TEMPERATURE OBSERVATIONS IN LOCH EARN. 759 



As this was after a prolonged period of calm it may be assumed that this distribu- 

 tion is typical for the whole loch. Applying the principles described in the previous 

 Loch Earn calculation, the discontinuity must be taken as occurring at a depth of 

 12 metres. The area of the surface of discontinuity at this depth is 1830 x 48010 

 square feet as compared with an area of 1683x48010 square feet for a depth of 

 16 metres in 1911. 



Assume that the minimum of the normal curves is proportional to <r(v) at the 

 deepest point in the loch, i.e. at sounding-line 10. In 1911 the value of <r(v) for 

 this line was '04104 units, and a similar calculation for the distribution of 1913 

 gives '02850 units. The calculated period for the temperature seiche in 1911 was 

 14'99 hours, hence, using the above formula, the corresponding period for 1913 is 



T= 14-99 x 1830 xJ4104 hopra 

 1683 x 72850 

 = 196 hours. 



This is the period of the uninodal seiche, and, assuming that the ratio between 

 the periods of the uninodal and binodal seiches is the same for the temperature as 

 for the ordinary seiche, the period of the binodal seiche would be 11 '0 hours. It 

 will be seen later that the agreement between the observed and the calculated period 

 is good in the case of the uninodal period, though not so good in the case of the 

 binodal period — probably because the assumptions on which the calculation is based 

 do not hold in the case of the higher nodalities as the ratio between the wave-length 

 and the depth of the loch becomes smaller. 



Periodogram Analysis. 



The observations at No. 2 boat during the last week were subjected to periodo- 

 gram analysis to determine the main periods which were present. In the case of 

 an oscillation which dies away so rapidly as do temperature seiches the ordinary 

 periodogram method as used for the analysis of astronomical observations cannot 

 be used, as there is not a sufficient number of periods to work with. A slight 

 modification of the method gives a good idea of the component periods of the 

 oscillation. 



For the purpose of the analysis the variation in depth of the 11° isotherm was 

 considered, as this isotherm seemed to be most nearly at the discontinuity on its 

 lower side, and therefore free from surface disturbances. The average depths of this 

 isotherm during successive intervals of 50 minutes were taken from the graph 

 drawn from the observations, and since the determination of the period is not 

 affected by the addition or subtraction of a constant from these depths, the constant 

 10 was subtracted to make the computation simpler. 



The numbers obtained are given in the following table : — 



