Movements of the Ground. 197 



lines through Q and P, it is evident that the parts Q D and 

 C E will expand by the same amount after a given change of 



Tig. 3. 



external temperature ; and the rise of P relatively to Q will 

 be due to the expansion of the part P C. Thus, as the tem- 

 perature rises, the end P of a level P Q will rise. 



As the temperature falls, on the other hand, the end P will 

 fall after a short interval, and the bubble of the level will pass 

 through its zero-point when the average temperature of P C 

 is equal to its initial value. 



Now M. Plantamonr finds that, with the ground sloping in 

 a direction nearly east, the rise and fall of the east end of the 

 level follow after a short interval the rise and fall of the 

 external temperature. 



Again, the length of the line P C is greatest when the line 

 P Q is perpendicular to the horizontal section of the isothermal 

 surface through Q, that is, when the line P Q is parallel to 

 the direction of the slope of the ground outside. Hence, the 

 directions of greatest change of inclination and of the general 

 slope of the ground should coincide. 



Also, since the range of temperature due to a given change 

 of external temperature diminishes as the depth below the 

 surface of the ground increases, the change of level due to that 

 change of external temperature must diminish as the distance 

 from the ground increases. So that two levels 'placed near one 

 another in the same cellar, hut at different distances from the 

 surface, should indicate different variations of level. And the 

 variations may even be in opposite directions when the changes 

 of external temperature take place in opposite directions. 



Other conditions being the same, moreover, the extent of 

 the movement varies as the tangent of the inclination of the 

 land ; and this shows the desirability of choosing level ground 

 for observatory-sites. 



