688 Mr. stokes, on THE VARIATION OF GRAVITY 



nearly balanced. To destroy the errors in high and mean latitudes without altering the others, he 

 has proposed to add a term - Jsin^Xcos°X, where X is the latitude. But a consideration of the 

 character of the stations seems sufficient, with the aid of the previous theory, to account for the 

 apparent anomaly. About latitude 45" the stations are all continental; in fact, ten consecutive 

 stations including this latitude are Paris, Clermont, Milan, Padua, Fiume, Bordeaux, Figeac, Toulon, 

 Barcelona, New York. These stations ought, as a group, to appear with considerable negative errors. 

 Mr. Airy remarks "If we increased the multiplier of sin'-X," and consequently diminished the 

 ellipticity, "we might make the errors at high latitudes as nearly balanced as those at the equator: 

 but then those about latitude 45° would be still greater than at present." 



The largeness of the ellipticity used in the comparison accounts for the circumstance that the 

 stations California, Maranham, Trinidad, appear with larger negative errors tlian any of the stations 

 about latitude 45", although some of the latter appear more truly continental than the former. On 

 the whole it would seem that the best value of the ellipticity is one which, supposing it left the errors 

 in high latitudes nearly balanced, would give a decided preponderance to the negative errors about 

 latitude 45" N. and a certain preponderance to the positive errors about the equator, on account of 

 the number of oceanic stations which occur in low latitudes. 



If we follow a chain of stations from the sea inland, or from the interior to the coast, it is 

 remarkable how the errors decrease algebraically from the sea inwards. The chain should not extend 

 over too large a portion of the earth's surface, as otherwise a small error in the assumed ellipticity 

 might affect the result. Thus for example, Spitzbergen + 4.3, Hammerfest — 0.4, Drontheim - 2.7. 

 In comparing Hammerfest with Drontheim, we may regard the former as situated at the vertex of a 

 slightly obtuse angle, and the latter as situated at the edge of a straight coast. Again, Dunkirk — O.I, 

 Paris - 1.9, Clermont - 3.9, Figeac - 3.8, Toulon - 0.1, Barcelona 0.0, Fomentera + 0.2. Again, 

 Padua + 0.7, Milan - 2.8. Again, Jamaica - 0.8, Trinidad - 5.2. 



24. Conceive the correction kg" calculated, and suppose it applied, as well as the correction 

 —g, to observed gravity reduced to the level of the sea, or to g, and let the result be g . Let e 

 be the ellipticity which would be determined by means of g^^, e^^ + Af,, the true ellipticity. Since 

 g ,1 ■= g - g' + k'g', and therefore g = g , + g — kg", we get by (27) 



45 

 Ae„=^m|(i-sin^/)(g''-A:^")j (32) 



Now g' = 2ircr/i = 27r^ = 2 7r2^,; and we get from (30) and (28) 



ug"=-k'pj-^=.k.^J^. 



° dr 2a 2j + 1 



All the terms ^j will disappear from the second side of (32) except ^.,, and we therefore get 



45 / ^\ 



Hence the correction Af,^ is less than that considered in Art. 18, in the ratio of 5 - A; to 5, and is 

 therefore probably insensible on account of the actual distribution of land and water at the surface of 

 the earth. 



25. Conceive the islands and continents cut off at the level of the sea, and the water of the sea 

 replaced by matter having the same density as the land. Suppose gravity to be observed at the 

 surface which would be thus formed, and to be reduced by Dr Young's rule to the level of what 

 would in the altered state of the earth be a surface of equilibrium. It is evident that g ^ expresses 

 tile gravity which would be thus obtained. 



The irregularities of the earth's coating would still not be wholly allowed for, because the surface 

 which would be formed in the manner just explained would no longer be a surface of equilibrium. 



