THE SEICHES OF LOCH EARN. 381 



Taking C.G.S. units, as before, let v be the volume of the statoscope cylinder 

 together with the connecting tube and the part of the well occupied by air ; 



w be the section, and a the diameter of the well, so that w = 7ra 2 /4 ; 



/ the length and b the diameter of the access tube ; 



x and y the heights above mean level at time t of the water-level in the well and 

 outside in the lake respectively ; 



p the pressure of the air inside the well and statoscope ; w the atmospheric pressure. 

 Then 



p- 0) = 0)WX/(v - wx) = (x)lVx/u . . . . (11)) 



since x is small. 



The equation (3) of p. 375 is therefore replaced by 



Hence we have 



where 

 so that 



— ira? dx { Oil ox . ) 7rZ/ 4 



§ + (4, + X ),: = x2/ .... (12), 



(14). 

 If now we consider a seiche of period 1-KJn, so that y = A sin nt, we get 



d> 7rcoa 2 , oho q<{> 

 ~ = and — = Ol 



X 4 ^ ® X 



x = ( , J A cos nr sin n(t - r) . . . (15), 



where 



tan nr = n/(cf) + x) ..... (16). 



The reading of the instrument is proportional to the difference between the pressure 

 in the cylinder and in the outside air, i.e. to p — v, which is equal to (wwjv)x. Using 

 (14), we get 



p- oi= {#<£/(<£ + x)} A cos nr sin ?i(t-r) . . . (17). 



Essentially, therefore, a statolimnograph acts like an ordinary limnograph whose 

 reduction constant has been increased by <f>. 



For the well actually used a = 14*3 cm. ; and v, which varied a little according as the 

 well was placed more or less deeply in the lake, would be about 1600tt cm. From these 

 data we find <f>/x to be about 33. Speaking roughly, therefore, the statolimnograph 

 acts like an ordinary limnograph whose reduction constant is <£ = 7T(y& 4 /128M^ ; or, more 

 exactly, in our particular arrangement, like an ordinary limnograph having a reduction 

 constant thirty-four times as large as that belonging to the well and access tube actually 

 used. 



The magnification for infinitely slow alterations of pressure was found by actual 

 experiment to be about 3*72. 



