III. MODELS. 23 



the Industrial Arts. It is only in small work, -which can be put into the 

 lathe, that the class of surfaces of revolution approaches them, in respect of 

 general utility. The most important surfaces of all, the plane, the right 

 cylinder, the right cone, and the common screw, belong to both classes. 



The representation of the surfaces by means of silk threads is of course 

 only approximate ; an approximation of the same character as the representa- 

 tion of a curve by a dotted or chain line, Fig. I, or by a series of right lines 

 touching the actual curve, Fig. 2. 



The 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 

 much greater variety of surfaces than if they were fixed. They are, how- 

 ever, too delicate to be much 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 who understands them, and they should not be 

 shifted without some good reason. 



FIG. 1. FIG. 2. 



Fig. 1 is an example of the first, and Fig. 2 of the second. In both cases, 

 the curve, although not actually drawn, is indicated with sufficient approxi- 

 mation for most practical purposes. Models Nos. 10 and 30 also afford illus- 

 trations of the principle exhibited in Fig. 2. 



Geometrical drawings of most of the surfaces represented by these models 

 are contained in BRADLEY'S Practical Geometry (2 vols., oblong folio, pub- 

 lished by Chapman and Hall). Many of them will also be found in the 

 French treatises on practical and descriptive geometry, such as LEROY, 

 ADHEMAR, LEFEBURE DE FOURCY, DE LA GOURNERIE, and in their treatises 

 on Stereotomy and Stone-cutting (coupe des pierres). Many of them are also 

 given in SONNET'S Dictionnaire des Math^matiques Appliqu6es. A catalogue 

 of this collection of models, with an appendix containing an account of the 

 application of analysis to their investigation and classification, was prepared 

 for the South Kensington Museum in 1872, by Mr. C. W. Merrifield, F.B.S. 

 The following descriptions are extracted from this catalogue : 



77. Hyperbolic Paraboloid generated by a single system 

 of right lines. 



Two bars, each pierced with holes, equally spaced. One bar is fixed, 

 the other swings round an axis, which, moreover, can be inclined at different 

 angles to the fixed bar. 



When the bars are parallel the strings indicate a plane. When they are 

 clined to one another, but still in the same plane, the strings still indicate a 



