ON GRArniC METHODS IN MECHANICAL SCIENCE. 423 



a new bridge or roof. Cremona ^ says of this branch of graphical methods, 

 ' No section of graphical statics is more brilliant, or shows more effectu- 

 ally the services that geometry is able to render to mechanics, than 

 the one dealing with reciprocal figures and framed structures with constant 

 load.' It is in the use of purely geometrical methods of reasoning as the 

 bases of graphical construction that the English engineers do not at 

 present claim much interest. 



That one or two leading minds have here and there made important 

 contributions to the subject, notably the late Professor Clerk Maxwell 

 in giving the world the theory of reciprocal figures, does not in any way 

 vitiate the general truth of the foregoing remarks. 



The fact is, that very few engineers in this country understand even 

 the nature of projective, modern, higher geometry, or geometry of 

 position, by all of which names it is variously called. This is not to be 

 wondered at, since it is scarcely taught at our colleges. Even at Cam- 

 bridge it has so insignificant a place as to be honoured with only one or 

 two questions in the Tripos. At Oxford the attention devoted to it is a 

 little more extended. Professor Henrici, whose article in the ' Encyclopaedia 

 Britannica ' places the elementary propositions of geometry clearly before 

 English readers," has always made the subject part of his mathematical 

 course of instruction, but it takes little, if any, part in the course of the 

 ordinary mathematical education of an engineer. 



But England does not stand alone in this respect, for the French 

 translators of Culmann's work — three engineers ^ — remark : — 



' The reading of this work requires the knowledge of what was termed 

 recently higher geometry, and which is now called geometry of position, 

 or projective geometry. Although this science is not officially taught in 

 our schools, we hope this will not prove an obstacle to the spreading of 

 graphic statics.' And Culmann himself said in the preface of the first 

 edition of his work : — 



' We have experienced unspeakable difficulties in securing for the 

 students attending our lectures a possession of the requisite preliminary 

 knowledge, by ensuring that geometry of position was made by the 

 educational authorities an obligatory subject of study. We have 

 lectured on graphic statics as long ago as 1860, yet it was not until 

 1864 that the students were provided with the requisite preliminary 

 instruction in geometry by means of an obligatory six-months course of 

 lectures.' But he goes on further to remark : ' For the engineer, and 

 for the technical man generally, geometrical instruction is no .less 

 important than analytical instruction ; he has always to deal with the 

 graphic representation of configurations of space. How useful, then, must 

 it be to him to have his stereographic perception trained and developed 

 to a certain extent, thus enabling him to resolve with ease plane pro- 

 jections into solid bodies, and to conceive in his mind a stereoscopic 

 view of the whole work of construction or machinery which is to be 

 executed. How much more progress might be made in graphic geometry, 



' Preface to English translation of Le Figvre Ttec'iproclte nella Statica Grafica 

 (L. Cremona, Milano, 1870), by Professor T. Hudson Bears. Clarendon Press, Oxford, 

 1890. 



- The excellent translation of Cremona's Geometria Progettica, by Mr. Charles 

 Leudesdorf, M.A., Clarendon Press, Oxford, should also be noted. 



' G. Glasson and J. Jacqmer, Ing^nieurs des Ponts et Chaussees, and A. Valet, 

 Ingenieur Civil. 



