GEXKRAL CONSIDERATIONS 



direction in which the corresponding point of the instrument would 

 be left ftve to move by the other bearings must be as nearly as possible 

 normal to the tangent plane at the bearing. 



(This condition implies that, of the normals to the tangent planes at the 

 bearings, no two coincide; no three are in one plane, and either meet in a 

 point or are parallel ; no four are in one plane, or meet in a point, or are 

 parallel, or, more generally, belong to the same system of generators of an 

 hyperboloid of one sheet. The conditions for five normals and for six are more 

 complicated.)* 



These uomjiiinnt are satisfied by the well-known method of forming on the 

 fixed base three V grooves, whose sides are inclined 45* to the base, and whose 

 directions meet in a point at angles of 120. The instrument has three feet ; 

 the end of each foot is, roughly speaking, conical, but so rounded off that it 

 bears against the two sides of the groove, and cannot reach the bottom. The 

 instrument has thus six solid bearings, and is kept in its place by its weight, 

 without being subjected to any unnecessary strain. 



Sir William Thomson, who has bestowed much attention on this subject, 

 has adopted a somewhat different arrangement in some of his instruments. A 

 triangular hole, like that formed by pressing an angle of a cube into a mass 

 of clay, is formed in the base, and a V groove is cut in a direction passing 

 through the centre of the hole. The three feet of the instrument are all rounded, 

 but of different lengths. The longest stands in the triangular hole, and has 

 three bearings ; the second stands in the V groove, and has two bearings ; and 

 the third stands on the horizontal plane of the base, and has one bearing. 

 There are, thus six bearings in all. This method, though it does not give so 

 large a margin of stability as the method of three grooves, has this advantage, 

 that as each of the three feet is differently formed, it is impossible to put 

 any but the proper foot into the hole without detecting the mistake. 



5. BEARINGS OF MIRRORS. 



In mounting mirrors it is especially important to attend to the number 

 and position of their bearings, for any stress on the mirror spoils its figure, 

 and renders it useless for accurate work. 



See Ball on the Theory of Screwt. 



