CHAP. IX.] TIDES 237 



immediately following the transit that occurs between 11^ and 

 12'\ then between 12'' and V\ then V' and 2', and so on to 10^ 

 and 1 V\ The mean of each class of transits being taken from 

 the mean of the high water following that transit, the remainder 

 shows the mean interval after that mean transit (see Table I.). 



5. Having thus obtained the twelve mean intervals, then, 

 on a sheet of squared paper (the horizontal lines being con- 

 sidered ordinates, and the vertical lines the abscissae), set ofi 

 the successive mean intervals as ordinates, the moon's transit 

 being the abscissae. 



Through the extremity of these ordinates draw a curve, and 

 the ordinate of this curve that corresponds to the moon's 

 transit O*' or 12^ is the time of H. W. F. and C. given on the 

 Admiralty charts (see Diagram I.), This is the vulgar estab- 

 lishment, the mean establishment being the mean of all the 

 intervals after the moon's transit. 



6. The heights of high and low water as ordinates are laid 

 off in a similar way to the intervals, the time of the moon's 

 transit, as before, being the abscissae. Through the extremity 

 of these ordinates draw a curve, and the difference betAveen the 

 minimum, or least height of low water, and the ynaximum, or 

 greatest height of high water, shows the mean spring range or 

 rise ; the difference between the inaximum height of low water 

 and the minimum height of high water gives the mean neap 

 range ; and the difference between the minimum height of low 

 water and the minimuin height of high water the mean neap 

 rise (see Diagram II.). Where the diurnal irregularity is 

 great, the results should be given both for the maximum and 

 minimum tides. 



7. The 7niniynum height of low water is assumed as the zero 

 or mean low-water level at springs, being the level to which 

 the soundings on the Admiralty charts are reduced, and also 

 the zero or standard level from which the heights given in the 

 Admiralty Tide Tables are calculated. The zero of the tide- 

 scale (as in Diagram II.) may be some feet below the mean 

 low water or zero here assumed, in order to embrace the 

 range of the equinoctial tides. 



As an example, Table I. shows the procedure described 

 above, the times and heights of high and low water being taken 

 from a series of tidal observations taken at Dunbar. 



