I 



ON GRAPHIC METHODS IN MECHANICAL SCIENCE, 425 



One man remarks that ' the interesting and practically useful results 

 which statics afford would already have found common use if the scientific 

 methods of modern geometry had not withheld many engineers from the 

 study of this subject.' The much -respected professor wishes to make 



it more elementary, but he cannot bring that about without d and J ; and 

 yet a knowledge of d and f requires a greater exercise of brain-power 

 than the elements of the geometry of position does. 



The question is, if the d and f have to be learnt (as they certainly 



should be) for a great number of other applications, and the engineer 

 finds it more easy to employ a method of reasoning with which he is 

 familiar, will he not certainly do so ? 



Lastly, there is the argument, so often adduced, of the intellectual value 

 of general methods, and doubtless it is true tliat a higher mental effort is 

 required to reason from the general to the special, such as is required in 

 the methods of projective geometry. However, teachers are almost 

 unanimous in agreeing that the average student finds it far more easy to 

 reason from the special to the general ; nay, it may be truly said that the 

 number of students who have the power of grasping generalisations, 

 such as are expected in the study which has just been discussed, is 

 extremely limited, and that the result of trying to introduce this method 

 is frequently disheartening to the majority of students, who would 

 otherwise acquire sufficient knowledge of the subject for all the practical 

 application they would ever have occasion for. 



So much space has been given for the setting forth of these views, 

 and to bringing forward various views on the subject because of its im- 

 portance, that the writer is unable for want of time to proceed further 

 in time for the presentation to the Association in the present year. 



The object in view at the commencement was to collect and summarise 

 all the problems of mechanical science for which graphical calculation 

 and methods were employed. That he is unable to do for the present, and 

 can only offer the following brief outline of the subject, dealing fully with 

 two sections, indicated below, leaving it for the Committee of the Section 

 to say whether they think it desirable that a further report should be 

 presented. 



Summary of Graphical Problems. 



1. The addition of parallel segments, including sliding calculation and 

 slide rules (which latter are dealt with in the present report). 



2. The addition or combination of non-parallel segments. 



3. The applications of graphical multiplication, including planimeters 

 and integrators, which are also dealt with. 



1. The first of these, as far as regards sliding calculation, has been 

 dealt with at tolerable length, and brought as far as possible up to date. 



There are numerous other applications of the addition of parallel 

 forces. The most important of these are the treatment of loads, including 

 the load on a beam, and the weight and buoyancy of a ship. 



These problems are dealt with in numerous works ; for example, the 

 subject of shearing forces, the construction of diagrams of which for 

 every possible kind of loading might form a subject of somewhat lengthy 

 treatment. 



