PREFACE. XXvii 



Airy's Function of Stress. The methods which in this paper were attended with so much 

 success, seem to have suggested to Maxwell a reconsideration of his former work, with the 

 view of extending the character of the reciprocity therein established. Accordingly in 1870 

 there appeared his fourth contribution to the subject, "On reciprocal figures, frames and 

 diagrams of forces." This important memoir was published in the Transactions of the Royal 

 Society of Edinburgh, and its author received for it the Keith Prize. He begins with a 

 remarkably beautiful construction for drawing plane reciprocal diagrams, and then proceeds 

 to discuss the geometry and the degrees of freedom and constraint of polyhedral frames, 

 his object being to lead up to the limiting case when the faces of the polyhedron become 

 infinitely small and form parts of a continuous surface. In the course of this work he 

 obtains certain results of a general character relating to inextensible surfaces and certain 

 others of practical utility relating to loaded frames. He then attacks the general problem of 

 representing graphically the internal stress of a body and by an extension of the meaning 

 of "Diagram of Stress," he gives a construction for finding a diagram which has mechanical 

 as well as geometrical reciprocal properties with the figure suppose^ to be under stress. It 

 is impossible with brevity to give an account of this reciprocity, the development of which 

 in Maxwell's hands forms a very beautiful example of analysis. It will be sufficient to 

 state that under restricted conditions this diagram of stress leads to a solution for the 

 components of stress in terms of a single function analogous to Airy's Function of Stress. 

 In the remaining parts of the memoir there is a discussion of the equations of stress, and 

 it is shewn that the general solution may be expressed in terms of three functions analogous 

 to Airy's single function in two dimensions. These results are then applied to special 

 cases, and in particular the stresses in a horizontal beam with a uniform load on its upper 

 surface are fully investigated. 



On the subjects in which Maxwell's investigations were the most numerous it has 

 been thought necessary, in the observations which have been made, to sketch out briefly 

 the connections of the various papers on each subject with one another. It is not how- 

 ever intended to enter into an account of the contents of his other contributions to science, 

 and this is the less necessary as the reader may readily obtain the information he may 

 require in Maxwell's own language. It was usually his habit to explain by way of 

 introduction to any paper his exact position with regard to the subject matter and to 

 give a brief account of the nature of the work he was contributing. There are however 

 several memoirs which though unconnected with others are exceedingly interesting in them- 

 selves. Of these the essay on Saturn's Rings will probably be thought the most important 

 as containing the solution of a difficult cosmical problem; there are also various papers on 

 Dynamics, Hydromechanics and subjects of pure mathematics, which are most useful con- 

 tributions on the subjects of which they treat. 



The remaining miscellaneous papers may be classified under the following heads: (a) 

 Lectures and Addresses, (6) Essays or Short Treatises, (c) Biographical Sketches, (d) Criticisms 



and Reviews. 



d 2 



