368 THE PRINCIPLES OF SCIENCE. [CHAP. 



We are sometimes able to eliminate fluctuations and 

 take a mean result by purely mechanical arrangements. 

 The daily variations of temperature, for instance, become 

 imperceptible one or two feet below the surface of the 

 earth, so that a thermometer placed with its bulb at that 

 depth gives very nearly the true daily mean temperature. 

 At a depth of twenty feet even the yearly fluctuations are 

 nearly effaced, and the thermometer stands a little above 

 the true mean temperature of the locality. In registering 

 the rise and fall of the tide by a tide-gauge, it is desirable 

 to avoid the oscillations arising from surface waves, which 

 is very readily accomplished by placing the float in a cis- 

 tern communicating by a small hole with the sea. Only a 

 general rise or fall of the level is then perceptible, just as 

 in the marine barometer the narrow tube prevents any 

 casual fluctuations and allows only a continued change of 

 pressure to manifest itself. 



Determination of the Zero point. 



In many important observations the chief difficulty con- 

 sists in defining exactly the zero point from which we are 

 to measure. We can point a telescope with great pre- 

 cision to a star and can measure to a 'Second of arc the 

 angle through which the telescope is raised or lowered ; 

 but all this precision will be useless unless we know 

 exactly the centre point of the heavens from which we 

 measure, or, what comes to the same thing, the horizontal 

 line 90 distant from it. Since the true horizon has 

 reference to the figure of the earth at the place of 

 observation, we can only determine it by the direction 

 of gravity, as marked either by the plumb-line or the 

 surface of a liquid. The question resolves itself then into 

 the most accurate mode of observing the direction of 

 gravity, and as the plumb-line has long been found 

 hopelessly inaccurate, astronomers generally employ the 

 surface of mercury in repose as the criterion of horizon- 

 tality. They ingeniously observe the direction of the 

 surface by making a star the index. From the laws 

 of reflection it follows that the angle between the 

 direct ray from a star and that reflected from a surface 

 of mercury will be exactly double the angle between the 



