1 PRACTICAL SIGNIFICANCE OF GEAPIHCAL STATICS. 



reason of the result obtained, which, in the substitution of numbers in a 

 formula, is not always the case. 



With tliis advantage goes hand in hand a disadvantage. This very 

 regularity of the process is a consequence of its special, we might almost 

 say numerical, character (I.). In a numerical analytical example greater or 

 less regularity has also but little effect. This numerical character has also 

 for consequence that we can never attain to general laws and relations 



(iv., vn.). 



The practical engineer becomes with time ever more familiar with the 

 dividers and rule, while facility in analytical operations gradually disap- 

 pears. A graphical construction once completed is not easily forgotten, or 

 a single glance at a similar figure suffices to recall the whole process. It is 

 indeed easy in clearly given formulae to substitute special numerical values ; 

 but formulae unfortunately are not always clearly given, in some cases can/- 

 not be so given, without presuming upon the thorough familiarity of the 

 reader with the processes involved ; these and the very many and various 

 systems of notation in nse leave to the constant, easily acquired and 

 remembered graphical solution many advantages. 



But here we may remark that graphical solutions can only be easily 

 acquired, retained or quickly recovered when the constructions are based 

 upon methods purely geometric, and not when they are simply the interpre- 

 tation of previously obtained analytical results. In the latter case we 

 must recall the process of development of the formula as well as the 

 graphical construction, and the method is thus too often confusing instead 

 of simple. 



Often it is desired to make visible the results of an investigation, as in 

 the case of the arch, where the graphical method is especially advan- 

 tageous, and has in France been long used (VII.). 



Errors relating to the mutual relation of strains are more easily discov- 

 ered in graphical solutions than in analytical, as a certain law of regularity 

 is always visible, which breaks abruptly for an error in construction. By 

 calculation, on the other hand, we can more easily select any one place in 

 the structure, and determine the strain there independently of the others. 



As to which of the two methods demands the least time is a matter of 

 minor importance. In a construction costing from thousands to millions, 

 it matters little whether the calculations require one or several days, more 

 or less, if only the results are clear and correct. It is a question also 

 which can hardly be decided in favor of one or the other, dependent as it 

 is upon elements other than those pertaining to the methods themselves 

 such as varying individual skill and capacity in either direction. The 

 declaration which is already sometimes encountered, that the numerical 

 calculation of a continuous girder requires about three times as much time 

 as the graphical solution, sounds questionable. Why not at once furnish 

 the statement with decimal places f In general, for ordinary cases, the ana- 

 lytical solution requires less time ; for irregular and more complicated cases, 

 the graphical. 



The exactness of the graphical solution is sufficient, but it, too, depends 

 upon the care and skill of the draughtsman. The greater the forces and 



