Opera posthuma [Opuscula astronomica]; viz. Astronomia Kepleriana, defensa & promota. Excerpta ex epistolis ad Crabtraeum suum. Observationum coelestium catalogus. Lunae theoria nova. Accedunt Guilielmi Crabtraei, Mancestriensis, Observationes coelestes. In calce adjiciuntur Johannis Flamstedii, Derbiencis, De Temporis Aequatione Diatriba. Numeri ad lunae theoriam horroccianam.

London: W. Godbid for J. Martyn, 1672-73.

First edition, very rare, of the principal published source of the short-lived “pride and boast of British astronomy,” as he was later described by Sir John Herschel. The works published here posthumously, edited by John Wallis, constitute almost all of Horrocks’ writings that survived the vicissitudes of the Civil War and the Great Fire of London. “There is no doubt about the influence of Horrocks on Newton, who pays tribute to [him] in the Principia” (Plummer). “Jeremiah Horrocks was, perhaps, the first man in England to comprehend fully the actual revolution [in astronomy] going on in continental Europe. He was the first Englishman (along with Crabtree and Gascoigne) to recognise the investigative power of the telescope in original research and drew conclusions that went beyond those of Galileo and Kepler. He was the first of his contemporaries to examine independently the Keplerian astronomy, improve upon it, and produce an analysis of the lunar orbit which would provide a working model for the rest of the solar system. But he was possibly the first man in Europe to recognise the methodological faults of post-Tychonian astronomy, discard tabular computation, and stress fundamental observation with specialised mathematical instruments as the only way to answer the dominating questions of the age … The high point of his short though remarkably fruitful scientific career, to both the first and subsequent generations of his admirers, lay in those thirty minutes before sunset on 1639 November 29 when he observed the transit of Venus” (Chapman). “In his extraordinary and short-lived career Horrocks turned his attention to almost every aspect of astronomy. He was an assiduous and careful observer, always anxious to extend the limits of precision and to seek out and eliminate sources of possible observational error. One of his aims was to carry on the work of Tycho, but by utilizing the new opportunities available in the age of the telescope. He re-determined the astronomical constants for several planets, imaginatively investigated the problem of the scale of the solar system, improved the theory of lunar motion, began a detailed study of the tides, and theorized about the forces responsible for the motions of the planets. As a theorist, Horrocks, although he was not in possession of the principle of inertia, represents a transition between the physical astronomy of Kepler and the fertile period 1660–1680 associated with the names of Borelli, Hooke, Halley, and Newton. His writings remained unpublished in his lifetime and the extent of his influence on his successors has yet to be explored” (DSB). The greater part of the book was printed in 1672 and some (incomplete) copies were issued in that year. The title varies between Opera posthuma and Opuscula astronomica according to the bookseller who sold it, but neither of the original publishers did at all well out of it. ABPC/RBH lists only the Macclesfield copy since Honeyman.

Horrocks (1618-41) grew up in Toxteth Park, then a small village about three miles from Liverpool. From 1632 to 1635 he attended Emmanuel College, Cambridge, but he left without taking a degree. He taught himself astronomy and familiarized himself with the chief astronomical works of antiquity and of his own time. Shortly after leaving Cambridge he befriended William Crabtree (1610-44), a clothier or merchant of Broughton, near Manchester. Crabtree had studied astronomy for several years and the two young and enthusiastic friends carried on an extensive correspondence on astronomical matters that continued until Horrocks’ death.

“In 1635 Horrocks began to compute ephemerides from Philip van Lansberge’s Tabulae motuum coelestium perpetuae (1632). Comparing the results of his calculations with his own and Crabtree’s observations, he concluded that Lansberge’s tables were not only inadequate but also based on a false planetary theory. Upon Crabtree’s advice he began to use Kepler’s Tabulae Rudolphinae (1627) and soon became convinced that the tables were superior to all others and the only ones founded on valid principles. He devoted the next few years to correcting their errors and improving their accuracy.

“Having some misgivings about Kepler’s physical theories, Horrocks turned to the study of Kepler’s works and soon became an ardent disciple. He accepted Kepler’s doctrines of elliptical planetary orbits, with the sun situated in the orbital planes, and of the constant inclination of these orbits to the ecliptic. Horrocks affirmed that he had carefully and repeatedly tested Kepler’s rule of the proportionality between the squares of the planetary periods and the cubes of their mean distances, and that he had found it to be absolutely true. With Kepler, he held that a planet moves more rapidly at perihelion than at aphelion and he believed planetary velocity to decrease proportionally with increasing distance from the sun. There is no mention in his surviving works of Kepler’s law of areas.

“Horrocks also accepted Kepler’s viewpoint on the unity of celestial and terrestrial physics and his program for the creation of a celestial dynamics. He tentatively put forward a dynamical model of his own, however, which he felt eliminated some of the worst features of his master’s. He started with Kepler’s hypothesis that the sun moves the planets both by its rotation and by the emission of a quasi-magnetic attractive force, which becomes weaker with distance and attracts the planets as well as acting as a series of lever-arms pushing them along. The specific shape of the planetary orbit is the result of a dynamic equilibrium between a lateral (pushing) and a central force. Horrocks repudiated Kepler’s idea that each planet has opposite sides ‘friendly’ and ‘unfriendly’ to the sun which cause it to be alternately attracted and repelled in different parts of its orbit and thus to move in an ellipse.

“Possibly influenced by his reading of Galileo’s Dialogue Concerning the Two Chief World Systems, Horrocks linked his celestial dynamics to the principles of falling bodies on earth and illustrated his conception by analogy with a pendulum. The planets may be seen as having a tendency to fall toward the sun or to oscillate about it freely, as the pendulum bob does about its mean position. But ‘Ye suns conversion doth turn the planet out of this line framing its motion into a circular, but the former desire of ye planet to move in a streight line hinders the full conquest of ye Sun, and forces it into an Ellipticke figure’.

“An analogy with a conical pendulum further illustrated his point. Horrocks pointed out that if a ball suspended by a string is withdrawn from its position at rest beneath the point of suspension, and given a tangential impulse, the ball will follow an elliptical path and its major axis will rotate in the direction of revolution—exactly as does the line of apsides of the lunar orbit. He further supposed a slight breeze blowing in the direction of the major axis, to support the analogy that the center of motion is in the focus of an ellipse rather than its center. According to Horrocks, therefore, and in contradistinction to Kepler, the planets tend always to be attracted to the sun and never to be repelled by it.

“Horrock’s conception of gravitation and his theory of comets also differed somewhat from Kepler’s. He hinted that the planets exert an attractive force on each other as well as on the sun; it is only because the sun is so massive compared to the other bodies in the solar system that it cannot be pulled from its place at the center. Originally, Horrocks proposed that comets are projected from the sun and tend to follow rectilinear paths. Like a stone thrown upward, they eventually reach a point of zero velocity and then return with accelerated motion; but since they are all the while influenced by the rotating force from the sun, they are thereby deflected into more or less circular paths. Horrocks later surmised that cometary orbits were elliptical.

“In mathematical planetary astronomy, he carefully re-determined the apparent diameters of several celestial bodies, examined afresh the manner of calculating their parallaxes, and obtained improved elements for several orbits. For the horizontal solar parallax, Horrocks proposed a figure of 14″ which he arrived at by an ingenious and novel line of reasoning spiced with a dash of metaphysical speculation. It was a value not to be improved on for many years and vastly superior to Tycho’s 3′ and Kepler’s 59″ and even to Hevelius’ 40″, a generation after Horrocks. He therefore obtained a figure for the radius of the earth’s orbit of ‘at least … 15,000 semidiameters of the earth,’ or about 60,000,000 miles. He reduced Kepler’s estimate of the solar eccentricity, and subtracted 1′ from the roots of the sun’s mean motion. Having discovered the irregularities in the motions of Jupiter and Saturn, he suggested specific corrections in the Rudolphine Tables for their mean longitudes and velocities, and he may have suspected that the increase in Jupiter’s velocity and the decrease in Saturn’s over a long span of time were periodic.

“His program of correcting Kepler’s tables led to Horrocks’ prediction of a transit of Venus, and he became the first astronomer to observe one. Consulting the tables of Lansberge, and afterward those of Reinhold, Longomontanus, and Kepler, he learned that there would be a conjunction of Venus and the sun some time in early December 1639. The four tables differed from each other in this estimate, however, by as much as two days. Horrocks discovered a small constant error in Kepler’s tables which displaced Venus about 8′ too much to the south, whereas Lansberge’s erroneously elevated its latitude by a still greater amount. Correcting Kepler’s error, Horrocks found that Venus would transit the lower part of the sun’s disk on 4 December and wrote to Crabtree urging that they both make careful observations upon the expected date of conjunction.

“Horrocks used a method of observation proposed for eclipses by Kepler and adapted to the telescope by Gassendi for the latter’s observation of the transit of Mercury of 1631. The sun’s light was admitted through a telescope into a darkened room so that the sun’s disk was reproduced on a white screen to a diameter of almost six inches; the screen was divided along the solar circumference by degrees and along the solar diameter into 120 parts. Crabtree, observing near Manchester, saw the transit for only a few minutes and failed to record the data precisely, but his general observations proved to be in agreement with those made by his friend. Horrocks was more successful, and his analysis of his observations enabled him to correct earlier data for the planet.

“Other astronomers had determined the apparent diameter of Venus as upwards of 3′, but Horrocks found it to be 1′ 16″ ± 4″, quite close to the modern value. The transit observation also enabled him to re-determine the constants for Venus’ orbit, yielding better figures for its radius, eccentricity, inclination to the ecliptic, and position of the nodes. As a result, he was also able to correct the figures for the rate of Venus’ motion; he determined it to be slower by 18′ over 100 years than Kepler’s tables showed.

“His contributions to lunar theory, to which he turned his earnest attention in 1637, were among his most important. Following Kepler, he had as the physical cornerstone of his lunar theory the assumptions that the lunar orbit is elliptical and that many of the moon’s inequalities are caused by the perturbative influence of the sun. In observation, he followed the practice initiated by Tycho of studying the moon in all its phases and not merely in the syzygies. Consequently, he was able to make improvements in the constants for several lunar inequalities, but his precepts were not reduced to tabular form until after his death. His most significant achievement in lunar theory was to account for the second inequality of longitude (evection, discovered in antiquity) by an unequal motion of the apsides and a variation in eccentricity. Depending on the moon’s distance from the sun, he added to the mean position of the apogee or subtracted from it up to 12° and altered the eccentricity within a range just over 20 percent about its mean value … Tables based on Horrocks’ lunar theory continued in use up to the middle of the eighteenth century, when they were superseded by Mayer’s” (DSB).

“The publication of the works of Horrocks has an interesting history. It concerns a group of three Emmanuel men, Horrocks himself, John Wallis and John Worthington on one side, and the Royal Society on the other. The papers of Horrocks were scattered. Some went to his brother Jonas in Ireland and were lost. A party of marauding soldiers at the beginning of the Civil War destroyed such as they found at his Toxteth home. Some notes went to Jeremiah Shakerley and were used in compiling his Tabulae Britannicae; these disappeared in the great Fire of London. But Crabtree gained possession of the remaining and, it may be hoped, the more important part of the papers and correspondence. These were bought by Worthington after Crabtree’s death …

“It was presumably through Wallis that the manuscript of Venus in Sole visa passed from Worthington into the hands of the Royal Society in its very earliest days. At a meeting it was voted worthy of publication by a majority, and Huygens who was present at the meeting received the MS. for transmission to Hevelius. It was published by the latter along with his own Mercurius in Sole visus and thus, as Wallis expresses it, the English Venus was mated with the Danzig Mercury. But this was in 1662, more than twenty years after the death of the man who had made the unique observation; and the MS. was not returned.

“It does not seem clear whether the other remains of Horrocks were delivered by Worthington to the Royal Society at the same time as the Venus in Sole visa or at some later date before his death in 1671. When this happened Wallis had returned to Oldenburg all the papers which had been entrusted to him for editing. They are now stated to be in the Bodleian Library, but how they came to be diverted from the ownership of the Royal Society, or in what state of completeness they may be, has not been ascertained.

“The critical work of Horrocks, which constitutes the main part of the Opera Postbuma, was reconstructed by Wallis in a connected form from a number of MSS. in different stages of development. The process of fusion has left visible traces in the repetition of certain passages. After this part the separate sections have each their own title page dated 1672 with the words ‘Impensis J. Martyn Regalis Societatis Typographi’ omitted. They contain the letters of Horrocks to Crabtree I636-40, translated into Latin by Wallis, observations made by Horrocks 1635-40, and observations made by Crabtree I636-38.

“These three sections nearly complete the volume, but there are two small additions. On Wallis fell the arduous task of literary editorship; but in the production of the work John Collins was associated with him. Collins was no doubt a good man of business, and he played a meritorious part in the scientific history of his time. But in this case he was not altogether happy … Collins was persuaded, and not without reason as the event showed, that the book could not be expected to sell without the addition of some more up-to-date material. In following this course he acted under the influence of John Flamsteed rather than of Wallis. The first piece added is a paper by Flamsteed on the equation of time and has nothing to do with Horrocks. But the other piece purports to give an account of the lunar theory of Horrocks, with tables and an explanation by Flamsteed. The description of the theory is conveyed by reproducing a letter from Crabtree to Gascoigne, while the original letter from Horrocks to Crabtree on the subject has been suppressed. This treatment of the matter caused intense annoyance to Wallis, who protested in vain and is free from responsibility. It is much to be regretted that a second-hand account was substituted, because the lunar theory of Horrocks probably marks his greatest advance on the ideas of his predecessors. Here there is no doubt about the influence of Horrocks on Newton, who pays tribute to his theory in the Principia” (Plummer, pp. 48-50).

A few copies of the Opera posthuma were issued with the original letter from Horrocks to Crabtree (dated December 20, 1638) on the lunar theory comprising signature 3O. Early in the print run, at the instigation of Flamsteed, this signature was cancelled and replaced (as here) by Flamsteed’s account of Crabtree’s letter to Gascoigne (dated July 21, 1642) expounding Horrocks’s theory. The edition was divided between two booksellers, John Martin (as here) and Robert Scott, the latter having the variant title Opuscula astronomica rather than Opera posthuma. A second edition appeared in 1678.

Crawford 242v; Houzeau and Lancaster :t1847; Lalande p 278; Wing H2870; Caspar (Anhang) 7 (1678 edition); Plummer, ‘Jeremiah Horrocks and his Opera posthuma’, Notes and Records of the Royal Society, 3 (1940), pp. 39-52. Chapman, ‘Jeremiah Horrocks. The Transit of Venus and the ‘New Astronomy’ in early 17th century England’, Quarterly Journal of the Royal Astronomical Society 31 (1990), pp. 333-357).

4to (199 x 156 mm), pp. [xvi], 496 and two engraved folding plates. Most of the sections have special title-pages, dated 1672 or 1673. Woodcut title vignettes, headpieces and historiated initials, numerous diagrams and tables (age-toned with some spotting). Contemporary calf, spine gilt in compartments.

Item #5368

Price: $50,000.00