784 REPORT — 1895. 



engineers, or, as in the case of several general principles and tidal calculations, 

 by mathematicians to their benefit; bat graphic statics will probably graduall}- 

 supersede analytical methods for the calculation of stresses, as more rapid in 

 operation, and less subject to errors, which are also more easily detected in graphic 

 diagrams. Pure mathematics, in its higher branches, appears to have a less direct 

 connection with engineering ; but applied mathematics is so largely dependent 

 upon pure mathematics, that the latter, including the calculus and ditferential 

 equations, cannot be safely neglected by the engineer, though certain branches, as, 

 for instance, probabilities, the theory of numbers, the tracing of curves, and some 

 of the more abstruse portions of the subject, ma)' be dispensed with. 



Phi/sics ill Relation to Emiineeriny. — Physics has been placed after mathematics, 

 as many physical problems are determined by mathematics ; but in several respects 

 physics, with its very wide scope in its relation to the various properties of matter, 

 is of equal importance to engineers, I'or there are few problems in engineering in 

 ■which no part is borne by physical considerations. 



The surveyor avails himself of physics when heights are measured by the 

 barometer, or by the temperature at which water boils ; and the spirit-level is a 

 physical instrument adapted by the surveyor for leyelling across land. Evapora- 

 tion, condensation, and latent heat are of great importance in regard to the 

 efficiency of steam-engines: and the expansive force of the gases generated or 

 exploded, the diminution of friction, and the retention of the heat developed are 

 essential elements in the economical working of heat-engines. Allowance for 

 expansion by heat and contraction by cold has to be made in all large structures ; 

 and detiections due to changes in temperature have to be taken into account. The 

 temperature, also, which decreases 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 temperature, by increasing about 

 1° Fahr. with every sixty feet below the surface of the earth, limits the depth at 

 Avhich tunnels can be driven under high mountain ranges. Congelation of the soil 

 is employed, as will be explained by Monsieur Gobert, in excavations through 

 watei-bearing strata. 



Compressed air is used by engineers for excluding the water from sub- 

 aqueous 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 heat on being liberated 

 and expanding in a chamber, are employed for refrigerating the chambers in which 

 meat and other perishable supplies are preserved. Compressed air is employed 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 efficient .systems fif automatic 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 perfect 

 vacuum than can be produced by the ordinary air-pump, might have been 

 supposed to be merely an interesting physical result ; ' 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 one- 

 two hundred milliontli 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 ; and 

 the refrangibility of the rays emitted, or the nature of their spectrum, should not 

 be disregarded, as upon this depends the power of a light to penetrate mist and 

 fog, which cut off the rays at the violet end of the spectrum, and have compara- 

 tively little influence on the least refrangible red rays." The effect also of the 



' Journal of the Chemical Society, June 1864. 

 ' Procecdiwjs Inst. C.E., vol. .57, pp. 145-148. 



