Robert Smith published 'A Compleat System of Opticks' in 1738. The
sections on telescope design and fabrication were the most important English
language manual for 18th century telescope makers; and the book remains the
best document of its era for use by current historians. As a preliminary
effort towards redressing contemporary neglect of this interesting person, 3
texts on Smith are posted here:
Barrow-Green, June. 'A Corrective to the Spirit of too Exclusively Pure
Mathematics': Robert Smith (1689-1768) and his Prizes at Cambridge
University. Annals of Science 56 (1999), 271-316.
Courtney, W.P. Robert Smith. Volume 18, pp517-519. Sidney Lee, ed.
Dictionary of National Biography. N.Y.: Macmillan, 1909.
Morse, Edgar W. Robert Smith. Dictionary of Scientific Biography. Charles
Gillispie, ed. New York: Scribner, 1970--.
Smith, Robert. A Compleat System of Opticks in Four Books, viz. A popular, a
mathematical, a mechanical, and a philosophical treatise. To which are added
remarks upon the whole. Cambridge, 1738. Vol.1, 280pp; Vol.2, pp281-455. 83
Steffens, Henry. The Development of Newtonian Optics in England. N.Y.:
Science History, 1977.
Barrow-Green, June (Faculty of Mathematics and Computing, The Open
University, Milton Keynes).
'A Corrective to the Spirit of too Exclusively Pure Mathematics': Robert
Smith (1689-1768) and his Prizes at Cambridge University. Annals of Science
56 (1999), 271-316.
The Smith's Prize competition was established in Cambridge in 1768 by the
will of Robert Smith (1689-1768). By fostering an interest in the study of
applied mathematics, the competition contributed towards the success in
mathematical physics that was to become the hallmark of Cambridge mathematics
during the second half of the nineteenth century. Perceptions of Smith's
intentions were to play a part in discussions about the content and balance
of the mathematics curriculum, as may be seen in the Airy quotation in the
title. In the twentieth century the competition acted to stimulate the
formalization of Cambridge postgraduate research in mathematics. Throughout
its existence the competition has played a significant role by providing a
springboard for graduates considering an academic career and the majority of
prize-winners have gone on to become professional mathematicians or
physicists. In seeking the reasons behind the competition's success,
attention has been paid to the life and work of Robert Smith, the intention
behind his bequest, and the history of the competition from its origins until
2. Robert Smith
Robert Smith was christened on 16 October 1689 at Lea in Lincolnshire, and
was the son of John Smith (d.1710), rector of Gate Burton, Lincolnshire. His
mother, Hannah Smith (d.1719), was the aunt of Roger Cotes (1682-1716). John
Smith, who had been educated at Trinity College, Cambridge, was well versed
mathematically and in the mid-1790s Cotes was sent to stay with him for
mathematical coaching prior to going to St Paul's School. John Smith was a
skilful tutor and when Cotes went up to Cambridge in 1699 his mathematical
preparation was well beyond what might have been expected.
Robert Smith entered Trinity College as a pensioner in 1708. He was
awarded a scholarship the following year and while an undergraduate he lodged
with Cotes. In 1707 Cotes had been elected the first Plumian Professor of
Astronomy and Experimental Philosophy, and when Smith arrived in Cambridge
Cotes provided work for him as his assistant. In 1711 Smith took his BA and
two years later was elected to a fellowship of the College. He held a variety
of college posts, and in 1716, on the death of Cotes, was elected to succeed
him as Plumian Professor, a position he retained until 1760. In 1742 he was
appointed Master of Trinity, and from then on resided in the College lodge
until his death in 1768. In 1742-3 he acted as Vice-Chancellor of the
During his tenure at Trinity Smith maintained a keen interest in college
affairs as well as in the university in general. (9) On the academic side,
he lectured on optics and hydrostatics, and, like his cousin, was one of the
early supporters of Newtonian philosophy. He edited his cousin's works (10)
and wrote two books of his own, one on optics and one on harmonics, both of
which enjoyed a high reputation for many years after his death.
Smith's 'Optics', (11) published in 1738 (with an abridged version in
1778) and translated into Dutch, French and German, was essentially the first
textbook on the subject and widely read. Voltaire, for example, congratulated
Smith upon it, while Desaguliers omitted optics altogether from his own
Course of Experimental Philosophy in favour of Smith's work. In the
nineteenth century, it found favour with both Lord Rayleigh and Hermann von
Helmholtz. And Rouse Ball, writing more than 150 years after the book's first
publication, considered it to be one of the best textbooks on the subject
available. It was especially renowned for promoting the particulate theory
of light, as well as other ideas from Newton's Optics. In one significant
result Smith shows that a certain relationship between the magnification and
location of object and image for one lens remains invariant for a system of
lenses. This result, later discovered independently by both Lagrange and
Helmholtz, is now sometimes referred to as the Smith-Helmholtz formula. (15)
The Optics also contains detailed descriptions of methods for making optical
instruments that were found to be extremely useful and led to increased
activity in the manufacture of such instruments. (16) The work concludes
with a history of telescopical discoveries. Taken as a whole, the Optics
shows that Smith had a deep understanding of the theory of the subject, and
an extensive knowledge of its history, as well as considerable didactic
Smith's Harmonics, which was published in 1749 with a second edition in
1759 and a postscript in 1762, also excited praise. In 1859 T. H. Safford
thought it 'an indispensable help in the study of a portion of our subject',
while in 1924 R. C. Archibald described it as 'the first English scientific
treatment of harmony, a work of high order' discussed in 'a manner attractive
even for a reader in the present day'. Smith's primary purpose in writing
the Harmonics was to provide a description of his 'Theory of Imperfect
Consonances'. This was a system for tempering a musical scale, or tuning a
keyboard instrument, by making all the consonances as equally harmonious as
possible. He constructed a mathematical theory to derive the equal harmonic
intervals and validated his results on an organ and a harpsichord. Despite
the book's academic success, the system never became popular in practice
owing to the difficulty and costs involved in constructing instruments
Smith's career was focused almost exclusively on Cambridge with few
exceptions. In 1718 he was elected a Fellow of the Royal Society but he
appears not to have played an active role in the Society, although he was a
signatory to the Society's certificate of approval given to John Harrison in
1737 in recognition of his work on the chronometer to solve the longitude
problem. Smith was also one of the eight commissioners of the Board of
Longitude which subsequently voted financial assistance to Harrison. (20) In
1728 Smith was appointed by warrant as Master of Mechanics to King George II,
the warrant being confirmed on the accession of King George III in 1760. (21)
In addition he was also appointed Professor of Astronomy to William, Duke of
Cumberland. (22) Both of these appointments involved work at the Kew House
Observatory although it is not clear what either entailed. (23)
Nevertheless, Smith and Cumberland certainly maintained communication with
one another. Smith dedicated both his edition of Cotes's lectures and his
Harmonics to Cumberland, while in 1740 Cumberland asked Smith to supply him
with a sea quadrant and a telescope. (24)
9. An account of some of Smith's forays into college and university politics
is contained in D. A. Winstanley, The University of Cambridge in the
Eighteenth Century (Cambridge, 1922).
10. On Cotes's death Smith collected most of Cotes's surviving papers. In
1722 he published Cotes's 'In Harmonia Mensurarum et alia opuscula
Mathematica' together with some of his own theorems, and in 1738 he
published, with notes, Cotes's 'Hydrostatical and Pneumatical Lectures'. A.
R. Hall and L. Tilling, The Correspondence of Isaac Newton, vol. 7
(Cambridge, 1977), 28-9, 98-9. N. Guicciardini, The Development of Newtonian
Calculus in Britain 1700- 1800 (Cambridge 1989), 30-1.
11. R. Smith, A Compleat System of Optics in Four Books, viz, A Popular, a
Mathematical, a Mechanical, and a Philosophical Treatise (Cambridge, 1738).
According to the Dictionary of National Biography (1968) this publication
earned Smith the nickname of Old Focus.
15. Smith (note 11), Book II, ch. 5. The Smith-Helmholtz formula is discussed
in detail in Lord Rayleigh, 'Notes Chiefly Historical, on Some Fundamental
Propositions in Optics', Philosophical Magazine, 21 (1886), 466-76.
16. R. T. Gunther, Early Science in Cambridge (Oxford, 1937), 104.
20. Edmund Halley, who was initially responsible for securing the Royal
Society's support for Harrison, was also one of the commissioners, and so too
was James Bradley, the Savilian Professor of Astronomy at Oxford. E. G. R.
Taylor, The Mathematical Practitioners of Hanoverian England 1714-1840
(Cambridge 1966), 20.
21. The Civil List of King George II for 1747 and 1748 records the payment
'To Rob Smith Master of Mechanics to Him on 150 p. ann 3 years to Midsm. 1747
450'. The Royal Archives, RA 53922A, 24. The Lord Chamberlain's records list
Smith as Professor of Astronomy to the King in 1736. The Royal Archives,
22. The Lord Chamberlain's records. The Royal Archives, LC.5.20 (265, 285),
LC.5.21 (13, 119, 369).
23. Taylor (note 20) 144.
24. Edleston, J., ed. Correspondence of Sir Isaac Newton and Professor Cotes.
(London 1850). 238-9.
Courtney, W.P. Robert Smith. Volume 18, pp517-519. Sidney Lee, ed.
Dictionary of National Biography. N.Y.: Macmillan, 1909.
SMITH, ROBERT (1689-1768), mathematician and founder of Smith's prizes at
Cambridge, was born in 1689, and probably at Lea, near Gainesborough, to
which living his father was instituted in October 1679. His father, John
Smith, had married Hannah (d.1719), the aunt of Roger Cotes [q. v.]; he
became rector of Gate Burton, Lincolnshire, and was buried at Lea on 28 Dec.
1710. Robert was educated at the Leicester grammar school and admitted
pensioner at Trinity College, Cambridge, on 28 May 1708, and scholar on 13
May 1709. At Trinity he was under the care of Cotes, his cousin, who was
then Plumian professor of astronomy, and lived with him as his assistant. He
graduated B.A. 1711, M.A. 1715, LL.D.1723, and D.D. per literas regias 1739.
He was elected minor fellow 1714, major fellow 1715, sublector quartus 1715,
lector linguae Latinae 1724, lector Iinguae Graecae 1725, lector primarius
1727, and senior fellow, 11 June 1739. He took pupils at Cambridge, was
master of mechanics to George II, and held the post of mathematical preceptor
to William, duke of Cumberland, from June 1739 to July 1740. Smith, like his
cousin Cotes, was throughout life the 'decided partizan' of Richard Bentley,
the master of Trinity, in his struggles with the fellows.
On 10 July 1716 Smith was elected to succeed Cotes as Plumian professor of
astronomy, and on 21 May 1718 he was admitted F.RS. Early in 1739 the
observatory over the great gate of Trinity College, for the use of the
professor, was completed under his direction (Bentley, Correspondence, ii.
448, 451, 786). The telescope in the library, which is described in Smith's
work on 'Opticks,' and is shown to strangers as Sir Isaac Newton's telescope,
was made for him. He retained the professorship until 1760.
Smith was literary executor to Cotes, and communicated notes for the
memoir of him in the 'General Biographical Dictionary'of Lockman and others
(1736, iv. 441-5). In 1722 he edited and augmented with some of his own
theorems Cotes's 'Harmonia Mensurarum et alia opuscula Mathematica,' and in
1738 he edited, with notes, his cousin's 'Hydrostatical and Pneumatical
Lectures' of Cotes. The first work was dedicated to Dr. Mead, the second
(which was republished in 1747 and 1776, and translated into French by
LeMonnier in 1720) to the Duke of Cumberland. He projected, but did not
proceed with, the publication of others of his cousin's works. The monument
to Cotes's memory, with the epitaph by Bentley, was erected at the cost of
Smith, and he presented to the library of the college in 1758 a marble bust
of his cousin by P. Scheemakers.
At Bentley's death Smith was appointed, on 20 July 1742, master of Trinity
College, and he also acted in 1742-3 as vice-chancellor of the university.
As master his 'equitable and judicious conduct healed all wounds and
conciliated all parties' (Monk, Life of Bentley, ii. 420). His acts of
kindness were numerous, and his influence in the university was considerable.
He recommended John Colson [q.v.] to come to Cambridge, and obtained for him
in 1739 the Lucasian chair. He advised Richard Cumberland to apply himself
to mathematics, and supported his claims to a fellowship. His encouragement
gave Bishop Watson, when an undergraduate 'a spur to his industry and wings
to his ambition,' for which the bishop always revered Smith's memory. Israel
Lyons, the younger, was aided by him in his studies, and in return dedicated
to Smith his 'Treatise of Fluxions', 1758. At the contest between Lords
Hardwicke and Sandwich for the post of high steward of the university of
Cambridge, he was a supporter of Sandwich. He was consequently introduced by
Churchill into the poem of the 'Candidate' (lines 615-620) as
'Black Smith of Trinity; on Christian ground
For faith in mysteries none more renowned.'
A recluse and a student, Smith, whose health was for many years
precarious, lived in the lodge with an unmarried sister, Elizmar (1683-1758),
who was buried in the ante-chapel at Trinity, and with a niece. He was fond
of music, and played the violon-cello. Smith died in the lodge on 2 Feb.
1768, and was buried on the south side of the communion table in the college
chapel, where he is commemorated by a Latin epitaph. A funeral oration in
Latin on his death was delivered by the Rev. Thomas Zouch in the chapel on 8
Feb. (Zouch, Works, 1820, i. 438-43).
Richard Cumberland records that he was thin in frame, with an aquiline
nose, a penetrating eye, and shrill nasal voice. A bust of Smith by P.
Scheemakers was placed in the library of the college in 1768, with the
inscription 'Praesenti tibi maturos largimur honores.' A portrait of him,
painted by Vanderbank in 1730, and given by Thomas Riddell, one of the
fellows, in 1827, hangs in the lodge; another, painted by J. Freeman in 1783,
and said to have been given by the Rev. Edward Howkins in 1779. is in the
hall. It was probably paid for by moneys bequeathed by Howkins for that
Smith's benefactions to the university and to Trinity College were
munificent. To the former he left by will the sum of 3,500 pounds. South
Sea stock, part of the interest to be applied in a dinner to the trustees,
and of the remainder, half to the Plumian professor, and half between two
junior B.A.s who have made the greatest progress in mathematics and natural
philosophy. The Smith's prizes, which now amount to about 23 pounds each,
'proved productive of the best results, and at a later time enabled the
university to encourage some of the higher branches of mathematics.' The
college, to which during his lifetime he had presented many pictures and
sculptures, obtained under the will the sum of 2,000 pounds of the same
stock, which was ordered to be sold on 15 Dec. 1770, and applied towards the
new combination-room in the great court, and the painted window, containing
nearly 140 square feet of glass, at the south end of the library. The
grotesque design (by Cipriani) for the window, which was completed by 1775,
represented George III under a canopy, giving a laurel chaplet to Sir Isaac
Newton, while Bacon is at the king's feet.
Smith published two works. The first was 'A compleat System of Opticks, in
four books,' 1738, 2 vols.; dedicated, with unusual warmth of expression, to
Right Hon., afterwards Sir Edward Walpole, a personal friend at Cambridge,
through whose aid the work was started and finished, and under Smith's will
and codicil Walpole received legacies of 2,000 pounds South Sea stock. The
'elementary parts' of these volumes, selected and arranged for the use of
students at the universities, were published separately at Cambridge in 1778.
They were translated, with additions, into German by Kaestner in 1755, and
into French, with additions, by Dural le Roy, at Brest in 1767, with a
supplement in 1783, and by L.P.P. [i.e. Ie Pere Pezenas] at Avignon in 1767.
Benjamin Robins [q.v.] published a criticism upon them in 1739. From this
treatise on optics, Smith went by the nickname of 'Old Focus.' Smith's
second volume was 'Harmonics, or the Philosophy of Musical Sounds,' 1749,
dedicated to the Duke of Cumberland; 2nd edit. 1759, and postscript, 1762.
The latter was inscribed to Sir Edward Walpole. Both works were of the
highest value. They were recommended to Gibbon by George Lewis Scott [q.v.],
with the words that the treatise on optics entered 'into too great details
for beginners,' and that the volume on harmonics 'is the principal book of
the kind' (Gibbon, Miscellaneous Work's 1837, pp. 232-3).
Smith left numerous papers on Cotes and Newton to the Rev. Edward Howkins,
who in 1779 bequeathed them to the college. From them was collected the
'Correspondence of Newton and Cotes,' edited by the Rev. J. Edleston in 1860,
and afterwards republished at Amsterdam. Twenty to thirty letters from
Newton to Cotes were borrowed from Smith by Conduitt for his projected life
of Newton, and never returned (Bentley, Correspondence, ii. 776-7). Letters
to Smith are printed in the 'Correspondence of Newton and Cotes' (pp. 231-9),
in Brewster's 'Memoirs of Newton' (2nd edit.), ii. 47-9, and in James
Bradley's 'Works and Correspondence' (1832), pp. 401-3. His name frequently
occurs in the diaries of John Byrom, with whom he was contemporary at
Cambridge, and Byrom's verses on John Gilbert Cooper's 'Epistles from
Aristippus in retirement' in a letter to Dr. S-, are supposed to be addressed
to Smith. When Zachary Grey [q.v.] published an 'Examination of the
Fourteenth Chapter of Newton's Observations on Daniel', Smith wrote 'Three
Observations' upon it which were not published.
[Gent. Mag. 1768, p. 94, Willis and Clark's Cambridge, ii. 500, 547-50,
583, 600, 606. Rouse Ball's Mathematics at Cambridge, 1889 pp. 91-101.
Wordsworth's Scholae Academicae pp. 67, 236. Corresp. of Newton and Cotes,
pp. xvi-xix, 199, 200, 227-9. Brewster's Memoirs of Newton, ii. 319-20.
Hartshorne's Cambr. Book Rarities, pp. 275, 481, 484-5. Byrom's Remains, i.
296, 623-34, ii. 34, 135, 206-7,833-841. Byrom's Poems, ed. Ward, vol. i.
pt. ii. p. 408. J. J. Smith's Cambr. Portfolio, p. 97. Monk's Bentley, i.
203, 401-2. Cumberland's Memoirs, 1806 edit. pp. 70, 107-9. Anecdotes of
Watson 1817, pp. 9, 21. Information from W. Aldis Wright, esq. of Trin.
(Smith, Robert.) Morse, Edgar W. (U.C. Davis, Cal State Sonoma). Dictionary
of Scientific Biography. Charles Gillispie, ed. New York: Scribner, 1970--.
Smith, Robert. (b. Lea, near Gainsborough, England, 1689; d. Cambridge,
England, 2 February 1768), physics.
Smith's father, John Smith, was rector of the parish of Lea; his mother,
Hannah Smith, was the aunt of Roger Cotes, Plumian professor of astronomy at
Cambridge. Smith was educated at the Leicester Grammar School and from 1708
at Trinity College, Cambridge, where he lived with and assisted his cousin
Cotes. Smith graduated B.A. in 1711 and M.A. in 1715. He was elected a fellow
of his college in 1714, Plumian professor in 1716, and fellow of the Royal
Society in 1718. He received the LL.D. in 1723 and the D.D. in 1739.
Appointed master of Trinity College in 1742, Smith was vice-chancellor of the
University in 1742- 1743, and he held the Plumian professorship until 1760.
Among his many bequests to the university and to his college, he founded the
two Smith's prizes for undergraduate attainment in mathematics and natural
Smith wrote on optics and harmonics. In 1738 he published 'A Compleat
System of Opticks in Four Books, viz. A Popular, a Mathematical, a
Mechanical, and a Philosophical Treatise'. Both comprehensive and reliable,
the work became probably the most influential optical textbook of the
eighteenth century. It was also published in Dutch in 1753, in German in
1755, and in two different French translations in 1767. In 1778 an abridged
version was published in English. In turn, its popularity helped to establish
the eighteenth century conviction that light is particulate.
Although Newton had expressed some uncertainty about the nature of light,
Smith asserted in the 'Popular Treatise' that there was no reason to doubt
that light consisted of material particles. He then gave a plausible
explanation of most known optical phenomena in terms of particles of light
that were acted upon by attractive and repulsive forces. In these
explanations Smith never even suggested that any vibrating medium might exist
to produce light or 'Newton's rings,' nor did he even mention Newton's theory
of 'fits.' Rather he repeated Newton's assertion that the rings were caused
by the disposition of varying thicknesses of air or films that reflect or
refract different colors of light.
In the 'Mathematical Treatise,' Smith developed a very comprehensive set
of geometric propositions for the computation of the focus, location,
magnification, brightness, and aberrations of systems of lenses and mirrors.
Apparently he was the first person to construct images by means of an
unrefracted central ray and a ray parallel to the axis that is refracted
through the focus. (1) He also derived a particular case of the relationship
now known as the Smith-Helmholtz formula or the theorem of Lagrange. Using a
relationship between the magnification and location of object and image for
one lens, Smith showed that the same relationship was invariant within a
system of any combination of lenses. (2)
In the 'Mechanical Treatise,' Smith gave methods for making optical
instruments, and in the 'Philosophical Treatise,' he gave an account of
In 1749 Smith published 'Harmonics or the Philosophy of Musical Sounds',
which had a second edition in 1759 and a postscript in 1762. Although it was
partly a textbook, Smith's principal objective was to describe his system of
tempering a musical scale by making 'all the consonances ... as equally
harmonious as possible....' (3) He derived the 'equally harmonic' intervals
by a mathematical theory and confirmed his results on an organ and a
harpsichord. Smith's temperament was an improvement on existing systems, but
its use required impractical mechanical changes in the instruments.
1. Ernst Mach. The Principles of Physical Optics (New York. 1953), 57.
2. Smith credits Roger Cotes with the discovery of the relationship for one
lens. See Smith, A Compleat System, bk. ll, ch. 5, esp. arts. 247-249, 261-
263. 267, 465-474. See also Lord Rayleigh, 'Notes, Chiefly Historical...,' in
Philosophical Magazine, 5th ser., 21 (1886). 466-469.
3. Smith, Harmonics (1749), p. vi
I. Original Works. Smith's works are:
'A Compleat System of Opticks in Four Books. viz. A Popular, a Mathematical,
a Mechanical, and a Philosophical Treatise (Cambridge. 1738). and
Harmonics, or the Philosophy of Musical Sounds (Cambridge, 1749; repr., New
II. Secondary Literature. There is no full biography of Smith. Biographical
information in this article is from the 'Dictionary of National Biography',
XVIII, 517- 519. Smith is mentioned in Ernst Mach, The Principles of
Physical Optics (New York, 1953), 57, 62. The most useful article on the
Smith-Helmholtz formula is Lord Rayleigh, 'Notes, Chiefly Historical, on Some
Fundamental Propositions in Optics,' in Philosophical Magazine, 5th ser., 21
(1886), 466-476. The best discussion of Smith's historical importance is in
a master's thesis by Henry John Steffens, 'The Development of Newtonian
Optics in England, 1738-1831' (Ithaca, New York: Cornell University, 1965).
On Smith's Harmonics, see Lloyd S. Lloyd, 'Robert Smith,' in Grove's
Dictionary of Music and Musicians, 5th ed., Vll (London. 1954), 857-858; and
'Temperaments,' ibid., VIII. 377.
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