Miscellaneous Works and Correspondence
(1832)

James Bradley FRS (March 1693 – 13 July 1762) was an English astronomer and served as Astronomer Royal from 1742, succeeding Edmond Halley. He is best known for two fundamental discoveries in astronomy, the aberration of light (1725–1728), and the nutation of the Earth's axis (1728–1748).

## Quotes

• My Instrument being fixed, I immediately began to observe such Stars as I judged most proper to give me light into the Cause of the Motion... There was Variety enough of small ones; and not less than twelve, that I could observe through all the Seasons of the Year; they being bright enough to be seen in the Day-time, when nearest the Sun. I had not been long observing, before I perceived, that the Notion we had before entertained of the Stars being farthest North and South, when the Sun was about the Equinoxes, was only true of those that were near the solstitial Colure: And after I had continued my Observations a few Months, I discovered what I then apprehended to be a general Law, observed by all the Stars, viz. That each of them became stationary, or was farthest North or South, when they passed over my Zenith at six of the Clock, either in the Morning or Evening. I perceived likewise, that whatever Situation the Stars were in with respect to the cardinal Points of the Ecliptick, the apparent Motion of every one tended the same Way, when they passed my Instrument about the same Hour of the Day or Night; for they all moved Southward, while they passed in the Day, and Northward in the Night; so that each was farthest North, when it came about Six of the Clock in the Evening, and farthest South when it came about Six in the Morning.
• When the year was completed, I began to examine and compare my observations, and having pretty well satisfied myself as to the general laws of the phenomena, I then endeavored to find out the cause of them. I was already convinced that the apparent motion of the stars was not owing to the nutation of the earth's axis. The next thing that offered itself was an alteration in the direction of the plumb-line with which the instrument was constantly rectified; but this upon trial proved insufficient. Then I considered what refraction might do, but here also nothing satisfactory occurred. At length I conjectured that all the phenomena hitherto mentioned, proceeded from the progressive motion of light and the earth's annual motion in its orbit. For I perceived that, if light was propagated in time, the apparent place of a fixed object would not be the same when the eye is at rest, as when it is moving in any other direction than that of the line passing through the eye and the object; and that, when the eye is moving in different directions, the apparent place of the object would be different.

### Miscellaneous Works and Correspondence (1832)

James Bradley, ed., Stephen Peter Rigaud

• I give all my printed books to Samuel Peach, son of Samuel Peach, in my Will named, and desire that this may be a codicil to my last Will and Testament, and taken as part thereof, as witness my hand, this third day of December. in the year of our Lord 1761.

#### To Mr. Cleveland Secretary of the Admiralty (April 14, 1760)

• Sir,
Having long deferred to make any report relating to the observations that were taken at sea by captain Campbell, in the year 1757, which you transmitted to me by order of the lords of the admiralty, I think it necessary to acquaint you, that, upon examining those observations, I perceived that they were not in all respects accompanied with such circumstances as are requisite for forming a right judgment of the accuracy and certainty with which observations proper for finding the longitude at sea by the moon can in fact be taken; for which reason I delayed giving my opinion upon this point till I could have an opportunity of comparing a greater variety of observations, made at different times, and with different instruments: such an opportunity having lately been given me by captain Campbell, who has favoured me with a copy of several observations that were made by him in 1758 and 1759, I now beg leave to lay before their lordships the result of the comparisons which I have made.
• But before I proceed farther it may be proper to take notice, that since the time when I gave their lordships an account of the near agreement of Mr. Professor Mayer's lunar tables with the observations that had been then made at the Royal Observatory, I have compared several others, which concurred to prove that the difference between the observed and computed places nowhere amounted to more than about one minute and a half; and I find that the difference (small as it is) may yet be diminished by making alterations in some of the equations, whose true quantity could not be determined without proper observations; after making the needful corrections it appeared, by the comparison of above eleven hundred observations taken here since the new instruments were fixed up, that the difference did nowhere amount to more than a minute: it may therefore be reasonably concluded, that so far as it will depend upon the lunar tables the true longitude of a ship at sea may in all cases be found within about half a degree, and generally much nearer.
• This fundamental and most important article being established upon such full evidence, it remained to be examined within what limits the errors arising from observations actually taken at sea could be contained.
In order to determine this point, I computed the ship's longitude from each of the observations made by captain Campbell, and, upon comparing the results of several that were taken near the same time and under the like circumstances, it appeared that in general the observer was not liable to err more than one minute in judging of the apparent contact of the moon's limb and the object with which it was compared. Now this being nearly the same error that would be found to obtain, if the like observations were to be made with the same instruments on land, it may hence be inferred, that in moderate weather the motion of the ship is no otherwise an impediment in this sort of observations, than as it renders the repetition of them more tedious and troublesome to the observer, which yet ought by no means to be omitted; because if each single observation be liable to an error of a minute only, by taking the mean of five or six, the error on this head may be so far diminished as to be of small moment.
• I would by no means attempt to infer from hence, that the longitude found by observations of this sort may in all cases be depended upon within one degree; but I beg leave to observe, that whatever extraordinary circumstances may have concurred to produce so near an agreement in this particular case, the event is such as may give reason to hope, however great the difficulties of finding the longitude by this method seem to be, that they are not insuperable, or such as ought to deter those whom it most nearly concerns from attempting to remove them.

#### Demonstration of the Rules relating to the Apparent Motion of the Fixed Stars upon account of the Motion of Light.

• If we suppose the distance of the fixed stars from the sun to be so great that the diameter of the earth's orbit viewed from them would not subtend a sensible angle, or which amounts to the same, that their annual parallax is quite insensible; it will then follow that a line drawn from the earth in any part of its orbit to a fixed star, will always, as to sense, make the same angle with the plane of the ecliptic, and the place of the star, as seen from the earth, would be the same as seen from the sun placed in the focus of the ellipsis described by the earth in its annual revolution, which place may therefore be called its true or real place.
But if we further suppose that the velocity of the earth in its orbit bears any sensible proportion to the velocity with which light is propagated, it will thence follow that the fixed stars (though removed too far off to be subject to a parallax on account of distance) will nevertheless be liable to an aberration, or a kind of parallax, on account of the relative velocity between light and the earth in its annual motion.
For if we conceive, as before, the true place of any star to be that in which it would appear viewed from the sun, the visible place to a spectator moving along with the earth, will be always different from its true, the star perpetually appearing out of its true place more or less, according as the velocity of the earth in its orbit is greater or less; so that when the earth is in its perihelion, the star will appear farthest distant from its true place, and nearest to it when the earth is in its aphelion; and the apparent distance in the former case will be to that in the latter in the reciprocal proportion of the distances of the earth in its perihelion and its aphelion. When the earth is in any other part of its orbit, its velocity being always in the reciprocal proportion of the perpendicular let fall from the sun to the tangent of the ellipse at that point where the earth is, or in the direct proportion of the perpendicular let fall upon the same tangent from the other focus, it thence follows that the apparent distance of a star from its true place, will be always as the perpendicular let fall from the upper focus upon the tangent of the ellipse. And hence it will be found likewise, that (supposing a plane passing through the star parallel to the earth's orbit) the locus or visible place of the star on that plane will always be in the circumference of a circle, its true place being in that diameter of it which is parallel to the shorter axis of the earth's orbit, in a point that divides that diameter into two parts, bearing the same proportion to each other, as the greatest and least distances of the earth from the sun.
• Hitherto we have considered the apparent motion of the star about its true place, as made only in a plane parallel to the ecliptic, in which case it appears to describe a circle in that plane; but since, when we judge of the place and motion of a star, we conceive it to be in the surface of a sphere, whose centre is our eye, 'twill be necessary to reduce the motion in that plane to what it would really appear on the surface of such a sphere, or (which will be equivalent) to what it would appear on a plane touching such a sphere in the star's true place. Now in the present case, where we conceive the eye at an indefinite distance, this will be done by letting fall perpendiculars from each point of the circle on such a plane, which from the nature of the orthographic projection will form an ellipsis, whose greater axis will be equal to the diameter of that circle, and the lesser axis to the greater as the sine of the star's latitude to the radius, for this latter plane being perpendicular to a line drawn from the centre of the sphere through the star's true place, which line is inclined to the ecliptic in an angle equal to the star's latitude; the touching plane will be inclined to the plane of the ecliptic in an angle equal to the complement of the latitude. But it is a known proposition in the orthographic projection of the sphere, that any circle inclined to the plane of the projection, to which lines drawn from the eye, supposed at an infinite distance, are at right angles, is projected into an ellipsis, having its longer axis equal to its diameter, and its shorter to twice the cosine of the inclination to the plane of the projection, half the longer axis or diameter being the radius.
Such an ellipse will be formed in our present case...
• For common purposes we may without sensible error suppose the earth's motion equable and neglect the corrections, and then the rule for the parallax of right ascension will be this:
Sine lat. : rad. : : cotang. A : cotang. C, or rad : sine lat. : : tang. A : tang. C; then long. star ${\displaystyle \mp }$ C = long. of λ.
Cosine C : cosine A : : semi transverse axis : z.
And cosine decl. cosine (ʘ - λ) :: z : x = parallax of right ascension.

by Thomas Hudson
• The invention of the telescope, the application of the pendulum to clocks, the invention of the micrometer, the combination of the telescope with the divided arc of a circle, invention of the transit circle by Roemer, with many improvements in minor apparatus, distinctly stamp the [17th] century as a remarkable period of preparation for achievements of the next century.
From the standpoint of the modern mechanician the instruments at the Greenwich Observatory in Bradley's time were very imperfect in design and construction, and yet on the observations obtained by his skill and perseverance depends the whole structure of modern fundamental astronomy. The use the quadrant reached its highest excellence under Bradley's management. ...
Bradley's observations furnish the data for Bessel's "Fundamenta Astronomiae," and many astronomers have since attempted by reductions to obtain improved positions for Bradley's stars. The value of these observations in the development of modern astronomy can hardly be exaggerated. Their importance in the determination of stellar proper motions increases with the lapse of time, and yet the accuracy of the original observations was far inferior to that obtained in ordinary routine work with modern methods and improved instruments.
Bradley's observations of γ Draconis and 35 Camelopardalis as reduced by Busch.
• When Bradley's observations of γ Draconis were corrected for abberation, they showed, according to himself, that the parallax of that star could not be as much as 1".0 or that the star was more than 200,000 times as distant from the earth as the sun.
• Seventy years have nearly elapsed since the death of Bradley and the generation of those who knew him has passed away some little however might be expected to remain in traditionary remembrance The rapid course of time would soon have swept away that little and have impaired some of the means which are still in our power for understanding what may exist in written documents It seemed desirable therefore to try what might yet be collected and though it proved to be far short of what could be wished I indulge the hope of its being authentic and accurate.
• Stephen Peter Rigaud, Preface (Nov. 29, 1831) in James Bradley, Miscellaneous Works and Correspondence (1832)

### Philosophical Transactions of the Royal Society of London, Vol. XII (1763-1769)

from their Commencement, in 1665, to the Year 1800, Ed. Charles Hutton, George Shaw, Richard Pearson (1809) source.
Table Deduced from Dr. Bradley's Observations, The Nautical Almanac and Astronomical Ephemeris, 1767.
• [Vol. LIV, Anno 1764] XLVIII. Concise Rules for Computing the Effects of Refraction and Parallax in Varying the Apparent Distance of the Moon from the Sun or a Star; also an Easy Rule of Approximation for Computing the Distance of the Moon from a Star, the Longitudes and Latitudes of both being given. By the Rev. Nevil Maskelyne, A.M. F.R.S. p. 263.
The following rules, excepting one, are the same which Mr. M. before communicated to the R.S., but without demonstration, in a letter from St. Helena, containing the results of his observations of the distance of the moon from the sun and fixed stars, taken in his voyage thither, for finding the longitude of the ship from time to time; since printed in vol. lii. of the Phil. Trans. The two rules for the correction of refraction and parallax, he had also communicated to the public in his British Mariner's Guide to the discovery of longitude from like observations of the moon; and added in the preface a rule for computing a second but smaller correction of parallax, necessary on account of a small imperfection lying in the first rule derived from the fluxions of a spherical triangle. To the rules he has here subjoined their demonstrations.
With respect to the usefulness of these rules, he entertains hopes that they will appear more simple and easy than any yet proposed; for the same purpose, the last rule, for computing the distance of the moon from a star, though only an approximation, being so very exact seems particularly adapted for the construction of a nautical Ephemeris, containing the distances of the moon from the sun and proper fixed stars, ready calculated for the purpose of finding the longitude from observations of the moon at sea; an assistance which, in an age abounding with so many able computers, mariners need not doubt they will be provided with, as soon as they manifest a proper disposition to make use of it.
A RULE. To compute the contraction of the apparent distance of any two heavenly bodies by refraction; the zenith distances of both, and their distance from each other being given nearly.
Add together the tangents of half the sum, and half the difference of the zenith distances; their sum, abating 10 from the index, is the tangent of arc the first. To the tangent of arc the first, just found, add the co-tangent of half the distance of the stars; the sum, abating 10 from the index, is the tangent of arc the second. Then add together the tangent of double the first arc, the co-secant of double the second arch, and the constant logarithm of 114″ or 2.0569: the sum, abating 20 from the index, is the logarithm of the number of seconds required, by which the distance of the stars is contracted by refraction: which therefore added to the observed distance gives the true distance cleared from the effect of refraction.
This rule is founded on an hypothesis, that the refraction in altitude is as the tangent of the zenith distance: and the refraction at the altitude of 45 degrees being 57″, according to Dr. Bradley's observations, therefore the refraction at any altitude, calling the radius unity, is 57″ × tangent of the zenith distance. This rule is exact enough for the purpose of the calculation of the longitude from observations of the distance of the moon from stars at sea as low down as the altitude of 10°, for there the error is only 10″ from the truth. But if the altitude of the moon or star be less than 10°, the rule may be still made to answer sufficiently, by only first correcting the observed zenith distances by subtracting from them 3 times the refraction corresponding to them, taken out of any common table of refraction, and making the computation with the zenith distances thus corrected. This correction depends on Dr. Bradley's rule for refraction, which he found to answer, in a manner exactly, from the zenith quite down to the horizon, namely that the refraction is = 57″ × tangent of the apparent zenith distance lessened by 3 times the corresponding refraction taken out of any common table.

### "Some Account of the late Dr. James Bradley, D.D. Royal Professor of Astronomy at Greenwich" (Sept. 1765)

The Gentleman's and London Magazine: Or Monthly Chronologer, 1741-1794 Vol. 35 pp. 533-538 John Exshaw, printer.
• Dr. James Bradley was the third son of William and Jane Bradley, and was born at Sherborne in Dorsetshire in the year 1692.
He was fitted for the university at North Leach [at] a boarding school... and from [there] he was sent to Oxford.
• His friends intended him for the church, and his studies were regulated with that view; and as soon as he was of sufficient age to receive holy orders, the bishop of Hereford, who had conceived a great esteem for him, gave him the living of Bridstow, and soon after he was inducted to that of Welfrie in Pembrokeshire. But, notwithstanding these advantages, from which he might promise himself still farther advancement in the church, he at length resigned his livings that he might be wholly at liberty to pursue his favourite study, the mathematics and particularly astronomy.
• He was nephew to Mr. Pound, a gentleman who is well known in the learned world by many excellent observations, and who would have enriched it with more, if the journals of his voyages had not been burnt at Pulo Condor, when the place was set on fire, and the English who were settled there cruelly massacred...
With this gentleman, Mr. Bradley passed all the time that he could spare from the duties of his function; and perhaps he sometimes trespassed upon them; he was then sufficiently acquainted with the mathematics to improve by Mr. Pound's conversation, yet it does not appear that in this study, he had any preceptor but his genius, or any assistant but his labour.
• He continued... to fulfill the duties [of holy orders]... though at this time he had made such observations as laid the foundation those discoveries which afterwards distinguished him as one of the greatest astronomers of his age.
Though these observations were made as it were by stealth, they gained him first the notice, and then the friendship of lord chancellor Macclessield, Mr. Newton, afterwards Sir Issac, and Mr. Halley, and many other members of the royal society, into which he was soon elected a member.
• About the fame time the chair of Savilian professor of astronomy at Oxford became vacant, by the death of the celebrated Dr. Keil; and Mr. Bradley was elected to succeed him on the 31st of October 1721, being then just nine and twenty years old; and his colleague was Mr. Halley, who was professor of Geometry on the same foundation.
• Bradley, upon his being elected into this professorship, gave up both his livings, and with great joy quitted a situation in which his duty was directly opposite to his inclination.
From this time he applied himself wholly to the study of his favourite science, and in the year 1727, he published his theory of the aberration of the fixed stars, which is allowed to be one of the most useful and ingenious discoveries of modern astronomy.
• It had been long observed that the position of the fixed stars were subject to some variations, which in no sort corresponded with the apparent motion of a degree in seventy-two years, which gives the precission of the equinoxes. The late abbe Picard had remarked these variations in the pole star in 1671, but he did not attempt either to reduce them to any settled rule, or to account for them. Dr. Bradley not only verified Picard's observations, but discovered many other variations which had never before been thought of; he found that some stars appeared to have, in the space of about a year, a variation of longitude backward and forward, but without any variation of latitude, that others, varied in latitude, but not in longitude, and others, by far the greater number, appeared to describe, in the space of a year, a small ellipsis, of different degrees of elongation.
The period of a year, in which all these motions, so different from each other, were performed, seemed to prove, that they had a connection with the revolution of the earth in its orbit; but the difficulty was to discover in what manner the stars were apparently influenced by that revolution; this was attempted for some time by Mr. Bradley, but without success; at last, however, his sagacity and his diligence surmounted all difficulties, and he found the cause of these seemingly capricious appearances in the successive motion of light co-operating with the motion of the earth round the sun.
• Light had long been supposed to move with a velocity physically infinite, but the late M. Roemer of the Royal Academy of Paris discovered the contrary... But however natural this theory might be, and however well it might be supported, it was then thought too bold, and poor Roemer did not live to see it adopted. It has, however, been since universally a agreed, that the motion of light is successive; and upon this successive motion of light, Mr. Bradley built his explanation of the irregular variations which he had observed in the stars, and which he called their aberation. His theory was this:
Let us suppose a series of very small particles, united into a thread, to fall in direction perpendicular to the horizon; and let several of these threads of particles fall at the same time, in he same direction, so as to be parallel to each other, in the same manner as drops of rain in a dead calm. Let us then suppose a tube to be placed in this rain, in a vertical position, and it is manifest that the drop of water which enters the aperture at the upper end of it, will issue at the aperture below, without touching the inside of the tube. But if the tube be moved parallel to itself, though still kept in a position parallel to the direction of the water, it is clear, that this motion of the tube will cause the drop that enters it to touch one of its sides, before it gets to the bottom; and that this contact will happen sooner, in proportion as the motion of the drops is slow, compared with the motion of the tube; and it is easy to demonstrate, that if the motion of the tube, and that of the rain are equal, the drop which falls in the center of the upper aperture of the tube, will come in contact with the inside of the tube, when it has passed down the tube the distance of half its diameter; and, consequently, that the line of its direction will make an angle of five and forty degrees with the axis of the tube: It follows, therefore, that, to prevent the drops of water from touching the inside of the tube, notwithstanding its motion, the tube must be inclined in an angle of five and forty degrees, on the side towards which it moves; and that, if this inclination should be successively made round in the circumference of a circle, the tube would describe round the vertical line, drawn from the centre of its base, a curve, the angle of which would be ninety degrees.
But what has been said, with respect to an inclination of the tube necessary to make the drop pass through it... depends upon the proportion between the motion of the tube, and the motion of the drop; and, in proportion as the motion of the drop is greater than that of the tube, the less the tube must be inclined: so that, if the motion of the drop be supposed to be infinite, no inclination at all of the tube would be necessary...
In order to apply this theory to the aberration of the fixed stars, we must substitute for the drops of water, uniting into a thread, the rays of light that come from those stars; and, for the tube, which we have supposed to be first at rest, and then in motion, that of the telescope used to determine the position of the stars, which is carried round with the Earth, in its revolution about the Sun; and we must suppose, that the velocity of the ray of light, having a finite relation to the velocity of the Earth's motion, the tube ought to change its inclination, in proportion as that motion changes its direction; whence it follows, that each star must have a series of different positions; or, which is the same thing, an apparent motion in the heavens, which causes it to describe, in the space of a year, ellipses more or less elongated according to its position. From the calculations of this gentleman it follows, that the velocity of light, as fixed by the aberrations of the stars, is the fame with what M Roëmer supposed it to be, and exactly quadrates with the retardation of the eclipses of the first satellite of Jupiter. A new proof of the truth of his hypothesis, if any new proof had been necessary.
• Such is the ingenious Theory of the Aberration, which Mr. Bradley published in the year 1727, and which was received by the whole learned world with the applause that it merited. M. Clairaut, of the acedemy of sciences at Paris, afterwards made this discovery the subject of a Memoir, which he printed in 1737: In this Memoir, he examines the principles on which the Theory of the Aberration is founded, and gives the necessary rules for putting it in practice.
• Three years after this discovery, by which Mr. Bradley acquired very great reputation, he was appointed Lecturer in Astronomy and Physic, at the Museum at Oxford.
He pursued his studies with equal application and delight; and in the course of his observations... he discovered that the inclination of the Earth's axis, upon the plane of the ecliptic, was not always the same, but that it varied backwards and forwards some seconds, and that the period of these variations was nine years. This period seemed altogether unaccountable, as it could not be supposed to have any thing in common with the revolution of the Earth, which is performed in one year. Mr. Bradley, however, discovered the cause of this phenomenon in the Newtonian system of attraction.
The first principle of that system is known to be, that all bodies mutually attract each other in the direct ratio of their masses, and in the inverse ratio of the squares of their distances. From this mutual attraction, combined with motion in a right line, Newton deduces the figure of the orbits of the planets, and particularly that of the Earth. If this orbit was a circle, and if the terrestrial globe was a perfect sphere, the attraction of the Sun would have no other effect than to keep it in its orbit, and would cause no irregularity in the position of its axis; but neither is the Earth's orbit a circle, nor its body a sphere; for the Earth is sensibly protuberant towards the equator, and its orbit is an ellipsis, which has the Sun in its focus. When the position of the Earth is such, that the plane of its equator passes thro' the centre of the Sun, the attractive power of the Sun acts only so as to draw the Earth towards it, still parallel to itself, and without changing the position of its axis, and this happens at the equinoxes. In proportion as the Earth recedes from those points, the Sun also goes out of the plane of the equator, and approaches that of one or other of the tropics; the semidiameter of the Earth, which is then exposed to the Sun, being no longer equal, the equator is more powerfully attracted than the rest of the globe, which causes some alteration in its position, and its inclination upon the plane of the ecliptic; and as that part of the orbit, which is comprized between the autumnal and vernal equinox, is less than that which is comprized between the vernal and the autumnal, it follows, that the irregularity caused by the Sun, during his passage through the northern signs, is not entirely compensated by that which he causes during his passage through the southern signs; and that the parallelism of the terrestrial axis, and its inclination with the ecliptic, will be a little changed. But though the irregularity is now accounted for, we are still at a loss for the cause of its happening in a period of nine years. This difficulty, however, will immediately disappear.
• The same effect which the Sun produces upon the Earth by its attraction, it also produced by the Moon which acts with greater force in proportion as it is more distant from the equator: Now, at the time when its nodes concur with the equinoxial points, its greatest latitude is added to the greatest obliquity of the ecliptic. At this time, therefore, the power which causes the irregularity in the position of the terrestrial axis, acts with the greatest force; and the revolution of the nodes of the Moon, being performed in eighteen years, it is clear, that in eighteen years the nodes will twice concur with the equinoxial points; and, consequently, that twice in that period, or once every nine years, the Earth's axis will be more influenced than at any other time; so that it will have a kind of balancing backward and forward, the period of which will he nine years, as Mr. Bradley had observed; and this ballancing he called the Nutation of the Terrestrial Axis.
He published this discovery in 1737, so that in the space of about ten years he communicated to the world two of the finest discoveries in modern astronomy, which will for ever make a memorable epocha in the history of that science.
• In the year 1744, he married Susannah Peach, the daughter of a gentleman of that name in Gloucestershire, by whom he had only one daughter.
• Mr. Bradley always preserved the esteem and friendship of Mr. Halley, who being worn out by age and infirmities, thought he could do nothing farther for the service of astronomy, than procure for Mr. Bradley the place of Regius Professor of Astronomy at Greenwich, which he had possessed himself many years with the greatest reputation. With this view, he wrote many letters, which have been since found among Mr. Bradley's papers, desiring his permission to apply for a grant of the reversion of it to him, and even offering to resign in his favour, if it should be thought necessary: But before Mr. Halley could bring this kind project to bear, he died. Mr. Bradley, however, obtained the place afterwards, by the favour and interest of my Lord Macclesfield, who was afterwards President of the Royal Society.
As soon as the appointment of Mr. Bradley to this place was known, the University of Oxford sent him a Diploma, creating him Doctor of Divinity.
• When Dr. Bradley was elected to the professor's chair at Oxford, he gave up his two livings, which were at such a distance, that he could not possibly fulfill the duties of them himself; but it happened, that after he was settled at Greenwich, the living of that parish became vacant, which is very considerable, and which was offered to him, as he was upon the spot to perform the duty, and had the claim of uncommon merit to the reward. This living, however, Dr. Bradley, very greatly to his honour, refused, fearing the duties of the astronomer would too much interfere with those of the divine.
• His majesty, however, hearing of the refusal, was so pleased with it, that he granted him a pension of 250I. a year, in consideration of his great abilities and knowledge in astronomy, and other branches of the mathematics, which had procured so much advantage to the commerce and navigation of Great Britain, as is particularly mentioned in the grant, which is dated the 15th of February 1752.
• Dr. Bradley, about the fame time, was admitted into the Council of the Royal Society. In the year 1748, he was admitted a member of the Royal Academy of Sciences, and the Belles Lettres of Berlin, upon the death of M. Crevier, first physician to his Catholic Majesty; in the year 1752, a member of the Imperial Academy at Petersbourg; and, in 1757, of that instituted at Bologne.
• His corporeal abilities... at length declined, though his intellectual suffered no abatement. In the year 1760, he became extremely weak and infirm, and towards he end of June 1762, he was attacked with a total supression of urine, caused by an inflammation of the reins, which, on the twelfth of July following, put an end to his life, in the seventieth year of his age.
He was buried at Mitchin Hampton in Gloucestershire, in the same grave with his mother, and his wife.
• He was remarkable for a placid and gentle modesty, very uncommon in persons of an active temper, and robust constitution. It was still more remarkable, that with this untroubled equanimity of temper, he was compassionate and liberal in the highest degree. Although he was a good speaker, and possessed the rare, but happy art of expressing his ideas, with the utmost precision and perspicuity, yet no man was a greater lover of silence, for he never spoke, but when he thought it absolutely necessary. He did indeed, think it necessary to speak when he had a fair opportunity to communicate any useful knowledge in his own way, and he encouraged those that attended his lectures, to ask him questions, by the exactness with which he answered, and the care he took to adapt himself to every capacity.
• He was not more inclined to write than to speak, for he has published very little; he had a natural diffidence, which made him always afraid, that his works should injure his character, therefore suppressed many, which probably, were well worthy of the public attention. He was even known as it were, in spight of himself; and, in spight of himself he was known much, and consequently much esteemed. ...He was honoured by all men of learning in general, and there was not an astronomer of any eminence in the world, with whom he had not a literary correspondence.
• No man cultivated greater talents with more success, or had a better claim to be ranked among the greatest astronomers of his age.

### Histoire de l'astronomie au dix-huitième siècle (1827)

Jean Baptiste Joseph Delambre, source
• James Bradley, l'astronome le plus célèbre qu'ait produit l'Angleterre, était né en 1692, à Shireborn, dans le comté de Glocester. Il était neveu de Pound, connu surtout par ses distances des satellites à leurs planètes principales, qu'il avait mesurées avec de très grandes lunettes. Pound était curé de Wansted; son exemple et ses leçons inspirèrent à son neveu le goût de l'Astronomie. En 1717 et 1718, Bradley présenta à la Société royale un recueil d'observations diverses. Sa famille l'avait destiné à l'état ecclésiastique, et lui avait fait obtenir une cure, à laquelle il renonça en 1721, quand il fut nommé à la chaire d'Astronomie fondée par Savil à Oxford, devenue vacante par la mort de Keill. On trouve de lui, dans les Transactions philosophiques de 1724, les observations qu'il avait faites d'une comète dans les derniers mois de l'année précédente. Dans le volume de 1726, il donna les longitudes de Lisbonne et du fort de New-York déterminées par les éclipses du premier satellite de Jupiter. Ces premiers essais n'annonçaient encore qu'un amateur d'Astronomie, d'un talent assez ordinaire; une occasion se présenta de se livrer à des recherches plus importantes; Bradley la saisit avec empressement, et elle le conduisit à une découverte qui a rendu son nom immortel.
• James Bradley, the most famous astronomer produced in England, was born in 1692 in Shireborn, Gloucester County. He was nephew of Pound, known above all for his determinations of distances to satellites from their principal planets, which he had measured with very large lenses. Pound was pastor of Wansted; His example and his lessons inspired his nephew with the taste for astronomy. In 1717 and 1718 Bradley presented to the Royal Society a collection of various observations. His family had appointed him to the ecclesiastical state, and had procured him a curate, which he renounced in 1721, when he was appointed to the chair of Astronomy founded by Savil at Oxford, made vacant by the death of Keill. We find in the Philosophical Transactions of 1724 the observations he made of a comet in the last months of the preceding year. In the volume of 1726 he gave the longitudes of Lisbon and the fort of New York, determined by the eclipses of the first satellite of Jupiter. These first experiments announced only an amateur of astronomy of a rather ordinary talent. Bradley seized her with eagerness an opportunity which presented itself of engaging in more important researches, and it led him to a discovery which made his name immortal.
• Nous avons dit que Bradley n'avait presque rien publié; c'est dix ans après sa mort que Mason donna une première édition de son catalogue de 389 étoiles principales. Les observations en contenaient trois mille, qui n'avaient pas encore été calculées. On en trouvait déjà 1041 réduites par Pilati, à la suite du nouveau catalogue de Piazzi. Ces réductions, que l'astronome royal et son assistant avaient négligées, ont été faites long-temps après sa mort, par M. Bessel, dans un ouvrage qu'il vient de publier sous ce titre:
Fundamenta astronomiae, pro anno 1755, deducta ex observationibus viri incomparabilis James Bradley in specula astronomica Grenovicensi per annos 1750-1762 institutis, auctore Friderico Wilhelmo Bessel. Regiomonti, 1818, petitin-folio.
• We said that Bradley had hardly published anything; It was ten years after his death that Mason gave a first edition of his catalog of 389 main stars. The observations contained three thousand, which had not yet been calculated. There were already 1041 reduced by Pilati, following the new catalog of Piazzi. These reductions, which the royal astronomer and his assistant had neglected, were made a long time after his death, by Mr. Bessel, in a work which he has just published under this title:
The Foundations of the Astvonomiæ, for the year 1755, have been deduced from observations of James Bradley an incomparable man of years 1750 -1762 in the Grenwich Astronomical Observatory, author Frederick William Bessel. Königsberg, 1818, slim folio.

### Miscellaneous Works and Correspondence (1832)

James Bradley, ed., Stephen Peter Rigaud, quotes by Regaud unless otherwise noted.
• Dr. Bradley had the whole British Catalogue calculated to the year 1744; and there are traces therein of his having examined almost every star in it. Indeed I have been well informed that Dr. Bradley observed the British Catalogue twice through; first with the old instruments of the Royal Observatory, previous to 1750; and afterwards with the new ones.

quotes by Stephen Peter Rigaud, unless otherwise noted.
• He had found that his instruments were inadequate to the accuracy which he was desirous of giving to his observations, and which he succeeded in attaining when the proper means were afterwards furnished for him. This however was not completed before 1750; and in the interval there were several other objects, of no small importance, which occupied Bradley's attention.
• The astronomical labours of 1743 would have afforded suflicient occupation to any common man; but notwithstanding all that he did in the observatory, Bradley found time, in this same year, to begin a course of experiments on the length of the seconds' pendulum. ...There are papers also on the same subject in Pound's handwriting, which indicate, that, like other scientific labours, it was pursued by them in common. Their apparatus was similar to that which was used by the earlier French philosophers... the length of the pendulum swinging seconds at that place was found to be between 39,14 and 39,168 inches. ...only valuable as the first approximations by which Bradley's mind became familiarized to the inquiry. ...Bradley found the lengths to be 39,13472 inches at a temperature of 68°, and 39,149 at 32°, which give 39,13710 inches for a temperature of 62°. In this no allowance is made for the resistance of the air...
• P. xxxiii. The time, within which the cause of aberration occurred to Bradley, is still further narrowed by the following extracts from the minutes of 1728, Nov 14: "Dr. Halley took occasion to speak concerning the late improvements in astronomy made from the new discovery of an annual motion of the fixed stars. ...his colleague, the Rev. Mr. Bradley, resolved to fix up another and more accurate instrument... and after fifteen months almost daily observations on fifteen different stars, has at length discovered not only the laws of the motions, but also the true and manifest cause of them." The instrument having been set up at Wansted on the 17th Aug. 1727, the fifteen months would only have been expiring, and from the expressions which are used, it is clear that the completion of the discovery was then quite recent. Halley, at the end of his report, "desired that a proper notice might be taken of this new discovery of Mr. Bradley, to prevent any other person from laying claim to it before he had sufficient time to prepare and adjust his observations and reflexions on this subject for the public." After the communication was finished, Halley concludes his report by saying, that Bradley was sufficiently convinced of his having discovered the true cause of the phenomena, since he was "able to foretell at any time, the situation of a star being given, how much the variation of it will amount unto, and that with so much exactness, that there does not remain any sensible part unaccounted for, which can be supposed to arise from parallax.—The President proposed that thanks might be returned to Mr. Bradley for the great care and pains which he has taken in his application to this subject, and likewise that it would be proper to advise Mr. Bradley, and hasten him to the publication of his thoughts, as soon as conveniently may be."
• He does not appear to have had much taste for mere abstract mathematics; but his papers prove that he was familiar with those branches which were most useful to him in their application. His demonstration of the laws of aberration is to be taken rather as an historical curiosity, than a test of his geometrical abilities. Every one, who has investigated a new problem, must be aware that the first solution which he devises has seldom been the best. Bradley's sole object, in this case, was to ascertain the rules by which he was to calculate; he had no view to publication; if he had, he might have improved the form, and condensed the substance, of his demonstration. But in this instance, as in others, he was probably checked by a fear of submitting his thoughts to the opinion of the world.
• He set too low a value on his own works, and always feared lest any thing might lower his reputation. His love of accuracy, likewise, acted as an impediment: those who take the most comprehensive views have the clearest knowledge of what may be deficient: he could see the improvements which were desirable, and while he had not yet attained them: he was unwilling to send out any thing to the public in a state which he considered to be imperfect. There was also another circumstance which operated against his publishing to any great extent: he certainly composed with difficulty; his writings are full of erasures; and after repeated transcriptions, his language was not always the happiest in its construction or arrangement. He was not remiss in noting what occurred to him, and making memoranda, where the words, which first occurred to him, were sufficient to register his thoughts, and recall them at any future time to his remembrance: but to dwell on the expressions which he should use, and to employ himself in polishing them for publication, seem to have been a task of irksome difficulty to him. No one writes well, who has not studied and practised it; and no one is inclined to acquire the habit, who does not enjoy some degree of facility in the execution of his purpose. It is not therefore astonishing that the voluminous historian of astronomy should have found that "Bradley n'avait presque rien publiée [Bradley had almost published nothing]." Besides the tables of Jupiter's satellites and a few others of no great extent, all that he could be found to have himself given to the world is comprised in seventy-two pages of the present volume. But when every thing is considered, we have no reason for regret; if he had written more for the press, he must have done less for our information;—the facts which he established, and the discoveries which he made, are of an intrinsic and inestimable value, beyond all comparison with any dissertations, in which he might have enlarged upon them.
• Euler's letter was probably intended for his notice, though addressed to Gael Morris; but there appears to have been no great inclination on Bradley's part to indulge a reciprocal desire. It may be said, that, as we have only the rough copies of his answers, which he may not in every instance have preserved, we do not know the number and extent of them. There certainly were many of which we have no remains; but still he seems to have seldom written unless some particular object required it, and there are repeated occasions on which his correspondents indicate the fact of his not having answered the letters which he had received. If, therefore, his great disinclination from studied composition made him remiss in keeping up an intercourse with such distinguished characters, it is not astonishing that a number of idle letters which were addressed to him may have been wholly unattended to. Many of these have been found among his papers which were wholly unfit for publication.

### Reduction of the Observations made by Bradley at Kew and Wansted (1838)

...to Determine the Quantities of Aberration and Nutation, August Ludwig Busch, source
• Of Bradley's original observations on Aberration and Nutation, those results only were known which Bradley himself published in the Philosophical Transactions (No. 406. vol. xxxv. p. 637. and No. 485. vol. xlv. p. I). It was known, however, that these observations were very complete; and it was supposed that a strict and accurate discussion of them would give the values of the constants of Aberration and Nutation with greater exactness, than had hitherto been attained: for, though Bradley himself had gone through the investigation, yet on account of the more extended developement, which the theory of Nutation has undergone in later times, and the recently invented methods of deducing the most probable results from observations, there was reason to expect that we might now obtain much greater precision.
• Mr. Rigaud... imparted his discovery to astronomers in a work, containing much valuable information relating to Bradley, published at Oxford in 1832, under the title of "Miscellaneous Works and Correspondence of the reverend James Bradley." This work contains not only the observations made by Bradley at Wansted, but those also which had been instituted at an earlier period by Molyneux at Kew, and continued there by Molyneux and Bradley conjointly. It contains likewise all the data requisite for a complete investigation of the constants of both elements resulting from Bradley's observations.

### History of Physical Astronomy (1852)

from The Earliest Ages to the Nineteenth Century, Robert Grant, source
• James Bradley, the third Astronomer Royal of Greenwich, was born at Sherbourn, in Gloucestershire, in the year 1692. In 1711 he entered Baliol College, Oxford, where he completed his education. Having qualified himself for the church, he was presented to a living in the year 1719. His predilection for astronomical pursuits, which evinced itself at an early age, was fostered by his uncle, the Rev. James Pound. with whom he resided for several years at Wanstead, in Essex. In 1721 he was appointed to the Savilian chair of astronomy in the University of Oxford, which had then become vacant by the death of Keill. His nomination by the Government, as successor to Halley in the Observatory of Greenwich, is dated February 2, 1742. His reputation as an astronomer was already well established in Europe by observations of a miscellaneous nature, and more especially by his immortal discovery of the Aberration of Light, and at the time of his appointment he was actually engaged in those researches which resulted in his discovery of the Nutation of the Earth's axis.
• Bradley's first object after his removal to Greenwich was to repair the instruments, and carefully to adjust their positions. Halley had confined himself to the use of the mural quadrant soon after its erection in 1725. Bradley, however, resolved to employ both the quadrant and the transit instrument in his observations. The former of these instruments was repaired by Graham, and the latter by Sisson, several important improvements being at the same time effected in their construction. Bradley's first observation with the quadrant was made on the 15th of June, 1742. His earliest transit observation is dated the 20th of July in the same year.
• The iron quadrant of Graham continued to be attached to the eastern face of the wall erected for its support in 1725, and was employed both by Halley and Bradley in observing the celestial bodies which passed the meridian to the south of the zenith. Bradley however was desirous of extending the plan of his observations and... presented a memorial to the Government in the year 1740, soliciting another quadrant, by means of which the stars that passed the meridian to the north of the zenith might be observed. The Government... at once acceded... and in the following year the observatory was furnished with a magnificent brass quadrant of eight feet radius constructed by Bird, who now took the place of Graham, as the most skilful divider of instruments in his day. ...these were finally subdivided by the micrometer screw to every 1″. The Government at the same time furnished the observatory with a new transit telescope by Bird, eight feet long, besides an excellent clock by Shelton...They also purchased of Bradley the famous zenith sector with which he discovered the phenomena of aberration and nutation, and appropriated it to the use of the observatory. This noble instrument was designed by Bradley to be henceforward employed in determining the errors of collimation of the quadrants, by making observations with it when its face was turned alternately east and west.
• Bradley being new in possession of instruments of unequalled perfection, proceeded to execute a series of preliminary observations for the purpose of ascertaining with greater accuracy the latitude of his observatory, the place of the equinox, the quantity and laws of refraction, and other fundamental points of astronomy. In pursuance of this design the brass quadrant was... employed in making observations of circumpolar stars. ...From them Bradley deduced the latitude of the observatory to be 51° 28′ 38½″. He also succeeded by means of them in constructing the elegant rule, so long used by astronomers, for finding the quantity of refraction corresponding to any assigned zenith distance, and any observed readings of the barometer and thermometer. He determined the absolute right ascensions of a few of the principal stars, by means of observations made near the equinoxes, according to the method of Flamsteed.
• As soon as Bradley had established these fundamental points he removed the brass quadrant from the western face of the meridian wall, and permanently attached it to the eastern face, where it was afterwards employed in observing the stars that passed the meridian to the south of the zenith. At the same time the iron quadrant was removed from the eastern face of the wall, and, after being re-divided by Bird, was attached to the western face, for the purpose of making observations with the telescope turned towards the north. Bradley now commenced the series of admirable observations which have formed the groundwork of so much valuable research to future enquirers, and which would have assured to him an immortal reputation, even independently of those great discoveries with which his name is inseparably associated. The sun, moon, and principal stars, and the planets when situate in favourable positions, were regularly observed with the transit instrument and the mural quadrants. Moreover, a multitude of small stars, chiefly those of Flamsteed's catalogue were included in the plan of observation. From the year 1750 may be dated the commencement of a series of observations which in point of accuracy may bear a comparison with those of modern times. Henceforward the records of Greenwich Observatory embody a collection of materials, which have almost exclusively formed the groundwork of every investigation undertaken in modern times, for the purpose of improving the solar, lunar, or planetary tables.
• Bradley, aided by only one assistant, continued with indefatigable assiduity to prosecute his labours at the Royal Observatory, until at length, in the autumn of 1761, he was compelled by the increasing frailties of old age, to retire from the duties of active life. ...he shortly afterwards withdrew to Chalford, in Gloucestershire, where he continued to reside among his wife's relations till his death, which took place on the 13th of July, 1762, having attained the age of 70 years.
• In 1751 a pension was granted to Bradley by George ll., not as an augmentation of salary, but as a gratuitous acknowledgment of his personal merit.
• The registers of Bradley's observations occupied thirteen folio volumes, and at his death were taken possession of by his executors. In 1767 the Government, under the impression of their being public property, commenced a law-suit with a view to their recovery, which, however, they abandoned in 1776. As soon as it was ascertained that the Government had relinquished their claim, the manuscripts were transmitted to Lord North, who was then Chancellor of the University of Oxford, to be presented by him to the University. They were finally printed, at the expense of the University, in two folio volumes. The first volume was published in 1798, under the superintendence of Dr. Hornsby. The second volume was prepared for the press by Dr. Robertson, and appeared in 1805. These two volumes contain the observations made by Bradley, from 1750 to 1762. The original manuscripts, as well as the registers of the observations made by Bradley, at Greenwich, previous to 1750, are deposited in the Bodleian Library, Oxford.
• The vast mass of observations made by Bradley... two volumes... continued inapplicable to any useful purpose, in consequence of their not being reduced, until... Bessel undertook to execute this task... The results of his labours were published in 1818, at Königsberg, in one folio volume, entitled Fundamenta Astronomiæ pro anno 1755, deducta ea Observationibus viri incomparabilis James Bradley, in specula Astronomica Grenovicensi per annos 1750 1762 institutis. In this work Bessel has determined, by a series of elaborate investigations, the quantity and laws of refraction, the maximum value of aberration, and other fundamental points of astronomy, as deducible from Bradley s observations.
• The observations made with the zenith sector at Kew and Wanstead, by the intercomparison of which Bradley was conducted to the discovery of aberration, were at one time supposed to be lost; but having been found among the papers of the late Dr. Hornsby, they were published by Professor Rigaud, in 1832, at the expense of the University, of which the immortal author of the discovery forms one of the brightest ornaments.

### Charles Mason and Jeramian Dixon (c. 1950)

Thomas D. Cope, source
• Charles Mason laid the foundation of his career at Greenwich where he worked from 1756 to 1760 as assistant observer to the Reverend James Bradley, Astronomer Royal. Bradley was then near the end of his career... As a young man he had discovered the aberration of light and the nutation of the axis of the Earth and had founded a new era of precise observations. He had enlarged the Greenwich Observatory and equipped it with new instruments. Mason acquired some of the spirit and the ideals of his preceptor and learned from him the use of instruments of precision and the art of observing. At Greenwich Mason made the acquaintance of the Reverend Nevil Maskelyne, a young astronomer who was assisting the Astronomer Royal in a study of atmospheric refraction. This association of Mason and Maskelyne continued as long as Mason lived.
• And at Greenwich Mason first learned to know Mayer's Tables of the Moon. ...Bradley first reported on Mayer's Tables on February 10, 1756, and finally on April 14, 1760. With the assistance of Charles Mason, Bradley had compared positions of the Moon as predicted in the Tables with positions as observed at Greenwich. Eleven hundred comparisons led to the comment:
So far as it will depend upon the lunar tables the true longitude of a ship at sea may in all cases be found within about half a degree and generally much nearer. It remained to be examined within what limits the errors arising from observations actually taken at sea could be contained.
This test was carried out for Bradley by Captain Campbell, of H.M.S. Royal George, on cruises near Ushant in 1758 and 1759. A sextant was made especially for the trials by John Bird, instrument maker for Greenwich Observatory. Bradley's final comment reads:
However great the difficulties of finding the longitude by this method seem to be, they are not insuperable, or such as ought to deter those whom it most nearly concerns from attempting to remove them.
James Bradley was now nearing the end of his days. His hand was faltering.
Nevil Maskelyne and Charles Mason received the torch he had carried. They made the development of the method of lunar distances for finding the longitude at sea a major concern of the rest of their lives.
• James Bradley's successor as Astronomer Royal was Nathaniel Bliss, who lived only two years after his appointment. Maskelyne succeeded him early in 1765 and thus became the fifth Astronomer Royal at Greenwich.
• The last quarter of Charles Mason's life was spent on projects that grew out of his earlier work at Greenwich Observatory as assistant observer to Astronomer Royal Bradley. From studies of Bradley's records Mason prepared tables for the Nautical Almanac and he was able to improve Mayer's Tables of the Moon by comparing them with the Greenwich records.
The Nautical Almanac was established by Nevil Maskelyne in 1767, immediately after his appointment as Astronomer Royal, and it has appeared annually ever since. In the first issue the latitude and longitude of Cape Town are given as found by Mason and Dixon in 1761. The comment follows that "it is probable that the Situation of few Places is better determined." To the Almanac for 1773 Mason contributed a catalogue of stars.
The preface, written by Maskelyne, states:
To this Ephemeris are annexed... a Catalogue of 387 fixed Stars.... adapted to the beginning of the year 1760... calculated from the late Dr. Bradley's Observations by Mr. Charles Mason, formerly his Assistant. ...After the Catalogue follow some Memoranda... communicated by the same Mr. Mason.
• The issue [of the Nautical Almanac] for 1774 first introduces Mason's improvements of Mayer's Lunar Tables. The preface written by Maskelyne on July 2, 1772, states:
To this Ephemeris are annexed 1220 Longitudes and Latitudes of the Moon deduced from the late Dr. Bradley's Observations. ...The greater part of these calculations were made during Dr. Bradley's Lifetime by himself and his Assistant Mr. Charles Mason; and what was left unfinished has been completed by Mr. Mason since, at the Instance and at the Expense of the Board of Longitude. A Series of Observations this for Number and Exactness far excelling anything of the kind which the World ever saw before... Accordingly the Board of Longitude have thought proper to employ Mr. Mason farther in making the necessary calculations for improving Mayer's printed Tables under my Direction...
• James Bradley had not published his Greenwich observations. In law they proved to be his personal property, and after his death they were claimed successfully by his only child, a daughter, and her husband, the Reverend Samuel Peach. They in turn gave the records to Oxford University where Bradley had studied and had held the Savilian professorship of Astronomy. The first of Bradley's records to be published was the catalogue of stars that Mason prepared for the Nautical Almanac of 1773. The Clarendon Press of Oxford University undertook the publication of all the records. The first volume appeared in 1798 under the editorship of Professor Thomas Hornsby. It includes Mason's star catalogue. Mason and Hornsby carried on an extensive correspondence about the Greenwich records that undoubtedly aided in preparing them for the press. The second volume, edited by Dr. Abram Robertson, appeared in 1805. Finally in 1832 there was published The Miscellaneous Works and Correspondence of Reverend James Bradley under the editorship of Professor S. P. Rigaud.