574 EEPORT — 1893. 



solutions of the various engineering problems at present scattered over 

 various books and papers in English and foreign literature. This should 

 convey a clear idea of the problems which can be dealt with, so that 

 their practical use can be estimated. The bare statement of the problems 

 would, however, be scarcely sufficient for this purpose, since not only 

 must the problems be such as are required, but the solution must not be 

 too difficult, or the ideas too abstruse for practical engineers. Some 

 application to practical results would, therefore, be advisable, leaving, 

 however, as a general rule, the proofs and explanation to be derived from, 

 the works which are quoted. This important work cannot be attempted 

 so as to do justice to it in the present report, which merely gives a 

 classified outline of the problems. 



It is not to be expected that the graphical methods will come into 

 general use unless special training and education on the subject can be 

 obtained at technical colleges and schools. As a good deal has been said 

 and written on this subject (vide second report), this report has been 

 supplemented with an account of the teaching of graphical methods in 

 engineering schools at home and abroad as explained on p. 608. 



The following is an outline of the scheme of the present report : — 



Division I. — Graphical Operations in General. 



Division II. — Summaiy of Problems which have graphical solu- 

 tions. 

 Division III. — The Teaching of Graphical Methods. 



Division I. — Gkaphical Operations in General. 



As already noted, graphical operations are distinguished from mere 

 geometrical operations by the fact that definite portions of lines repre- 

 sent quantities, and only such geometrical operations are of interest as 

 enable definite numerical results to be obtained. 



It is true that a very common graphical operation is that of finding 

 the direction of the line in which the resultant of various given forces act ; 

 but direction itself, though it may not always be numerically expressed, 

 is capable of being so expressed if required. Indeed, it is this particular 

 power of being able to deal directly with the directions in which forces 

 act, or motion takes place, and with positions in space, instead of first 

 translating these measurable quantities into mathematical symbols and 

 calculating the results by means of trigonometry or algebra, and finally 

 effecting their reconversion into some geometrical mode of representation, 

 that constitutes the great value of graphical methods. It is this that 

 has led to the discovery of the solution of such a large number of 

 engineering problems and its growing popularity amongst scientific men. 



We may treat graphically many problems in which direction or 

 position is not either of them the factors which actually occur, but in 

 which they simply become a part of the process of performing mathe- 

 matical operations ; thus treatises on graphic statics frequently com- 

 mence by stating the means by which multiplication, extraction of roots, 

 solution of equations, &c., may be graphically performed. It is tolerably 

 clear that the reason why the operation of these numerical calculations by 

 graphic methods has never been put to any practical use is because such 

 work is most easily performed arithmetically. 



The problems which arise in engineering are, however, to a large 



