TEMPERATURE OBSERVATIONS IN LOCH EARN. 763 



When subjected to harmonic analysis the 20-hour oscillation is found to be : — 



14-99 + 172 cos (0 - 332°) + I'M) cos (20 - 172°) + 0*10 cos (30 - 185°) 

 + 0*14 cos (40 - 300°) + 0'14 cos (50 - 125°). 



It is thus shown that the uninodal and binodal constituents of this curve are very 

 much more important than those of higher nodality. It will be seen from other 

 considerations that the periods of the trinodal and quadrinodal seiches arc about 

 8 '5 hours and 6"0 hours respectively, and, as these are not approximate aliquot parts 

 of 20 hours, the terms cos 30 and cos 40 cannot be taken to be the mathematical 

 correspondents of the physical trinodal and quadrinodal seiches. 



Harmonic Analysis. 



In order to investigate the variations of the amplitudes and of the periods of 

 the several component seiches during the series of observations which were subjected 

 to periodogram analysis, the harmonic analysis of the 11° isothermal at both 

 stations, and of the 10° isothermal at Station 2, was undertaken. 



The period chosen was 20 hours. This period is exactly 24 of the " intervals " 

 used above, and hence the method of 24 ordinates could be immediately applied 

 to the numbers given in Table IV without any troublesome interpolation. All 

 the calculations were made on the harmonic-analysis computation forms devised 

 by Professor Whittaker for use in the Mathematical Laboratory of the University 

 of Edinburgh. 



The results for the 11° isothermal are given in Table VII (page 764). The numbers 

 in italics refer to Station 1, and those in Roman type to Station 2. The results are 

 also shown graphically in fig. 17, the dotted curve referring to Station 1 and the 

 continuous line to Station 2. 



The whole series of 140 intervals was divided into groups of 24 intervals each, 

 viz., 1-24, 25-48, etc., and, in addition, intermediate groups were taken — 13-36, 

 37-60, etc. The time of the middle point of these groups is shown in the column 

 of time in the table. 



We shall now examine the curves composing fig. 17. 



1. The Amplitude of the Uninodal Seiche. — The amplitude is seen to be about 

 2"0 metres for the first period, and to rise through 2*5 metres to a maximum of about 

 3*6 metres at the group whose mid-time was 25th August 17 h. On the 24th and 

 25th there was an alternation of westerly winds of moderate strength with calms, and 

 these may have been so timed as to build up the uninodal seiche in preference to 

 the binodal. The increase of amplitude may also have been partly due to the 

 gradual resolution of a travelling bore into a steady wave, as is suggested on page 758, 

 where there is also a description of the weather conditions before the commencement of 

 the series. During the next 36 hours there is a gradual fall in the amplitude of the 



