158 RECORD AND RESULTS OP 



That low water which follows the moon's upper transit (about 17 hours) when 

 she has north declination is the lower of the two, provided it happens ten days after 

 the zero declination ; if before, it is the higher of that day. A similar restriction, 

 of two days only, applies to the rule for the highest high water. 



Diurnal Inequality in Time. — The inequality in time is best exhibited by means 

 of diagrams, the abscissae of which are the times of high or low water, and the ordi- 

 nates the corresponding lunitidal intervals, both taken from Table II. Lunitidal 

 intervals from the upper transits are indicated by dots ; intervals from the lower 

 transits by small circles. The observations of the winter series proved somewhat 

 too rough for the elucidation of this inequality — they were taken every half hour ; 

 the diurnal mequality, nevertheless, is sufficiently indicated to make out its general 

 law. I shall here confine this investigation to the second series, for which we have 

 observations every ten minutes ; the results are given on Plate II for high water 

 and low water separately. The inequality, proper, is shown imderneath, where the 

 middle line between the full and broken curves of inequality is straightened out 

 and forms the axis of abscissae, upon which the time inequalities, as ordinates, have 

 been plotted. From these curves we find the retard of the time inequality for high 

 water from three intersections with the axis equal 11.0 days, and that of low water 

 equal 2.2 days. A comparison of these time-curves of Plate II with the height- 

 curves of Plate I, indicates a strong similarity in character between the height 

 inequality oihigh water and the time inequality of low water; for these curves the 

 average epoch is two days, and the alternation each semi-lunation of the signs or 

 full curves above and heloio the axis correspond ; a similar correspondence of epoch, 

 which is on the average 10.4 days, and of alternation of the signs exists in the time 

 inequality of high water and the height inequality of low water. This is not an 

 accidental relation, but has been recognized at other stations, the first and conspi- 

 cuous notice of it I find in the U. S. Coast Survey Report for 1853, p. *79 in the 

 tidal discussion by A. D. Bache, Superintendent, of Rincon Point, San Francisco, 

 California. 



The greatest range of the time inequality is for the high waters 46", and for the 

 low waters 58"", the first from two, the last from three determinations. 



Eespecting the relative magnitude of the inequality we have, on the one hand, 

 the smaller time and greater height inequality in high water, and on the other, the 

 greater time and smaller height inequality in low water. 



A similar relation of magnitudes occurs at Rincon Point, but it is the reverse of 

 that just stated, in conformity with the more prominent development of the diurnal 

 inequality in the height of low waters in San Francisco Bay. 



The interval of that high water which follows the moon's upper transit (about 11 

 hours) when she has north declination will be the smaller one, provided it happens 

 11 days after the moon's zero declination ; if before, it will be the greater of the twa 

 of that day. The interval of that low water which follows the moon's upper transit 

 (about 17 hours) when she has north declination will be the greater of the two pro» 

 vided it happens two days after the moon's zero declination ; if before, it will be 

 the earlier one. The reverse takes place for south declination, or for lower transit. 



The time-inequality of the low water of the second series can be represented well 



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