374 EEPORT— 1892. 



omissions, because descriptions of many such instruments have not been 

 published ; heuce the object of the writer in dealing with this part of the 

 report has been to give a concise statement of the progress and present 

 state of the subject. 



At the same time thte difiBculty of ascertaining what subjects in 

 mechanical engineering have been treated graphically in current litera- 

 ture is very great, and nothing less than an examination of every page of 

 engineering journals and scientific papers suffices for this purpose, since 

 no intimation of graphical treatment is usually given in the index. 

 Hence a list of references has been added to this report, arranged under 

 suitable headings of the more important applications of mechanical 

 science, wherever such applications have been graphically treated. In 

 one column the names of the subjects are given under which the article 

 is found in the journal ; in another, the description of the graphic 

 diagram ; in another, the author's name. The arrangement of matter 

 under each heading is in the order of the year of publication, so that 

 anyone searching for graphical records on a certain subject will see at ■ 

 once what is old and what is new. 



(2) Very different, however, is the case of the graphical treatment of 

 problems. This is a subject of very divided opinion, whereas the mere 

 representation of results has settled down into recognised lines and 

 methods of operation. Great as the progress has been in this direction, 

 it will be seen that there is a wide field for discussion in the present 

 state of the question ; hence in this portion of the report an attempt has 

 been made to present the views of different schools of thought, and to 

 state the results achieved up to the present. At the same time, the 

 question is far too wide to be treated in the present report in a way at all 

 justified by its importance, and it is a question for the Association to decide 

 whether a further report, dealing more fully with foreign literature and 

 practice in graphic methods in relation to mechanical science, is not 

 desirable. 



To the treatment of the subject thus divided there is prefixed a 

 statement of the geometrical principles involved in the methods of 

 graphical representation. This preliminary statement is necessary to 

 show both the possibilities and methods of graphical records, as well 

 as to premise the considerations in the second portion, dealing with 

 calculation. 



The foregoing remarks will explain the following scheme of the 

 report : — 



Scheme of Report. 



I. Geometrical considerations involved in (1) the representation of 

 results graphically, and in (2) gi-aphical calculations : — 



1. Use of one dimension of space corresponding to measurement 



from one fixed point in a plane, enabling one vai'iable to be 

 dealt with. The use of two dimensions of space corresponding 

 to the measurement from two fixed points in a plane, enabling 

 two variable quantities to be represented by the position of a 

 point. The use of three dimensions, or of representation of 

 three variables by the positions of a point, involves the use of 

 models or stereotomy, and is excluded from consideration in 

 treating of graphical methods. 



2. Practical distinction between analytical treatment and geometry 



of position. The Graphical Calculus. 



