TRANSACTIONS OF SECTION G. 783 



since its bounds are unlimited, and equally so must be the researclies of its prO' 

 feasors.' If the fall sig-nificaiice of these statements maj' be accepted as correct, 

 engineers mi<rht fairly claim to have a right to say, ' As engineers we are neces- 

 sarily men of science, and no branch of science is outside our province.' It might, 

 however, be said that no engineer, with his absorbing professional avocations, would 

 have the time to acquire even the rudiments of the principal branches of science 

 with their ever-increasing developments, to the study of each of which the life- 

 work of many earnest searchers into the secrets of nature is wholly devoted. 

 Nevertheless, a few branches of science, such as physiology, biology, aiid botany, 

 appear to be beyond the scope of practical engineering; whilst a moderate 

 acquaintance with some others might suffice for the needs of the engineer, except 

 in certain special branches, supplemented as it can readily be by the advice of a 

 specialist in complicated case.-'. 



Among the branches of science necessary for the engineer, two may be regarded 

 as of the highest importance, namely, mathematics and physics, upon which the 

 science of engineeriiio- mainly depends ; and without an adequate knowledo-e of 

 these no person should be able at the present day to enter the profession of a^civil 

 engineer. Other sciences of considerable, though of comparatively minor, import- 

 ance to engineers in general, are chemistry, geology, and meteorology ; but each 

 of these assumes an enhanced value in special branches of engineerino-. 



Mathematics in Itdat.ion to Enejineering. — The pre-eminent importance of 

 mathematics in relation to engineering may be accepted as fully established ; and a 

 President of the Institution of Civil Engineers would not now tell a pupil, at their 

 first interview, that he had done very well without mathematics, a remark made 

 to me by a justly celebrated engineer over thirty years ago. 



Surveying, which is the handmaid of civil engineering, depends upon the 

 principles of geometry for its accuracy ; and ordinary triangulation, geodesy, and 

 the rapid method of surveying and taking levels in rough country, known as 

 tacheometry, are based on trigonometry and aided by logarithms. Tacheometry, 

 indeed, though carried out by means of a specially constructed theodolite, may be 

 regarded as the practical application of the familiar problem in trigonometry of 

 finding the height and distance of an inaccessible tower. A proposition of Euclid 

 forms the basis of the simplest and speediest method of setting out circular curves 

 for railways ; whilst astronomy has been resorted to for facilitating surveying in 

 unexplored regions. The laws of statics are involved in the design of bridges, 

 especially those of large span, and also of masonry dams, roofs, floors, columns^ 

 and other structures ; whilst torsion, internal ballistics, the trajectory of a pro- 

 jectile, the forces of impact, and the stoppage of a railway train are dynamical 

 problems. Hydrostatics and hydrodynamics provide the foundation of hydraulic 

 engineering ; though, owing to the complicated nature of the flow of water, obser- 

 vations and experiments have been necessary for obtaining correct formulte of 

 discharge. Geometrical optics has been employed for determining the forms of 

 the lenses for giving a parallel direction to the rays proceeding from the lamps of 

 a lighthouse, in accordance with the principles laid down by Fresnel. The theory 

 of the tides, the tide tables giving tlie predicted tidal rise at the principal ports, 



and wave motion — questions of considerable importance to the harbour engineer 



depend upon mathematical and astronomical calculations ; whilst the stability and 

 rolling of ships, the lines for a vessel of least resistance in passing through water, 

 and the dimensions and form of screw-propellers, to obtain the greatest speed with 

 a given expenditure of power, have been determined by mathematical considera- 

 tions aided by experiment. Electrical engineering depends very largely upon 

 mathematical and physical problems, guided by the results of practical experience ; 

 and the possibility of the commercial success of the first Atlantic cable, depending 

 upon the rate of transmission of the signals and the loss of electrical intensity in 

 that long journey, has been shown by Dr. John Hopkinson, in his ' James Forrest ' 

 lecture, to have been determined by Lord Kelvin by the solution of a partial 

 difierential equation.' 



All branches of applied mathematics have, accordingly, been utilised by 

 ' Proceedings Inst. C.E„ vol. 118, p. 339. 



