Mr. W, Parkes on the Tides of Bombay and Kurrachee. 231 



water time. In particular cases, the actual values of height and time 

 of diurnal tide may he directly deduced from the values of diurnal 

 inequality, From these it was found that diurnal tide follows the 

 moon's movements at a much shorter interval than semidiurnal, the 

 retardation of the former being from two to three hours only, while 

 that of the latter is from thirty-four to thirty-six hours. 



The mode adopted for identifying the varying values of diurnal 

 inequality with their physical causes was then explained. A hypo- 

 thetical series of diurnal tides, based on the varying values of the 

 declination of the sun and moon, was calculated, the necessary local 

 constants being deduced from the particular cases in which their 

 values could be directly obtained. These hypothetical diurnal tides 

 hemg combined with a series of semidiurnal tides deduced from the 

 diagram of ohservations, the diurnal inequalities so obtained were com- 

 pared with the actual diurnal inequalities. It was then found that a 

 further element was wanting, which was approximately and provi- 

 sionally obtained by the introduction of a second empirical diurnal 

 lunar tide of twelve inches maximum half-range at Bombay, and 

 six inches at Kurrachee. This tide was assumed, like the first and 

 principal diurnal tide, to be dependent on the moon's declination, 

 but to vanish at intervals of two or three days, before the moon 

 crossed the equator. The author expresses an opinion that this em- 

 pirical correction might probably be superseded by one more con- 

 sistent with physical causes, if more extended and more correct 

 observations were subjected to investigation. 



Lastly, the comparison of calculated heights and times with the 

 records of observations for four months at Bombay and eight months 

 at Kurrachee were given. This showed that three calculated tides 

 out of four were correct within three inches in height and fifteen 

 minutes in time, the errors of the remainder ranging up to nine 

 inches in height, and thirty minutes in time. 



Since receiving the observations made at Bombay and Kurrachee 

 in the year 1867, the author has subjected them to another process 

 for obtaining the actual times and heights of diurnal tide, which 

 has been more successful than that described in the paper. 



The only data made use of were the diurnal inequalities in height 

 at high and low water — the range of semidiurnal tide and the diurnal 

 inequality in time, which were necessary to the previous process, 

 being now altogether disregarded. 



The diurnal inequalities in height were obtained by measuring the 

 widths of the brown spaces where they were crossed by the vertical 

 lines representing noon on successive days. The two daily values 

 thus obtained are respectively the sine and cosine of an angle which 

 represents the difference in time between semidiurnal and diurnal 

 tide. Dividing the low-water by the high-water value gives the 

 cotangent of that angle, and thence the angle itself. Thus the time 

 of actual diurnal tide (first in relation to the time of semidiurnal low 

 water, and then in relation to solar time) was obtained. 



The actual range of diurnal tide was obtained by adding together 

 the squares of the high-water and low- water values (sine and cosine), 

 and taking the square root of the sum. 



