GEOMETRICAL INSTRUMENTS AND MODELS. 5 1 



importance. The cardboard models of Professor Henrici admit 

 of deformation in a similar manner, since the angle at which the 

 two planes of circular section are inclined to one another may be 

 changed. 



(4.) Models of certain Special Surfaces. 



(a) The Surfaces of Plucker. 



In very recent times the properties of systems of lines in 

 space have been studied with great ardour, chiefly by the German 

 geometers. The consideration of such systems is suggested by 

 many geometrical problems (for example, the study of the straight 

 lines which cut a given surface at right angles, the so-called nor- 

 mals of the surface), but it is also forced upon our notice in all 

 those optical researches in which the properties of systems of rays 

 form the subject of inquiry. A further interest attaches to the 

 study of systems of straight lines in space, inasmuch as an exami- 

 nation of their properties would seem to be an indispensable pre- 

 liminary to the more general inquiry into the properties of systems 

 of curves ; such systems of curves meeting us at every tarn in 

 Physics ; as stream lines in Hydrodynamics, as lines of flow in the 

 theory of the conduction of Heat, as lines of force in the theories 

 of Electricity and Magnetism. 



The present Collection contains a beautiful series of models of 

 a class of surfaces which are found to play an important part in the 

 theory of rectilinear systems. A certain historical interest attaches 

 to these models; they are copies of those exhibited in 1866, at 

 the Nottingham Meeting of the British Association, by the cele- 

 brated mathematician, Julius Plucker, to whom, more than to any 

 other single person, we are indebted for our knowledge of the 

 geometry of systems of lines. They were made by Epkens, of 

 Bonn, and were presented by Dr. Hirst to the London Mathe- 

 matical Society. Professor Hennessy, of the Royal College of 

 Science for Ireland, also exhibits a series of models illustrative of 

 the researches of Plucker. 



(V) The Wave Surface. 



E 2 



