INSTRUMENTS USED IN MEASUREMENT. 59 



-metres or centimetres. But if it has to be expressed with greater 

 accuracy, it must be described in hundredth, or thousandth, or 

 millionth parts of a millimetre ; and this is still done by comparing 

 it with a scale. 



But in order to estimate a length in terms of these very small 

 quantities, it must be magnified; and this is done in three ways. 

 First, geometrically, by what is called a vernier scale. This is a 

 movable scale, which gains on the fixed one by one-tenth in each 

 division. To measure any part of a division, we find how many 

 divisions it takes the vernier to gain so much as that part ; this is 

 how many tenths the part is. The quantity to be measured is 

 here geometrically multiplied by ten. Next, optically, by looking 

 at the length and scale with a microscope or telescope. Third, 

 mechanically, by a screw with a disc on its head, on which there 

 is a graduated rim, called a micrometer screw. If the pitch of the 

 screw is one-tenth and the radius of the disc ten times that of the 

 screw, the motion is multiplied by one hundred. The two latter 

 modes are combined together in an instrument called a micrometer- 

 microscope. Another mechanical multiplier is a mirror which 

 turns round and reflects light on a screen at some distance, as in 

 Thomson's reflecting galvanometer. 



Properly speaking, however, any description of a length by 

 counting of standard lengths is imperfect and merely approximate. 

 The true way of indicating a length is to draw a straight line 

 which represents it on a fixed scale. And this is done by means 

 of self-recording instruments, which measure lengths from time to 

 time on a cylinder in the manner described above. It is only by 

 this graphical representation of quantities that the laws of their 

 variation become manifest, and that higher branch of measure- 

 ment becomes possible which determines the nature of the con- 

 nection between two simultaneously varying quantities. 



W. K. CLIFFORD. 



