380 Uoyal Society, 



Tides. Seventh Series. On the Diurnal Inequality of the Height of 

 the Tide, especially at Plymouth and at Sincapore : and on the Mean 

 Level of the Sea." By the Rev. W. Whewell, A.M., F.R.S., Fellow 

 of Trinity College, Cambridge. 



The diurnal inequality which the author investigates in the present 

 paper, is that by which the height of the morning tide differs from that 

 of the evening of the same day j a difference which is often very con- 

 siderable, and of great importance in practical navigation, naval offi- 

 cers having frequently found that the preservation or destruction of 

 a ship depended on a correct knowledge of the amount of this varia- 

 tion. In the first section of the paper he treats of the diurnal ine- 

 quality in the height of the tides at Plymouth, at which port good tide 

 observations are regularly made at the Dock Yard 3 and these obser- 

 vations clearly indicate the existence of this inequality. As all the 

 other inequalities of the tides have been found to follow the laws of 

 the equilibrium theory, the author has endeavoured to trace the laws 

 of the diurnal inequality by assuming a similar kind of correspond- 

 ence with the same theory; and the results have confirmed, in the 

 most striking manner, the correctness of that assumption. By taking 

 the moon's declination four days anterior to the day of observation, 

 the results of comj)utation accorded, with great accuracy, with the 

 observed heights of the tides : that is, the period employed was the 

 fifth lunar transit preceding each tide. 



In the second section, the observations made on the tides at Sin- 

 capore from August 1834 to August 1835, are discussed. A diurnal 

 inequality was found to exist at that place, nearly agreeing in law and 

 in amount with that at Plymouth ; the only difference being that, in- 

 stead of four days, it was found necessary to take the lunar declina- 

 tion a day and a half preceding the tide ; or, more exactly, at the in- 

 terpolated, or north lunar transit, which intervened between the se- 

 cond and third south transit preceding the tide. The diurnal inequality 

 at Sincapore is of enormous magnitude, amounting in many cases to 

 six feet of difference between the morning and evening tides ; the 

 whole rise of the mean tide being only seven feet at spring tides, and 

 the difference between mean spring and neap tides not exceeding two 

 feet. 



In the third section, the author considers the diurnal inequalities 

 at some other places, and the general law of its progress. The change 

 which the epoch, (that is, the anterior period at which the moon's de- 

 clination corresponds to theamountand direction of the inequality,) in 

 particular, undergoes, is a subject of great interest. At Liverpool, 

 the epoch is found to be about six days and a quarter ; at Bristol, it 

 is nearly six days ; and at Leith, it is as much as twelve days. On 

 the east coast of America, it appears to be zero. On the coasts of 

 Spain, Portugal, and France, it is successively two, and three days j 

 and on those of Cornwall and Devonshire, four days 3 thus observing 

 a tolerably regular augmentation as it is traced along the line of coast 

 from the shores of the Atlantic to the Firth of Forth, but travelling 

 more slowly than the other inequalities. 



