing the luminous point nearer to the mirror, new aberrations would reappear, which in their turn might be corrected by a similar process, and then the ellipsoid to which the surface of the mirror belongs would be increased in length.

"Pursuing the same course by a small quantity at a time the ellipsoid is lengthened progressively until it is transformed into a paraboloid of revolution, that is to say, until the mirror has acquired the property of reflecting light to an infinite distance without any perceptible aberration.

"This method was first applied to a mirror of 25 centimètres (9.8 inches) in diameter, and was carried out only to a certain limit, so that the instrument collected in one focus only the rays emitted from a distance of 10 mètres (32.8 feet). However it has been thought desirable to maintain the instrument in this condition, in order that it may undergo other experiments, which, upon being repeated on a limited space, would demonstrate in a most decisive way the efficacy of the reflexion of the rays by the whole surface.

"A second mirror of the same diameter, the figure of which has been corrected in such a way that it became almost parabolical, and formed in the tube of the telescope at the distance of 1 mètre (3.28 feet) an image free from aberration, of objects placed at an indefinite distance.

"A third mirror, the diameter of which was 33 centimètres (13 inches), and the focal length of which was 2m.25 (8feet.87), prepared like the others, above mentioned, with much care in Mr. Secretan's workshop, presented, just after being taken from the workman's hand, a figure of revolution well centred upon its axis, but which deviated very much from the figure of a sphere. Upon being subjected to a slight re-touching it was very much improved, and the parts which were most salient have completely disappeared. Subsequently a second retouching, effected in a very short time, gave to the mirror a parabolic figure, and upon being directed towards celestial objects it was found to perform correctly.

"Although a surface of glass reflects onlyth part of the incidental light, it is not necessary to have the mirror silvered in order to become acquainted with the state of the surface. The light of a lamp transmitted towards the observer, by means of a partial reflexion upon the glass mirror, possesses sufficient intensity for exhibiting all the details which are interesting for the discovery of the formation of the focus. As for the asperities which modify the geometrical properties of curvature, they are in reality so infinitely small that a single rubbing of the polisher is sufficient to cause them to disappear, without the necessity of continuing the process too long. In the dimensions I have operated on until now it has taken me

only six hours to retouch a whole surface; a few minutes suffice to exhibit a sensible change. This mode of attacking the substance of glass admits of the operation being suspended at any time, and definitively terminated as soon as it is thought that the real figure has been acquired. Then comes the silvering, which increases the reflecting power without the least alteration of curvature being apprehended."

The author then proceeds to explain a method imagined by him for ascertaining the limit of the optical power of the instrument. He concludes with the following account of a trial which he made with a mirror of 33 centimètres (13 inches) aperture, and 2.25 mètres (8feet-865) focal length :

"On the night of the 21st of July, under a pretty favourable condition of the atmosphere, we undertook an attentive examination of y Andromeda. This star (which, in refracting telescopes of 33 centimètres or less, is seen double, the principal star being of a yellow colour mixed with a little red, and the other a blue star of a greenish tint) is really triple, as Struve has shown with the Pulkowa refractor. The duplicity of the blue star is well known.

"During the whole night this feature of the double star remained doubtful; but at three o'clock in the morning, as the first rays of the sun were perceptible, the definition became very much improved; and upon applying a magnifying power of 600, the star was seen plainly divided into two small points

very near each other.

"Two days afterwards, at the same hour, but with not so good definition, this observation was confirmed. Moreover, in order to guard against any imperfection which might attach to the instrument, a single star was observed, in order to ascertain if the image of the star was perfectly free from duplicity.

"An experienced observer took part in this examination. We have drawn on paper, separately and at sight, the same impressions; and afterwards, when the catalogue was consulted, we have succeeded in ascertaining that the positions

were exact.

"It is, then, an established fact that the star y Andromeda was seen double with a parabolic mirror of silvered glass 13 inches in diameter and 8.865 focal length.

"These results, very satisfactory in themselves, also offer interest on account of the small expenditure which has sufficed to obtain them. Thanks to the liberal disposition, to the disinterestedness of the learned artist Mr. Secretan, who for

MISCELLANEOUS INTELLIGENCE.

Death of Dr. Wichmann.

190, 191

Died on the 7th of February, 1857, at five o'clock in the

morning, Dr. Moritz Ludwig George Wichmann, Observer of the Königsberg Observatory. Death gently terminated a long course of suffering, which a milder climate might have alleviated, but could hardly have removed.

Wichmann was born on the 14th of September, 1821, at Celle, in the kingdom of Hanover. He first studied at Göttingen, and subsequently, in 1843, proceeded to Königsberg. Here, in 1844, he was appointed by Beud Assistant at the Observatory. In 1847 he established himself as a tutor in the University, and upon Dr. Busch being appointed Director of the Observatory in 1849, he obtained in the following year the situation of observer in that institution, which he continued to hold till his death.

He had been long in delicate health, but in 1853 he fell seriously ill from a complaint of the chest, and in the following year he proceeded to Italy in hopes of deriving benefit from the climate of that country. In August 1855 he returned, his health somewhat improved, to Königsberg after an absence of fourteen months. He now, in conjunction with Professor Luther, discharged the duties attached to the directorship of the observatory, which had become vacant by the death of Dr. Busch. About the middle of December in last year he was attacked by a severe illness which terminated in death.*

Admiral Smyth has forwarded to the Editor a copy of the Report of the Committee of the Overseers of Harvard University, appointed in February of last year to visit the Observatory of Harvard College. The visitation took place on the 15th of December last, and it acquires a melancholy interest from the circumstance of its being the last at which our late distinguished Associate, Professor W. C. Bond, officiated as Director. We extract the following passages from the Report :

"The Director acknowledges that the dome as well as the pier which supports the great equatoreal are all that can be desired. Indeed, the fact that for several years there has been no re-adjustment of the polar axis of the telescope, furnishes

the mechanical resources of a great establishment, the expense of the process for obtaining them has been confined within such limits that a private individual would have borne them easily. I have no doubt that, by the expenditure of a sum of money comparable to what is usually laid out on astronomical instruments, it is possible to construct a telescope of comparatively moderate dimensions which would be capable of revealing regions of space hitherto inaccessible to vision."

At the close of the proceedings the Astronomer Royal favoured the meeting with an oral exposition of his views on the Motion of the Solar System in Space. An abstract of a paper embodying his recent researches on this important subject will be found at page 175.

sustains it. This noble instrument, the Committee are happy to say, is still in perfect preservation; and continues to give the satisfaction of former years. The lenses of the object-glass have been separated during the last year, and no enlargement of the minute spots heretofore noticed has been detected. The observations and measurements made by this instrument appear to the committee to be of the utmost value in extending astronomical science; and the course pursued by the observers, not so much to accumulate observations on the same object, as to apply its power to the examination of the more remote ones, appears to us to be judicious. Observations for the revision of the position and magnitude of the stars in the interesting nebula of Orion, were commenced in October 1857, and brought to a close in March 1858. A systematic and thorough examination of this astonishingly rich region of the heavens was called for by singular variations recognised at different periods. From the data thus obtained, a chart may be constructed, which will faithfully represent the relative position and brightness of the separated stars. The great equatoreal has also been applied to the frequent examination of the planets Jupiter, Saturn, and Neptune, as well as many of the asteroids and comets.

"Since our last visit to the Observatory, the improved Bowditch comet-seeker, in the hands of Mr. Horace P. Tuttle, has been surprisingly successful. No fewer than five independent discoveries have crowned his efforts. The fourth in the order of these discoveries was the great comet of Donati, first seen at Cambridge on the 28th of June last; and it having early, and while yet telescopic, given promise of great brilliancy, extensive preparations were made to subject it to close scrutiny. The expectations of the observers were fully realised; and from the 28th of June to the 25th of October, their exertions were unremitting. If we except the comet of 1811 (its rival in beauty and its superior in the period of its visibility), no recorded comet gave greater facilities for the investigation of its physical properties. Of these favourable circumstances the observers availed themselves; and the fruits of their labours, so far as we have been able to learn, are unequalled. The various drawings of this interesting object, faithfully and skilfully executed by Mr. Henry G. Fette and the young Bond were examined by the Committee with admiration. They exhibit at a glance the various changes and vagaries of the comet. These drawings have since been engraved, and in connexion with the explanations and observations of the assistant have been published and circulated extensively in a treatise which reflects the highest honour upon the Observatory and upon its enlightened author.

"In their last year's report, the Committee dwelt upon the labours of the preceding year in the delineation of celestial objects by photography. They believed they then saw the germ of an invaluable mode of celestial research. In this they have not yet been disappointed. Their anticipations of the progress of a single year have been more than realised. The Director in his report of last year, alluded to the possibility of distinguishing stars by their chemical action, and the investigations of the assistant observer leave no question of its practicability; and the curious fact is given that the stars a Lyræ and Arcturus, though of nearly the same magnitude as seen by a telescope, or unassisted vision, yet in photographic power the former surpasses the latter by seven times.

"Finally, the Committee are satisfied from the report of the Director, and much other testimony and observation, that a great amount of labour has been performed, and well performed, during the last year, and they regret that the means are not in hand to give to the world, by way of publication, the large collection of results which are constantly accumulating."

The Report concludes with an allusion to the death of Mr. Bond, expressed in the following terms:

"The Committee have hitherto dwelt on matters of an interesting and pleasing character. They come now to a most melancholy part of their duty, it is to speak of the death of the able Director of the Observatory, Prof. William Cranch Bond, which occurred on the evening of the 29th ult. On the 15th of December last, in somewhat feeble but usual health, and depressed by a family affliction, the death of Mrs. George P. Bond, he read to us in his wonted dignity and calmness his annual report, from which most of the facts in this report are derived. His oral communications on the occasion, though given with his characteristic calmness, were strongly marked

with the zeal in his favourite pursuit which has distinguished his whole life. Known and appreciated as an accurate and truthful observer, wherever the science of astronomy is cultivated, his death will be justly deemed a great loss to science. Several members of this Committee have enjoyed the privilege of his counsel and friendship for more than thirty years, and in yielding to the mandate that time to him shall be no longer, their humble consciousness is, that a great and a good man is no more."

The Society will be gratified to learn that Mr. G. P. Bond has been appointed Director of the Observatory of Harvard College in the room of his lamented father.

RECENT PUBLICATIONS.

Report on the Recent Progress of Theoretical Dynamics.

By A. Cayley.*

In this report Mr. Cayley confines himself to the general theories of dynamics. The special problem of the variation of the elements of a planet's orbit is alone alluded to in consequence of its historical connexion with the subject of the report. The author gives a masterly survey of the progress of research from Lagrange's establishment of the equations of motion by a combination of the principle of virtual velocities with D'Alembert's principle, down to the labours of the geometers of the present day. At the close of his report he sums up the leading steps in the series of investigations. These are: first, the establishment of the Lagrangian form of the equations of motion; secondly, Lagrange's theory of the variation of arbitrary constants, a theory perfectly complete in itself, and it would not have been easy to see, à priori, that it would be less fruitful in results than the theory of Poisson; thirdly, Poisson's theory of the variation of arbitrary constants, and the method of integration thereby afforded; fourthly, Sir W. R. Hamilton's representation of the integral equations by means of a single characteristic function determinable à posteriori, by means of the integral equations assumed to be known, or by the condition of its simultaneous satisfaction of two partial differential equations; fifthly, Sir W. R. Hamilton's form of the equations of motion; sixthly, Jacobi's reduction of the integration of the differential equations to the problem of finding a complete integral of a single partial differential equation, and the general theory of the connexion of the integration of a system of ordinary differential equations, and of a partial differential equation of the first order, a theory, however, of which Jacobi can be considered only as the second founder; seventhly, the notion arising from the researches of Lagrange and Poisson, and ulterior development of the theory of a system of canonical integrals.

Ordnance Trigonometrical Survey of Great Britain and Ireland:-Account of the Observations and Calculations of the Principal Triangulations; and of the Figure, Dimensions, and Mean Specific Gravity of the Earth as derived therefrom. Published by order of the Master General and Board of Ordnance. Drawn up by Captain Alexander Ross Clarke, R.E., F.R.A.S., under the direction of Lieut.Col. H. James, R.E., F.R.S., M.R.I.A., &c., Superintendent of the Ordnance Survey, pp. 782. 4to. London, 1858. (Accompanied with a volume of Plates.)

It is well known that the Triangulation of the British Isles originated in an operation undertaken in the year 1783, under * Report of the Twenty-seventh Meeting of the British Association for the Advancement of Science for 1857. London, 1858.

the superintendence of General Roy, for the purpose of establishing a geodetical connexion between the observatories of Greenwich and Paris. Details of the subsequent operations have been published from time to time by the Ordnance department. It has been already mentioned in the Monthly Notices (vol. xviii. p. 113) that the operations embrace an arc of the meridian, extending from Dunnose in the Isle of Wight to Saxavord in the Shetland Isles, and possessing an amplitude of 10° 10' 31" 43. The present volume contains a systematic exposition of the entire triangulation, with an investigation of the figure, dimensions, and mean density of the earth hence deducible. With reference to the preparation of the work Colonel James makes the following statement:

"The voluminous computations connected with the reduction of the observations have been made by Lieut.-Colonel Yolland, Captain Cameron, and Captain Alexander Clarke, assisted by Quarter-Master Young and Mr. O'Farrell, and a great number of computers; but the chief and most important portion of the work, including all the calculations connected with the determination of the figure, dimensions, and mean specific gravity of the earth, has been performed by Captain Clarke."

A listis given of the officers and non-commissioned officers who were personally engaged, either in the measurement of the bases or in taking the trigonometrical or astronomical observations.

We can of course do little more than merely give a state

ment of the principal contents of this immense volume.
The work is divided into fourteen sections.
Section I.-Description of Stations.
Section II. Description of Instruments.

The principal instruments used in the triangulation were four large theodolites: two of these were three feet in diameter, another was two feet, and the fourth was eighteen inches. The two largest of these instruments and the 18inch instrument were constructed by Ramsden; the remaining theodolite, of two feet in diameter, was constructed by Troughton and Simms, at the commencement of the Irish Survey.

For the determination of latitudes, the instrument used from the commencement of the survey till the year 1836 was a zenith sector constructed by Ramsden.* It consisted of an arc of 15o, divided to every 5', and having a micrometrical division by which quantities of about a tenth of a second could be estimated. The radius of the arc was eight feet, and the aperture of the telescope was four inches. The instrument was read off by means of a plumb-line. The apparatus for placing it truly vertical, for reversing its position, and for bringing the plumb-line over the centre of the instrument, were all very perfect; but notwithstanding the general excellence of the instrument, it was not well adapted to constant transport from station to station, by reason of its complex construction and the number of separate parts of which it was composed. The necessary reversal of the instrument on successive nights, and the consequent delay during bad weather, was also a source of considerable inconvenience.

"In consequence of these deficiencies, an application was made to the Astronomer Royal by Major-general Colby for a new zenith sector, by which the observations of a single night might give an accurate determination of the latitude. The design was furnished, and eventually the construction of the instrument superintended by Mr. Airy.

"The first principle in this instrument, now known as Airy's zenith sector, was the arrangement for making successive observations in two positions of the instrument, face east and face west, at the same transit. The second principle was the substitution of a level or system of levels for the usual plumb-line. The third principle was the casting in one piece, as far as practicable, of each of the different parts of the instrument, in order to avoid the great number of screws and

195, 196

fastenings with which most instruments are hampered, and to secure, if possible, perfect rigidity."

These remarks are followed by a description of the instrument, and of the method of making observations with it.

Section III. Reduction of Observations. - In this section an exposition is given of the method, founded on the theory of probabilities, for reducing the observed to the most probable mean bearings.

Section IV. Observations, Terrestrial and Astronomical, for the principal Triangulations. The first part of this section contains extracts from the reduced theodolite observations of terrestrial objects; the second part contains the principal azimuthal observations in detail, and the results of those which are less important, together with their range and probable error; the third part contains the results of the observations made with Airy and Ramsden's zenith sectors for the latitudes of various points in the triangulation.

Section V. Measurement of Base Lines. - Some details relative to the subject of this section have been already given in the Monthly Notices for April 1858 (vol. xviii. p. 221).

Section VI. Principles of Calculation. - The theory of spheroidal triangles is investigated. The error resulting from the solution of such triangles by spherical trigonometry is demonstrated to be inconsiderable. It is further shown that no appreciable error can arise from the application of Legendre's theorem to the computation of spheroidal triangles. This theorem is accordingly employed in the calculations, in preference to the chord method which was exclusively used in the earlier part of the operations. Formulæ are then investigated for calculating the longitudes, latitudes, and azimuths. section concludes with an exposition of the method employed for determining the most probable values of the corrections to the observed mean bearings of the triangulation.

The

Section VII. Reduction of the Triangulation. - In order to obtain the most probable values of the corrections to the observed bearings, Colonel Yolland directed that the whole triangulation should be reduced according to the method of least squares. As the number of equations of condition amounted to 920, their solution in one mass was impracticable. However, a mode of treatment was devised which was equally effective for the object in view, and was naturally suggested by the relations in which the corrections stood towards each other in the equations. This consisted in breaking up the triangulation into a number of separate parts or figures, each of which afforded a limited number of equations of condition, and then applying the theory of probabilities to the solution of each group of equations.

Section VIII. Triangles and Distances. - The definitive values of the absolute distances are made to depend on the Lough Foyle and Salisbury Bases. The distance between the parallels of Dunnose and Saxavord is found to be 3,729,334.07 feet. The distance between Easington and Saxavord was computed by two different series of triangles. By the one the distance was found to be =2,288,427.29 feet; by the other it came out =2,288,427.38 feet. Both Easington and Saxavord lie nearly on the same meridian. The distance of Saxavord from the meridian of Easington was found

By the first train of calculations = 222'56 feet.
By the second

"

Difference

=221.94 "

0.62

Section IX. Observed Zenith Distances and Altitudes.The theory of probabilities is applied to the determination of the mean observed zenith distances. The coefficient of refraction is investigated in two different ways: first, by direct ob

* This instrument was destroyed by the fire which happened in the Tower of London in 1841.

servation from one point to another, the heights of both points being exactly ascertained by levelling; secondly, by combining reciprocal observations of zenith distance. The results are interesting. With regard to 31 values of the coefficient deduced from levelled heights, it is found that in the cases wherein the rays cross the sea, the mean value of the coefficient amounts to 0.0817; while for the rays which pass over the land, the mean value of the coefficient is 0.0772. Omitting the case of Ben Nevis, in which the atmosphere appears to have been in an abnormal state, the value of the coefficient is found to be 0.0756 for rays not crossing, the sea. The following are the results deduced from pairs of reciprocal observations:-In 35 cases wherein the ray passes for a considerable portion of its length over the sea, the value of the coefficient k = 0.0801; in 13 cases wherein the ray passes also over the sea, but for a smaller portion of its length, the value of h = 0.0778; in the remaining cases, wherein the ray is inland, the value of h = 0.0744. The definitive result is,

The heights of a considerable number of the stations were determined by spirit-levelling; the heights of others were deduced from the levelled heights, combined with the observed zenith distances. Thus from the levelled heights of Ben Nevis (4406.3 feet) and Ben Lomond (3192.2 feet), the heights of four other stations were determined. In this way the height of Ben Macdui was found to be 4295.6 feet. This result has recently received a remarkable confirmation. By levelling up the western side of the mountain, the height has been found to be 4295.70 feet; and by levelling down the eastern side, the result was 4295.76 feet.

Section X. Connexion of Geodetical and Astronomical Observations. - In this section the subject of local attraction is generally considered, and formulæ are investigated for computing the amount of deflection upon various suppositions with respect to the disturbing mass. From observations made at Arthur's Seat, near Edinburgh, in 1855, the relative deflection at the north and south stations of the hill was found to amount to 4".07, whence the mean density of the earth was concluded to be 5.316 ±√3.725 82 + 0029, & being the probable error of the mean density of the hill, which is assumed by Colonel James to be 2.75, from the examination of a great many sub

stances.

a = 20,927,005±295. c* = 280.4±8.3.

Section XIII. Of the Length of the Degree, &c.: Longitudes and Latitudes and Directions of the Meridian at the different Stations. The following is the expression obtained for the length of a degree of the meridian in the British Isles:

Length = 364,5941 - 1953.8 cos 2 2 + 4.4 cos 4 λ the unit being a foot.

Section XIV. Figure of the Earth.

In the Philosophical Transactions for 1856 there is a paper containing a new determination of the Figure of the Earth, founded upon the arcs used by Bessel, but including the extensions of the English and Indian arcs (Monthly Notices, vol. xviii. p. 220). The investigation in the present volume includes also the Russo-Scandinavian arc, extending from Ismail, in lat. 45° 20′, to Fuglenas, in lat. 70° 40′, and having, consequently, an amplitude of 25° 20′ (Monthly Notices, vol. xiii. p. 201). The data of this arc were furnished to the Ordnance by Professor Struve; the latitudes are not final, but the probable errors of the latitudes stated are less than half a second. The elements of the earth's figure are determined on two suppositions, the non-elliptic and the elliptic. On the first hypothesis the mean value of a correction to an observed latitude is ± 2".064; on the second the mean value is ± 2".098. The figure deduced, independently of the elliptic assumption, does not differ sensibly from a spheroid of the same axes, the amount of the protuberance of a meridional section being represented by

dr = (177 feet-5 ± 70.9) sin2 2 2,

Combining Colonel Everest's Indian are from Daumergida to Kaliana with the English arc from St. Agnes to Saxavord, the value of the mean degree is found to be 364,623.50±7.15 and a : b = 292.39: 291.39; probable error ±2.67.

Combining the same Indian arc with the Russian arc, the value of the mean degree is found to be = 364,616.07 ± 6.59 and a : b = 294.58: 293.58; probable error ± 2.27.

The three arcs combined together give 364,619.19 ± 6.14 for the value of the mean degree, and a : b = 294 44: 293.44; probable error ± 2.26.

The foregoing determinations conclude with this remark:"Until the exact latitudes of the thirteen stations in the Russian arc are known we cannot state the precise elements best representing all the geodetical operations. They cannot, however, be far from the following:

Mean Degree of Meridian Ratio of Semi-Axes

364,616 feet of Ordnance Standard 293: 294."