ON GRAPHIC METHODS IN MECHANICAL SCIENCE. 375 



II. The representation of results: — 



1. The plotting of diagrams ; the use of squared paper. Growth of 



the method. Plotted tables. Contributions on Naval Archi- 

 tecture, by Mr. H. H. West; and on Electrical Work, by 

 Mr. F. G. Baily. Applications in civil and mechanical 

 engineering. 



2. Instruments for drawing known curves used with graphical 



methods. Improvements in simple drawing-instruments. 

 BUiptographs. Drawing the parabola. Harmonic curves : the 

 involute ; cycloid ; spirals, &c. The Gabarit. The Integraph. 



3. Self-recording instruments. Marking arrangements. Modes of 



actuating surface for receiving the recoi-d. The movement of 

 the recording arrangement. Instruments for recording (a) 

 levels ; (b) pressure ; (c) magnetic attraction ; (d) velocity ; 

 (e) temperature; (/) vibrations and shocks; (g) results of 

 mathematical operations ; (h) chronographic results. 



III. Graphical solution of problems : — 



1. Consideration of modern methods of graphical calculation, chiefly 



in view of Continental usage and opinions concerning the appli- 

 cation of projective geometry in graphic statics. 



2. Addition of parallel segments. Sliding calculation and slide 



rules. Shearing force and load diagrams. 



3. Addition of non-parallel segments. Summary of the applications 



of the principle of reciprocal figures. 



4. The applications of graphical multiplication. The rectiBcation 



and calculation of areas. Summary of the problems in 

 engineering to which methods of graphical multiplication are 

 applied. 



I. Geometrical Considerations. 



Let us suppose we have a plane surface, or what may be developed 

 into a plane surface, e.g., a paper wrapped upon a cylindrical barrel, which 

 we propose to use for graphical purposes. 



If we take any point upon the surface, we can represent any numerical 

 quantity by its distance from some other fixed points, the position of 

 which we suppose to be known, writing beside the point, or representing 

 by means of some notation, what particular thing the numerical quantity- 

 is supposed to refer to. By taking a number of points we may represent 

 any number of numerical quantities by their distances from the fixed 

 point, and there is no limit to the number of ways in which we may do 

 this ; for instance, we may take them ranged along one straight line, just 

 as in the graduation of scales and similar instruments, where each reading 

 measures the distance from the zero of the scale ; as, for instance, the kind 

 of graphic record of magnitudes represented by the distances OA, OB, 

 OC, OD, and OE in fig. 1. 



Fig. 1. 



B A D C 



Instead of a point being taken alcmg a straight line, i.e., in one direc- 

 tion, the same points may be taken in different directions, as shown in 



