There is a well-known correlation between music and mathematics, amply demonstrated in the account of the life of William Herschel (1738–1822). The son of a German musician, William Herschel was himself a professional organist before becoming fascinated by the stars—a fascination that led him to become one of the greatest of all astronomers and a pioneer in the improvement of telescopes used for watching the night sky.
Isaak Herschel was a musician in a German military regiment. In 1755, when the regiment was transferred to England for several months, Isaak took his family with him. His young son, Wilhelm, also played in the regimental orchestra, but he had not signed up as a soldier and when his father’s regiment was transferred he decided to stay in England in the hope of making a living from his musical talents. Wilhelm was successful in this endeavor, and he was employed to play in the Duke of Richmond’s private orchestra. He moved to Leeds where he remained for four years, before moving to Halifax for a short time. In December 1766 Herschel was appointed as the organist at the Octagon Chapel in the fashionable city of Bath. Wilhelm Herschel was then 28 years of age, and about this time he changed his Christian name from Wilhelm to the anglicized version of William.
However, it was not as a musician that William Herschel became famous. But it was through the patterns in his music that Herschel became interested in mathematics, and this in turn led him on to an interest in astronomy. Soon he became fascinated by what he could see in the night sky, and he found that he was spending all his spare time studying the stars. Simple telescopes were easy to come by, but after a short time they were not good enough for Herschel’s observations. No matter how far into the sky he could see he always wanted something better so he could see further. The local opticians and spectacle makers supplied him with better lenses and eyepieces, but even they were found to be of limited use.
He knew that reflecting telescopes could be purchased from London instrument makers, but they were very expensive and Herschel could not afford one. He also knew that in the previous century Isaac Newton (1642–1727) had made his own reflecting telescope. Herschel knew that the reflecting telescope had many advantages over the refracting telescopes of the time. The mirrors were free from the colored fringes that appeared in the refracting telescope, a defect known as chromatic aberration. The mirrors were easier to manufacture than lenses, and because they could be supported from the back they could also be made much larger. Herschel’s only solution was to set about casting and grinding his own mirrors. It was painstaking work. He cast larger and larger mirrors for his telescopes, but he also met with many failures. The larger the mirror the more likely it was to crack during the cooling process. Even when Herschel had cast a perfect mirror his problems were not over. He had to spend hours and hours polishing the mirrors to achieve the perfect parabolic surface. He mastered this and other techniques, and he also made his own eyepieces. He persevered with larger and larger telescopes year after year, and by the time he had mastered all the optical techniques he was building the best telescopes in the world.
Herschel was ably supported in his endeavors by his sister, Caroline (1750–1848), who was also a musician and a professional singer. Caroline undertook all the household duties at their Bath residence in New King Street, and she made sure that her fanatical brother was properly fed. She also spent hours and hours helping to grind and polish the mirrors to perfection. Without the support of his sister, Herschel would never have become the most famous astronomer of his time.
When his first reflecting telescope was ready for observing, one of the first tasks tackled by William Herschel was to study the Moon. He knew the distance to the Moon, so he could estimate the height of the mountains from the shadows they cast on the surface. He made a survey and he drew maps of his findings. Then he looked deeper into space. His reflecting telescope could see far more stars than were visible with the naked eye and more than were listed in the most up-to-date star catalogs. He became interested in the different types of stars, and he studied objects such as nebulae (gas clouds) that were not stars at all. He soon realized that a large number of stars were not single stars like our Sun but were paired, or binary, stars. Others were triple stars or even clusters of several stars all rotating about each other. He went on to make a detailed study of the binary stars, and he was able to distinguish genuine binary stars from others that looked to be paired or clustered but in reality just happened to lie in the same direction and were in fact light years apart.
With his reflecting telescope William Herschel was able to see much further into the sky than others before him. His catalog of binary stars eventually grew to 700 entries, and soon the number of known double stars in the sky grew to nearly 10 percent of the number of single stars like the Sun. He discovered many new nebulae to add to the French astronomer Charles Messier’s collection, and the extended catalog added up to about 250 objects. His sister Caroline was keen to do more than look after the house and polish telescope mirrors and so he supplied her with one of his telescopes. It was not long before Caroline Herschel had also discovered new objects to add to the Messier catalog, plus binary stars and several new comets.
The Herschels became well known in Bath, and sometimes received visits from local residents and others who wanted to talk about astronomy and look through the telescope. One of the visitors was none other than Nevil Maskelyne (1732–1811), the Astronomer Royal and director of the Royal Greenwich Observatory.
The Herschels made excellent progress as they continued to map the skies and build up catalogs of new objects. Both were fanatical about their work and for years they were happy to be making additions to the catalogs. Then, on March 13, 1781, William Herschel made a discovery that was every astronomer’s dream. For some time he had been watching a star that he suspected was moving against the background of the other stars. It had no tail and so it was certainly not a comet. Nor was it listed in the Messier catalog. After more observation Herschel became convinced that the object really was moving, and furthermore he was also convinced that it was moving in a nearly circular orbit. There seemed to be only one possible explanation for the motion. William Herschel had discovered a new planet!
The discovery of a new planet launched Herschel’s career. The invention of the telescope had paved the way for countless additional stars to be detected by astronomers. Many new comets and even other galaxies had been discovered, but nobody had found a new planet since earliest times. It was thought that all the planets had been discovered at the dawn of astronomy, and thousands of years of gazing at the heavens since then had not changed this belief. When the position and direction of motion of Herschel’s new planet had been measured it was easy for other astronomers to verify the find. As the path of the new object in the sky was plotted, there was no doubt that it was further from the Sun than Saturn. After a time it became obvious that it was obeying Kepler’s and Newton’s laws, and it was following an elliptical course around the Sun. Now all that remained was to name the new planet. Some suggested that it be called planet Herschel. Others suggested the rather pompous name of Georgium Sidus to honor King George III, but after his incompetent handling of the American Revolution George was not the most popular of kings.
In the best classical style the name Uranus was eventually agreed upon. A few years later Herschel discovered two moons orbiting Uranus and they became known as Titania and Oberon, thereby seemingly disclosing his taste for the plays of William Shakespeare. William Herschel seems to have been too modest to name the moons himself and the names were actually given many years later by his son John.
Some would say that the discovery of Uranus was the high point of Herschel’s career, and in the sense that it brought him fame and fortune this is true. He was given a pension by the king and he moved to Berkshire where he was able to set up his own observatory. It was only then, when he had royal sponsorship, that he was able to make his most significant contribution to the advance of astronomy. In 1785 he and his sister Caroline moved to a house called Clay Hall in Old Windsor. Socially it was a very acceptable address, but the Herschels did not own the property and in 1786 they were obliged to move to a new residence in nearby Slough. His dwelling became known as Observatory House. He found Slough to be very amenable, and it was there that he met his wife, a widow called Mary Pitt. On May 7, 1788 they were married at St. Laurence Church in Slough. William’s sister Caroline moved into nearby lodgings and continued her work as his assistant.
During his long career it has been estimated that William Herschel made about 400 telescopes. His salary as the court astronomer was supplemented by an income from the sale of his telescopes. He became so well known as a telescope maker that his customers included the king of Spain, the prince of Canino and the Russian emperor. He made telescopes for export to Berlin and he even sold one of his instruments to China.
The largest and most famous was his great reflecting telescope with an aperture of 1.2 meters (4 ft) and a focal length of 12 meters (40 ft). The telescope was completed in February 1787 but Herschel was not satisfied with the mirror; it was too thin and it bent under its own weight of half a ton. He ordered a new disc to be cast but it cracked in the cooling process. Then he cast a third mirror 8 centimeters (3 in) thick and weighing nearly a ton. It was polished and ready for use in August 1789. It was with this telescope that Herschel discovered two moons of Saturn within the first month of observation. They became known as Mimas and Enceladus and, as with the moons of Uranus, it was his son who chose the names long after William’s death. The discovery of the moons took place just one month after news arrived in England of the storming of the Bastille in Paris and the outbreak of the French Revolution.
The great telescope needed a complex system of scaffolding and pulleys to raise it to the desired elevation. The whole structure was mounted on a large turntable that needed to be winched round to the correct azimuth to point it toward the required object in the sky. This type of mounting made it very difficult to follow a star as the Earth rotated, and consequently the great telescope was only used to follow up discoveries from smaller instruments. The smaller but more maneuverable 6-meter (20-ft) telescope was the one Herschel used for most of his observing.
Herschel wanted to know more about the distribution of the stars in the sky. To accomplish this he divided the sky into 683 regions and then set about trying to count the number of stars in each region. He produced a model showing the distribution of the stars in the Milky Way. It consisted of a great spinning disc in which he placed the Sun, our own star, near the center. His model of the galaxy was the most advanced produced at that time but in fact it contained one of the few mistakes made by Herschel. The Sun is actually situated on one of the spiral arms of the galaxy, quite a long way from the center where Herschel put it.
Herschel was well acquainted with Newton’s work on the spectrum and he was one of the first to realize that there were other colors (or wavelengths) that lay outside the visible spectrum. He passed a beam of sunlight through a glass prism and he held a thermometer just beyond the red end of the spectrum. The thermometer indicated a temperature rise. Herschel came to the conclusion that there must be an invisible form of light beyond the red wavelength. It became known as infrared radiation. Herschel was an excellent scientist but he still held some unconventional views that may have appealed to science fiction readers. He thought, for example, that every planet was inhabited by intelligent life, and he also believed that there was a temperate region beneath the surface of the Sun where there lived a race of beings with very large heads who had fully adapted to their environment.
In Herschel’s time nobody had any idea of the true size of the universe. It seemed impossible that anybody would ever be able to measure a parallax for the stars. Some of the “fixed” stars were not quite in the positions given by Ptolemy and Hipparchus, however, and this gave reliable evidence that they had moved over a time span of nearly 2000 years. The nebulous smudges of light revealed by the large telescope for the objects in the Messier catalog were thought to be clouds of luminous gas; some of the Messier objects were in fact distant galaxies much further way than the stars, but in Herschel’s time no one imagined that they were any more distant than other objects in the sky. In Herschel’s time the calculations of the French mathematicians Lagrange and Laplace implied that the Newtonian model of the universe reigned supreme.
In 1816 William Herschel was made a knight of the Royal Guelphic Order by the Prince Regent. In 1820 he was a founder member of the Astronomical Society of London, which became the Royal Astronomical Society in 1831. He and his wife Mary had one child, christened John, who was born at Observatory House in Slough on March 7, 1792. John Herschel had the best possible start in life for an astronomer, and he grew up to follow his father and become a leading figure in the astronomical world. While he was at Cambridge University John Herschel (1792–1871) befriended Charles Babbage (1791–1871), well known in computing circles as the designer of his difference engine, as well as the mathematician George Peacock (1791–1858). These three started a movement to abolish what they called the “dotty notation” of the differential calculus. The notation was widely used in England but it was not as logical as the dy/dx and d2y/dx2 terminology used by mathematicians on the Continent.
Between 1786 and 1802 William and Caroline Herschel compiled three catalogs giving a total of about 2500 positions of star clusters, nebulae and galaxies. Caroline’s efforts as her brother’s assistant were recognized by the crown, and in 1787 she was awarded a royal pension of £50 a year. She lived until 1848 and she was only a few days short of her 98th birthday when she died.
When John Herschel became involved with astronomical work one of his major tasks was the reobservation of the double stars already cataloged by his father. Using the large telescopes he was able to detect movements of some of these pairs of stars as they rotated about each other, and this was the first positive proof that Newton’s law of gravitation was still valid outside the solar system. John Herschel was fortunate to find a competent collaborator called James South (1785–1867) who was wealthy enough to afford the refined instruments needed for this kind of work. The catalog compiled between 1821 and 1823 by John Herschel and James South was published by the Royal Society in 1824, and it earned them both the Gold Medal of the Royal Astronomical Society and the Lalande Prize from the Paris Academy of Sciences.
In 1829 John Herschel married Margaret Stewart, who was to bear him a large family of three sons and nine daughters. He was very keen to complete his father’s work in astronomy and he knew that his father’s researches were confined to the Northern Hemisphere. He therefore decided to undertake a journey south of the equator to survey the skies not visible in England. He began planning his expedition in 1832 while he was still living at Observatory House in Slough. He took his wife and children with him, and in November of that year John and his family set sail for South Africa, taking with them a large reflecting telescope for observing faint nebulae. They also carried an extensive selection of astronomical instruments including a refracting telescope for observing double stars. The Herschel family set up home and established themselves in a farmhouse a short distance to the south of Cape Town.
For four years John Herschel studied the clear skies of the Southern Hemisphere and made excellent progress during that time. By the time he and his family embarked for home in March of 1838, John Herschel had recorded the locations of thousands of stars and in addition he had amassed long catalogs of nebulae and double stars. He added 1700 new entries to his father’s catalog, making a total number of 68,948 stars in the Herschel catalogs. After his return to England John Herschel was given the post of Master of the Mint—after Isaac Newton had held this post it was not uncommon for it to be offered to a scientist. John Herschel did not enjoy the pressures of the job at the Royal Mint, however, and he suffered a nervous breakdown in 1854.