386 REPORT — 1892. 



we may use either geometrical construction or mathematical calculation 

 of trigonometry and algebra; that is to say, the analytical process may be 

 employed to follow the same operations and register the same results. 



As a result of the increasing introduction of graphical methods, a 

 science known as the Graphical Calculus has arisen, ihough until a few 

 years ago there was no complete treatise in the EngHsh language under 

 this head. Now, thanks to Professor T. Hudson Beare's translation, 

 there is available for English readers the ' Calcolo Grafico ' of Professor 

 Cremona.' This work deals with the modern use of lines in geometry, 

 as initiated by Moebius, and then in subsequent chapters the combination 

 or addition of a number of segments, which is made use of chiefly for 

 reciprocal figures of framework in graphic statics ; graphical multiplica- 

 tion, which is apphed in such important problems as bending moment, 

 moment of inertia, deflection, and other matters; the extraction of roots; 

 reduction of plane figures, so as to enable their area to be found 

 o-raphically ; the finding of the centre of parallel forces, under the title of 

 ' centroids ' ; and finally some useful propositions on the rectification of 

 the circular arc. Many of these propositions the author in a preface to 

 the English translation states are not new, and have been known to 

 English writers, but there is much that has never been previously written 

 in English, or brought together in one book. 



It is therefore unnecessai-y to refer in detail to these applications of 

 geometry treated of in the above work, but it may be remarked that the 

 more careful use of lines and notation on the principles set forth by 

 Moebius would often prevent much confusion and unnecessary explana- 

 tions — sometimes not even then leaving the subject particularly clear — in 

 various books dealing with graphical applications. 



II. Graphical Representation of Results. 



1. The Plotting of Diagrams. 



The plotting of experimental results of all kinds, usually by the use 

 of Cartesian co-ordinates, has become a universal practice. Scarcely a 

 paper containing numerical results is presented to the scientific world in 

 which this system is not employed, while in connection with experimental 

 research in all laboratories in which instruction is given, the operation 

 has become probably nearly as common as the use of arithmetic. This 

 has led to the use of ' squared ' paper, which lias greatly facilitated the 

 process of plotting, and the annexed figure (fig. 12) gives a number of 

 different examples of squared paper in common use. 



For many purposes where special work is done, ruled paper of a 

 particular kind is used instead of squared paper. For instance, in 

 plotting the results of experiments with the Thurston Testing Machine 

 for torsion the lines are ruled radially, as shown in MacLay's book on 

 'Loci' (p. 60). 



There are three principal purposes for which plotting of results may 

 be employed : — 



(1) For experimental work, in which the results of a certain number 

 of experiments are plotted, and the curves drawn through them, so as to 



' Graphical Statics, by Luigi Cremona, translated by Thomas Hudson Beare. 

 Clarendon Press, Oxford, 1890. 



