A SCIENTIFIC APPARATUS. 



our instruments are solid, but not rigid. They are liable to 

 change of form under stress, but such change of form is not 

 desirable, except in certain special parts, such as springs. 



Hence, if a solid piece is constrained in more than six ways it 

 will be subject to internal stress, and will become strained or dis- 

 torted, and this in a manner which, without the most exact micro- 

 metrical measurements, it would be impossible to specify. 



In instruments which are exposed to rough usage it may some- 

 times be advisable to secure a piece from becoming loose, even at 

 the risk of straining and jamming it ; but in apparatus for accurate 

 work it is essential that the bearings of every piece should be 

 properly defined, both in number and in position. 



4. METHODS OF PLACING AN INSTRUMENT IN A DEFINITE 

 POSITION. 



When an instrument is intended to stand in a definite position 

 on a fixed base it must have six bearings, so arranged that if one 

 of the bearings were removed the direction in which the corre- 

 sponding point of the instrument would be left free 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 compli- 

 cated.)* 



These conditions are satisfied by the well-known method of 

 forming on the fixed base three V grooves, whose sides are in- 

 clined 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 

 * See Ball on the Theory of Screws. 



