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

William Kingdon Clifford William Kingdon Clifford (4 May 18453 March 1879) was a British 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 university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...

. 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. The algebra of quater ...

product of

William Rowan Hamilton Sir William Rowan Hamilton (4 August 1805 – 2 September 1865) was an Irish astronomer, mathematician, and physicist who made numerous major contributions to abstract algebra, classical mechanics, and optics. His theoretical works and mathema ...

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 ...

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 for other symmetric bilinear forms, for example in a pseudo-Euclidean space. Not to be confused wit ...

. This separation of the quaternion product into two was followed by J. W. Gibbs in his development of vector analysis, first in a pamphlet acknowledging Clifford's ''Kinematic'', and later in a textbook published by

Yale University Yale University is a Private university, private Ivy League research university in New Haven, Connecticut, United States. Founded in 1701, Yale is the List of Colonial Colleges, third-oldest institution of higher education in the United Stat ...

, called ''

Vector Analysis Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, \mathbb^3. The term ''vector calculus'' is sometimes used as a ...

''. He apparently remained unaware of Clifford's seminal paper on the unification of these two products into what he termed a

geometric algebra In mathematics, a geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is built out of two fundamental operations, addition and the geometric pr ...

. ''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 , , , on a line, their cross ratio is defin ...

for a four-

argument An argument is a series of sentences, statements, or propositions some of which are called premises and one is the conclusion. The purpose of an argument is to give reasons for one's conclusion via justification, explanation, and/or persu ...

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 Vector (mathematics and physics), vectors, also known as ''dual vectors'' – such as Angular velocity, angular and linear velocity, or forces and Moment (physics), moments – that arise in th ...

that had recently been introduced by Robert Stawell Ball.

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)" Dictionary of National Biography#Oxford Dictionary of ...

'' explained for prospective readers that

kinematics In physics, kinematics studies the geometrical aspects of motion of physical objects independent of forces that set them in motion. Constrained motion such as linked machine parts are also described as kinematics. Kinematics is concerned with s ...

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 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 intent on promoting their v ...

'' (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 called pop-science or popsci) is an interpretation of science intended for a general audience. While science journalism focuses on recent scientific developments, popular science is more broad ranging. It may be written ...

'' 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, Blairgowrie) and Ann Small. He s ...

spoke at

Lehigh University Lehigh University (LU), in Bethlehem, Pennsylvania, United States, is a private university, private research university. The university was established in 1865 by businessman Asa Packer. Lehigh University's undergraduate programs have been mixed ...

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 the university press of the Massachusetts Institute of Technology (MIT), a private research university in Cambridge, Massachusetts. The MIT Press publishes a number of academic journals and has been a pioneer in the Open Ac ...

: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