GRAPHICAL REPRESENTATION. 



V. 



GRAPHICAL REPRESENTATION. 



Graphical representation, in the widest sense of the word, includes every 

 visible result of writing or drawing. The written sentence is the graphi- 

 cal representation of a thought the drawn line the graphical indication of 

 an idea. In such generality we naturally do not here regard graphical 

 representation. In a narrower sense we understand the graphical represen- 

 tation of the diversity or dependence of numerical quantities. In this 

 sense we cannot speak of the graphical representation of pure geometry. 

 This last was introduced into analysis by Vleta (1540-1603). Here the 

 figure merely aids the conception, while the equation embraces the charac- 

 teristics of the phenomena (I.), and ensures the independent character of 

 the drawn lines. Thus the clearness of geometry is combined with the 

 fruitf ulness of analysis. 



If the graphical representation is constructed from a number of suitably 

 chosen and calculated values, the intermediate values can be directly meas- 

 ured and, by means of the scale, reconverted into numbers. The graphical 

 representation, then, replaces numerical tables. Illustrative examples often 

 occur in practice. We instance, for example, the graphical representation 

 of maximum moments and shearing forces in the continuous girder. If 

 the several values are calculated from a formula, their graphical union gives 

 a simultaneous view a picture of the law which the formula represents. 

 If these values are merely known observed, for example their graphical 

 combination may enable us to deduce the law which connects them. Thus 

 the graphical representation is of assistance in the deduction of empirical 

 formulae, and indirectly in the discovery of exact relations. Illustrations 

 of such application occur frequently in applied mathematics, especially in 

 astronomy and meteorology. 



In this connection we may also remark that graphical representation 

 plays also an important part in statistics. By its aid a comprehensive view 

 is obtained of a series of separate results. Or it may be applied to still 

 higher problems for example, from comparison of simultaneous but differ- 

 ent series of observations to determine an inner connection. 



In engineering practice, graphical representations have in recent times 

 notably multiplied. All graphical constructions, so far as they do not de- 

 pend upon analytical formulas, and therefore are not directly given by 

 geometrical laws, are nothing more than consequences of graphical repre- 

 eentation. 



