Method of finding the longitude, meridian, time, culmination of the fixed stars, and the variation of the compass, at sea or on land, independently of refraction and parallax, by one simple observation

Method of Finding the Longitude (1823)
John Tyrrell Baylee

2051316Method of Finding the Longitude1823John Tyrrell Baylee

METHOD

OF

FINDING THE LONGITUDE, MERIDIAN, TIME,

CULMINATION OF THE FIXED STARS,

AND THE

VARIATION OF THE COMPASS,

AT SEA OR ON LAND,

Independently of Refraction and Parallax,

BY ONE SIMPLE OBSERVATION.

BY

JOHN TYRRELL BAYLEE.

LONDON:

PUBLISHED FOR THE AUTHOR,

BY

R. HUNTER, 72, ST. PAUL'S CHURCHYARD.

1823.

CHARLES WOOD, Printer,
Poppin's Court, Fleet Street, London.

METHOD

OF

FINDING THE LONGITUDE,

&c. &c.

To find the Meridian:—When two, or any number of fixed stars, which have the same right ascension, appear in a right line (or right circle), and perpendicular to the horizon of any observer, if a right line be drawn on the earth's surface, or on any plane parallel to that horizon, and perpendicular to the line of fixed stars which is then perpendicular to that horizon, the right line so drawn will give, accurately, the meridian line of that observer. For, let the right line (or right circle), ${\begin{matrix}\mathrm {M} \\|\\\mathrm {E} \end{matrix}}$ , represent the meridian, and the right line (or right circle), H—O, the horizon of any observer, at any parallel of latitude: now, as all the parallels of latitude are parallel to the equator, and as the equator is the boundary of the rational horizon, to which the sensible horizon is parallel; and as when any point in any right line (or right circle), ${\begin{matrix}\mathrm {M} \\|\\\mathrm {E} \end{matrix}}$ , is perpendicular to any other right line (or right circle), H—O, the whole of ${\begin{matrix}\mathrm {M} \\|\\\mathrm {E} \end{matrix}}$ will be perpendicular to H—O; and, further, as any number of fixed stars, which have the same right ascension, must be all in the same right line (or right circle); it follows, that, if among any number of fixed stars, which have the same right ascension, any one of them coincide with any meridian, ${\begin{matrix}\mathrm {M} \\|\\\mathrm {E} \end{matrix}}$ , the whole of them must coincide with that meridian; and hence (and also from the definition of a meridian) it follows, that the whole of these fixed stars will be perpendicular to the horizon H—O. When any fixed star, X, has not exactly the same right ascension as any other fixed star, Y, the culmination of the fixed star X can be found just as if it had the same right ascension as the fixed star Y: for, when the fixed star X is on the meridian, the deflection of the fixed star Y, from the perpendicular at the fixed star X, will be accurately the difference in right ascension between the fixed stars X and Y, and vice versa.^[1]

To find the Time:—When one line, or any number of lines, of fixed stars culminate, that is, come to the meridian, let a good common watch, or watches, be then set as to noon, or twelve o'clock, for each line of stars respectively; and the time indicated by that watch, or those watches, when the same line, or lines, of fixed stars is, or are, on the same meridian the following evening, plus the sun's (or more properly speaking the earth's) motion during twenty-four hours, converted into time, will give a result so very near the true time, as to leave scarcely any error capable of affecting the observation for the longitude^[2].

To find the longitude:—Assume any meridian, A, as a first meridian, and find the time of the culmination of any fixed star, with respect to the meridian A: the difference between the time so found, and the time of the culmination of the same fixed star for the same day of any year, with respect to any other meridian, B, will give the difference of longitude between any places which are under the two meridians A and B. For, the diurnal motion of the earth on its axis being equable and uniform, at least so far as has been hitherto practically noticed, it follows, that equal relative spaces of the firmament must pass over equal and absolute spaces of the earth's surface in equal times. The times of the respective culminations should be found by observation, and not by calculation only.^[5]

To find the Variation:—When the meridian is found the variation is found: but the meridian has been found, by the method here presented, and therefore the variation is found.^[6]

In the Advertisement and in the Notes to this Method, some expressions, such as "the efficiency of my method," may appear as originating from self-sufficiency; but I can with truth assure my readers they have originated from the opposite principle. Attached to the system I had studied, the reflection of many years had influence scarcely sufficient to induce me to depart from it in any degree; because the high respect I cherish for the distinguished characters who had shone in the walks of science, and who had themselves tenaciously adhered to that system, and to whose attainments mine are comparatively nothing, would not admit me to think of any other: it was not, therefore, until conviction, arising from a long series of experiments and observations, founded on a regular inductory procedure, had arrested my attention, that I ventured to think I could do any thing out of the usual course; and even then I was apprehensive, that the novelty of my method would operate against every prospect of success; an apprehension which has been, for the moment, painfully realised; though I have no doubt that a short but fair trial will establish the method which I have with much respect and diffidence ventured to present. Long and intense application to the phenomena of nature, and in particular to the solar system, led me to suppose, that the noble simplicity, which is observable in the laws which those phenomena obey, did not require much apparatus or abstruse calculus to develop them; and it struck me, that the reason why they were not generally understood and practically applied was, because the technical language through which they are presented was more difficult to know than the laws themselves. I ventured to investigate Nature in her own simple attire; and, thus investigating, I found I could do in a few months what would before require the labour of as many years. I feared I had deceived myself in the conclusion, because I had previously studied the subject in another way; and, in consequence, I selected two of my pupils, in whom I could confide, and who were new to the subject, and I was favoured with success beyond what I had hoped to meet. When I speak of much apparatus and abstruse calculus, I do not mean to decry either apparatus or calculus; I mean nothing more than to keep them in their proper place; that is, to keep them subordinate to Nature, and not (vain labour!), to substitute the complexity of Art for the simplicity of Nature! Since I visited this city, I have sighed during my solitary walks through her streets, when I have viewed the greatest artists in the world looking at their admirable productions, which lay comparatively neglected: and why? Because more is expected from them than human effort can accomplish.^[7] Let the phenomena to which those admirable productions are skilfully adapted be well understood, the value of them will then be known, their application will become familiar, and the artists will be stimulated to excel, because they will meet an adequate remuneration. Our corporeal organs being subject to decay, we are obliged to resort to various contrivances to remedy the defects; and it also often happens, that in some persons an original malconformation is exhibited. The profane sceptic generally lays hold of those apparent defects to support his wild system, which consigns to fortuitous causes the laws of the universe: but to him who through Divine grace takes a calm survey of the order established by Omniscience,

"Reason's eye refined clears up apace,"

and he is led to adore the wisdom which is conspicuous in those apparent defects. Such a man sees that they operate as a stimulus to the exercise of the inventive powers, and

"Make heedless, rambling impulse learn to think;"

for while the effort to remedy those apparent defects gives employment to thousands, the minds of those who are employed, as well as the minds of those who avail themselves of their inventions, acquire a knowledge of the human frame, and of the general operations of nature, to which they would have remained strangers had no necessity been laid upon them. But the profane sceptic may, in his impious wisdom, ask, "If Omniscience directs the universe, why does imperfection appear!" But as it invariably costs a man more effort to be vicious than to be good, the answer does not require as much labour as the question. Our ideas of organic perfection are merely relative. The myope may complain of the short focal distance of his eye; while that very circumstance enables him to see minute objects with greater distinctness, and fits him for performing what others dare not undertake, without risking the total loss of sight. Other cases may be adduced; but to every pious mind one general observation is sufficient: these apparent imperfections shew us that this earth is not our abiding place; they lead us to look for help from on high; they call forth the kindly feelings, and teach us mutual dependence, while they counteract the supineness of corrupt nature, and are thus instrumental in conducting man to the end of his creation— to be virtuous and useful. I am led to make these observations, because those who do not know me may think I affect to despise those helps, which the imperfection or the imbecility of our organs require, when I speak of the efficiency of my Method, and the ease with which a competent knowledge of it may be attained; while the fact is, that my Method tends to render the application of those helps more general, by bringing the objects to which they are applied more within the range of familiar notice. To every enlightened and unprejudiced mind, simplicity in design and facility in execution must prove the strongest recommendations; while to those who think differently, utility must remain for ever undefined, and talent and empiricism become terms of similar import.

The Author of the foregoing Method proposes to engage in a Course of Astronomy, should a sufficient number of Students offer; and accordingly he begs respectfully to present the following

OUTLINES

OF

A COURSE OF ASTRONOMY,

ON

A SYSTEM STRICTLY SCIENTIFICAL,

Yet so easy of Attainment, that any Person, though previously unacquainted with Astronomy, may, in a short time, with moderate attention, become profoundly versed in it.

The Places of the Fixed Stars and of the Planets; their Rising, Culmination, Setting, Altitude.—The Periods, Distances, Magnitudes of the Planets; their Positions, as affecting their Motions in their Orbits with respect to the Laws of Gravity.—The Aspect of the Firmament at all times, by night or day, including the Medium Cœli and the Nonagesimal Degree, with accuracy and precision, and without recurring to tedious calculation, or to instruments or apparatus of any description, taking as centres, successively, the Zenith Point, the Poles of the Equinoctial, and those of the Ecliptic.—The Position of Terrestrial Objects, as indicated by the Fixed Stars and by the Planets.—Terrestrial Latitude.—Terrestrial Longitude.—Theory of the Tides.

The object of the system on which this Course of Astronomy is founded is to render that noble science accessible without the toil of abstruse calculation or the expense of extensive apparatus. Through the medium of this system it is confidently expected this object will be attained by the attentive student in a short time, and with comparatively small effort, though with a strict adherence to the rigour of scientifical demonstration, as found in Newton's Principia, La Place's Mecanique Celeste, &c., to which constant reference will be had, but without labour to the student; nor will any expense be incurred beyond the fee, which is moderate; for the necessary instruction as to data will be given elegantly printed and free of expense, though extensive. No plates, no complex apparatus will be presented; the Firmament alone will be the object of contemplation; and this glorious display of the Creator's "handy-work," it is hoped, under his gracious assistance, the student will read soon and with intelligence, and so as to apply, without hesitation, to valuable practical purposes the heads above stated, and also a considerable mass of important particulars which has been, for the moment, omitted, in order to avoid fastidious display; but it will be found, that the system now presented will enable any attentive student, far within the limits of the time generally requisite, to conduct a ship round the globe, so far as nautical astronomy is concerned, unaided by any other apparatus than a good common watch, a common quadrant, and a sea compass, with which last the student could dispense if the firmament were clear at all times: and by this system the attentive student will also readily learn to depict, from nature, all the regions, kingdoms, &c., of the globe, an object which it is vain to attempt except through the medium of astronomy.

Letters directed to 40, Philip-street, Kingsland Road, and No. 72, St. Paul's Churchyard.

ADVERTISEMENT.

The method of finding the longitude, &c., which I have now, with high respect, the honour of presenting to the British Public, I had also the honour of presenting to the Board of Longitude, with the high respect and deference due to that learned body, on the seventh instant, but unaccompanied by any elucidation, because I had been, on inquiry at the admiralty, informed, that an outline only was necessary: and, on the evening of the eighth instant, I was honoured with a negative from the Board of Longitude, through their secretary, as follows:—

Admiralty, 7th November, 1822.

Sir;

I am directed to inform you, that your communication respecting a method of finding the longitude, the meridian, the variation, and the time, of this day's date, has been taken into consideration by the Board of Longitude: but that the Board is of opinion, that no satisfactory result can be obtained by the method you propose.

I have the honour to be, Sir, ⁠
Your very obedient servant,⁠
(A copy, signed)⁠Thomas Young, M. D.⁠

Sec. Bd. Longit.

Mr. John Tyrrell Baylee, Old Slaughter's
Coffee House, St. Martin's Lane.

If a feeling, which to me is dearer than life, did not induce me to give candour her full sanction, by stating the opinion which the Board of Longitude has expressed of my method, the disclosure would become an imperative obligation; because any address to England, the queen of nations, must be not only founded in truth, but it must also be supported by candour: for the lofty fame which England has acquired by her strict adherence to those main pillars of society renders it impossible for her to act without resting on them; and it is because she thus acts, that the King of kings has vouchsafed to give her wisdom and power to overcome the united effort of the surrounding nations, to whom she stands, and will, I trust, remain, a bright example.

In presenting my Method, after having received the negative just stated, I must necessarily feel diffident: but my diffidence arises from the high respect and deference due to the rank and talent of the Board of Longitude; and not, in any measure, from an apprehension of any material error in my Method; for it has not been until I had spent many years in inquiry and observation, and in examining the highest works of our own countrymen as well as those of most other nations, that I have ventured to meet the public on principles, which certainly have never before been presented to the world in the manner in which I apply them; for though the phenomena of nature, hitherto existing, cannot be new; yet the mode of applying those phenomena to practical purposes admits of endless variety: and, as I stand on the undeviating laws ordained by the Almighty, I well know the efficiency of my Method; and that conviction leads me to conclude, that the simple guise in which the outline of my Method appeared, or a press of important business, was the cause why the Board of Longitude omitted all inquiry, of me, into my Method, which is now presented in a more expanded form; not, however, with the presumptuous intention of controverting the opinion of the Board of Longitude, but because I conceive my Method is efficient, and that, if it be found so, it must prove a very high acquisition to the greatest maritime people in the world—the British Public.

JOHN TYRRELL BAYLEE.

40, Philip Street, Kingsland Road.

Copy of the Outline, which I presented to the Board of Longitude on the 7th instant.

METHOD

OF

FINDING THE LONGITUDE,

THE MERIDIAN, THE CULMINATION OF THE FIXED STARS, THE VARIATION OF THE COMPASS, AND THE TIME, AT SEA, INDEPENDENTLY OF PARALLAX AND REFRACTION, BY ONE SIMPLE OBSERVATION.

To find the Longitude:—Assume any meridian, R, as a first meridian, and find the time of the culmination of any fixed star, for any day of any year, with respect to the meridian R: the difference between the time so found and the time of the culmination of the same fixed star, for the same day of any year, with respect to any other meridian, S, will give the difference of longitude between the two meridians, R and S. The times of the respective culminations should, for greater accuracy, be found by observation, and not by calculation only.

To find the Meridian:—Let the right line (or right circle), ${\begin{matrix}\mathrm {M} \\|\\\mathrm {E} \end{matrix}}$ , represent the meridian, and the right line (or right circle), H—O, the horizon of any place at any parallel of latitude: now as all the parallels of latitude are parallel to the equator; and as the equator is the boundary of the rational horizon; and as when any point in any right line (or right circle) ${\begin{matrix}\mathrm {M} \\|\\\mathrm {E} \end{matrix}}$ , is perpendicular to any right line (or right circle), H—O, the whole of ${\begin{matrix}\mathrm {M} \\|\\\mathrm {E} \end{matrix}}$ will be perpendicular to H—O and, further, as any number of fixed stars which have the same right ascension must be in the same right line (or right circle); it follows, that if among any number of fixed stars, having the same right ascension, any one of them coincide with any meridian, ${\begin{matrix}\mathrm {M} \\|\\\mathrm {E} \end{matrix}}$ , the whole of them must coincide with that meridian; and hence, and also from the definition of a meridian, it follows, that the whole of them will be perpendicular to the horizon, H—O. When any fixed star, X, has not exactly the same right ascension as any other fixed star, Y, the time of the culmination of X can be found, by the method here presented, as if X had the same right ascension as Y; for let the fixed star X be on the meridian, and then will the deflection of the fixed star Y, from the perpendicular at X, be accurately the difference in right ascension between X and Y, and vice versa.

To find the variation of the Compass:—When the meridian is found the variation is found; but the meridian is found by the method here presented, and therefore the variation is found.

To find the Time:—Having found the times of the culminations of two or three fixed stars, let good common watches be set to each of these times respectively, considering the time of each culmination as noon: the time thus found, compared with the time found by computing the difference of the right ascensions of those stars, will give a result so near the true time, as to leave scarcely any error capable of affecting the observation for the longitude.

I have no doubt but the longitude will be found with ease and facility by my method, within eight miles of absolute distance, and perhaps within half that distance: and with respect to tracing the firmament, I may, I conceive, from long experience and extensive research, challenge all the publications extant for a method which will bear any moderate competition with what I am prepared to present, in point of simplicity, accuracy, or easiness of attainment.

The corrections applicable to the several particulars here presented are obvious; and I do ardently desire to undergo the most severe scrutiny.

JOHN TYRRELL BAYLEE.

London, Eleventh Month 7, 1822.

THE END.

CHARLES WOOD, Printer,
Poppin's Court, Fleet , London.

Notes:

↑ The method here presented, for ascertaining the meridian of any observer, will be found accurate, within limits so very narrow, as at first view to appear incredible: but when it is considered, that this method is no way affected by refraction or by parallax, the former of which constitutes the grand natural obstacle to accuracy in all astronomical observations which are made according to the methods heretofore practised; and the latter, on account of its intimate connection with the former, presents serious difficulties; I say, when it is considered, that the method here presented is not clogged by those insuperable impediments, doubt will subside; and according as observations are made pursuant to this method, which substitutes the simplicity of nature for the complexity of art, doubt will give place to confidence. That this method is no way affected by refraction or by parallax is clear; because it does not require any recurrence to the elevation or to the depression of the celestial bodies; and as light moves only in right lines, the position of those bodies can be affected only with respect to their elevation and to their depression by refraction: and the fixed stars, which are the only celestial bodies to which this method has a primary regard, have no sensible parallax.

The method now in use for ascertaining the meridian of an observer, by the altitudes of any of the celestial bodies above the horizon of that observer, is attended by several impediments, which constitute an insurmountable bar to the accuracy which most observations demand. Every person, however slightly conversant in those subjects, knows, that the refractive powers of any medium is proportionate to its density; and that, of all media, the atmosphere is subject to the greatest fluctuations: those fluctuations are very numerous, and many of them have hitherto eluded the utmost effort of investigation, though aided by the nicest experimental tests. And, besides, the causes of many of them are wholly unknown: and, again, the causes of some of them, though known as to their general operation, cannot be traced in particular instances, in which it often happens, that the knowledge of them is most wanting: so that to say when the refractive power of the atmosphere is a maximum (or at its greatest power), or when it is a minimum (or at its least power), has been hitherto found absolutely impossible: and the knowledge of its intermediate powers, for the same reasons, is so obscure as to render results which are affected by atmospherical refraction extremely doubtful.

If this were the proper place, it would be quite easy to show, that the labours of the closet on the subject of atmospherical refraction, however aided by experiment and adorned with the specious intricacy of theoretical calculus, have always some latent assumption mixed up with them; and not only so, but that experiments made with the greatest care, at the same time of the same day, in the same latitude and temperature, &c., but not in the same place and with the same identical instrument, never indicate the same results: and further, that even under all the same circumstances, as nearly similar as possible, amongst several observations scarcely any two of them will indicate the same results; so that after all the labour which has been expended, atmospherical refraction remains still—a fugitive principle, and the observations affected by it remain shaded by obscurity and by doubt.

The difficulty of ascertaining the horizon with tolerable accuracy is another insurmountable impediment to finding a meridian within the necessary limits. Several days pass, during which the horizon remains undefined, in consequence of clouds, mists, &c.; and even when the firmament is quite clear and the weather calm, the undulations of the sea, the motion of the vessel, the dip of the horizon, &c. are adverse to accuracy of observation; insomuch, that seamen are known frequently to take an average for the dip, and even to lump, as they term it, the dip and the refraction! On land, not bordering on the sea, any mode of attempting to ascertain the horizon amounts almost to absurdity. Another obstacle to ascertaining the horizon is parallax, which, though in itself it is ascertainable, admitting the earth to be a perfect sphere, yet as the observation for parallax is necessarily affected by refraction, it must, inevitably, partake of the uncertainty which is always attendant on refraction: other considerations might easily be adduced, but more would appear unnecessary.
↑ Let the fixed stars, Alpharetz, α, in the head of Andromeda, and Algenib, γ, in the wing of Pegasus, be the fixed stars taken, suppose for the twelfth of next month^[3]: now, if a good watch be set as to noon, or twelve o'clock, when those stars culminate, that is, when they are on the meridian, on the evening of the eleventh; that watch will on the evening of the twelfth, when those stars are again on the same meridian, indicate 24 hours, minus the motion of the sun (more properly speaking, the motion of the earth) in its orbit, converted into time, during the interval between those two observations: and if a meridian line be traced as directed by this method, and the sun's culmination, that is, his coming on that line, be observed; the same watch will indicate the difference in right ascension, converted into time, between the sun and those stars, minus the motion of the sun in its orbit, converted into time, during the interval between the observation of the stars and the time indicated by the watch at the culmination of the sun. As similar observations may be made on several lines of fixed stars during the same night, such a number of means present themselves as will reduce any error that may arise to a nullity, so far as respects the observation for the longitude.

The method heretofore in use for finding true time, by comparing the culmination of the sun with twelve o'clock, as indicated by a well-regulated clock, requires a correction which is compounded of two elements. The unequal motion of the earth in its orbit, and the obliquity of the earth's axis to the sphere of its orbit: the latter of these, the obliquity of the earth's axis, may be understood by viewing the relative position of the equinoctial and the ecliptic on a celestial globe; but the former, the unequal motion of the earth in its orbit, can be discovered only by observations on the sun, or, which is much better, by observations on the fixed stars.

The method now presented is materially different. With the orbits of the fixed stars we are wholly unacquainted; their distances mock human conception, and lay the pretensions of science in the dust. The distance between the sun and the earth is very great indeed; but brought into competition with the distance between the fixed stars and the sun, it becomes like the tiny mote, which we behold floating in the sun's beams, compared with the united bulk of all the vast globes which revolve about our sun; and we may include in the enormous bulk our sun itself, which is, at least, a million of times larger than our earth! In consequence of their distance their diameters are so minute, that in observation for finding the times of their culminations an error in finding their centers becomes a nullity. Here then is one advantage which the method here presented possesses over all others; and another, and a still greater advantage, is, that the motion of the earth is no way affected by them; and, as they are quite beyond her orbit, her position compared with theirs may be depended on within very narrow limits; for it is only the precession of the equinoxes and the nutation of the earth's axis that can affect her position with respect to theirs; and the precession is known and amounts to only a small quantity in a year, while the nutation exhibits a progressive annual change, which experiences a progressive annual compensation. Again: the sun being the center round which the earth annually revolves, the sun and the earth are always at diameters^[4] from each other, so far as respects their apparent relative positions with respect to the fixed stars; and as the fixed stars do not affect either the sun or the earth, so far as mortals have hitherto discovered, we may indifferently take the sun's place or the earth's place amongst the fixed stars; and, consequently, by finding the time of the culmination of a fixed star, the right ascension of which is known, we have the right ascension of the sun; and we have, also, the time of the culmination of the sun; for the difference of those right ascensions, in times plus or minus, according as the sun is in antecedentia, or in consequentia, with respect to the fixed star, applied to either of those culminations will give the time; and thus, as we can by observation ascertain the quantity of the earth's motion in its orbit, true time can be known, so as to give the longitude at sea or on land, within seven miles of absolute distance. Whereas the method now in use compares the culmination of the sun with twelve o'clock, as indicated by a good clock, which can never be exact, because the clock is itself regulated by the culmination of the sun, and must, of course, partake of the errors in finding that culmination; and as the motion of the sun is in reality nothing else than the motion of the earth, and as the earth is affected by the sun, as well as by other agents, the time found by the sun's culmination cannot be depended on for the longitude, particularly when we take into the account the errors which are inseparable from observations on refraction and parallax. The case is still worse with the lunar observations, as I shall probably have occasion to show hereafter.
↑ These two fixed stars are selected merely because the square of Pegasus is a remarkable constellation, which just now culminates at a convenient hour in the evening: the other two stars in this square may be taken, but at an earlier hour.
↑ In the case under consideration, finding the time, I take no greater liberty than what is universally assumed, namely, that in consequence of the distance of the sun from the earth, the excentricity of the earth's orbit may be neglected; in point of fact it can have no influence on my method.
↑ The mean motion of the sun is stated to be about fifty-nine minutes of a degree for each day; because as every circle, according to the English division, contains 360 degrees, and as our years are between 365 and 366 days, therefore,
Days.
365
plus :
Degrees.
360
::
Day.
1
:
Minutes.
59 plus.
But this mean is taken on the presumption of the annual motion being equal and uniform, in equal times, through the entire orbit; but a slight inspection of the sun's right ascension (to go no further), as presented in the Nautical Almanack, will be quite sufficient to prove the absurdity of applying this mean in particular cases; and I need not hesitate to say, that the irregularity of the earth's annual motion has a sensible effect on the earth's diurnal motion on its axis; which effect, I apprehend, demands particular notice.
↑ I shall reserve my observations on the variation of the compass for another occasion, as I wish to enter more largely on it than I can do at this moment, in consequence of the pressing demands of a large family, to whom my absence, which has been already too long, may be highly injurious.
↑ "I cannot read with your spectacles," said the clown, "though you have over your door—'Spectacles, to help people to read!'" "Perhaps," replied the artist, "you could not read before you put them on." The reply of the artist is worth remembering; it may save many mistakes.

This work was published before January 1, 1929, and is in the public domain worldwide because the author died at least 100 years ago.

Public domainPublic domainfalsefalse

[p4-1] The method here presented, for ascertaining the meridian of any observer, will be found accurate, within limits so very narrow, as at first view to appear incredible: but when it is considered, that this method is no way affected by refraction or by parallax, the former of which constitutes the grand natural obstacle to accuracy in all astronomical observations which are made according to the methods heretofore practised; and the latter, on account of its intimate connection with the former, presents serious difficulties; I say, when it is considered, that the method here presented is not clogged by those insuperable impediments, doubt will subside; and according as observations are made pursuant to this method, which substitutes the simplicity of nature for the complexity of art, doubt will give place to confidence. That this method is no way affected by refraction or by parallax is clear; because it does not require any recurrence to the elevation or to the depression of the celestial bodies; and as light moves only in right lines, the position of those bodies can be affected only with respect to their elevation and to their depression by refraction: and the fixed stars, which are the only celestial bodies to which this method has a primary regard, have no sensible parallax.

The method now in use for ascertaining the meridian of an observer, by the altitudes of any of the celestial bodies above the horizon of that observer, is attended by several impediments, which constitute an insurmountable bar to the accuracy which most observations demand. Every person, however slightly conversant in those subjects, knows, that the refractive powers of any medium is proportionate to its density; and that, of all media, the atmosphere is subject to the greatest fluctuations: those fluctuations are very numerous, and many of them have hitherto eluded the utmost effort of investigation, though aided by the nicest experimental tests. And, besides, the causes of many of them are wholly unknown: and, again, the causes of some of them, though known as to their general operation, cannot be traced in particular instances, in which it often happens, that the knowledge of them is most wanting: so that to say when the refractive power of the atmosphere is a maximum (or at its greatest power), or when it is a minimum (or at its least power), has been hitherto found absolutely impossible: and the knowledge of its intermediate powers, for the same reasons, is so obscure as to render results which are affected by atmospherical refraction extremely doubtful.

If this were the proper place, it would be quite easy to show, that the labours of the closet on the subject of atmospherical refraction, however aided by experiment and adorned with the specious intricacy of theoretical calculus, have always some latent assumption mixed up with them; and not only so, but that experiments made with the greatest care, at the same time of the same day, in the same latitude and temperature, &c., but not in the same place and with the same identical instrument, never indicate the same results: and further, that even under all the same circumstances, as nearly similar as possible, amongst several observations scarcely any two of them will indicate the same results; so that after all the labour which has been expended, atmospherical refraction remains still—a fugitive principle, and the observations affected by it remain shaded by obscurity and by doubt.

The difficulty of ascertaining the horizon with tolerable accuracy is another insurmountable impediment to finding a meridian within the necessary limits. Several days pass, during which the horizon remains undefined, in consequence of clouds, mists, &c.; and even when the firmament is quite clear and the weather calm, the undulations of the sea, the motion of the vessel, the dip of the horizon, &c. are adverse to accuracy of observation; insomuch, that seamen are known frequently to take an average for the dip, and even to lump, as they term it, the dip and the refraction! On land, not bordering on the sea, any mode of attempting to ascertain the horizon amounts almost to absurdity. Another obstacle to ascertaining the horizon is parallax, which, though in itself it is ascertainable, admitting the earth to be a perfect sphere, yet as the observation for parallax is necessarily affected by refraction, it must, inevitably, partake of the uncertainty which is always attendant on refraction: other considerations might easily be adduced, but more would appear unnecessary.

[p5-2] Let the fixed stars, Alpharetz, α, in the head of Andromeda, and Algenib, γ, in the wing of Pegasus, be the fixed stars taken, suppose for the twelfth of next month^[3]: now, if a good watch be set as to noon, or twelve o'clock, when those stars culminate, that is, when they are on the meridian, on the evening of the eleventh; that watch will on the evening of the twelfth, when those stars are again on the same meridian, indicate 24 hours, minus the motion of the sun (more properly speaking, the motion of the earth) in its orbit, converted into time, during the interval between those two observations: and if a meridian line be traced as directed by this method, and the sun's culmination, that is, his coming on that line, be observed; the same watch will indicate the difference in right ascension, converted into time, between the sun and those stars, minus the motion of the sun in its orbit, converted into time, during the interval between the observation of the stars and the time indicated by the watch at the culmination of the sun. As similar observations may be made on several lines of fixed stars during the same night, such a number of means present themselves as will reduce any error that may arise to a nullity, so far as respects the observation for the longitude.

The method heretofore in use for finding true time, by comparing the culmination of the sun with twelve o'clock, as indicated by a well-regulated clock, requires a correction which is compounded of two elements. The unequal motion of the earth in its orbit, and the obliquity of the earth's axis to the sphere of its orbit: the latter of these, the obliquity of the earth's axis, may be understood by viewing the relative position of the equinoctial and the ecliptic on a celestial globe; but the former, the unequal motion of the earth in its orbit, can be discovered only by observations on the sun, or, which is much better, by observations on the fixed stars.

The method now presented is materially different. With the orbits of the fixed stars we are wholly unacquainted; their distances mock human conception, and lay the pretensions of science in the dust. The distance between the sun and the earth is very great indeed; but brought into competition with the distance between the fixed stars and the sun, it becomes like the tiny mote, which we behold floating in the sun's beams, compared with the united bulk of all the vast globes which revolve about our sun; and we may include in the enormous bulk our sun itself, which is, at least, a million of times larger than our earth! In consequence of their distance their diameters are so minute, that in observation for finding the times of their culminations an error in finding their centers becomes a nullity. Here then is one advantage which the method here presented possesses over all others; and another, and a still greater advantage, is, that the motion of the earth is no way affected by them; and, as they are quite beyond her orbit, her position compared with theirs may be depended on within very narrow limits; for it is only the precession of the equinoxes and the nutation of the earth's axis that can affect her position with respect to theirs; and the precession is known and amounts to only a small quantity in a year, while the nutation exhibits a progressive annual change, which experiences a progressive annual compensation. Again: the sun being the center round which the earth annually revolves, the sun and the earth are always at diameters^[4] from each other, so far as respects their apparent relative positions with respect to the fixed stars; and as the fixed stars do not affect either the sun or the earth, so far as mortals have hitherto discovered, we may indifferently take the sun's place or the earth's place amongst the fixed stars; and, consequently, by finding the time of the culmination of a fixed star, the right ascension of which is known, we have the right ascension of the sun; and we have, also, the time of the culmination of the sun; for the difference of those right ascensions, in times plus or minus, according as the sun is in antecedentia, or in consequentia, with respect to the fixed star, applied to either of those culminations will give the time; and thus, as we can by observation ascertain the quantity of the earth's motion in its orbit, true time can be known, so as to give the longitude at sea or on land, within seven miles of absolute distance. Whereas the method now in use compares the culmination of the sun with twelve o'clock, as indicated by a good clock, which can never be exact, because the clock is itself regulated by the culmination of the sun, and must, of course, partake of the errors in finding that culmination; and as the motion of the sun is in reality nothing else than the motion of the earth, and as the earth is affected by the sun, as well as by other agents, the time found by the sun's culmination cannot be depended on for the longitude, particularly when we take into the account the errors which are inseparable from observations on refraction and parallax. The case is still worse with the lunar observations, as I shall probably have occasion to show hereafter.

[3] These two fixed stars are selected merely because the square of Pegasus is a remarkable constellation, which just now culminates at a convenient hour in the evening: the other two stars in this square may be taken, but at an earlier hour.

[4] In the case under consideration, finding the time, I take no greater liberty than what is universally assumed, namely, that in consequence of the distance of the sun from the earth, the excentricity of the earth's orbit may be neglected; in point of fact it can have no influence on my method.

[5] The mean motion of the sun is stated to be about fifty-nine minutes of a degree for each day; because as every circle, according to the English division, contains 360 degrees, and as our years are between 365 and 366 days, therefore,
Days.
365
plus :
Degrees.
360
::
Day.
1
:
Minutes.
59 plus.
But this mean is taken on the presumption of the annual motion being equal and uniform, in equal times, through the entire orbit; but a slight inspection of the sun's right ascension (to go no further), as presented in the Nautical Almanack, will be quite sufficient to prove the absurdity of applying this mean in particular cases; and I need not hesitate to say, that the irregularity of the earth's annual motion has a sensible effect on the earth's diurnal motion on its axis; which effect, I apprehend, demands particular notice.

[6] I shall reserve my observations on the variation of the compass for another occasion, as I wish to enter more largely on it than I can do at this moment, in consequence of the pressing demands of a large family, to whom my absence, which has been already too long, may be highly injurious.

[7] "I cannot read with your spectacles," said the clown, "though you have over your door—'Spectacles, to help people to read!'" "Perhaps," replied the artist, "you could not read before you put them on." The reply of the artist is worth remembering; it may save many mistakes.

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