TRANSACTIONS OF THE SECTIONS. 53 



to zero at the extreme limit. The particles within the superficial stratum subjected 

 to this disturbance are maintained in equilibrium by the combined action of mole- 

 cular repulsion and the earth's attraction, till at a small distance from the extreme 

 limit, -where the abnormal variation of density ceases, the density is such as might 

 result from a very small constant pressure applied at all points of a surface bounding 

 a terminal densitj- of finite value. (Views of this liind respecting the condition of 

 the atmosphere at its superior limit were entertained by Poissou.) On these prin- 

 ciples it is eas}^ to find a mathematical relation between the terminal density and 

 the heiglit of the atmosphere. The author lias, in fact, made the calculation on 

 the supposition that the atmosphere is GO miles high, and obtains a terminal density 

 equal to six-millionths of that at the earth's surface. 



According to the above views a particle at tlie superior boundary may be sup- 

 posed to remain at the surface, and to be of the same density, in successive instants. 



This condition is expressed by equating the complete difierential coefficient (^) 



to zero. By moans of this additional equation the value of the constant C can be 

 calculated on assuming a certain height for the atmosphere. Supposing the ]iei"-ht 

 to be 60 miles, the author obtains C = 0-000000830 /z. ° 



The arbitrary quantities being determined, tlie following results are readily 

 obtained : — 



Height of tide above the polar colunm, expressed in feet, 



= 1-084 cos- X4- 1-275 cos= X cos 2((9-/xO. 



At the equator, where X=0, difterence between high and low tide =2-55 feet. 

 Excess of barometer-reading above that at the pole, expressed in inches, 



=0-00117 cos=X + O-OO139cos=Xcos2(0-iLi<). 



At the equator the maximum difterence of the barometer-readings =0-00278 in. 



The data employed in calculating these coefticients were : — 



G ~ 70' R ~ ti(>3' y ~ 82^ ^ 289' 



the density of air =0-0013, the density of mercury =13-568. 



The above determination of the maximum difterence of barometer-readings at the 

 equator admits of comparison with the results of barometric observations made at 

 St. Helena and at Singapore, as given in p. 129 of the Philosophical Transactions 

 for 1852. These results agree ■with the theory in placing the high tide immediately 

 imder the moon ; but the maximum difterence of readings is 0003G5 in. at St. Helena 

 and 0-00570 in. at Singapore. Both consequently are in excess of the theoretical value 

 0-00278 in. But it is to be remarked that the latter depends on the assumption 

 that the atmosphere is 00 miles high; if it had been supposed of less height, say 

 40 miles, there would have been a closer agreement between the observed and theo- 

 retical values. 



The author's theory accounts in a remarkable manner for the fact that although 

 for the atmosphere high tide occurs under the moon, there is reason to say that for 

 a general ocean of the uniform depth of three or four miles it would be low tide 

 under the moon. The explanation given by the theory is, that there is a certain 

 depth of ocean or height of atmosphere for which the tide becomes infinite, namely, 

 when the rate of propagation of waves, as due to the earth's attraction, is equal to 

 the rate of the moon's relative rotation about the eartli. In that case the tide 

 would be accumidative, and might be of unlimited amount. This critical deptli, 

 or height, is shown by the theory to be about 8-4 miles for each fluid. It is because 

 the actual mean depth of the ocean is less, and the actual height of the atmospliere 

 greater, than this critical value, that the ocean-tide imder the moon is the opposite 

 of the atmospheric tide. 



Bemarlcs on Acricd Currents. By Prof, Colding. 



