CHAP. L, 2.] 



MATHEMATICS PHYSICS MECHANICAL AETS. 



i) 



'30.) The commencement of a better era originated, early 



in the present century, with Woodhouse at Cambridge, 

 Edinburgh, and Playfair in Edinburgh, by both of whom the con- 

 and Dublin, tinental methods were introduced into the studies of 

 their respective universities ; whilst Ivory, a native of 

 Scotland, was the first to challenge, by his writings, a 

 place in the list of great living mathematicians. The 

 systematic form of the Me"canique Celeste rendered the 

 subject more accessible than were the countless me- 

 moirs by men of the highest name, which then filled 

 the Transactions of Paris, Turin, Berlin, and StPeters- 

 burg. But the notation of differentials, which could 

 alone break down the barrier between the British and 

 foreign mathematicians, was first introduced at Cam- 

 bridge by the efforts of Sir John Herschel and Dean 

 Peacock about 1816, soon after which the transla- 

 tion of Lacroix's Differential Calculus, which they 

 superintended, came into use as an university text- 

 book. From this time the works of foreign mathe- 

 maticians began to be more generally read, particu- 

 larly the writings of Laplace and Poisson ; and 

 within ten or a dozen years subsequently, a few 

 active and undaunted men, chiefly of the Cambridge 

 school, such as Mr Airy and Sir John Lubbock, 

 grappled with the outstanding difficulties of physical 

 astronomy, whilst a larger number applied them- 

 selves to the most difficult parts of pure analysis, 

 and acquired great dexterity in its use in the solu- 

 tion of geometrical and mechanical problems. Such, 

 for example, were Mr Babbage, Mr De Morgan, Mr 

 Murphy, and Mr Green ; and at Dublin Sir William 

 R. Hamilton and Mr MacCullagh, whose names will 

 occur in other parts of this Dissertation. 



No new calculus or great general method in ana- 

 teln" lysis has resulted from these persevering labours, 

 ntegra- whether of British or foreign mathematicians, but 

 ion. an increased facility and power in applying the ex- 



isting resources of mathematics to the solution of 

 large classes of problems previously intractable, or 

 resolved only indirectly or by approximation. The 

 Integral Calculus, in particular, affords an almost 

 boundless field for research, and each branch of 

 science in succession not only Physical Astronomy, 

 but Optics, Heat. Electricity, and Civil Engineering 

 has offered problems of great importance, which 

 awaited only the skill of the pure mathematician to re- 

 Solve in a practical and finite form. 1 Every year, and 

 every civilized community, contribute to these real 

 i m P rovemen * s ' The principle of discontinuity, con- 



spicuously introduced into the doctrine of the con- 

 duction of Heat in consequence of the abrupt varia- 

 tion of physical circumstances at the boundary of 

 the conducting body, enters largely into the specula- 

 tions of mathematicians of the present century ; and 

 the doctrine of definite integrals so intimately con- 

 nected with it has received a proportional extension. 

 Next, analytical geometry has acquired a very great Analytical 

 enlargement and by attention principally to symmetry g eometI 7- 

 in the arrangement of the results, solutions other- 

 wise the most intricate are obtained with facility and 

 directness. Of this we shall find examples in our 

 history of the Undulatory Theory of Light. Lastly, The Calcu- 

 notwithstanding the pre-eminently practical charac- lus . of P e - 

 ter of the mathematics of the last age, speculative ra 

 geometers and analysts have found time to discuss 

 the metaphysics of their respective sciences, both as 

 regards the foundations of the Differential Calculus 

 and as to the use of imaginary and other symbols in 

 Algebra. An almost new branch of abstract science 

 (though faintly foreshadowed by Leibnitz) has come 

 into existence the separation of symbols of opera- 

 tion from symbols of quantity, and the treatment of the 

 former like ordinary algebraic magnitudes. In some 

 cases remarkable simplicity is thus introduced into 

 the solution of problems, although perhaps few ma- 

 thematicians would choose to depend implicitly upon 

 the method in untried cases. Sir John Herschel and 

 the late Mr Gregory 2 were amongst the most active in- 

 troducers of this new algebra, but few of the more 

 eminent living British or foreign mathematicians 

 have failed to contribute their share to this more 

 metaphysical department of analysis. 



I shall now attempt to consider more particu- (32.) 

 larly the reciprocal relations of pure physical science Conne ction 

 and the mechanical arts. $* 



This is evidently a very intimate one. The dis- the arts, 

 coveries of pure physics (such as Astronomy, Acous- ( 33> ) 

 tics, Magnetism), are the results of either observation 

 or experiment, and they consist in generalizations, 

 by means of which a multitude of facts are reduced 

 under one simple expression of a more general fact 

 or principle. But instruments often very compli- 

 cated are necessary for observation and for experi- 

 ment ; as telescopes in astronomy, organs in acoustics, 

 properly magnetized and suspended steel bars in 

 magnetism. Art is required to construct these. The 

 highest possible degree of science, and the utmost 



1 For example the Lucasian Professor at Cambridge, Mr Stokes, has effected two previously impracticable integrations, one 

 occurring in the theory of the rainbow, the other in that of railway girder bridges. 



3 Mr Duncan Gregory, a promising mathematician who died 23d February 1844, at the early age of 30, was the youngest Mr Duncan 

 son of Dr James Gregory, the late distinguished Professor of Medicine at Edinburgh. His name deserves a passing record, not only Gregory, 

 from the influence he exercised on the progress of the English mathematics of his time, but as having revived the dormant charac- 

 ter for this peculiar kind of talent, so long connected with the family of Gregory. He was, in fact, the lineal descendant of the 

 inventor of the reflecting telescope. Mr Gregory was the first editor of the Cambridge Mathematical Journal, and author of an 

 excellent book of Examples in the Differential and Integral Calculus, both of which have exercised a beneficial influence on the 

 progress of science in England. He also wrote several original memoirs on the subjects referred to in the text. Mr Leslie Ellis, 

 a man of congenial ability, has written a short but pleasing biography of his friend. 



