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William Hyde Wollaston

William Hyde Wollaston

A course on the physician who left medicine to refine platinum, found palladium and rhodium, saw the dark lines of the Sun before Fraunhofer, and filled the instrument cases of his age, with lessons on powder metallurgy, platinum-group chemistry, equivalents, refraction, optical instruments, crystals and electricity.

Born 6 August 1766, East Dereham Died 22 December 1828, London Discoveries palladium 1802, rhodium 1804 Level advanced undergraduate → graduate
The camera lucida (patented 1806). Two total internal reflections at faces meeting at 135° turn the ray through 90° without inverting the image. Half the pupil sees the scene, half the paper.
Lesson 00

How to use this course

William Hyde Wollaston is one of the great names of early nineteenth-century science that few people now recognize. In London between 1800 and 1828 he was regarded, with Humphry Davy, as the leading chemist in England. He discovered two elements, made platinum workable, gave strong early evidence for John Dalton’s atomic theory, and invented instruments that artists, mineralogists and chemists used for a century. He also saw the dark lines in sunlight twelve years before Joseph von Fraunhofer. He worked alone, published briefly, and guarded his methods, which partly explains why his reputation faded.

Prerequisites for Part II
  • General chemistry: moles, equivalents, simple redox and precipitation reactions (Lessons 04 to 06).
  • Geometrical optics: Snell’s law, total internal reflection, thin lenses (Lessons 07 and 08).
  • Elementary solid geometry and vectors (Lesson 09).
  • Basic mechanics and electrostatics: momentum, kinetic energy, charge and current (Lesson 10).

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. The lessons group his work by theme: platinum metals (1800–1828), atomic chemistry (1808–1814), optics (1802–1812), crystals (1809–1822), and electricity, mechanics and physiology (1801–1824).

Reference

Timeline

1766Born 6 August at East Dereham, Norfolk, to Francis Wollaston, clergyman and astronomer, and Althea Hyde; one of seventeen children.
1774–78Charterhouse School, London.
1782Enters Gonville and Caius College, Cambridge, to study medicine.
1787Graduates in medicine; elected fellow of Caius, a fellowship he holds until his death.
1793Doctor of Medicine, Cambridge. Fellow of the Royal Society.
1797Moves his practice from Bury St Edmunds to London.
1799His brother George transfers to him £8,000 of Bank of England stock.
1800Gives up medicine. December: with Smithson Tennant, buys crude platinum ore.
1801Shows that frictional and voltaic electricity act alike.
1802Refractive indices by total reflection; dark lines in the solar spectrum. Palladium found by July. Copley Medal.
1803April: palladium offered for sale anonymously. Periscopic spectacles.
1804Announces rhodium. Secretary of the Royal Society (to 1816).
1805Bakerian Lecture on the force of percussion. Admits authorship of palladium.
1806Patent for the camera lucida.
1808Paper on super-acid and sub-acid salts: multiple proportions.
1809The reflecting goniometer.
1810Cystic oxide (cystine), a new urinary calculus.
1812Bakerian Lecture on the elementary particles of crystals. Joins the Geological Society.
1814The synoptic scale of chemical equivalents.
1818Board of Longitude (to 1828).
1820Interim President of the Royal Society after the death of Joseph Banks.
1821Electromagnetic rotation: dispute over Faraday’s discovery.
1822On the finite extent of the atmosphere.
1824On semi-decussation of the optic nerves.
1828Publishes his platinum method in his last Bakerian Lecture, read 20 November by Henry Warburton. Royal Medal. Gifts to the Royal Society and the Geological Society. Dies 22 December in London, aged 62.
Part I · Formation
Lesson 01

A family of naturalists, 1766–1782

William Hyde Wollaston was born on 6 August 1766 at East Dereham in Norfolk, the seventh child and third son among the seventeen children of Francis Wollaston and Althea Hyde. His father was a clergyman, a Fellow of the Royal Society and an observational astronomer who later compiled a large star catalogue, the Fasciculus astronomicus of 1800. Science ran through the family. His great-grandfather, also William Wollaston, had written the popular moral treatise The Religion of Nature Delineated (1724). His uncle William Heberden was among the most eminent physicians in London. His elder brother Francis John Hyde Wollaston lectured in mathematics at Cambridge and in 1792 succeeded Isaac Milner as the university’s lecturer in chemistry.

He was educated at Charterhouse School in London from 1774 to 1778. From his father he learned to observe the sky with care and to keep exact records. This habit of quiet, precise observation, made with small means, became the signature of his work.

Lesson 02

Cambridge and medicine, 1782–1800

In 1782 Wollaston entered Gonville and Caius College, Cambridge, as a medical student. He graduated in 1787 and was elected a fellow of Caius, which he remained for life. At Cambridge he also studied chemistry, astronomy, botany and mineralogy. He took the degree of Doctor of Medicine in 1793 and was elected a Fellow of the Royal Society the same year.

He practised as a physician in Huntingdon and Bury St Edmunds, and in 1797 moved to London. He was conscientious but found the anxieties of practice hard to bear, especially when he could do nothing for a patient. In 1800 he failed to be appointed physician at St George’s Hospital, and he left medicine for good. Money made this possible. In 1797 his uncle West Hyde had left an estate to Wollaston’s brother George, and in March 1799 George transferred £8,000 of Bank of England stock to William.

Medicine left a mark on his science. He wrote on urinary stones, discovering in 1810 a new kind made of what he called cystic oxide, now known to be the amino acid cystine. In 1811 he reported his search for sugar in the blood of diabetic patients. His last major physiological paper, of 1824, drew on his own episodes of half-blindness (Lesson 10).

Lesson 03

The platinum partnership, 1800–1805

Wollaston’s close friend Smithson Tennant, a chemist from Cambridge, had shown in 1797 that diamond is pure carbon. In 1800 the two formed a private partnership to purify platinum. In December 1800 they made their first purchase of crude platinum ore from South America, for £794. Platinum was in demand: it resists acids and fire, so it was ideal for crucibles, and the sulfuric acid industry wanted platinum boilers. But nobody in Britain could make it into sound, workable metal.

The work split naturally. Tennant studied the black insoluble residue left after dissolving the ore, and found in it two new elements, osmium and iridium, announced in 1804. Wollaston studied the solution and found two more: palladium, by July 1802, and rhodium, announced in 1804 (Lesson 05). Wollaston also worked out a method to turn purified platinum powder into dense, malleable metal (Lesson 04). He kept the method secret for more than twenty years, and for most of that time he was effectively England’s sole supplier of malleable platinum. His profits were substantial: estimates in the literature range from about £15,000 to about £17,000.

The palladium episode showed his secrecy at its strangest. In April 1803 he advertised the new metal anonymously for sale at a shop in Soho. The Irish chemist Richard Chenevix bought the stock, analysed it and declared it an alloy of platinum and mercury. An anonymous offer of £20 followed for anyone who could make the supposed alloy. Nobody could. In February 1805 Wollaston admitted that he was the discoverer.

Part II · The science
Lesson 04

Malleable platinum

For the general reader. Platinum melts at about 1770 °C, far hotter than any furnace of 1800 could reach. So it could not be cast like gold or iron. Wollaston’s answer was to avoid melting altogether. He made a very fine pure powder, pressed it hard into a cake, heated the cake until the grains welded together, and then hammered it into a solid bar. This is the basic idea of powder metallurgy, which now makes tungsten lamp filaments, hard-metal tools and many machine parts.

Goals
  • Follow the chemistry of platinum purification through ammonium chloroplatinate.
  • Understand why each mechanical step of Wollaston’s method matters.
  • Compute yields and drawing ratios, including Wollaston’s fine wire.

Purification

Crude ore was dissolved in aqua regia, a mixture of nitric and hydrochloric acids, which oxidizes platinum to the hexachloroplatinate ion. Ammonium chloride then precipitates the sparingly soluble yellow salt:

\[ \begin{aligned} 3\,\mathrm{Pt}+4\,\mathrm{HNO_3}+18\,\mathrm{HCl}&\longrightarrow 3\,\mathrm{H_2PtCl_6}+4\,\mathrm{NO}+8\,\mathrm{H_2O},\\ \mathrm{H_2PtCl_6}+2\,\mathrm{NH_4Cl}&\longrightarrow (\mathrm{NH_4})_2\mathrm{PtCl_6}\downarrow+2\,\mathrm{HCl}. \end{aligned} \]

Gentle heating drives off ammonium chloride, hydrogen chloride and nitrogen, leaving spongy platinum, a soft grey mass of very fine particles. Wollaston used dilute aqua regia and left part of the ore undissolved, so as to reduce contamination by iridium, which makes platinum brittle. Platinum left in the mother liquor was recovered with iron.

Wollaston’s process (published 1828)
  1. Heat the chloroplatinate only enough to decompose it, so that the particles do not cohere.
  2. Rub the sponge gently between the hands and grind it in a wooden mortar, never burnishing it.
  3. Wash and let the powder settle in water, keeping only the finest fraction.
  4. Press the wet mud strongly in a brass barrel with a lever (toggle) press, forming a firm cake.
  5. Dry, heat the cake to a high temperature in a charcoal fire, then forge it hot on an anvil.

Each step serves a purpose that modern sintering theory explains. Fine particles have a large surface energy, which drives them to bond and densify when hot. Burnished particles would have hard, smooth faces that resist bonding. Pressing under water excludes air pockets and brings particles into contact over large areas. Heating below the melting point lets atoms diffuse across contacts, closing pores. Hot forging closes the remaining porosity and gives a metal that can be rolled and drawn. Wollaston was proud of the result: his platinum was denser than any made before.

Wollaston wire

He also made platinum wire far finer than could be drawn directly. A platinum wire is set along the axis of a silver cylinder, and the composite is drawn down through dies. The platinum shrinks in the same ratio as the silver. Nitric acid then dissolves the silver, leaving a platinum filament of a few micrometres. Such wire was used for cross-hairs in telescopes and, later, in hot-wire instruments and fuses.

Exercise 4.1What mass of platinum can be obtained from 100 g of pure ammonium chloroplatinate, \((\mathrm{NH_4})_2\mathrm{PtCl_6}\)? (Pt 195.08, N 14.007, H 1.008, Cl 35.45.)

Show solution
\(M=2(18.04)+195.08+6(35.45)=36.08+195.08+212.70=443.86\). Platinum is \(195.08/443.86=43.95\%\), so 43.9 g.

Exercise 4.2A platinum wire of diameter 0.076 mm is placed in a silver rod of diameter 2.5 mm. The composite is drawn to 0.051 mm. What is the final platinum diameter? Why must the platinum and silver be drawn together rather than the platinum alone?

Show solution
Every cross-section scales by the same factor, \(0.051/2.5=0.0204\), so the platinum ends at \(0.076\times0.0204=1.55\ \mu\mathrm m\). A bare platinum wire this thin would break in the die: the silver carries the drawing force and supports the core. This is Wollaston’s trick.

Exercise 4.3A pressed platinum cake has 35% porosity. After sintering and forging its density is 21.3 g/cm\(^3\) (pure platinum 21.45 g/cm\(^3\)). By what fraction has the volume of the cake shrunk, assuming no mass loss?

Show solution
Initial density \(0.65\times21.45=13.94\) g/cm\(^3\). The volume ratio is \(13.94/21.3=0.655\), so the volume has shrunk by about 35%. Nearly all the pore space has been removed.
Lesson 05

Palladium and rhodium

For the general reader. After the platinum had been taken out of the dissolved ore, small amounts of other metals stayed behind in the liquid. Wollaston worked through this leftover solution with a few drops at a time, testing it with one reagent after another. He found two new elements: palladium, named after the asteroid Pallas discovered a few months before, and rhodium, named after the rose colour of one of its salts. Both are now essential in catalytic converters.

Goals
  • Follow the separation scheme that isolated palladium and rhodium.
  • Understand how Wollaston proved palladium was an element, not an alloy.
  • Use stoichiometry to test claims of composition.

Palladium (1802)

Wollaston neutralized the solution left after the platinum had been precipitated, and added mercuric cyanide. A pale precipitate of palladium(II) cyanide formed; heating decomposed it to the metal:

\[ \mathrm{Pd^{2+}}+\mathrm{Hg(CN)_2}\longrightarrow\mathrm{Pd(CN)_2}\downarrow+\mathrm{Hg^{2+}},\qquad \mathrm{Pd(CN)_2}\xrightarrow{\ \text{heat}\ }\mathrm{Pd}+(\mathrm{CN})_2. \]

His notebook records a new noble metal in July 1802. He named it in August after Pallas, found by Heinrich Olbers in March of that year. It is lighter than platinum, melts lower, and dissolves in nitric acid alone, which platinum does not.

Rhodium (1804)

After platinum had been removed, zinc precipitated a mixture of copper, lead, palladium and rhodium. Dilute nitric acid took up the copper and lead. The remainder was redissolved in aqua regia and treated with sodium chloride. On evaporation a rose-red salt crystallized, now written \(\mathrm{Na_3[RhCl_6]}\cdot n\mathrm{H_2O}\). Alcohol removed the palladium salt, and zinc reduced the rose salt to rhodium metal. He announced rhodium, from the Greek rhodon, rose, in 1804, and in the same paper discussed palladium.

The case against the alloy

An element is a substance that cannot be separated into others by any chemical treatment. Chenevix claimed palladium was platinum combined with mercury. Wollaston’s reply had two parts: no one could produce palladium by combining platinum and mercury, and palladium’s density, solubility in nitric acid and other properties were not intermediate between those of the supposed components, as an alloy’s should be.

Exercise 5.1Heating 1.000 g of palladium(II) cyanide gives what mass of palladium? (Pd 106.42, C 12.011, N 14.007.)

Show solution
\(M(\mathrm{Pd(CN)_2})=106.42+2(26.018)=158.46\), so the yield is \(106.42/158.46=0.672\) g.

Exercise 5.2Chenevix’s hypothetical alloy would need a density between those of platinum (21.45) and mercury (13.53 g/cm\(^3\)). Palladium’s density is 12.0 g/cm\(^3\). What does this alone show, assuming no large volume change on alloying?

Show solution
Mixing two substances without large contraction or expansion gives a density between the two. Palladium is less dense than either supposed component, so it cannot be a simple alloy of them. Wollaston’s own determinations of density were among the arguments he used.

Exercise 5.3Why does zinc precipitate palladium and rhodium from solution, but leave zinc ions behind? Use the standard reduction potentials \(E^\circ(\mathrm{Zn^{2+}/Zn})=-0.76\) V, \(E^\circ(\mathrm{Pd^{2+}/Pd})\approx+0.95\) V.

Show solution
For \(\mathrm{Zn}+\mathrm{Pd^{2+}}\to\mathrm{Zn^{2+}}+\mathrm{Pd}\), \(E^\circ_{\text{cell}}=0.95-(-0.76)=1.71\) V \(>0\), so the reaction is strongly spontaneous. Zinc, the more active metal, displaces the nobler metals from solution and enters it itself.
Lesson 06

Multiple proportions and the scale of equivalents

For the general reader. In 1808 John Dalton proposed that matter is made of atoms that combine in small whole-number ratios. Wollaston gave some of the cleanest early evidence: salts of the same acid and base, made in different ways, contain exactly one, two or four times as much acid. In 1814 he built a sliding scale, a slide rule for chemists, that let anyone read off combining weights at a glance.

Goals
  • State the law of multiple proportions and see Wollaston’s evidence for it.
  • Understand equivalent weights and why Wollaston preferred them to atomic weights.
  • Explain how a logarithmic scale turns proportion into addition.
Law of multiple proportions (Dalton, 1803–1808)

If two substances \(A\) and \(B\) form more than one compound, the masses of \(B\) that combine with a fixed mass of \(A\) stand in ratios of small whole numbers.

Super-acid and sub-acid salts (1808)

Wollaston heated the bicarbonate of potash and measured the carbon dioxide driven off: it contained exactly twice as much acid per unit of alkali as the ordinary carbonate. He then studied the oxalates of potash and found three salts, with acid in the proportions 1 : 2 : 4 per unit of potash. Similar ratios appeared in sulfates. He remarked that a full explanation would need the geometry of the atoms themselves, an early hint at the arrangement of atoms in space. In the same year Thomas Thomson published related evidence from the oxalates of strontia.

Equivalents and the synoptic scale (1814)

Combining weights determined by analysis are unambiguous, but atomic weights depend on guessing formulas, which in 1814 nobody could do reliably. Wollaston therefore proposed to work with equivalents: the weight of each substance that combines with or replaces a fixed weight of a standard, which he took to be oxygen. He laid out the equivalents of many acids, bases and salts on a scale ruled logarithmically, with a sliding central rule of numbers.

Principle of the synoptic scale

If quantities are placed at distances proportional to their logarithms, then a fixed separation corresponds to a fixed ratio. Setting the slide so that the number \(m_A\) stands against substance \(A\), every other number \(m_X\) on the slide stands against substance \(X\) and gives the mass of \(X\) equivalent to \(m_A\) of \(A\):

\[ \log m_X-\log m_A=\log E_X-\log E_A \iff \frac{m_X}{m_A}=\frac{E_X}{E_A}. \]

Exercise 6.1Potassium oxalate \(\mathrm{K_2C_2O_4}\), potassium hydrogen oxalate \(\mathrm{KHC_2O_4}\), and the “quadroxalate” \(\mathrm{KHC_2O_4\cdot H_2C_2O_4}\). Show that the oxalic acid per potassium is in the ratio 1 : 2 : 4.

Show solution
Oxalate groups per K: \(1/2\), \(1\), \(2\). Ratios \(\tfrac12:1:2=1:2:4\). Wollaston found these ratios by weighing what was needed for neutralization, before such formulas could be written.

Exercise 6.2On a synoptic scale, how far apart (in units of the decade length) are substances whose equivalents are 49 (half the mass of a mole of sulfuric acid) and 53 (half the mass of a mole of sodium carbonate)? How much sodium carbonate neutralizes 20 g of sulfuric acid?

Show solution
Separation \(\log_{10}(53/49)=0.034\) of a decade. Mass: \(20\times53/49=21.6\) g. On the scale one simply sets 20 against sulfuric acid and reads 21.6 against sodium carbonate.
Lesson 07

Refraction, dark lines and invisible rays

For the general reader. In 1802 Wollaston devised a way to measure how strongly a substance bends light, using only a drop of it pressed against a glass prism. In the same work he looked at sunlight through a narrow slit and a prism and saw that the colours were crossed by a few fine dark lines. He took them for natural boundaries between colours and moved on. Twelve years later Fraunhofer found hundreds of them, and half a century later Kirchhoff and Bunsen showed they reveal the chemistry of the Sun.

Goals
  • Derive the critical-angle method for measuring refractive index.
  • Understand what Wollaston saw in the solar spectrum and why his slit mattered.
  • Place his work on ultraviolet light in context.

Index by total reflection

Place a sample of index \(n\) in contact with the base of a prism of known higher index \(N\). Light inside the prism meeting the base at angle \(\theta\) is partly transmitted into the sample if \(\theta<\theta_c\) and totally reflected if \(\theta>\theta_c\). The boundary between bright and dimmer reflection is sharp and easy to locate.

Critical-angle relation

For light passing from a medium of index \(N\) to one of index \(n<N\), total internal reflection occurs for angles of incidence above \(\theta_c\), where

\[ \sin\theta_c=\frac{n}{N}. \]

Measuring \(\theta_c\) gives \(n=N\sin\theta_c\). Only a thin film of sample is needed, and opaque or coloured substances can be measured by reflection.

This is the principle of the refractometers made later by Ernst Abbe and still used to measure sugar content and the purity of oils. Wollaston used it on dozens of substances, solid and liquid, and found surprising behaviour in some of them. He also confirmed by measurement Christiaan Huygens’s construction for the extraordinary ray in Iceland spar, evidence for the wave theory of light.

The dark lines

Viewing a slit of daylight about a twentieth of an inch wide through a flint-glass prism held close to the eye, Wollaston saw the spectrum divided by dark lines. He described a handful of them, labelled with letters, and interpreted the strongest as the edges separating red, yellow-green, blue and violet. He saw nothing to show that they were features of the light source. The narrow slit was the important innovation: a broad source blurs neighbouring colours together and hides fine lines, which is why Isaac Newton, using a round hole, never saw them.

Chemical rays

In 1801 Johann Wilhelm Ritter found that silver chloride blackens fastest beyond the violet end of the spectrum, where the eye sees nothing. Wollaston independently made similar observations with silver chloride and with gum guaiacum, which changes colour in light. These invisible “chemical rays” are ultraviolet light.

Exercise 7.1A prism of flint glass with \(N=1.62\) gives a critical angle of \(55.4^\circ\) for a liquid sample. Find the liquid’s index. What is the largest index this prism can measure?

Show solution
\(n=1.62\sin55.4^\circ=1.62\times0.823=1.333\): water. The method needs \(n<N\), so the limit is \(1.62\), reached as \(\theta_c\to90^\circ\). Wollaston used a dense glass for this reason.

Exercise 7.2Wollaston’s slit was about 1.3 mm wide, viewed from a few metres. The dispersion of a flint prism between the red C line (656 nm) and the blue F line (486 nm) is about \(1.5^\circ\). If the slit subtends \(0.02^\circ\), what is the smallest wavelength difference his arrangement could resolve? Could he separate the two sodium D lines, 0.6 nm apart?

Show solution
On average \(1.5^\circ\) spans 170 nm, about \(0.0088^\circ\) per nm. The slit width \(0.02^\circ\) corresponds to about 2.3 nm, and somewhat less in the blue, where flint disperses more. The D lines (0.6 nm) would merge into one, which is what Wollaston saw. Fraunhofer’s telescope and theodolite magnified the spectrum and reduced the effective slit angle.
Lesson 08

Optical instruments

For the general reader. Wollaston had a gift for simple, clever optical devices. His camera lucida lets an artist see a scene and the drawing paper at once and trace one over the other. His curved spectacle lenses gave clear vision when the eye looked sideways through them. His prism of calcite splits light into two beams polarized at right angles. All three are still found in laboratories or textbooks.

Goals
  • Trace the rays through the camera lucida prism and explain why the image is upright.
  • Understand the advantage of the meniscus (periscopic) lens.
  • Compute the beam separation of a Wollaston prism.

The camera lucida (1806)

The prism has four faces, with angles of \(90^\circ\), \(67.5^\circ\), \(135^\circ\) and \(67.5^\circ\). Light from the scene enters the face next to the right angle, is totally reflected at the two faces meeting at \(135^\circ\), and leaves through the other face next to the right angle, travelling up to the eye. The eye is placed over the edge of the prism so that part of the pupil receives this light and part looks straight past the prism at the paper. The brain fuses the two, and the scene appears to lie on the paper. Johannes Kepler had described the basic optics in 1611, but Wollaston made the first practical instrument.

Two-mirror theorem

Two successive reflections at plane mirrors whose surfaces meet at angle \(\beta\) (in a plane containing the ray) rotate the ray by \(2\beta\), whatever the angle of incidence. Two reflections leave the handedness of the image unchanged, so the image is neither reversed nor inverted relative to a direct view.

Proof. A reflection in a line at angle \(\varphi\) sends a direction at angle \(\psi\) to \(2\varphi-\psi\). Composing reflections in lines at \(\varphi_1\) and \(\varphi_2\) gives \(\psi\mapsto2\varphi_2-(2\varphi_1-\psi)=\psi+2(\varphi_2-\varphi_1)\), a rotation by twice the angle between the mirrors, independent of \(\psi\). Each reflection reverses handedness, so two restore it. In the camera lucida the reflecting faces make an angle of \(45^\circ\) between their lines (the internal angle is \(135^\circ\)), so the ray turns through \(90^\circ\). The \(67.5^\circ\) angles make both reflections occur at \(67.5^\circ\) incidence, well above the critical angle of glass (about \(41^\circ\)), so no silvering is needed.

Periscopic spectacles

Spectacle lenses of his day were biconvex or biconcave. Light passing obliquely through such a lens is badly blurred by astigmatism, so the wearer had to turn the head rather than the eyes. From 1803 Wollaston advocated meniscus lenses, curved like a watch glass, with the concave side toward the eye. Oblique rays then pass more nearly perpendicular to both surfaces, and the field of clear vision widens. Almost all spectacle lenses today are menisci. In 1812 he designed a meniscus lens for the camera obscura with a stop in front of it, an early landscape lens.

The Wollaston prism

Two right-angled wedges of calcite (or quartz) are cemented together with their optic axes perpendicular to each other and to the light. A ray that is ordinary in the first wedge becomes extraordinary in the second and vice versa, so the two polarizations are bent in opposite directions at the interface. Two orthogonally polarized beams leave symmetrically.

Exercise 8.1For a Wollaston prism of wedge angle \(\theta\) and small birefringence \(\Delta n=|n_e-n_o|\), show that the angular separation of the emerging beams is approximately \(2\Delta n\tan\theta\). Evaluate for calcite (\(\Delta n=0.172\)) and \(\theta=15^\circ\).

Show solution
At the interface one beam goes from index \(n_o\) to \(n_e\), the other from \(n_e\) to \(n_o\). For a nearly normal ray the interface tilt is \(\theta\), and a small index step \(\pm\Delta n\) deviates each beam by about \(\pm\Delta n\tan\theta\) (from Snell’s law linearized about \(\theta\)). Refraction at the exit face scales these slightly but leaves the total near \(2\Delta n\tan\theta\). Calcite: \(2\times0.172\times0.268=0.092\) rad \(\approx5.3^\circ\).

Exercise 8.2Rotate the camera lucida prism by \(5^\circ\) in the plane of the diagram. By how much does the outgoing ray turn? What would happen with a single mirror?

Show solution
Both mirror lines turn by \(5^\circ\), so their difference is unchanged, and by the theorem the outgoing ray is still turned through exactly \(90^\circ\) from the incoming one. Its direction does not change at all; it is only shifted sideways. (Refraction at the entry and exit faces adds a small correction, which nearly cancels because those faces are perpendicular.) A single mirror turned by \(5^\circ\) would turn the reflected ray by \(10^\circ\). The two-reflection design makes the instrument tolerant of small misalignment, the same principle as the pentaprism and the constant-deviation prism.
Lesson 09

Crystals, the goniometer and atoms

For the general reader. Crystals of the same mineral have the same angles between their faces, but to use this for identification the angles must be measured accurately, often on tiny crystals. Wollaston’s reflecting goniometer of 1809 did this by watching reflections rather than touching the faces. He also suggested that crystal shapes arise from the packing of spherical atoms, and he argued from the edge of the Earth’s atmosphere that atoms really exist.

Goals
  • Explain how the reflecting goniometer measures an interfacial angle.
  • Relate crystal forms to sphere packings.
  • Follow Wollaston’s argument for a finite atmosphere.

The reflecting goniometer (1809)

The crystal is fixed on a horizontal axis with the edge between two faces parallel to the axis. The observer sees in the first face the reflection of a distant horizontal line, such as a window bar, and brings it into coincidence with a second line seen directly. The crystal is then turned until the second face gives the same reflection in the same place.

Goniometer relation

The angle \(\rho\) through which the crystal is rotated equals the angle between the normals of the two faces. The interfacial angle, measured inside the crystal, is \(180^\circ-\rho\).

A reflection depends only on the direction of the face normal, so bringing the second face’s normal to the first face’s former position needs a rotation by the angle between normals. The faces can be millimetre-sized and need only reflect light. Contact goniometers, which pressed two arms against the faces, were accurate to about half a degree; Wollaston’s instrument reached a few minutes of arc. With it he measured the cleavage angle of calcite as \(105^\circ\,5'\), essentially the modern value, and the instrument became standard in mineralogy.

Crystals from spheres (1812)

In his Bakerian Lecture, read on 26 November 1812, Wollaston proposed that the octahedra and tetrahedra of crystallography arise naturally if the ultimate particles are spheres in close packing, and that rhombohedral forms arise from slightly flattened spheroids. The idea anticipated the sphere-packing models used in crystallography after X-ray diffraction.

The finite atmosphere (1822)

If matter were infinitely divisible, Wollaston argued, the atmosphere would thin out without limit and extend through space, and the Sun would gather a dense atmosphere around itself by gravity. Atoms of finite weight would instead let the atmosphere end where the gravitational pull on a particle balances the elastic force of the gas. He looked for refraction of the light of Venus as the planet passed close to the Sun in May 1821, and found none. He concluded that the atmosphere is finite and matter atomic. The argument is now seen as flawed: an atmosphere in a gravitational field thins exponentially whatever the nature of matter, and the solar atmosphere’s extent depends on its temperature.

Exercise 9.1Between reflections from two cleavage faces of a calcite rhomb, the goniometer turns through \(74^\circ\,55'\). What is the interfacial angle? What angle does the obtuse edge make?

Show solution
Interfacial angle \(180^\circ-74^\circ55'=105^\circ5'\). This is the obtuse angle between cleavage faces; the acute one is \(74^\circ55'\).

Exercise 9.2Show that in a face-centred cubic packing of equal spheres the packing fraction is \(\pi/(3\sqrt2)\approx0.740\), and identify the octahedral face in this packing.

Show solution
The cubic cell of side \(a\) contains 4 spheres, which touch along the face diagonal: \(4r=a\sqrt2\). Fraction \(=4\cdot\frac43\pi r^3/a^3=\frac{16\pi}{3}\big(\frac{\sqrt2}{4}\big)^3=\frac{\pi\sqrt2}{6}=\frac{\pi}{3\sqrt2}\approx0.740\). The \((111)\) planes are hexagonal close-packed layers, and the eight \(\{111\}\) planes bound an octahedron, the form Wollaston built from stacked spheres.

Exercise 9.3In an isothermal atmosphere the pressure falls as \(p=p_0e^{-z/H}\) with scale height \(H=k_BT/(mg)\). Compute \(H\) for air (\(m=29\) u) at 250 K. How does this undercut Wollaston’s argument?

Show solution
\(H=\frac{1.381\times10^{-23}\times250}{29\times1.661\times10^{-27}\times9.81}=7.33\) km. The density falls by \(e\) every 7 km but never reaches zero at any height. A continuous fluid in a gravitational field gives the same exponential profile, so the rapid thinning of the atmosphere does not distinguish atoms from a continuum. Whether the Sun captures an atmosphere depends on temperature and on escape, not on atomicity.
Lesson 10

Electricity, force and vision

For the general reader. Wollaston touched many other questions briefly but well. In 1801 he showed that electricity from a friction machine and from a voltaic battery are the same thing in different quantities. In 1805 he argued that the true measure of a moving body’s “force” is its mass times the square of its speed, close to the modern idea of kinetic energy. In 1821 he tried to make a wire carrying current spin, and in 1824 he explained, from his own attacks of half-blindness, how the nerves from the two eyes cross.

Goals
  • Compare the charge delivered by a friction machine and a voltaic pile.
  • Distinguish momentum and vis viva in collisions.
  • Explain semi-decussation and predict visual-field defects.

One electricity (1801)

A voltaic pile decomposes water copiously, but sparks from a friction machine seemed to do little. Wollaston sealed a very fine gold wire in glass so that only its tip was exposed, and passed the discharge of an electrical machine through water between two such points. He obtained streams of gas bubbles, as from a battery. He concluded that the two kinds of electricity differ only in quantity and intensity, not in nature. Michael Faraday made the quantitative comparison in 1833.

The force of percussion (1805)

In his Bakerian Lecture of 1805 Wollaston took the side of Gottfried Wilhelm Leibniz in the old dispute over the measure of force. He argued that the mechanical effect of a moving body, such as the depth it penetrates soft material or the work it can do against a constant resistance, is proportional to \(mv^2\), the vis viva, rather than to the momentum \(mv\).

Work–energy theorem

A body of mass \(m\) brought to rest from speed \(v\) by a constant resisting force \(F\) travels a distance \(d=\dfrac{mv^2}{2F}\). It is brought to rest in a time \(t=\dfrac{mv}{F}\). So penetration depth measures \(\tfrac12mv^2\), while stopping time measures \(mv\).

Electromagnetic rotation (1821)

After Hans Christian Ørsted’s discovery of 1820, Wollaston suggested that a current-carrying wire near a magnet should rotate about its own axis. An attempt at the Royal Institution, with Davy present, failed. On 3 and 4 September 1821 Faraday found a different effect: a wire free to move circles continuously around a magnetic pole. Rumours spread that Faraday had used Wollaston’s idea without credit. Faraday went to Wollaston, who said he did not feel wronged. In March 1823 Davy nonetheless told the Royal Society that Wollaston had first suggested the rotation.

Semi-decussation (1824)

In a paper read on 19 February 1824 Wollaston described two attacks in which he lost half of his visual field in both eyes for a quarter of an hour or so: once the left half, once the right. He concluded that each optic nerve carries fibres from both sides of the brain. Fibres from the outer (temporal) half of each retina stay on the same side, and fibres from the inner (nasal) half cross at the optic chiasm. Each side of the brain thus receives the opposite half of the visual field from both eyes.

Exercise 10.1Two lead balls, A of 1 kg at 4 m/s and B of 4 kg at 1 m/s, strike the same block of clay. They have equal momentum. Which penetrates deeper, and by what factor, if the clay exerts a constant resistance?

Show solution
Kinetic energies are \(\tfrac12(1)(16)=8\) J and \(\tfrac12(4)(1)=2\) J. Depth is proportional to kinetic energy, so A goes 4 times deeper, although both are stopped in the same time. This is the kind of example Wollaston used for vis viva.

Exercise 10.2A friction machine produces sparks totalling about \(5\ \mu\mathrm C\) each, at 10 sparks per second. A small voltaic pile drives 50 mA through acidified water. Compare the hydrogen produced per second.

Show solution
Machine: \(50\ \mu\mathrm C/\mathrm s=5\times10^{-5}\) A. Pile: \(5\times10^{-2}\) A, 1000 times more. Hydrogen: \(I/(2F)\) mol/s, so \(2.6\times10^{-10}\) versus \(2.6\times10^{-7}\) mol/s. The machine’s electricity has enormous tension but tiny quantity, which is why Wollaston needed fine points to see any decomposition.

Exercise 10.3Using semi-decussation, predict the visual-field loss from (a) a lesion of the left optic tract, behind the chiasm, and (b) a lesion at the centre of the chiasm.

Show solution
(a) The left tract carries the temporal fibres of the left eye and the nasal fibres of the right eye, which serve the right half of the visual field of each eye: right homonymous hemianopia, the kind Wollaston experienced. (b) The crossing fibres come from the nasal retinas, which see the temporal fields: loss of both outer halves, bitemporal hemianopia, typical of a pituitary tumour pressing on the chiasm.
Part III · Life and legacy
Lesson 11

The Royal Society years, 1804–1827

Wollaston received the Copley Medal of the Royal Society in 1802 and was its Secretary from 1804 to 1816. On the death of Sir Joseph Banks in June 1820 he served as interim President until the election of Davy in November, and he was Vice-President thereafter. He served on the Board of Longitude from 1818, and on royal commissions on weights and measures: in 1814 he recommended the imperial gallon, adopted in 1824, and in 1819 he opposed adopting the metric system. He was elected a foreign member of the Royal Swedish Academy of Sciences in 1813 and a foreign associate of the Académie des Sciences in 1823.

He lived alone in London, kept a private laboratory to which visitors were seldom admitted, and was known for working with minute quantities: a few grains of a mineral, a drop of a solution, tested on a glass slide. Jöns Jacob Berzelius met him in London in 1812, and Fraunhofer, Faraday and Dalton all knew his work. He was reserved and exact in speech and print. His papers are short, and he published only what he was sure of.

He was also a scientific ally of geology. A member of the Geological Society from 1812, he supported its work with instruments and analyses, and his goniometer became a tool of mineral identification.

DiscussionWollaston kept his platinum method secret for over twenty years and announced palladium anonymously. Davy and Faraday, by contrast, lectured publicly and published quickly. How did secrecy shape his finances, his reputation and the progress of the science he worked on?

Lesson 12

Last year, death and legacy, 1828

In 1828 Wollaston fell ill with a brain tumour, confirmed after his death. He knew the illness was fatal and spent his last months putting his work in order. He dictated descriptions of his unpublished inventions, among them his doublet microscope lens, and his paper on making platinum malleable, which Henry Warburton read as the Bakerian Lecture on 20 November 1828. The Royal Society awarded him a Royal Medal that year. He gave £2,000 to the Society to found a Donation Fund for experimental research and £1,000 to the Geological Society, whose income funds the Wollaston Medal, its highest award, first given to the geologist William Smith.

He died in London on 22 December 1828, aged 62, and was buried at Chislehurst in Kent. Some sources give 28 December.

Legacy

  • Chemistry: palladium and rhodium; strong early evidence for Dalton’s atomic theory; equivalents and the slide rule of combining weights; cystine.
  • Metallurgy: the first practical powder-metallurgy process, and malleable platinum for laboratories and industry; Wollaston wire.
  • Optics: the critical-angle refractometer, the first sighting of the dark solar lines, the camera lucida, the meniscus lens, the Wollaston prism.
  • Crystallography and physiology: the reflecting goniometer, sphere-packing models of crystals, and semi-decussation of the optic nerves.
  • Names: the mineral wollastonite, the lunar crater Wollaston, Wollaston Lake in Canada, and the Wollaston Medal.

Final projectChoose one of Wollaston’s instruments or methods: the platinum process, the critical-angle refractometer, the camera lucida, the goniometer or the synoptic scale. Explain its principle in two pages, work one realistic example with numbers, and describe the modern instrument or technique that descends from it.

Reference

Connections

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

Influenced by

Influenced

Colleagues and collaborators

Rivals

  • Richard Chenevix 1803-1805

Friends

Family

  • Francis John Hyde Wollaston
  • Francis Wollaston
  • William Heberden

Also mentioned in this life

Fields

On CoursesHub

Reference

Sources and further reading

Biography

  1. William Hyde Wollaston, Wikipedia; German Wikipedia.
  2. D. C. Goodman and M. C. Usselman, Wollaston, William Hyde, Dictionary of Scientific Biography and supplement, via Encyclopedia.com.
  3. M. C. Usselman, Pure Intelligence: The Life of William Hyde Wollaston, University of Chicago Press, 2015.
  4. William Hyde Wollaston, Encyclopaedia Britannica.
  5. F. A. J. L. James, Davy, Faraday and electro-magnetic rotations, Davy Notebooks Project.

Science

  1. W. H. Wollaston, A method of examining refractive and dispersive powers, by prismatic reflection, Phil. Trans. 92 (1802).
  2. W. H. Wollaston, On a new metal, found in crude platina, Phil. Trans. 94 (1804).
  3. W. H. Wollaston, On super-acid and sub-acid salts, Phil. Trans. 98 (1808).
  4. W. H. Wollaston, Description of a reflective goniometer, Phil. Trans. 99 (1809).
  5. W. H. Wollaston, The Bakerian Lecture: On the elementary particles of certain crystals, Phil. Trans. 103 (1813).
  6. W. H. Wollaston, A synoptic scale of chemical equivalents, Phil. Trans. 104 (1814).
  7. W. H. Wollaston, On semi-decussation of the optic nerves, Phil. Trans. 114 (1824).
  8. W. H. Wollaston, The Bakerian Lecture: On a method of rendering platina malleable, Phil. Trans. 119 (1829).
  9. Palladium, Rhodium, Camera lucida and Wollaston wire, Wikipedia.
  10. High Altitude Observatory, Solar physics historical timeline, 1800–1999.