''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 his ...

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 teach an ...

. 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 quatern ...

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, anticipating the complete severance seen in ''

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

'' (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, the ...

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 dialectic ...

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

Reviews

A review in the '' Philosophical Magazine'' explained for prospective readers that

kinematics Kinematics is a subfield of physics, developed in classical mechanics, that describes the Motion (physics), motion of points, Physical object, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause ...

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'' (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 Athenaeum may refer to: Books and periodicals * ''Athenaeum'' (German magazine), a journal of German Romanticism, established 1798 * ''Athenaeum'' (British magazine), a weekly London literary magazine 1828–1921 * ''The Athenaeum'' (Acadia U ...

'' 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 spoke at Lehigh University 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 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 publish ...

: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