Repository: UIHistories Project: Mathematical Models Catalog of a Collection of Models of Ruled Surfaces [PAGE 4]

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Fig- 1 is an example of thefirst,and Fig. 2 of the second. In both cases, the curve, although not actually drawn, is indicated with sufficient approximation for most practical purposes. Models Nos. 10 and 30 also afford illustrations of the principle exhibited in Fig. 2. T h e models are constructed with especial reference to the possibility of changing their shape, by moving some of the supports of the strings, by altering the lengths or positions of certain parts, or by converting upright forms into oblique. This possibility of deformation, as the process is technically called, greatly enhances the value of the models, by allowing them to represent a m u c h greater variety of surfaces than if they were fixed. They are, however, too delicate to be m u c h pulled about, and, unless they are very cautiously handled, the strings are apt to become entangled or break. They should never be used except by a person w h o understands them, and they should not be shifted without some good reason. In order to m a k e this collection as useful as possible to the student of geometry, it has been thought advisable to give, in an appendix, a short account of the application of analysis to the investigation of these surfaces, and of their properties. T h e statement of these properties is scattered over a great number of treatises and tracts, and there exists no single work which gives a full account of ruled surfaces. T h e appendix, of course, requires some knowledge of analytical geometry of three dimensions. A n y of the smaller modern treatises, such as A l d i s or L e r o y , contain more than is necessary as an introduction to the subject. T h e statements in the appendix have been chiefly taken from M o n g e ' s Applications de I''Analyse a la Geometrie. Geometrical drawings of most of the surfaces represented by these models are contained in Bradley's Practical Geometry (2 vols., oblong folio, published by C h a p m a n and Hall). M a n y of them will also be found in the French treatises on practical and descriptive geometry, such as

Leroy, Adhemar, Leeebcjre de Fourcy, De la

Gottrnerie, and in their treatises on Stereotomy and Stonecutting (coupe des pier res). M a n y of them are also given in Sonnet's Dictionnaire des MatEematiques Appliquees.