CONCERNING SCIENTIFIC APPARATUS. 509 



For small mirrors it is best to make one face of the mirror rest against 

 three solid bearings, and to keep it in contact with these by three spring 

 bearings placed exactly opposite to them against the other face of the mirror. 

 These will prevent any displacement of the mirror out of its proper plane. The 

 bearings against the edges of the mirror, by which it is prevented from shifting 

 in its own plane, are, in the case of small mirrors, of less importance. 



When the mirror is large, as in the case of the speculum of a large 

 telescope, a greater number of bearings is required to prevent the mirror from 

 becoming strained by its own weight ; but in all cases the number of fixed 

 bearings at the back of the mirror must be three and only three, otherwise 

 any warping of the framework will entirely spoil the figure of the surface. 



6. BEARINGS OP STANDARDS OF LENGTH. 



It is of the greatest importance that the standard measure of length, by 

 which the national unit of length is defined, should not be exposed to strain. 



The box in which the standard yard is kept in the Exchequer Chamber 

 is provided with bearings, the positions of which have been arranged so that 

 the bar may rest on them with as little strain throughout its substance as is 

 consistent with the fact that it is a heavy body. 



7. ON THE BEARINGS OF MOVABLE PARTS. 



The most important kinds of motion with one degree of freedom are, 

 (1) Rotation round an axis; (2) Motion of translation without rotation; and 

 (3) Screw motion, in which a definite rotation about an axis corresponds to a 

 definite motion of translation along that axis. 



For one degree of freedom five solid bearings are required, the sixth con- 

 dition being supplied by that part of the instrument which regulates the motion 



of the piece. 



The construction of pieces capable of rotation about an axis is better 

 understood than any other department of mechanism. 



In astronomical instruments, four of the bearings are supplied by the two 

 Y's on which the cylindrical end-pieces of the axle rest, and the fifth by the 

 longitudinal pressure of a bearing against one end of the axle, or a shoulder 

 formed upon it. The weight of the instrument is generally sufficient to keep 



