ON GRAPHIC METHODS IN MECHANICAL SCIENCE. 609 



without any instruction. The solution of problems, on the other hand, has 

 of recent years received a great deal of attention, under the title of ' Graphic 

 Statics,' which is the most important, and indeed at present almost the 

 only, special branch of the application of graphical construction. This 

 branch is in many engineering schools dignified by a special course of 

 lectures and classes, with even a special professor for the subject, while 

 in many other schools the subject is not taught at all ; and, again, the 

 opinions held by practical men, and apparently also by professors in the 

 engineering science, would seem to differ in a most remarkable manner as 

 to the value of graphical methods. It is believed that this difference of 

 opinion is apparent, and not real ; and the very fact that so much attention 

 has been devoted to the subject, in w^hich at present there is no uniformity 

 in the teaching or general agreement as to methods, amply justified the 

 treatment of this subject before a congress ; and it was with the hope 

 that some authoritative expression of opinion might be obtained that it 

 was brought forward. 



The two divisions may be dealt with in order, taking first the plotting 

 of results. This method is now universal, not only in the mechanical 

 sciences, but in almost any case where statistics of any kind are employed, 

 as it enables I'esults, which would otherwise be difficult to grasp, to be at 

 once made clear by a simple inspection. The various methods of plotting 

 and the vai'ious instruments which have come into use for automatically 

 recording such results were too familiar to need discussion. [A sketch 

 of that portion of the report presented last year relating to the plotting 

 of results was then given.] Now it appears to be the common idea that 

 the interpolation of results, no less than the actual plotting, is a sort of 

 intuitive process which is readily acquired and requires no sort of train- 

 ing ; but on careful investigation the contrary is found to be the case. 

 This was illustrated by various examples. The series of diagrams relating 

 to the action of the crank and connecting-rod of an ordinary engine which 

 were exhibited, and which were drawn for a meeting of an engineering 

 society, were noticed to be in some respect novel, giving a satisfactory 

 arrangement, so as to include four sets of diagrams, each of which in- 

 cludes a linear, central polar, and circumferential polar diagram of the 

 same results. To many of those present these diagrams were no doubt 

 perfectly familiar, but it was found that there wei-e many practical 

 engineers to whom, not only did the different series of diagrams have no 

 definite meaning, but the difference between the three diagrams and 

 the various points which are thereby brought out were obviously not 

 easily grasped ; and, moreover, from year to year, when bringing these 

 diagrams before students, it has been found that only after considerable 

 repetition, and after the student has constructed for himself a series of 

 similar diagrams, is he able to deal with such problems or to grasp their 

 general meaning. 



With regard to the solution of problems the case is entirely different, 

 for this subject receives a certain amount of attention in every en- 

 gineering course of instruction. In England such instruction is given, 

 as a rule, in most colleges incidentally when the subjects of statics, 

 machines, or hydraulics are being dealt with, although recently in some 

 cases special training in graphical methods is being Introduced as a part 

 of the course of engineering instruction, in several cases being given as a 

 branch of descriptive geometry. Thus in the Science and Art Depart- 

 ment, both under the heads of descriptive geometry and also machine 

 1803. RR 



