James Bradley's 1747 letter read to the Royal Society

The letter James Bradley wrote, read to the Royal Society in 1747, is remarkable in that it gives us a very clear understanding of how Bradley worked and details his careful approach to verifying his hypotheses. We give below a version of the first part of this long letter:


A Letter to the Right honourable George Earl of Macclesfield concerning an apparent Motion observed in some of the fixed Stars. By James Bradley D.D. Astronomer Royal, and F.R.S.

Read at a meeting of the Royal Society, February 14, 1747.

My Lord,

The great Exactness, with which Instruments are now constructed, hath enabled the Astronomers of the present Age to discover several Changes in the Positions of the heavenly Bodies; which, by reason of their Smallness had escaped the Notice of their Predecessors. And although the Causes of such Motions have always subsisted, yet Philosophers had not so fully considered, what the Effects of those known Causes would be, as to demonstrate a priori the Phenomena they might produce; so that Theory itself is here, as well as in many other Cases, indebted to Practice, for the Discovery of some of its most elegant Deductions. This points out to us the great Advantage of cultivating this as well as every other Branch of Natural Knowledge, by a regular Series of Observations and Experiments.

The Progress of Astronomy indeed has always been found, to have so great a Dependence upon accurate Observations, that, till such were made, it advanced but slowly: For the first considerable Improvements that it received, in point of Theory, were owing to the renowned Tycho Brahe; who far exceeding those that had gone before him, in the Exactness of his Observations, enabled the sagacious Kepler to find out some of the principal Laws, relating to the Motion of the heavenly Bodies. The Invention of Telescopes and Pendulum-Clocks affording proper Means of still farther improving the Praxis of Astronomy; and these being also soon succeeded by the wonderful Discoveries made by our Great Newton, as to its Theory; the Science, in both respects, had acquired such extraordinary Advancement, that future Ages seemed to have little room left, for making any great Improvements. But, in fact, we find the Case to be very different; for, as we advance in the means of making more nice Inquiries, new Points generally offer themselves, that demand our Attention. The Subject of my present Letter to your Lordship, is a Proof of the Truth of this Remark: for, as soon as I had discovered the Cause, and settled the Laws of the Aberrations of the fixed Stars, arising from the Motion of Light, &c. whereof I gave an Account in No. 406 of the Philosophical Transactions; my Attention was again excited by another new Phenomenon, viz. an annual Change of Declination in some of the fixed Stars which appeared to be sensibly greater about that time, than a Precession of the Equinoctial Points of 50" in a Year would have occasioned. The Quantity of the Difference, though small in itself, was rendered perceptible, through the Exactness of my Instrument, even in the first Year of my Observations; but being then at a Loss to guess, from what Cause that greater Change of Declination proceeded, I endeavoured to allow for it in my Computations, by making use of the observed annual Difference, as mentioned in p. 652. of the same Transaction.

From that time to the present, I have continued to make Observations at Wansted, as Opportunity offered, with a View of discovering the Laws and Cause of this Phenomenon: For, by the Favour of my very kind and worthy Friend Matthew Wymondefold Esq, my Instrument has remained, where it was first erected; so that I have been able, without any Interruption, which the Removal of it to another Place would have occasioned, to proceed on with my intended Series of Observations, for the Space of twenty Years: a Term somewhat exceeding the whole Period of the Changes, that happen in this Phenomenon.

When I shall mention the small Quantity of the Deviation, which the Stars are subject to, from the Cause that I have been so long searching after; I am apprehensive, that I may incur the Censure of some Persons, for having spent so much Time in the Pursuit of such a seeming Trifle: But the candid Lovers of Science will, I hope, make due Allowance for that natural Ardour, with which the Mind is urged on towards the Discovery of Truths, in themselves perhaps of small Moment, were it not that they tend to illustrate others of greater Use.

The apparent Motions of the heavenly Bodies are so complicated, and affected by such a Variety of Causes; that in many Cases it is extremely difficult to assign to each its due Share of Influence; or distinctly to point out, what Part of the Motion is the Effect of one Cause, and what of another: And whilst the joint Effects of all are only attended to, great Irregularities and seeming Inconsistencies frequently occur; whereas, when we are able to allot to each particular Cause its proper Effect, Harmony and Uniformity usually ensue.

Such seeming Irregularities being also blended with the unavoidable Errors, which Astronomical Observations must be always liable to, as well from the Imperfection of our Senses, as of the Instruments that we make use of, have often very much perplexed those, who have attempted to solve the Phenomena: and till Means are discovered, whereby we can separate and distinguish the particular Part of the whole Motion, that is owing to each respective Cause, it will be impossible, to be well assured of the Truth of any Solution. For these Reasons, we generally find, that the more exact the Instruments are, that we make use of, and the more regular the Series of Observations is, that we take; the sooner we are enabled to discover the Cause of any new Phenomenon. For when we can be well assured of the Limits, wherein the Errors of the Observations are contained; and have reduced them within as narrow Bounds as possible, by the Perfection of the Instruments which we employ; we need not hesitate to ascribe such apparent Changes, as manifestly exceed those Limits, to some other Causes. Upon, these Accounts it is incumbent upon the practical Astronomer, to set out at first with the Examination of the Correctness of his Instruments; and to be assured that they are sufficiently exact for the Use he intends to make of them: or at least he should know, within what Limits their Errors are confined.

This Practice has, in an eminent manner, been lately recommended by your Lordship's noble Example; who having, out of a singular Regard for the Science of Astronomy, erected an Observatory, and furnished it with as complete an Apparatus of Instruments, as our best Artists could contrive; would not fully rely on their Exactness, till their Divisions had undergone the strictest Re-examination: whereby they are probably now rendered as perfect in their kind, as any extant, or as human Skill can at present produce.

The Lovers of this Science in general, cannot but acknowledge their Obligations to your Lordship on this Account; but I find myself more particularly bound to do it; since, by means of your Lordship's most accurate Observations, I have been enabled to settle some principal Elements; which I could not at present otherwise have done, for want of an Instrument at the Royal Observatory, proper for that Purpose: For the large mural Quadrant, which is there fixed to observe Objects lying Southward of the Zenith, however perfect an Instrument it may be in it self, is not alone sufficient to determine, with proper Exactness, either the Latitude of the Observatory, or the Quantity of Refraction corresponding to different Altitudes: For it being too heavy to be conveniently removed; and the Room wherein it is placed, being too small to admit of its being turned to the opposite Side of the Wall, whereon it now hangs; I cannot, by actual Observations of the circumpolar Stars, settle those necessary Points; and therefore have endeavoured to do it, by comparing my own with your Lordship's Observations: and until this Defect in the Apparatus belonging to the Royal Observatory be removed, we must be indebted to your Lordship, for the Knowledge of its true Situation.

A Mind intent upon the Pursuit of any kind of Knowledge, will always be agreeably entertained, with what can supply the most proper means of attaining it: Such, to the practical Astronomer, are exact and well-contrived Instruments; And I reflect with Pleasure on the Opportunities I have enjoyed, of cultivating an Acquaintance and Friendship with the Person, that, of all others, has most contributed to their Improvement. For I am sensible, that if my own Endeavours have, in any respect, been effectual to the Advancement of Astronomy; it has principally been owing to the Advice and Assistance given me by our worthy Member Mr George Graham; whose great Skill and Judgment in Mechanics, joined with a complete and practical Knowledge of the Uses of Astronomical Instruments, enable him to contrive and execute them in the most perfect manner.

The Gentlemen of the Royal Academy of Sciences, to whom we are so highly obliged for their exact Admeasurement of the Quantity of a Degree under the Arctic Circle, have already given the World very convincing Proofs of his Care and Abilities in those Respects; and the particular Delineation, which they have lately published, of the several Parts of the Sector, which he made for them, hath now rendered it needless, to enter upon any minute Description of mine at Wansted; both being constructed upon the same Principles, and differing in their component Parts, chiefly on account of the different Purposes, for which they were intended.

As mine was originally designed to take only the Differences of the Zenith Distances of Stars, in the various Seasons of the Year, without any View of discovering their true Places; I had no Occasion to know exactly, what Point on the Limb corresponded to the true Zenith: and therefore no Provision was made in my Sector, for the changing of its Situation for that Purpose. Neither was it necessary that the Divisions or Points on the Arc should be set off, with the utmost Accuracy, Equidistant from each other; because, when I observe any particular Star, the same Spot or Point being first bisected by the Plumb-line, and then the Screw of the Micrometer turned until the Star appears upon the middle of the Wire, that is fixed in the common Focus of the Glasses of the Telescope, I can thereby collect, how far the Star is from that given Point at the Time of Observation: and afterwards, by comparing together the several Observations that are made of it, I am able to discover what apparent Change has happened. The Quantity of the visible Alteration, in the Position of the Stars, being expressed by Revolutions and Parts of a Revolution, of the Screw of the Micrometer, I endeavoured to determine, with great Care, the true Angle answering thereto: and after various Trials, I thoroughly satisfied myself, both of the Equality of the Threads of the Screw, and of the precise Number of Seconds corresponding to them.

But although these Points could be settled with great Certainty, I was nevertheless obliged to make one Supposition; which perhaps to some Persons may seem of too great Moment in the present Inquiry, to be admitted without an evident Proof from Facts and Experiments. For I suppose, that the Line of Collimation of my Telescope has invariably preserved the same Direction, with respect to the Divisions upon the Arc, during the whole Course of my Observations. And indeed it was on account of the Objections, which might have been raised against such a Postulate, that I thought it necessary, to continue my Series of Observations for so many Years, before I published the Conclusions, which I shall at present endeavour to draw from them.

Whoever compares the Result of the several Trials, that have been made by the Gentlemen of the Academy of Sciences, for determining the Zenith Point of their Sector, since their Return from the North; will, I presume, allow that mine is not an unreasonable or precarious Supposition: since it is evident, from their Observations, that the Line of Collimation of that Instrument underwent no sensible Change in its Direction, during the Space of more than a whole Year; although it was several times taken down, and set up again in different and remote Places; whereas mine hath always remained suspended in the same Place.

But besides such a strong Argument for the Probability of the Truth of my Supposition, I have the Satisfaction of finding it actually verified by the Observations themselves; which plainly prove, that at the End of the full Period of the Deviations which I am going to mention, the Stars are found to have the same Positions by the Instrument, as they ought to have, supposing the Line of Collimation to have continued unaltered from the Time when I first began to observe.

I have already taken notice, in what manner this Phenomenon discovered itself to me at the End of my first Years Observations, viz. by a greater apparent Change of Declination in the Stars near the Equinoctial Colure, than could arise from a Precession of 50" in a Year; the mean Quantity now usually allowed by Astronomers. But there appearing at the same time, an Effect of a quite contrary Nature, in some Stars near the Solstitial Colure, which seemed to alter their Declination less than a Precession of 50" required; I was thereby convinced, that all the Phenomena, in the different Stars, could not be accounted for, merely by supposing, that I had assumed a wrong Quantity for the Precession of the Equinoctial Points.

At first, I had a Suspicion, that some of these small apparent Alterations in the Places of the Stars, might possibly be occasioned by a Change, in the Materials, or in the Position of the Parts of my Sector: But, upon considering how firmly the Arc, on which the Divisions or Points are made, is fattened to the Plate, wherein the Wire is fixed that lies in the Focus of the Object-Glass; I saw no Reason to apprehend, that any Change could have happened in the Position of that Wire and those Points. The Suspension therefore of the Plummet being the most likely Cause, from whence I conceived any Uncertainty could arise; and the Wire of which had been broken three or four times in the first Year of my Observations: I attempted to examine, whether Part of the aforementioned apparent Motions might not have been owing, to the different Plumb-lines that had been made use of. In order to determine this, I adjusted a particular Point of the Arc to the Plumb-line, with all the Exactness I could; and then taking off the old Wire, I immediately hung on another, with which the same Spot was again compared. I repeated the Experiment three or four times, and thereby fully satisfied myself, that no sensible Error could arise from the Use of different Plumb-lines; since the various Adjustments of the same Point agreed with each other, within less than half a Second.

Having then, from such Trials, sufficient Reason to conclude, that these second unexpected Deviations of the Stars, were not owing to any Imperfection of my Instrument; after I had settled the Laws of the Aberrations arising from the Motion of Light, etc. I judged it proper to continue my Observations of the same Stars; hoping that, by a regular and longer Series of them, carried on through several succeeding Years, I might, at length, be enabled to discover the real Cause of such apparent Inconsistencies.

As I resided chiefly at Wansted, after my Sector was erected there in the Year 1727 till the Beginning of May 1732 when I removed from thence to Oxford: I had, during my Abode at Wansted, frequent Opportunities of repeating my Observations; and thereby discovered so many Particulars relating to these Phenomena, that I began to guess what was the real Cause of them.

It appeared from my Observations, that, during this Interval of Time, some of the Stars near the Solstitial Colure, had changed their Declinations 9" or 10" less, than a Precession of 50" would have produced; and, at the same time, that, others near the Equinoctial Colure, had altered theirs about the same Quantity more, than a like Precession would have occasioned: the North Pole of the Equator seeming to have approached the Stars, which come to the Meridian with the Sun, about the Vernal Equinox and the Winter Solstice; and to have receded from those, which come to the Meridian with the Sun, about the Autumnal Equinox and the Summer Solstice.

When I considered these Circumstances, and the Situation of the Ascending Node of the Moon's Orbit, at the time when I first began my Observations; I suspected, that the Moon's Action upon the Equatorial Parts of the Earth might produce these Effects: For, if the Precession of the Equinox be, according to Sir Isaac Newton's Principles, caused by the Actions of the Sun and Moon upon those Parts; the Plane of the Moon's Orbit being at one time, above ten Degrees more inclined to the Plane of the Equator, than at another; it was reasonable to conclude, that the Part of the whole annual Precession, which arises from her Action, would in different Years be varied in its Quantity; whereas the Plane of the Ecliptic, wherein the Sun appears, keeping always nearly the same Inclination to the Equator; that Part of the Precession, which is owing to the Sun's Action, may be the same every Year: And from hence it would follow, that, although the mean annual Precession, proceeding from the joint Actions of the Sun and Moon, were 50"; yet the apparent annual Precession might sometimes exceed, and sometimes fall short, of that mean Quantity, according to the various Situations of the Nodes of the Moon's Orbit.

In the Year 1727 when my Instrument was first set up, the Moon's Ascending Node was near the Beginning of Aries; and, consequently, her Orbit was as much inclined to the Equator, as it can at any time be; and then the apparent annual Precession was found, by my first Year's Observations, to be greater than the mean: which proved, that the Stars near the Equinoctial Colure, whose Declinations are most of all affected by the Precession, had changed theirs, above a tenth Part more than a Precession of 50" would have caused. The succeeding Years Observations proved the same Things and in three or four Years time the Difference became so considerable, as to leave no Room to suspect, that it was owing to any Imperfection, either of the Instrument or Observations.

But some of the Stars, which I had observed, that were near the Solstitial Colure, having appeared to move, during the same time, in a manner contrary to what they ought to have done, by an Increase in the Precession; and the Deviations in them being as remarkable as in the others, I perceived that something more, than a mere Change in the Quantity of the Precession, would be requisite to solve this Part of the Phenomenon. Upon comparing my Observations of Stars near the Solstitial Colure, that were almost opposite to each other in Right Ascension; I found, that they were equally affected by this Cause for whilst gamma Draconis appeared to have moved Northward, the small Star, which is the 35th Camelopardali Hevel in the British Catalogue, seemed to have gone as much towards the South: which showed, that this apparent Motion, in both those Stars, might proceed from a Nutation in the Earth's Axis; whereas the Comparison of my Observations of the same Stars, formerly enabled me to draw a different Conclusion, with respect to the Cause of the annual Aberrations arising from the Motion of Light. For the apparent Alteration in gamma Draconis from that Cause, being as great again as in the other small Star, proved, that that Phenomenon did not proceed from a Nutation of the Earth's Axis; as, on the contrary, this may. Upon making the like Comparison between the Observations of other Stars, that lie nearly opposite in Right Ascension, whatever their Situations were with respect to the Cardinal Points of the Equator, it appeared, that their Change of Declination was nearly equal, but contrary; and such as a Nutation or Motion of the Earth's Axis would effect.

The Moon's Ascending Node being got back towards the Beginning of Capricorn in the Year 1732, the Stars near the Equinoctial Colure appeared, about that time, to change their Declinations no more, than a Precession of 50" required; whilst some of those near the Solstitial Colure altered theirs above 2" in a Year less, than they ought. Soon after, I perceived the annual Change of Declination of the former to be diminished, so as to become less than 50" of Precession would cause; and it continued to diminish till the Year 1736 when the Moons Ascending Node was about the Beginning of Libra, and her Orbit had the least Inclination to the Equator. But by this time, some of the Stars near the Solstitial Colure had altered their Declinations 18" less, since the Year 1727 than they ought to have done from a Precession of 50". For gamma Draconis, which in those nine Years should have gone about 8" more Southerly, was observed in 1736 to appear 10" more Northerly, than it did in the Year 1727.

As this Appearance in gamma Draconis indicated a Diminution of the Inclination of the Earth's Axis to the Plane of the Ecliptic; and as several Astronomers have supposed that Inclination to diminish regularly; if this Phenomenon depended upon such a Cause, and amounted to 18" in nine Years, the Obliquity of the Ecliptic would, at that rate, alter a whole Minute in thirty Years; which is much faster than any Observations, before made, would allow. I had Reason therefore to think, that some Part of this Motion at the least, if not the whole, was owing to the Moon's Action upon the Equatorial Parts of the Earth; which I conceived, might Cause a libratory Motion of the Earth's Axis. But as I was unable to judge, from only nine Years Observations, whether the Axis would entirely recover the same Position, that it had in the Year 1727 I found it necessary to continue my Observations through a whole Period of the Moon's Nodes; at the End of which I had the Satisfaction to see, that the Stars returned into the same Positions again; as if there had been no Alteration at all in the Inclination of the Earth's Axis: which fully convinced me, that I had guessed rightly as to the Cause of the Phenomenon. This Circumstance proves likewise, that if there be a gradual Diminution of the Obliquity of the Ecliptic; it does not arise only from an Alteration in the Position of the Earth's Axis, but rather from some Change in the Plane of the Ecliptic itself: because the Stars, at the End of the Period of the Moon's Nodes, appeared in the same Places, with respect to the Equator, as they ought to have done, if the Earth's Axis had retained the same Inclination to an invariable Plane.

During the Course of my Observations, our ingenious Secretary of the Royal Society, Mr John Machin, being employed in considering the Theory of Gravity; and its Consequences, with regard to the Celestial Motions; I acquainted him with the Phenomena that I had observed: and at the same time mentioned, what I suspected to be the Cause of them. He soon after sent me a Table, containing the Quantity of the annual Precession in the various Positions of the Moon's Nodes, as also the corresponding Nutations of the Earth's Axis; which was computed upon the Supposition, that the mean annual Precession is 50", and that the Whole is governed by the Pole of the Moon's Orbit only: and therefore he imagined, that the Numbers in the Table would be too large; as in Fact they were found to be. But it appeared, that the Changes which I had observed, both in the annual Precession and Nutation, kept the same Law, as to increasing and decreasing, with the Numbers of his Table. Those were calculated upon the Supposition, that the Pole of the Equator, during a Period of the Moon's Nodes, moved round in the Periphery of a little Circle, whose Centre was 23° 29' distant from the Pole of the Ecliptic; having itself also an angular Motion of 50" in a Year, about the same Pole: The North Pole of the Equator was conceived to be in that Part of the small Circle, which is farthest from the North Pole of the Ecliptic, at the Time when the Moon's Ascending Node is in the Beginning of Aries: and in the opposite Point of it, when the same Node is in Libra.

Such a Hypothesis will account for an Acceleration and Retardation of the annual Precession; as also for a Nutation of the Earth's Axis: And if the Diameter of the little Circle be supposed equal to 18"; which is the whole Quantity of the Nutation, as collected from my Observations of gamma Draconis: then all the Phenomena in the several Stars which I observed, will be very nearly solved by it.


JOC/EFR November 2018

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