RELATIONS OF CIVIL ENGINEERING 563 



has forgotten. Strictly speaking, though, engineers in their daily 

 tasks utilize applied mechanics, almost without recognition; for 

 stresses, moments, energy, moments of inertia, impact, momentum, 

 radii of gyration, etc., are all conceptions of applied mechanics; 

 and these are terms that the engineer employs constantly. 



There are some branches of the higher mathematics of which as 

 yet engineers have made no practical use, and prominent among 

 these is quaternions. When it first appeared the conciseness of its 

 reasoning and its numerous short-cuts to results gave promise of 

 practical usefulness to engineers, but thus far the promise has not 

 been fulfilled. 



Notwithstanding the fact that the higher mathematics are of so 

 little use to the practicing engineer, this is no reason why their 

 study should be omitted from or even slighted in the technical 

 schools; because when an engineer has need in his work for the 

 higher mathematics he needs them badly; besides, the mental 

 training that their study involves is almost a necessity for an en- 

 gineer's professional success. 



Geology (with its allied branch, or more strictly speaking subdi- 

 vision, petrology) and civil engineering are closely allied. Civil 

 engineers are by no means so well versed in this important science 

 as they should be. This, perhaps, is due to the fact that the instruc- 

 tion given on geology in technical schools is mainly from books, 

 hence most graduates find difficulty in naming properly the ordin- 

 ary stones that they encounter, and are unable to prognosticate 

 with reasonable assurance concerning what a proposed cutting 

 contains. 



Geology is important to the civil engineer in tunneling, railroad- 

 ing, foundations, mining, water-supply, and many other lines of 

 work; consequently, he needs to receive at his technical school 

 a thorough course in the subject given both by text-books and by 

 field instruction. 



A knowledge of petrology will enable the engineer to determine 

 readily whether building-stone contains iron which will injure its 

 appearance on exposure, or feldspar which will disintegrate rapidly 

 under the action of the weather or of acids from manufacturing 

 establishments. 



Next to mathematics, physics is undoubtedly the science most 

 essential to civil engineering. The physicist discovers and form- 

 ulates the laws of nature, the engineer employs them in "direct- 

 ing the sources of power in nature for the use and convenience of 

 man." The forces of gravitation, adhesion, and cohesion; the press- 

 ure, compressibility, and expansibility of fluids and gases; the 

 laws of motion, curvilinear, rectilinear, accelerated, and retarded; 

 momentum; work; energy; the transformation of energy; thermo- 



