1868.] Bombay and Kurrachee, 415 



The character of the diurnal tide and the highly complex conditions 

 under which its constantly varying solar and lunar component parts are 

 combined are then traced. Being entirely dependent on the declinations 

 of the sun and moon, the solar element vanishes twice a year, and the 

 lunar element twice a month, each reappearing after the solar or lunar 

 equinox, with its times of high and low water reversed. 



The diurnal tide produces a diurnal inequality in height and time of 

 high and low water, affecting simultaneously respectively high-water time 

 and low-water height, and high-water height and low-water time. In par- 

 ticular cases, the actual values of height and time of diurnal tide may be 

 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 sem.idiurnal, the retard 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 inequa- 

 lity with their physical causes was then explained. A hypothetical 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 being combined with a series of semidiurnal tides 

 deduced from the diagram of observations, the diurnal inequalities so obtained 

 were compared with the actual diurnal inequalities. It was then found that 

 a further element was wanting, which was approximately and provisionally 

 obtained by the introduction of a second empirical dhu-nal lunar tide of 

 twelve inches maximum half-range at Bombay, and six inches at Kurra- 

 chee. 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 an opinion that this empirical correction might probably be superseded by 

 one more consistent 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 Kurra- 

 chee 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 suc- 

 cessful 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 ine- 



