186 Dr. C. Ctiree on Applications of Physics 



or in seconds of arc 



slope at O = 0"-033 (26) 



Taking next c = 2b, we replace (26) by 



slope at O = // -10 (27) 



If, for instance, the river be 100 yards broad, the first 

 station is 400, the second 100 yards from the bank. 



§ 17. As rivers are seldom straight, I have supplemented 

 the above by calculating the slope at the centre of a semi- 

 circular channel of width "2b, supposed small compared to the 

 radius R. For a difference h in the level of high and low 

 water, 1 find as a first approximation 



difference of slope at centre of semicircle = 2(1 — rj)gb hjirnR. (28) 



To aid the imagination, the river may be supposed to enter 

 and leave the semicircle by straight channels forming con- 

 tinuations of the limiting diameter, so that the semicircular 

 portion alone need be considered. 



It will be noticed that (22) and (28) are identical if 



c = R, and p=gli. 



In other words, the semicircular tidal river has exactly the 

 same influence on the slope of the station at its centre as it 

 would have if the channel were straight throughout and came 

 within the same distance of the station. 



§ 18. The results of the last two paragraphs point to changes 

 of water-level in tidal rivers and estuaries as more likely to 

 appreciably affect the level of neighbouring observatories 

 than any probable differential peculiarities of rainfall or 

 evaporation. In making this observation I exclude of course 

 the direct action of water on the foundations of the building. 



In all cases similar to those treated in §§ 14-17 the direct 

 gravitational action of the load must be taken into account to 

 obtain the full result. For instance, in the case of an anti- 

 cyclone, the horizontal attraction of the surplus air must be 

 considered as well as the excess of pressure over the area 

 covered by the anti-cyclone. 



Pressure Effects below the Surface. 



§ 19. As the foundations of most buildings are below the 

 ground-level, the slope at some little depth possesses con- 

 siderable interest. The general formula (14) for the depression 

 at any depth due to a loaded rectangle, though easily evaluated 

 for specified numerical values of z 9 x, &c, is somewhat com- 



