ON HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 327 



Besides the above there is the constituent M, of speed y — a which consists 

 partly of that of variable amplitude of the principal diurnal species and partly of 

 that of amplitude inversely proportional to the fourtli power of the moon's distance. 

 There is also the ter-diurnal constituent M3 of speed 3(7 — o-) and amplitude 

 inversely proportional to the fourth power of the moon's distance. 



Shallow Water Constituents. 



In shallow water a harmonic constituent is accompanied by others having for 

 their phases multiples of the phase of the primary constituent. Also, two harmonic 

 constituents are accompanied by two others, having for their phases the sum and 

 diflference of the phases of the primary constituents. Some of these shallow water 

 constituents have speeds the same as those of certain primarj' constituents. In the 

 following tables only those shallow water constituents are mentioned which it has 

 been the custom to consider hitherto. 



Primary Constituents affected by Shallow Water Constituents. 



Primary Constituents of 



Meteorological Constituents. 



The observed values of Ssa and Sa are largely of meteorological origin, as also 

 those of S, of speed 7 — rj. 



Besjilts of Analysis. 



5. In order to show how far the results of harmonic analysis of hourly heights 

 represent harmonic constants we give some figures relating to ten different analyses 

 for Bombay. The tidal observatory chosen is regarded as one of the most satisfac- 

 tory, and the results of the analyses of the records taken there are about the most 

 consistent from year to year. 



Each entry in the tables refers to ten different determinations of what ought to 

 be the same constant ; by ' standard deviation ' is meant the square root of the mean 

 of the squares of the differences from the mean. 



It will be noticed that apart from 



M„ S,„ Nj, K„ K„ 0„ P, 



