AT THE SURFACE OF THE EARTH. 687 



Let S„ be the mean value of S throughout a circle with an angular radius \J/, then the part of 

 V^ which is due to an annulus having a given infinitely small angular breadth rfx// is proportional to 



S„ cos ^ , or to S„, nearly when r// is not large. If we regard the depth of the sea as uniform, we 



may suppose ^ = for the sea, and transfer the defect of density of the sea with an opposite sign to 

 the land. We have seen that if we set a circle of land i mile high of 1000 miles radius surrounding 

 one station against a circle of sea 3^ miles deep, and of the same radius, surrounding another, we get 

 a difference of about ^ x 1.64 x 6.35, or 3I nearly, in the number of vibrations performed in one 

 day by a seconds' pendulum. It is hardly necessary to remark that high table-land will produce 

 considerably more effect than land only just raised above the level of the sea, but it should be 

 observed that the principal part of the correction is due to the depth of the sea. Thus it would 

 require a uniform elevation of about 2.1 miles, in order that the land elevated above the level of the 

 sea should produce as much effect as is produced by the difference between a stratum of land 

 3i miles thick and an equal stratum of water. 



23. These considerations seem sufficient to account, at least in a great measure, for the 

 apparent anomalies which Mr. Airy has noticed in his discussion of pendulum experiments*. The 

 first table at p. 230 contains a comparison between the observations which Mr. Airy considers first- 

 rate and theory. The column headed " Error in Vibrations" gives the number of vibrations per 

 diem in a seconds' pendulum corresponding to the excess of observed gravity over calculated 

 gravity. With respect to the errors Mr. Airy expressly remarks " upon scrutinizing the errors of 

 the first-rate observations, it would seem that, cceteris paribus, gravity is greater on islands than on 

 continents." This circumstance appears to be fully accounted for by the preceding theory. The 

 greatest positive errors appear to belong to oceanic stations, which is just what migiu be expected. 

 Thus the only errors with the sign + which amount to 5 are. Isle of France + 7.0 ; Marian 

 Islands + 6.8 ; Sandwich Islands + 5.2 ; Pulo Gaunsah Lout (a small island near new Guinea and 

 almost on the equator,) -t- 5.0. The largest negative errors are, California - 6.0; Maranham — 5.6; 

 Trinidad — 5.2. These stations are to be regarded as continental, because generally speaking the 

 stations which are the most continental in character are but on the coasts of continents, and Trinidad 

 may be regarded as a coast station. That the negative errors just quoted are larger than those that 

 stand opposite to more truly continental stations such as Clermont, Milan, &c. is no objection, 

 because the errors in such different latitudes cannot be compared except on the supposition that the 

 value of the ellipticity used in the comparison is correct. 



Now if we divide the 49 stations compared into two groups, an equatoreal group containing the 

 stations lying between latitudes 35''N. and 35°S., and a polar group containing the rest, it will 

 be found that most if not all of the oceanic stations are contained in the former group, while the 

 stations belonging to the latter are of a more continental character. Hence the observations will 

 make gravity appear too great about the equator and too small towards the poles, that is, they will 

 on the whole make gravity vary too little from the equator to the poles ; and since the variation 

 depends upon ^m ~ e, the observations will be best satisfied by a value of e which is too great. 

 This is in fact precisely the result of the discussion, the value of e which Mr. Airy has obtained 

 from the pendulum experiments (.003535) being greater than that whith resulted from the dis- 

 cussion of geodetic measures (.003352), or than any of the values (.003370, .003360, and .003107), 

 obtained from the two lunar inequalities which depend upon the earth's oblateness. 



Mr. Airy has remarked that in the high north latitudes the greater number of errors have the 

 sign -f , and that those about tiie latitude •1'5" have the sign — ; those about the e(|ual()r being 



Encydopadia Metropotitana, Art. Figure of the Kiirth. 



4 T 2 



