William Herschel

How to use this course

William Herschel came to astronomy in his mid-thirties, as a professional musician who read books on harmony and optics in his spare time. Within a decade he had found the first planet unknown to the ancients. Within three decades he had changed the questions astronomers asked. Before him, astronomy measured the positions of the Sun, Moon and planets. Herschel asked how the stars are arranged in space, how they move, and what nebulae are made of. He is often called the founder of sidereal astronomy for this reason.

This course follows the man and the work together. Part II takes seven of his scientific contributions and treats each as a short technical lesson, using modern notation and modern values where they help.

Each technical lesson opens with an italic paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. Companion modules cover his sister Caroline Herschel, who shared nearly all of his observing life, and his son John Herschel, who carried his surveys to the southern sky.

Timeline

Hanover and the regimental band, 1738–1757

Friedrich Wilhelm Herschel was born in Hanover on 15 November 1738, one of ten children of Isaac Herschel and Anna Ilse Moritzen. Hanover was then ruled by the King of Great Britain, George II, as Elector. Isaac was an oboist in the band of the Hanoverian Foot Guards. He had little formal education himself but valued learning, and he pointed out the constellations to his children on clear nights. His daughter Caroline Herschel later recalled being shown a comet by him.

William and his elder brother Jacob followed their father into the band as oboists. Their mother saw no point in educating her daughters, but the boys went to the garrison school, and William was an eager pupil. Music filled the household; William also played the violin.

In 1756, with war with France approaching, the Guards were sent to England to guard against invasion. They were stationed at Maidstone in Kent. William learned English there and bought a copy of John Locke’s Essay Concerning Human Understanding, which he read closely. The regiment returned home and in July 1757 was in the defeat at Hastenbeck. William left the army and, with Jacob, made his way to England, where a skilled musician could earn a living.

A musician in England, 1757–1772

Herschel arrived in England with little money and found work as a musician. In 1760 he became head of the band of the Durham Militia, living at Richmond in Yorkshire. In 1761 he moved to the north-east, played first violin and soloist for Charles Avison’s orchestra in Newcastle for a season, and composed steadily. By the mid-1760s he had written some two dozen symphonies and a set of concertos for oboe, violin and viola. Recordings of several symphonies now exist, and the music is competent and lively in the style of the 1760s.

From 1762 to 1766 he was director of concerts at Leeds. In 1766 he took the post of organist at the new Octagon Chapel in Bath, the fashionable spa town, and gave his first concert there on 1 January 1767. He taught many private pupils, conducted oratorios and in 1780 became director of the Bath orchestra.

From harmony to optics

The route to astronomy ran through music theory. Herschel read Robert Smith’s Harmonics, a mathematical treatise on tuning and consonance. Smith had also written a Compleat System of Opticks, which described how to build telescopes, and Herschel moved on to it. On 10 May 1773 he bought James Ferguson’s Astronomy. He also studied Euclid in Robert Simson’s edition and William Emerson’s Trigonometry.

In August 1772 Herschel brought Caroline from Hanover to keep house and to train as a singer. She became principal singer at his oratorio concerts and, soon after, his assistant in a very different enterprise.

Bath: from mirrors to a new planet, 1773–1782

In September 1773 Herschel hired a small Gregorian reflector. It disappointed him, and good telescopes of any size were expensive. He decided to make his own. By the end of 1773 he was grinding and polishing mirrors of speculum metal, a brittle alloy of copper and tin. The house filled with tools; his brother Alexander, a skilled mechanic, helped with the metalwork, and Caroline read aloud and fed him while he polished for hours without stopping. He opened his observing journal on 1 March 1774.

His instruments soon outperformed those at the Royal Observatory. Through the Bath Philosophical Society he met William Watson, a physician and Fellow of the Royal Society, who became his friend and introduced his papers in London. In October 1779 he began a systematic review of every star down to a set brightness with a 7-foot reflector of 6.2-inch aperture, looking for close pairs. Lesson 06 explains why.

13 March 1781

On the night of 13 March 1781, examining stars near η Geminorum from the garden of his house at 19 New King Street, Herschel saw an object that showed a small disc. Stars remain points however much they are magnified; this object grew with the magnification. A few nights later it had moved. He reported a comet. His paper was read to the Royal Society on 16 April 1781. Within months Anders Lexell and others found that the orbit was nearly circular and far beyond Saturn. It was a planet, the first discovered since antiquity (Lesson 05).

Fame followed fast. Herschel received the Copley Medal in November 1781 and was elected a Fellow of the Royal Society on 6 December. He proposed to name the planet Georgium Sidus, the Georgian Star, after George III. In 1782 the king granted him a pension of £200 a year on condition that he live near Windsor and show the heavens to the royal family. Herschel gave his last professional musical performance in May 1782 and moved with Caroline to Datchet in August. He was 43, and from then on he was an astronomer.

Reflecting telescopes and penetrating power

For the general reader. A telescope does two separate jobs. It collects light, which lets you see fainter objects, and it separates fine detail, which lets you split close pairs and see discs. Both improve with the width of the mirror. Herschel understood this better than anyone of his time and built a sequence of ever larger reflectors, ending with a mirror four feet across. He also introduced the idea of a telescope’s “power of penetrating into space”: how much deeper than the naked eye it can see.

The instruments

Herschel’s main instruments were Newtonian reflectors with speculum mirrors. The 7-foot of 1779 had a 6.2-inch aperture. The “large” 20-foot, which carried his sweeps of the sky from October 1783, had an 18.7-inch mirror. The 40-foot, paid for by a royal grant of £4,000 in 1785 and completed in 1789, had a mirror about 48 inches (1.2 m) across and remained the largest telescope in the world for more than fifty years. Over his life he cast, ground and polished several hundred mirrors and sold at least sixty complete telescopes.

Speculum metal reflects well under two-thirds of the light and tarnishes within months. In a Newtonian, light strikes the primary and then a small diagonal mirror, so it suffers two reflections. Herschel removed the diagonal. He tilted the primary slightly so that the image formed near the mouth of the tube, where he viewed it with an eyepiece from a platform. This front-view or Herschelian arrangement costs a little sharpness off-axis but saves an entire reflection.

Light grasp and penetrating power

Let a telescope have aperture \(D\) and total transmission \(\tau\) (the product of the reflectivities). The eye’s pupil has diameter \(p\). A star of luminosity \(L\) at distance \(r\) delivers flux \(F=L/4\pi r^2\), and the power collected is \(F\cdot\tau\pi D^2/4\). A star is just visible when that power reaches a fixed threshold \(P_{\min}\).

Proof. The threshold condition is \(\dfrac{L}{4\pi r^2}\cdot\dfrac{\tau\pi D^2}{4}=P_{\min}\) for the telescope and \(\dfrac{L}{4\pi r^2}\cdot\dfrac{\pi p^2}{4}=P_{\min}\) for the eye. Solving each for \(r\) and dividing gives \(r_{\text{tel}}/r_{\text{eye}}=\sqrt{\tau}D/p\). \(\square\)

Herschel stated this principle in a paper of 1800 on the power of penetrating into space. It made the aperture, not the magnification, the measure of a telescope for deep-sky work, and it is the reason he kept building larger mirrors.

Resolution and the figure of the mirror

To reach this limit, every ray from a distant star must arrive at the focus in phase, which requires a paraboloidal mirror. A spherical mirror of radius of curvature \(R\) has sag \(z_s(r)=R-\sqrt{R^2-r^2}=\dfrac{r^2}{2R}+\dfrac{r^4}{8R^3}+\cdots\), while the paraboloid with the same focus has \(z_p(r)=\dfrac{r^2}{2R}\) exactly. The mirror-maker must therefore remove a layer of thickness about \(r^4/8R^3\) at the edge, a fraction of a micrometre to a few micrometres. Herschel did this by hand and tested the result on stars.

Uranus and its moons

For the general reader. Uranus is just visible to the naked eye and had been recorded as a star many times before 1781. John Flamsteed catalogued it in 1690 as 34 Tauri. Herschel recognized it because his telescope was good enough to show its tiny disc. The discovery doubled the known size of the solar system. Six years later he found its two largest moons, and their orbits gave the first measurement of the planet’s mass.

A disc and a motion

Uranus has an equatorial diameter of about 51,000 km and is about 18 AU from Earth at opposition, so it subtends less than 4 arcseconds. A star subtends far less than 0.01 arcsecond, and its telescopic image is set by diffraction and seeing, which do not scale with the magnification. Herschel used eyepieces of increasing power. The stars stayed the same size; the new object grew. Its slow motion against the stars then showed it was in the solar system.

Herschel and the astronomers who first computed its path assumed a comet. Anders Lexell, and independently others, found that a nearly circular orbit at about 19 AU fitted the observations. Johann Elert Bode proposed the name Uranus, which became standard in the nineteenth century; Herschel’s name, the Georgian Star, was used in Britain for decades, and French astronomers for a time called the planet Herschel.

The Titius–Bode rule

In 1766 Johann Daniel Titius noticed, and Bode popularized, that planetary distances roughly fit \(a_n=0.4+0.3\times2^n\) AU with \(n=-\infty,0,1,2,\dots\) for Mercury, Venus, Earth, Mars, and \(n=4,5\) for Jupiter and Saturn, leaving a gap at \(n=3\). For \(n=6\) the rule gives 19.6 AU. Uranus, at 19.2 AU, fitted, and the success encouraged the search for a planet at 2.8 AU that led Giuseppe Piazzi to Ceres in 1801. The rule fails badly for Neptune and has no accepted physical basis.

Titania, Oberon and the mass of Uranus

On 11 January 1787 Herschel found two faint satellites of Uranus. His son John later named them Titania and Oberon. Their orbits give the mass of the planet directly from Kepler’s third law, with no reference to the Sun.

Double stars become binary stars

For the general reader. Herschel started collecting close pairs of stars in order to measure distances. If one star of a pair is much nearer than the other, the Earth’s yearly motion makes the near one wobble against the far one. Twenty-five years of measurement showed something else. Many pairs were turning around each other. Gravity, it seemed, worked between the stars as it does in the solar system.

The parallax plan

As the Earth orbits the Sun, a star at distance \(d\) parsecs traces a small ellipse on the sky of semi-major axis \(\varpi=1/d\) arcseconds. Absolute positions could not be measured to a fraction of an arcsecond in the 1780s, but the separation of two stars in one field could. Galileo had suggested the idea. If a pair consists of a near star at \(d_1\) and a distant one at \(d_2\gg d_1\), the separation oscillates yearly with amplitude \(\varpi_1-\varpi_2\approx\varpi_1\). Herschel catalogued 269 pairs in 1782 and 434 more in a second catalogue soon after, looking for candidates. No stellar parallax was measured until 1838.

Chance or physical?

In 1767 John Michell argued from probability that close pairs and clusters such as the Pleiades are too common to be accidental. The modern version of his argument uses the Poisson distribution.

The count of neighbours in a disc of area \(\pi\rho^2\) is approximately Poisson with mean \(n\pi\rho^2\), giving the first statement. Summing over the \(N\) stars counts each pair twice. When the expected number is far below the observed number, most pairs must be physical.

Orbital motion (1802–1803)

In his 1802 catalogue Herschel used the word binary for a pair of stars bound together. In 1803 he published an account of the changes in the relative positions of double stars over the preceding twenty-five years. For several pairs, Castor among them, the position angle had changed steadily in one direction, while the separation stayed nearly constant. Parallax would produce a yearly oscillation; this was a slow, one-way rotation. He concluded that these stars revolve about a common centre under mutual attraction. The first full orbit, of ξ Ursae Majoris, was computed by Félix Savary in 1827; John Herschel’s method of 1833 is the subject of a lesson in his module.

Mars: rotation, axis and polar caps

For the general reader. Before photography, the only way to study a planet was to watch it night after night and draw what one saw. Herschel did this for Mars between 1777 and 1783. By timing the return of dark markings he found that a Martian day lasts about 24 hours and 39 minutes. He measured the tilt of its axis and watched the bright polar caps grow and shrink with the seasons, and he concluded that Mars was the planet most like the Earth.

Rotation

If a marking crosses the central meridian at times \(t_1\) and \(t_2\), and the planet turns \(k\) times in between, then \(P=(t_2-t_1)/k\). Over a long baseline the error in \(P\) is the timing error divided by \(k\). The integer \(k\) must be fixed first from short intervals, where the ambiguity is resolved by rough estimates. Herschel reported a sidereal rotation of 24 h 39 m and some seconds in the Philosophical Transactions for 1781, within about two minutes of the modern value of 24 h 37 m 23 s.

In time \(S\) the planet turns through \(2\pi S/P\) relative to the stars, while the direction to the Sun advances by \(2\pi S/T\). The Sun returns to the meridian when these differ by \(2\pi\).

Axis and seasons

In his 1784 paper on the remarkable appearances at the polar regions of Mars, Herschel described bright polar spots that changed size and inferred an axis tilted by roughly thirty degrees to the pole of the ecliptic. The modern obliquity of Mars to its own orbit is 25.2°, close to Earth’s 23.4°. He argued that the bright spots were ice and snow that melt in the Martian summer.

At the pole the Sun circles the sky at constant altitude \(\varepsilon\) for the whole day. At the equator the Sun has declination \(\varepsilon\); the flux on the ground is \(S\cos\varepsilon\cos h\) at hour angle \(h\), and averaging over \(|h|\le\pi/2\) and the night gives \(S\cos\varepsilon/\pi\). For Mars, \(\pi\tan25.2^\circ\approx1.48\): in midsummer the pole receives more energy per day than the equator, and the cap retreats.

The motion of the Sun

For the general reader. Drive through a forest and the trees ahead seem to part and stream past you on either side. In 1783 Herschel looked at the slow drifts of a small number of bright stars measured over decades by earlier astronomers and saw the same pattern. The stars seemed to spread away from a point in the constellation Hercules. He concluded that the Sun, carrying its planets, is moving towards that point.

Reflex motion

Let the Sun move with velocity \(\mathbf V\) through a population of stars at rest. A star at distance \(d\) in direction \(\mathbf u\) has position \(\mathbf r=d\,\mathbf u\) relative to the Sun, and \(\dot{\mathbf r}=-\mathbf V\).

Proof. Differentiate \(\mathbf u=\mathbf r/|\mathbf r|\): \(\dot{\mathbf u}=\dot{\mathbf r}/d-\mathbf u\,(\mathbf u\cdot\dot{\mathbf r})/d\). Substituting \(\dot{\mathbf r}=-\mathbf V\) gives the formula. The vector \(\mathbf V-(\mathbf V\cdot\mathbf u)\mathbf u\) is the component of \(\mathbf V\) perpendicular to \(\mathbf u\), which lies in the plane of \(\mathbf u\) and \(\mathbf V\), so the motion is along that great circle. \(\square\)

Real stars also have their own random motions. Herschel used proper motions from the catalogues of Nevil Maskelyne and Jérôme Lalande and looked for the point that best accounted for the common trend. He placed the apex near λ Herculis. Modern determinations put it at roughly right ascension 18 h 28 m and declination +30°, about ten degrees from Herschel’s point, with a solar speed relative to nearby stars of about 13 to 20 km/s depending on the reference population.

Nebulae and the construction of the heavens

For the general reader. When Herschel began, about a hundred nebulae were known, mostly from Charles Messier’s list. With Caroline Herschel he swept the sky from Datchet and Slough for twenty years and catalogued about 2,500. He also tried to map the Milky Way by counting stars. He concluded that we live inside a flattened system of stars, and later that some nebulae are clouds of luminous fluid that may condense into stars. Both ideas shaped astronomy for a century.

Sweeps and catalogues

From October 1783 Herschel observed with the 20-foot telescope fixed near the meridian, moving it slowly up and down while the Earth’s rotation carried a strip of sky past. Caroline sat at a desk indoors and wrote down the objects he called out, with the clock time and the telescope’s height, from which positions followed. The results appeared in the Philosophical Transactions as three catalogues: a thousand new nebulae and clusters (1786), a second thousand (1789) and five hundred more (1802). He sorted the objects into eight classes: bright, faint and very faint nebulae (I–III), planetary nebulae (IV), very large nebulae (V), very compressed rich clusters (VI), compressed clusters (VII) and coarsely scattered clusters (VIII). The term “planetary nebula”, for a round disc-like glow, is his.

Star gauges

In On the Construction of the Heavens (1785) Herschel counted the stars visible in the field of the 20-foot, about 15 arcminutes across, in hundreds of directions. He assumed the stars are roughly uniformly spaced and that the telescope sees to the edge of the system.

The cone has solid angle \(\pi\alpha^2\) and volume \(\pi\alpha^2R^3/3\). From hundreds of gauges Herschel drew a section of the Galaxy: a flattened, irregular stratum, the “grindstone”, with the Sun near the middle. The method assumes no absorption, uniform density and a telescope that reaches the edge. Herschel himself later doubted the last assumption, finding that larger telescopes kept revealing more stars. The lesson on star gauges in John Herschel’s module discusses how interstellar dust distorts the counts.

Nebulae: unresolved stars or true nebulosity?

At first Herschel thought that all nebulae were distant clusters, resolvable with enough aperture. In 1790 he observed a star surrounded by a faint, uniform glow (now NGC 1514). A cluster so far away that its stars merged could not contain one star much brighter than the rest at the same distance, so he concluded that the glow was a “shining fluid” of a nature unknown. In later papers (1811 and 1814) he arranged nebulae in a sequence from diffuse light to condensed clusters, suggesting that gravity gathers nebulous matter into stars, an idea close to the nebular hypothesis that Laplace proposed for the solar system in 1796.

At distance \(d\) an object of luminosity \(L\) and linear size \(\ell\) gives flux \(L/4\pi d^2\) spread over a solid angle about \(\ell^2/d^2\); the ratio does not involve \(d\). Hence a nebula’s brightness does not reveal its distance. Herschel’s clue for NGC 1514 came from structure, the central star, rather than from brightness. The proposition fails over cosmological distances, where surface brightness falls as \((1+z)^{-4}\).

Invisible rays: the discovery of infrared

For the general reader. Herschel observed the Sun through coloured glass filters and noticed that some colours let through much more heat than others. In 1800 he spread sunlight into a spectrum with a prism and placed thermometers in each colour. The temperature rose from violet to red, and it kept rising beyond the red, where nothing could be seen. He had found radiation invisible to the eye, now called infrared. It was the first discovery of light outside the visible range.

The experiment

Herschel passed sunlight through a slit and a glass prism onto a table. He placed a thermometer with a blackened bulb in one colour and kept two others alongside, out of the beam, as controls for the room temperature. He moved the first thermometer step by step from violet to red, then beyond. The heating effect increased towards the red and was still greater beyond it. He presented the results to the Royal Society in 1800 and called the invisible radiation “calorific rays”. Further experiments showed that these rays obey the same laws of reflection and refraction as visible light.

The solar spectrum

The Sun’s effective temperature is 5,772 K, so \(\lambda_{\max}\approx502\) nm, in the green. Yet integrating Planck’s law shows that about half of the energy of a 5,772 K black body lies beyond 700 nm. The infrared carries a large share of sunlight.

Why the prism moved the maximum

A thermometer at a point in a prism spectrum measures energy per unit angle, not per unit wavelength. Glass disperses blue light strongly and red light weakly, so the red and infrared are squeezed into a narrow angle and their energy is concentrated.

Derivation. \(dE/d\theta=B_\lambda\,|d\lambda/d\theta|\), and \(d\theta/d\lambda\propto dn/d\lambda=-2B/\lambda^3\), so \(dE/d\theta\propto\lambda^3B_\lambda\propto\lambda^{-2}(e^{x}-1)^{-1}\propto x^2/(e^x-1)\). Setting the derivative with respect to \(x\) to zero gives \(2(e^x-1)=xe^x\). \(\square\)

For the Sun this puts the peak near \(\lambda=hc/(1.594\,kT)\approx1.6\ \mu\)m, well beyond the red. In reality glass absorbs strongly beyond a few micrometres and the atmosphere has absorption bands, but the dispersion effect alone explains why Herschel’s thermometers read highest past the visible end.

Slough, 1782–1807

Herschel’s title was the King’s Astronomer, a private post distinct from that of the Astronomer Royal at Greenwich. The pension of £200 was modest for a man who had earned more as a musician, and he made up the difference by selling telescopes to observers and princes across Europe. The house moved from Datchet to Clay Hall in Old Windsor in June 1785 and, on 3 April 1786, to a house on the Windsor Road at Slough, later called Observatory House. There he and Caroline carried out the sweeps of Lesson 09. In 1787 the king granted Caroline a salary of £50 a year as her brother’s assistant.

The 40-foot telescope was built in the garden between 1785 and 1789. The first mirror, cast in 1785, proved too thin to hold its figure, and a thicker one was cast in 1788. Herschel looked at the Orion Nebula through the unfinished instrument in February 1787. In its first weeks of service, in August and September 1789, he found two new moons of Saturn, now called Enceladus and Mimas. The telescope became a landmark and a tourist sight, but it was cumbersome, slow to set up and quick to tarnish, and Herschel did most of his work with the 20-foot.

On 8 May 1788 he married Mary Pitt, née Baldwin, the widow of a neighbour and friend, at St Laurence’s Church, Upton. Her fortune ended his money worries. Their only child, John Frederick William Herschel, was born on 7 March 1792. Caroline moved to lodgings nearby and continued to work with her brother.

In 1802 Herschel visited Paris, met Laplace, Messier, Joseph Lalande and Jean-Baptiste Delambre, and was presented to Napoleon Bonaparte, then First Consul. He was unimpressed by Napoleon’s show of knowledge. In 1807 he suffered a serious illness, and his observing slowed thereafter, though his papers continued.

Last years, death and legacy, 1807–1822

In his last fifteen years Herschel published long papers on the arrangement of the stars and the nature of nebulae, and in 1821 a final catalogue of 145 double stars. In 1816 he was made a Knight of the Royal Guelphic Order, a Hanoverian honour, and was known thereafter as Sir William. The same year his son John came home from Cambridge and began to learn the craft of the telescope from him. When the Astronomical Society of London was founded in 1820, Herschel became its first president.

He died at Observatory House on 25 August 1822, aged 83, and was buried at St Laurence’s Church, Upton. Caroline returned to Hanover within weeks. John took up the work, re-examined his father’s nebulae and double stars, and in 1834 carried the survey to the southern sky. John dismantled the 40-foot telescope around 1840; a section of its tube survives at Greenwich and its first mirror is in the Science Museum in London.

Legacy

• Planets: Uranus, four new moons (Titania, Oberon, Enceladus, Mimas), the rotation and seasons of Mars. The motion of Uranus later led Urbain Le Verrier and John Couch Adams to Neptune.
• Stars: more than 800 double stars, the proof that binary stars orbit under gravity, and the motion of the Sun towards the apex.
• Nebulae and the Galaxy: about 2,500 nebulae and clusters, the classification that introduced planetary nebulae, the first quantitative model of the Milky Way, and the idea that nebulae condense into stars. His catalogues, enlarged by John, became the basis of the New General Catalogue.
• Physics: infrared radiation, and the concept of a telescope’s penetrating power.
• Honours: Copley Medal (1781), Fellow of the Royal Society (1781), Royal Swedish Academy of Sciences (1813), Royal Guelphic Order (1816). His name is carried by the large crater on Mimas, a lunar crater, the 4.2-metre William Herschel Telescope on La Palma, and the European Space Agency’s Herschel Space Observatory (2009–2013), an infrared telescope. His house at 19 New King Street, Bath, is now the Herschel Museum of Astronomy.

Connections

People linked to William Herschel across this collection. A name without a link has no page here yet. See William Herschel in the network of all 337 lives →

Influenced by

• Charles Messier
• James Ferguson
• John Michell

Colleagues and collaborators

• Pierre-Simon Laplace 1802
• Anders Johan Lexell 1781
• Johann Elert Bode
• Nevil Maskelyne

Friends

• Mary Somerville
• William Watson

Family

• Caroline Herschel 1772-1822
• John Herschel

Also mentioned in this life

• George Biddell Airy
• Friedrich Wilhelm Bessel
• Augustin-Louis Cauchy
• Euclid
• John Flamsteed
• Galileo Galilei
• Johannes Kepler
• Urbain Le Verrier
• Max Planck
• Siméon Denis Poisson
• Lord Rayleigh

Fields

• astronomy 50 lives
• optics 38 lives

On CoursesHub

• Astrophysics for Beginners
• Optics & Photonics

Sources and further reading

Biography

1. J. J. O’Connor and E. F. Robertson, Frederick William Herschel, MacTutor History of Mathematics.
2. William Herschel, Wikipedia (with extensive references).
3. 40-foot telescope, Wikipedia.
4. M. Hoskin, Discoverers of the Universe: William and Caroline Herschel, Princeton University Press, 2011.
5. M. Hoskin, The Herschel Partnership, as Viewed by Caroline, Science History Publications, 2003.
6. R. Holmes, The Age of Wonder, HarperPress, 2008, chapters on the Herschels.
7. J. L. E. Dreyer (ed.), The Scientific Papers of Sir William Herschel, 2 vols., Royal Society and Royal Astronomical Society, 1912.

Science

1. W. Herschel, Account of a comet, Phil. Trans. R. Soc. 71 (1781).
2. W. Herschel, On the proper motion of the Sun and solar system, Phil. Trans. R. Soc. 73 (1783). See Solar apex.
3. W. Herschel, On the remarkable appearances at the polar regions of the planet Mars, Phil. Trans. R. Soc. 74 (1784).
4. W. Herschel, On the construction of the heavens, Phil. Trans. R. Soc. 75 (1785).
5. W. Herschel, Catalogue of one thousand new nebulae and clusters of stars, Phil. Trans. R. Soc. 76 (1786); second thousand, 79 (1789); 500 new nebulae, 92 (1802).
6. W. Herschel, On nebulous stars, properly so called, Phil. Trans. R. Soc. 81 (1791).
7. W. Herschel, Experiments on the refrangibility of the invisible rays of the Sun, Phil. Trans. R. Soc. 90 (1800). See Infrared.
8. W. Herschel, Account of the changes that have happened, during the last twenty-five years, in the relative situation of double-stars, Phil. Trans. R. Soc. 93 (1803). See Binary star.
9. Moons of Uranus, Wikipedia (discovery dates and orbital elements).
10. C. Hutton, Mars, A Mathematical and Philosophical Dictionary, 1795 (Herschel’s Mars measurements).