ON GRAPHIC METHODS IN MECHANICAL SCIENCE. 573 



The Development of Graphic Methods in Mechanical Science. — 

 Third Report by Professor H. S. Hele Shaw, M.lnst.G.E. 



Graphical Solution of Problems. 



The first and preliminary report on thia subject was presented in 1889. 

 The second report was presented last year, and was divided into four 

 parts. 



1. General geometrical considerations. 



2. The representation of results graphically. 



3. Graphical solution of problems. 



4. A tabulated list of reference to graphic methods to be found in 



the scientific literature of this country. 



Only a brief treatment of the third division was possible. This in- 

 cluded quotations from various authors concerning the development of 

 the subject and a summary of graphical problems, though a more com- 

 plete account was given of two of these branches, viz., slide rules and 

 naechanical integrators. 



The present Committee was appointed to prepare a third report on 

 the subject, dealing as completely as possible with the unfinished portion 

 of the report, viz., ' The Solution of Problems.' 



The study of the second report, particularly of the classified list of 

 references, conclusively shows that graphical solutions have in this 

 country at any rate proceeded almost entirely on two lines. 



1. Interpolation of plotted results. 



2. Use of reciprocal diagrams in structures. 



The former, although arriving at results which would be difficult, if 

 not impossible, to obtain in any other way, is itself a remarkably simple 

 operation, the chief part of the work really consisting in the preparation 

 of the diagrams in which the interpolation is made. This matter was 

 treated very fully in the second report, both for plotted curves and 

 instrumental methods for obtaining them. 



The latter, viz., use of reciprocal diagrams, is largely employed, 

 chiefly because of its simplicity. It forms, however, only one branch of 

 what is now known as ' Graphical Statics,' which in turn only includes 

 one class, although the most important class of graphical problems. 

 Moreover, the cases treated by its means are nearly always the simplest, 

 and do not involve the use of more complete solutions which have been 

 given by various writers for cases of more difficult problems in struc- 

 tures. There has been, however, a large amount of research in connection 

 with the subject, of which little practical use is at present made, and 

 while, on the one hand, many writers strongly advocate the application 

 in practice of graphical statics (vide ' Quotations,' pp. 420-426, second 

 report), on the other hand there is a large amount of scepticism as to 

 the use which may be derived from the study of the subject. 



What is apparently needed is a definite statement of the general 

 nature of graphical operations followed by a concise account of the 



