The unfathomed Milky

Herschel continued his observations with his 20- and 40-foot telescopes through the first decade of the 1800s, and continued to try to fit his observations of nebulae into a comprehensive theory of nebular evolution. Alexander helped with the mirror polishing and other duties. Caroline continued to assist William and to care for the family — when the irresponsible younger brother Dietrich showed up again, penniless, in 1809, she complained she had ''not a day's respite from accumulated trouble and anxiety'' until he left for Hanover four years later.54 Meanwhile William's son John (figure 4.10) grew up and entered St. John's college at Cambridge University, where, as an undergraduate, he distinguished himself in mathematics.

In 1816, Alexander, then 71 years old, retired to Hanover, supported by an annuity from William. Perhaps his departure, and the loss of his assistance to William, precipitated some crisis at Slough, for in this year John decided to give up his

Figure 4.10 John Frederick William Herschel (1792-1871). (Credit: National Portrait Gallery, UK.)

graduate studies in law and go home to take up his father's ''star-gazing.''55

Herschel read one of his last major papers to the Royal Society in 1817, when he was 78 years old. He had reluctantly given up on finding the absolute distances to the stars: he knew that the parallax of even the nearest stars must be less than one arcsecond, and he had no hope of obtaining any satisfactory result from this method of triangulation. But he still sought to map the positions of the stars in three dimensions, or what he called ''longitude, latitude, and Profundity.''56 Accordingly, he devoted much time in his later years to developing a quantitative method of comparing the relative distances to the stars. The 1817 paper describes his method, and his application of the method to the problem of ''the construction and extent of the milky way.''57 His final conclusions on the subject are embodied in a sketch of the Milky Way, replacing the diagram he had earlier drawn from his star gauges.

To begin with, Herschel cast aside the notion of ''big'' and ''small'' stars, even though he commonly used such terms in his own observing notebooks. His method required him to admit ''a certain physical generic size and brightness'' of the stars, and besides, he felt, ''we cannot really mean to affirm that the stars of the 5th, 6th, and 7th magnitudes are really smaller than those of the 1st, 2d, or 3d.''58 In that case, Herschel noted, the difference in the apparent magnitudes of the stars must be due to their different distances, rather than their different sizes. This overly simplistic but very common assumption has been called by a modern astronomer the ''faintness means farness'' axiom; as we shall see in chapters 8 and 9, astronomers continued to rely on it until the early years of the twentieth century, and it still may be used in some cases as an approximation to the truth if stars of one particular type are considered.59 In fact, the intrinsic luminosity of a star may range from more than 10 000 times greater than that of the Sun, down to 1/100 times or less, so the assumption that faint stars are distant ones and bright stars are near, is a very poor one.

Next, Herschel pointed out, correctly, that the amount of light from a star is inversely proportional to the square of its distance. That is, a star of a given brightness at a distance of one unit (say, one light-year) will appear to be only a quarter as bright if removed to a distance of two units (or two light-years). The fact that this property was known meant that Herschel could put his relative distances on a quantitative basis.

To actually find the relative brightnesses and hence the relative distances, Herschel used two similar telescopes side-by-side to compare target stars with standard stars in what he called the method of ''the equalisation of starlight.'' He equipped the telescope to be used on standard stars with an optical diaphragm (like the kind used in a modern camera) so that its aperture could be stopped down or fixed to smaller sizes. The telescope to be used on target stars was left ''unconfined.''60

Herschel pointed the first telescope to a chosen standard such as the bright star Arcturus in the constellation Bootes. He stopped down the aperture to a quarter, and viewed Arcturus this way. Then he searched through the second telescope for stars that seemed equally bright as the dimmed-down Arcturus. This search required him to move many times between the two telescopes, comparing the two views. He rejected many target stars that seemed slightly dimmer or brighter than the dimmed-down Arcturus, but finally found that the star Alpha Andromeda seemed to be a perfect match. Thus he established that Alpha Andromeda is twice as far as Arcturus, and by repeating this laborious equalization method with other targets and standards, he established the relative distances to other, more distant stars. A star of the ''second order of distances'' such as Alpha Andromeda could itself be used as a standard star. So, for example, Alpha Andromeda stopped down to a quarter of its brightness was found to be equal to the star Mu Pegasi.61

The ''equalization'' technique allowed Herschel to assign a ''space penetrating power'' to each of his larger telescopes. This in turn allowed him to measure, in a crude way, the ''profundity'' of the Milky Way system in various directions. For example, he turned one of his smaller telescopes to a spot of the Milky Way in Perseus, and saw stars which he knew must be of the 12th to the 24th order of distances (i.e. 12 to 24 times as far as his standard star). With a somewhat larger telescope, more stars became visible, and a whitish background appeared. These stars he estimated were at the 48th to 96th order of distance. With the 7-foot telescope he saw yet more stars, up to what he estimated was the 204th order of distances, and so on.

In this way he mapped out the relative depth of the stars on the celestial sphere in different directions. In some directions of the sky, perpendicular to the plane of the Milky Way, he thought he reached the limit of the stars, but within the Milky Way itself some parts seemed out of reach. ''[Tjhe utmost stretch of the space-penetrating power of the 20 feet telescope could not fathom the Profundity of the milky way, and the stars which were beyond its reach must have been farther from us than the 900dth order of distances,'' he the temperamental 40-foot telescope in such a study, he wrote, but he predicted that even this great aperture instrument would not reach the end of the stars. ''From the great diameter of the mirror of the 40 feet telescope we have reason to believe, that a review of the milky way with this instrument would carry the extent of this brilliant arrangement of stars as far into space as its penetrating power can reach, which would be up to the 2300dth order of distances, and that it would then probably leave us again in the same uncertainty as the 20 feet telescope,'' he wrote.63

Herschel illustrated his new conception of the Milky Way with a simple diagram (see figure 4.11). The circle in the middle represents a sphere containing stars visible to the naked eye, that is, in his notation, to the 12th order of distances. The parallel lines show the stratum of the Milky Way. From the center of the circle where we sit to the top or bottom edge of the stratum, Herschel believed, is the 39th order of distance. For the purposes of this sketch he called the depth of the Milky Way along its greatest extent the 900th order of distances — but his illustration of the stratum is open, to show that the greatest depths have yet to be fathomed.

His illustration appears so tentative and imprecise, it is easy to overlook as the sum of his life's work on the construction of the heavens. He must have been acutely disappointed that he could not provide a better map of our stellar system after years of building and designing ever larger telescopes, counting the stars in laborious ''star gages,'' and, late in life, starting afresh with the ''equalization'' technique of determining relative distances. Yet he retained to the very end a youthful and infectious enthusiasm for his subject.

Herschel's friend, the poet Thomas Campbell, said after a visit in 1813, when Herschel was 76, ''[Hjis simplicity, his

Figure 4.11 Herschel's ''Unfathomable'' Milky Way. The circle represents the limit to which the naked eye can see; the parallel lines delimit the Milky Way system as Herschel conceived it late in life, when he believed the system extended to an unknown distance in breadth.

kindness, his anecdotes, his readiness to explain, and make perfectly perspicuous too, his own sublime conceptions of the Universe, are indescribably charming____[Ajnything you ask, he labours with a sort of boyish earnestness to explain.''64

Herschel died in August 1822, at the age of 83. Caroline, who was then 72, was despondent. She made a hasty and much-regretted decision to return to Hanover and live with her brother Dietrich. She always expected to live only a short time more herself, but endured another 26 years as a local celebrity, complaining all the time about incompetent servants and the ''useless'' life she led. In 1828 the Royal Society awarded her its Gold Medal for her arrangement of a catalog of nebulae and for her lifelong assistance to her brother.

John Herschel, who was destined to become one of the most prominent English astronomers of the nineteenth century, continued his father's work on double stars—now interesting in their own right as probes of the law of gravitation—and verified his father's observations of nebulae. He helped establish the Royal Astronomical Society, which met first in 1821, shortly before William Herschel's death. After his mother Mary's death, John and his wife and children sailed for the Cape of Good Hope, where John swept the skies for southern hemisphere nebulae and double stars.

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