50^ 



NA TURE 



[September 19, 1895 



Miit/umatics in AWatinii to Eiigiiueriiig. — The pre-eminent 

 impirtance of mathematics in relation to engineering may be 

 accepted as fully established ; and a President of the Institution 

 of CiNTl Engineers would not now tell a pupil, at their first 

 interWew, that he had done verj' well without mathematics, a 

 remark made to me by a justly celebrated engineer over thirty 

 years ago. 



Suri-ej-ing, which is the handmaid of civil engineering, depends 

 upon the principles of geometrj- 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 s|>ecially constructed theodolite, 

 may \x regarde<l 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 facilitat- 

 ing sur\eying in une.\plored 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 

 stmctures ; whilst torsion, internal ballistics, the trajectory of a 

 projectile, 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, observations and 

 experiments have been necessary for obtaining correct formula; of 

 discharge. Geometrical optics has been employed for deter- 

 mining the forms of the lenses for giving a parallel direction to 

 the rays i>rix:eeding front the lamps of a lighthouse, in accord- 

 ance with the jirinciples laid down by I'resnel. The theory 

 of the tides, the tide tables giving the predicted tidal rise at the 

 principal ports, and wave motion — questions of considerable 

 importance to the harb<™r engineer — depend upon mathematical 

 and astronomical calculations ; whilst the stability and rolling of 

 ships, the lines for a vessel of least resistance in pa.ssing through 

 water, and the dimensions and form of screw-propellers, to 

 obtain the greatest s[x'ed with a given expenditure of power, 

 have lx*en determine*! by mathematical considerations 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 llopkinson in 

 his "James Eorrest " lecture, to have been determined by Lord 

 Kelvin by the solution of a partial difierential equation (Proceed- 

 ings Inst. C.E. vol. cxviii. p. 339). 



All liranchcs of applied mathematics have, accordingly, been 

 utilised by engineers, or, as in the case of .several general prin- 

 ciples and tidal calculations, by mathematicians to their benefit ; 

 hut graphic statics will proljably gradually supersede analytical 

 methods for the calculation of stresses, as more rapid in opera- 

 tion, and less subject to errors, which are also more easily de- 

 lected in graphic diagrams. Pure mathematics, in its higher 

 branches, appears to have a less direct connection with engineer- 

 ing : but applied mathematics is so largely dependent upon pure 

 mathematics, that the latter, including the calculus and difieren- 

 tial ef|uations, cannot \k safely neglected by the engineer, though 

 certain branches, as, for instance, probaliililies, the theory of 

 numbers, the tracing of curves, and some of the more abstruse 

 portions of the subject, may be dis|x:nsed with. 



Physits ill Kelation to Eiigiiueriiig. — Physics has been 

 placed after mathematics, as many physical problems are deter- 

 mined by mathematics ; but in several respects physics, with its 

 very wide scope in its relation to the various pro|ierties of 

 matter, is of c<|ual importance to engineers, for there are few 

 problems in engineering in which no part is borne by phy.sical 

 (-,,. .,1....,:..,..,^ 



I .r avails himself of physics when heights arc 



ni the barometer, or by the temperature at which 



water bolls : and the spirit-level is a physical instrument adapted 

 by ih" -nrv.-y.ir f'lr levelling across land. Evajxiration, con- 

 di I ii are of great nnportance in regard to 



111 ii".;ines; and the ex|Mnsive force of the 



g.i ' I ■ \| led, the diminution of friction, and the 



re le heat developed arc essential elements in the 



vi .rViiiL' '.f Ileal engines. Allow.tnce for ex|xinsion 



by heat and ' by cold has to lie made in all large 



.itruclures ; .n is due to changes in tcni|K-rat»re have 



NO. 1.35 1, VOL. 52] 



to be taken into account. The temperature, also, which de- 

 creases with the elevation above the sea-level, and the distance 

 from the equator, limits the height to which railways can be 

 carried without danger of blocking by snow ; whilst the tem- 

 perature, by increasing about 1° Y. with every 60 feet below 

 the surface of the earth, limits the depth at which tunnels can 

 be driven under high mountain ranges. Congelation of the 

 soil is employed, as will be exi>lained by M. Clobert, in 

 excavations through water-bearing strata. 



Compressed air is used by engineers for excluding the water 

 from subaqueous foundations, so that excavations can be 

 made and foundations laid, at considerable depths below the 

 water-level, with the same certainty as on dry land. The 

 compression of air, and its subsequent absorption of heal on being 

 liberated and expanding in a chamber, are employed for re- 

 frigerating the chambers in which meat and other [lerishable 

 supplies are preserved. Compressed air is em|>loycd for working 

 the boring machinery in driving long tunnels through rock, and 

 provides, at the same time, means of ventilation ; and it also 

 serves to convey parcels along pneumatic underground tubes. 

 Moreover, the compressed-air and vacuum brakes are the most 

 efiicient systems of automatic and continuous brakes, which have 

 done .so much to promote safety in railway travelling, and in 

 reducing the loss of time in the pulling up of frequently stopping 

 trains. The production of a more jjcrfect vacuum than can be 

 produced by the ordinary air-pump, might have been supposed 

 to be merely an interesting physical result (^/oiiriial of the 

 Chemical Society, June 1864) : but, in fact, the preservation of 

 the heated filament of carbon in the incandescent electric light 

 has been rendered possible only by the far more perfect vacuum 

 obtained by the Sprengel vacuum-pump, by which the air is 

 exhausted down to so low a pressure as a Iw o-hundred millionth 

 of an atmosphere. 



The illuminating power of different sources of light is of great 

 importance in determining the distance at which the concentrated 

 rays from a lighthouse can be rendered visible, as well as in 

 relation to the lighting of streets and houses ; ami the re- 

 frangibility of the rays emitted, or the nature of their spectrum, 

 should not be disregarded, as upon this deiiends the power of a 

 light to penetrate mist and fog, which cut olT the rays at the 

 violet end of the spectrum, and have comparatively little in- 

 fluence on the least refrangible red rays {Pi-o,t;ji)igs Inst. 

 C.E., vol. Ivii. pp. 145-148). The eftect also of the colouring 

 of lights on their visibility is of interest in determining the 

 sh.ades of colour to be used for signals and ship-lights, and also 

 the relative power of the lights reijuired for difl'ercnt colours to 

 secure equal illuminating power. Distinctions of colour are 

 essential in these case-; ; but for distinguishing lighthouses, the 

 use of coloured glasses has been abandoned, on account of their 

 im]>airing the light emitted : and the desire<t indication has been 

 effected by varying the number and duration of the flashes and 

 eclipses in each lighthouse. The detection of colour-blindness 

 is of interest to engineers, as this physical infirmity incapaci- 

 tates men from acting as engine-drivers, signalmen, or navigat- 

 ing seamen. Fhe use of compressed oil-gas enables buoys and 

 beacons to give a warning or guiding light for about three 

 months without requiring attention ; and the electric light has 

 accelerated the passage through the .Suez Canal from 30.4 hours 

 to 20 hours, and htis greatly increased the ca|«cily of the canal 

 for traflic by enabling navigation to be carrie<l on at night. The 

 electric light also affords an excellent, safe, and cool light in the 

 confined caliins on board ship, in the headings of long tunnels, 

 and in the working-chamlK-rs filled with compressed air used for 

 sinking subaqueous foundations. 



Acoustics might seem to have little relation to engineering ; 

 but the soundness of the wheels of a train are tested by the 

 noise they give when struck with a hammer ; warning notes are 

 emitted by railw.ay and steamship whistles, the foghorn on 

 board ship, and the whistling and bell-buoys employed for 

 marking snoals or the navigable channel ; whilst the striking of 

 bells, the blast of steam sirens, and the explosion of compressed 

 gun-cotton cartridges and rockets indicate the position of light- 

 houses in foggy weather. The most powerfiil sounds that can 

 be produced by the help of steam appear to have a very limited 

 range as compared with light ; for, under ordinary conditions, 

 the most powerful siren cea.ses to be audible at a distance of six 

 or seven miles ; whilst the transiiiissiim of sound is very much 

 affectefl by the wind anil the condition of the atmi>sphere. It 

 seems possible that lourl detonations at short intervals may be 

 more re.tdily hear<l than the continuous bl.tsl of a steam Irunipet. 



