PAPER BY MAX MARGULES. 



317 



This is the same as equation (13) of the previous section, only here G 

 replaces E, and H replaces A (go). 



G= 



3 kMS 2 

 4 P 3 



(a A sin 4 Go-\-ot 6 sin' J «+ 



• ) 



„ 1 3hMS 2 , . . . . x 



-E=j5-m j — ™- (sin 2 Go—aCi&UTGo— a 6 rsin 6 co— ...).. (17) 



For a given value of T therefore, or 4 , « 6 , etc., are the same constants 

 as in Section ix. 



u m 



m 



is the mass of the earth ; -™ = g ; M = 355000 m.; P = 24000 S; 



3uMS 2 

 4 P 3 



1.203 



Hence on the equator when 4 ft = 10, or T = 298.7, we have 



760 s = 287 x 298.7 x 1 ' 203 x 1L26 x cos ( 2 n1 x 2A ) 

 =0.12 (mm) cos(2^ + 2A) 



Thus by the sun's attraction a semi-diurnal variation of the barome- 

 ter of 0.24 mm. would arise at the equator ; but through the moon's action 

 one that is three times greater, 0.7 mm. 



Laplace, in Meeanique Celeste, book iv, chapter 5, computed the 

 atmospheric tide with the same value of A-, but for an atmosphere over 

 an ocean of constant depth, whose tides influence those of the air, 

 whereas here the atmosphere over a rigid earth is alone considered. 

 For our case the same formulae obtain as for an ocean of uniform depth 

 equal to I. In the equations (15) and subsequently, we have only to 

 put gl in place of R T, and gy in place of R T a, when y is the elevation 

 of the surface of the sea above the mean level. 



The lunar tides computed from equations (17) with any allowable 

 value of T are very much too large in comparison with those deduced 

 from the barometer observations.* One can scarely wonder at this 



* Besides the observations of Bouvard mentioned in Book xm, Meeanique Celeste 

 and which, arranged by syzygies and quadratures, show scarcely any difference in the 

 daily variation of the barometer (note that only the observations of 9 a. m. and 3 

 p. m. were used), there are at hand for later dates computations of series of hourly 

 observations for certain tropical stations that Professor Hann has poiuted out to me. 

 These give the following barometer variations produced by the lunar tides : 



The results for Singapore aud St. Helena are remarkable in that the maxima 

 occur precisely at the moment of lunar culmination ; at Batavia the high tide is 50 

 minutes late. 



