xui.J MEASUREMENT OF PHENOMENA. 287 



approach a delicately balanced needle without disturbing 

 it. Under these circumstances the only mode of proceed- 

 ing with accuracy, is to attach a very small mirror to the 

 moving body, and employ a ray of light reflected from 

 the mirror as an index of its movements. The ray may 

 be , considered quite incapable of affecting the body, and 

 yet by allowing the ray to pass to a sufficient distance, 

 the motions of the mirror may be increased to almost any 

 extent. A ray of light is in fact a perfectly weightless 

 linger or index of indefinite length, with the additional 

 advantage that the angular deviation is by the law of 

 reflection double that of the mirror. This method was 

 introduced by Gauss, and is now of great importance ; 

 but in Wollaston's reflecting goniometer a ray of light 

 had previously been employed as an index. "Lavoisier 

 and Laplace had also used a telescope in connection with 

 the pyrometer. 



It is a great advantage in some instruments that they 

 can be readily made to manifest a phenomenon in a greater 

 or less degree, by a very slight change in the construction. 

 Thus either by enlarging the bulb or contracting the tube 

 of the thermometer, we can make it give more conspicuous 

 indications of change of temperature. The ordinary baro- 

 meter, on the other hand, always gives the variations of 

 pressure on one scale. The torsion balance is remark- 

 able for the extreme delicacy which may be attained 

 by increasing the length and lightness of the rod, and the 

 length and thinness of the supporting thread. Forces so 

 minute as the attraction of gravitation between two balls, 

 or the magnetic and diamagnetic attraction of common 

 liquids and gases, may thus be made apparent, and even 

 measured. The common chemical balance, too, is capable 

 theoretically of unlimited sensibility. 



The third mode of measurement, which may be called 

 the Method of Eepetition, is of such great importance and 

 interest that we must consider it in a separate section. It 

 consists in multiplying both magnitudes to be compared 

 until some multiple of the first is found to coincide very 

 nearly with some multiple of the second. If the multipli- 

 cation can be effected to an unlimited extent, without the 

 introduction of countervailing errors, the accuracy with 

 which the required ratio can be determined is unlimited 



