''Elements of Dynamic'' is a book published by

William Kingdon Clifford William Kingdon Clifford (4 May 18453 March 1879) was an English mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in hi ...

in 1878. In 1887 it was supplemented by a fourth part and an appendix. The subtitle is "An introduction to motion and rest in solid and fluid bodies". It was reviewed positively, has remained a standard reference since its appearance, and is now available online as a ''Historical Math Monograph'' from

Cornell University Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to tea ...

. On page 95 Clifford deconstructed the

quaternion In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. Hamilton defined a quater ...

product of

William Rowan Hamilton Sir William Rowan Hamilton Doctor of Law, LL.D, Doctor of Civil Law, DCL, Royal Irish Academy, MRIA, Royal Astronomical Society#Fellow, FRAS (3/4 August 1805 – 2 September 1865) was an Irish mathematician, astronomer, and physicist. He was the ...

into two separate "products" of two vectors:

vector product In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and is d ...

and

scalar product In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an alge ...

, anticipating the complete severance seen in ''

Vector Analysis Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3. The term "vector calculus" is sometimes used as a synonym for the broader subjec ...

'' (1901). ''Elements of Dynamic'' was the debut of the term

cross-ratio In geometry, the cross-ratio, also called the double ratio and anharmonic ratio, is a number associated with a list of four collinear points, particularly points on a projective line. Given four points ''A'', ''B'', ''C'' and ''D'' on a line, t ...

for a four-

argument An argument is a statement or group of statements called premises intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three main perspectives: the logical, the dialecti ...

function frequently used in geometry. Clifford uses the term ''twist'' to discuss (pages 126 to 131) the

screw theory Screw theory is the algebraic calculation of pairs of vectors, such as forces and moments or angular and linear velocity, that arise in the kinematics and dynamics of rigid bodies. The mathematical framework was developed by Sir Robert Stawe ...

that had recently been introduced by

Robert Stawell Ball Sir Robert Stawell Ball (1 July 1840 – 25 November 1913) was an Irish astronomer who founded the screw theory. He was Royal Astronomer of Ireland at Dunsink Observatory. Life He was the son of naturalist Robert Ball, and Amelia Gresley He ...

Reviews

A review in the ''

Philosophical Magazine The ''Philosophical Magazine'' is one of the oldest scientific journals published in English. It was established by Alexander Tilloch in 1798;John Burnett"Tilloch, Alexander (1759–1825)" Oxford Dictionary of National Biography, Oxford Univer ...

'' explained for prospective readers that

kinematics Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a fiel ...

is the "study of the theory of pure motion". Noting the nature of "progressive training" required for mathematics, the reviewer wondered "For what class of readers is the book designed?"

Richard A. Proctor Richard Anthony Proctor (23 March 1837 – 12 September 1888) was an English astronomer. He is best remembered for having produced one of the earliest maps of Mars in 1867 from 27 drawings by the English observer William Rutter Dawes. His map w ...

noted in ''

The Contemporary Review ''The Contemporary Review'' is a British biannual, formerly quarterly, magazine. It has an uncertain future as of 2013. History The magazine was established in 1866 by Alexander Strahan and a group of intellectuals anxious to promote intellig ...

'' (33:65) that there are "few errors in the work, and even misprints are few and far between for a treatise of this kind." He did not approve of Clifford's coining of "odd new words as squirts, sinks, twists, and whirls." Proctor quoted the last sentence of the book: "Every continuous motion of an infinite body may be built up of squirts and vortices." In a "Sketch of Professor Clifford" in June 1879 the journal ''

Popular Science ''Popular Science'' (also known as ''PopSci'') is an American digital magazine carrying popular science content, which refers to articles for the general reader on science and technology subjects. ''Popular Science'' has won over 58 awards, incl ...

'' said "It will probably not take high rank as a university text-book, for which it was intended, but is much admired by mathematicians for the elegance, freshness, and originality displayed in the treatment of mathematical problems." After Clifford had died, and ''Book IV and Appendix'' were published in 1887, the literary magazine '' Athenaeum'' said "we have here Clifford pure and simple." It explained that he "had entirely shaken off the concept of force as an explanatory cause." It also expressed "the oft-told regret that Clifford did not live to reshape the teaching of elementary dynamics in this country, and we wait somewhat impatiently for his successor in this labour, who seems long in appearing." In 1901

Alexander Macfarlane Alexander Macfarlane FRSE LLD (21 April 1851 – 28 August 1913) was a Scottish logician, physicist, and mathematician. Life Macfarlane was born in Blairgowrie, Scotland, to Daniel MacFarlane (Shoemaker, Blairgowire) and Ann Small. He s ...

spoke at

Lehigh University Lehigh University (LU) is a private research university in Bethlehem, Pennsylvania in the Lehigh Valley region of eastern Pennsylvania. The university was established in 1865 by businessman Asa Packer and was originally affiliated with the Epi ...

on Clifford. Reviewing ''Elements of Dynamic'' he said :The work is unique for the clear ideas given of the science; ideas and principles are more prominent than symbols and formulae. He takes such familiar words as ''spin, twist, squirt, whirl'', and gives them exact meaning. The book is an example of what he meant by scientific insight,... In 2004 Gowan Dawson reviewed the situation of the book's publication. On the basis of a letter from

Lucy Clifford Lucy Clifford (2 August 1846 – 21 April 1929), better known as Mrs. W. K. Clifford, was an English novelist, playwright and journalist. Biography Lucy Clifford was born Lucy Lane in London, the daughter of John Lane of Barbados. She married ...

to Alexander MacMillan, the publisher, Dawson wroteGowan Dawson (2004) "Victorian periodicals and the making of William Kingdon Clifford's posthumous reputation", pages 259 to 284 in ''Science Serialized'', Geoffrey Candor & Sally Shuttleworth editors,

MIT Press The MIT Press is a university press affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts (United States). It was established in 1962. History The MIT Press traces its origins back to 1926 when MIT publ ...

:Clifford, by the time of his death, had published just a single monograph, ''The Elements of Dynamic'', and that had been rushed through the presses in an incomplete form only during the last months of his life. Clifford's standing as both a leading mathematical specialist and an iconoclastic scientific publicist had instead been forged largely in the pages of the Victorian periodical press... File:Clifford-2.jpg, Volume 1 (1878) containing books I-III and Volume 2 containing book IV (1887) of Clifford's "''Elements of Dynamic''" File:Clifford-2-4-vol 1-3.jpg, Table of contents page of Volume 1 (1878) containing books I-III of Clifford's ''"Elements of Dynamic"'' File:Clifford-2-3-vol 1-3.jpg, First page of Volume 1 (1878) containing books I-III of Clifford's "''Elements of Dynamic''"

References

Elements of Dynamic, books I,II,III
(1878) London: MacMillan & Co; on-line presentation by

''Historical Mathematical Monographs''. * *{{Internet Archive, elementsofdynami02clifiala, Book IV (1887) 1887 non-fiction books Mathematics books Physics books