ON GRAPHIC METHODS IN MECHANICAL SCIENCE. 611 



Take, as an example of this proposition, the ellipse of inertia and the 

 central ellipse, which are only applied to force, and which are given as if 

 they only referred to the problem of the beam. These theorems, how- 

 ever, have an equally important bearing on hydrostatics and rigid 

 dynamics, the ellipsoid of inertia having the properties, for instance, of 

 the momental ellipsoid of Cauchy, the central ellipsoid, and those of the 

 equimomental ellipsoid of Legendre. Indeed, there is every indication of 

 a gradual tendency towards the development of the science of graphical 

 calculation, quite apart from that of graphic statics. Thus we find 

 graphical constructions originally devised and given by writers (notably 

 Rankine) as they were needed in works of mechanics. Next we have the 

 first collection of graphical calculation, already referred to, of whicli 

 there are remarkable examples in the little work of Cremona, ' II Calcolo 

 grafico,' in the preface of the English edition of which he acknowledges 

 the work of Culmann. Cremona, however, goes considerably beyond that 

 author, particularly in adding the important chapter on ' Centroids,' in 

 which the properties of the centre of gravity are treated from a purely 

 geometrical point of view, without any reference whatever to force. A 

 still more recent work is that of Favaro, who, in his ' Lessons on Graphic 

 Statics,' devoted his second volume entirely to the subject of graphical 

 calculations. 



From this it is clear that a course of instruction might be given, under 

 the head of Graphical Methods, which, might be taught in the same way 

 as descriptive geometry, and which ought, indeed, to be worked in con- 

 junction with that subject. This subject should deal with the construc- 

 tions of such geometrical figures as are important for graphical applica- 

 tion. It should also deal with the plotting of results and the general 

 properties of plane curves, as far as the student is able to numerically 

 efiect measurements with it, which he can check by calculation. A 

 student should be expected to do his work with great accuracy, and to 

 regard the results he obtains as accurate enough to be useful in practical 

 work, although such examples need not at the time be applied to any 

 practical engineering problems. Thus, for instance, the propositions of 

 projective geometry, so far as the null or focal system is concerned, and 

 the projective properties of bodies, and of the pole and antipolar, might 

 be taught; but a systematic treatment of the subject of projective 

 geometry is not necessary for engineers. With regard to projective 

 geometry, it may be said that, unless it is desired to study the higher 

 branches of the subject, there is no necessity whatever of a treatment 

 such as Culmann has given in his chapters on the 'projective relations 

 between the polygon of forces and the funicular polygon ' and ' the rela- 

 tion of a system of forces with the focal system, and with curves of the 

 third degree,' or with the central axis of a system of forces, or colinear 

 and reciprocal relations of the funicular or force polygon. 



There appears to be no reason, therefore, why an elementary course of 

 a general nature, specially arranged so as to include all that an ordinary 

 engineering student requires to know of graphical methods, should not 

 be introduced as a regular subject in engineering schools, and the follow- 

 ing arguments, may be brought forward in support of this view : — 



(1) Although the time-tables of an engineei-ing department are 

 already full, yet it will be found that a course such as that suggested 

 really includes much of what is taught at present in a desultory way, and 

 such a course would obviate some of the teaching given under the heading 



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