320 Royal Society, 



The height of the sea and "the corresponding height of the mer- 

 cury in the barometer, at every hour in each day, from the 1st No- 

 vember to the 18th December 1848 are given in tables. In these 

 the arithmetic mean of the hourly heights of the sea for each day is 

 taken as the mean level of the sea for that day, and the mean of 

 the hourly heights of the barometer is taken as the corresponding 

 height of the barometer. These mean levels and corresponding 

 mean barometric heights are given in another two-column table, 

 arranged in the order of the days of observation ; and in a third 

 table these are arranged in the order of the heights of the barometer 

 with the corresponding mean levels, without regard to the dates of 

 observation, for the purpose of showing the dependence which the 

 latter have on the former. 



On these tables the author makes the following remarks. The 

 forty-seven days of hourly observations give for the mean height of 

 the barometer 29*874 inches, and of the mark of the mean level of 

 the sea 21 feet 0*21 in. 



^^^r^/LV/re^^^^^^ ^^ «^ corresponding level 20 feet 8-4 inch. 



The mean of three days l 29.559 ^^^ ^^ corresponding level 21 feet 5-4 inch. 

 least pressure was ... J *^ ° 



Diff. +0-668 Diff. -9-0 



Thus a difference of pressure equal to 0668 inch produced a differ- 

 ence of 9 inches in the mean level of the sea. As the ratio of 9 to 

 •668 is 13'467 to 1, the author considers that the effect of the pres- 

 sure of the atmosphere on the level of the sea is 13*467 times as 

 great as the effect it produces on the mercury in the barometer, or 

 very nearly in the inverse ratio of the specific gravities of sea-water 

 and mercury. He however states that this remarkable coincidence 

 must be considered in a great measure accidental, for if a greater 

 number of days' observation be taken in order to deduce the mean 

 greatest and mean least pressure, and the corresponding mean levels, 

 a different result will be obtained. From these observations however 

 he considers that he has been enabled to deduce results which plainly 

 point to the law which governs the effect of the pressure of the atmo- 

 sphere on the mean level of the sea, and may be encouraged to 

 pursue the investigation through a more extended series of observa- 

 tions, in order to arrive at the most accurate conclusion that the ob- 

 served facts may justify. 



In conclusion a formula is given for determining the correct height 

 of the tide, or of the mean level of the sea : — 



Let L denote the correct height of the tide, or of the mean level 

 of the sea ; 

 B the mean pressure of the atmosphere ; 

 X the observed height of the tide, or of the mean level of the 



sea; 

 /3 the corresponding height of the barometer ; 

 D the ratio of the specific gravity of mercury to that of sea- 

 water : 

 then L=X-f(3-B)D. 



Examples are given of the application of this formula. 



