XXVI PREFACE. 



Hamilton's characteristic function for a narrow beam of light," he considers the more general 

 question of the passage of a ray from one isotropic medium into another, the two media 

 being separated by a third which may be of a heterogeneous character. He finds the most 

 general form of Hamilton's characteristic function from one point to another, the first being 

 in the medium in which the pencil is incident and the second in the medium in which 

 it is emergent, and both points near the principal ray of the pencil. This result is then 

 applied in two particular cases, viz. to determine the emergent pencil (1) from a spectroscope, 

 (2) from an optical instrument symmetrical about its axis. In the third paper (1875) he 

 resumes the last-mentioned application, discussing this case more fully under a somewhat 

 simplified analysis. 



It may be remarked that all these papers are connected by the same idea, which was 

 first to study the optical effects of the entire instrument without examining the mechanism 

 by which these effects are produced, and then, as in the paper in 1858, to supply whatever 

 data may be necessary by experiments upon the instrument itself. 



Connected to some extent with the above papers is an investigation which was published 

 in 1868 " On the cyclide." As the name imports, this paper deals chiefly with the geometrical 

 properties of the surface named, but other matters are touched on, such as its conjugate 

 isothermal functions. Primarily however the investigation is on the orthogonal surfaces to 

 a system of rays passing accurately through two lines. In a footnote to this paper Maxwell 

 describes the stereoscope which he invented and which is now in the Cavendish Laboratory. 



In 1868 was also published a short but important article entitled " On the best arrange- 

 ment for producing a pure spectrum on a screen." 



The various papers relating to the stresses experienced by a system of pieces joined 

 together so as to form a frame and acted on by forces form an important group connected 

 with one another. The first in order was "On reciprocal figures and diagrams of forces," 

 published in 1864. It was immediately followed by a paper on a kindred subject, " On 

 the calculation of the equilibrium and stiffness of frames." In the first of these Maxwell 

 demonstrates certain reciprocal properties in the geometry of two polygons which are related 

 to one another in a particular way, and establishes his well-known theorem in Graphical 

 Statics on the stresses in frames. In the second he employs the principle of work to 

 problems connected with the stresses in frames and structures and with the deflections 

 arising from extensions in any of the connecting pieces. 



A third paper "On the equilibrium of a spherical envelope," published in 1867, may 

 here be referred to. The author therein considers the stresses set up in the envelope by 

 a system of forces applied at its surface, and ultimately solves the problem for two normal 

 forces applied at any two points. The solution, in which he makes use of the principle 

 <>f inversion as it is applied in various electrical questions, turns ultimately on the deter- 

 mination of a certain function first introduced by Sir George Airy, and called by Maxwell 



