426 EEPOET— 1892. 



2. The second division, viz., the addition of non-parallel segments, 

 •covering, as it does, the whole range of the most fertile branch of graphic 

 statics, is worthy of a separate report. It must suffice here to give the 

 following as amongst the different headings nnder which it might be 

 treated : — 



(a) The study of reciprocal figures. 



(h) Diagrams of forces for framed structure. 



(c) The polygon of forces, and its application to arches and suspen- 



sion bridges. 



(d) The subject of internal stress and the ellipse of stress. 



(e) Machine problems dealing with the efficiency of machinei'y, as 



proposed by Fleeming Jenkin, and the ' method of instan- 

 taneous centres,' applied with such effective results by Pro- 

 fessor Kennedy in his ' Mechanics and Machinery.' 



(/) Velocity of machine parts. 



(g) Hydro-mechanics. , 



(h) Crank effiart diagrams, &c. 



3. As to the thiz'd division almost a wider range opens out, com- 

 mencing with the principle of what Culmaun calls ' the rope polygon,' or 

 ' funicular polygon,' and which he treats in his book under the heading 

 ■of ' Summation.' By means of this be shows how not only single but 

 whole series of lines of different ratios may be multiplied together, and 

 which, under the title of ' Culmann's Method,' is employed for the purpose 

 of bending moment, moment of inertia, finding the central ellipse and 

 the kern of sections, and still further applied in problems of deflection 

 and continuous girders. 



How fertile this graphic method may be made may be seen from 

 the following remark in Cotterill's ' Applied Mechanics,' second edition, 

 p. 303 :— 



' Thus it appears that the curves of deflection, slope, and bending 

 moment are related to each other in the same way as the curves of bending 

 moment, shearing force, and load. 



' The five curves, in fact, foi-m a continuous series, each derived from 

 the next succeeding by a process of graphical integration.' 



These are only a few of the problems to which graphical method 

 lends itself, and in connection with which there is abundant scope for 

 investigation and original research. 



Addition of Parallel Segments, Sliding Calculation, and Slide Rules. 



Shortly after the invention by John Napier, in 1614, of logarithms, 

 Edmund Gunter, Gresham Professor, laid them down on a scale, so that 

 by means of a pair of compasses arithmetical questions might be solved. 

 Mr. Heather, in his work on mathematical instruments,' gives a full 

 explanation of the use of ' Gunter's lines,' as they were called, which 

 included not only logarithms of numbers, but other lines graduated so as 

 to represent logarithms of the sines, tangents, &c., and other calculated 

 values useful to navigators. 



Gunter's scale and its uses are also described. The sliding: Guntei-'s 



a 



^ Mathematical Instruments, hy J. F. Heather, M.A., 1880. Crosby, Lockwood, 

 & Co. 



