322 Mr. Ivory on the Ellipticity of the Earth 



upon applying the general formula for the length of the pen- 

 dulum which has been deduced from the whole of the experi- 

 ments, to every individual case, the discrepancies of calcula- 

 tion will show the consistency of the experiments, and will en- 

 able us to judge of the degree of accuracy with which they 

 are represented by one figure. But on the other hand, it may 

 be alleged that the mean figure deduced from a great num- 

 ber of experiments may be considerably different from the 

 true figure belonging to the consistent observations alone; 

 and that the discrepancies of calculation are therefore not 

 an unexceptionable means of forming a just notion of the dis- 

 tribution of gravity on the earth's surface, and of the anoma- 

 lies to which it is subject. In one case only there is no doubt 

 that the mean figure coincides with the true one ; and that is, 

 when all the errors of calculation are small, and of the same 

 order with the errors of observation. But when the errors 

 are more considerable, the mean ellipticity deduced from a 

 great number of experiments, cannot be adopted, without 

 further investigation, as a safe determination of the figure of 

 the earth. In order to ascertain this point on sure principles, 

 it seems necessary to subdivide the whole of the experiments 

 into partial combinations; to investigate the ellipticity of 

 every separate combination ; and finally, to examine whether 

 all the results agree or disagree. If they agree with one an- 

 other and with the ellipticity obtained from the whole of the 

 experiments, we are then certain that the figure of the earth 

 has been rightly determined. But if the results are discor- 

 dant, the proper inference is, not that the earth has any par- 

 ticular ellipticity, but that the observed quantities are incon- 

 sistent with one another ; and no exact knowledge with re- 

 spect to the distribution of gravity on the earth's surface, can 

 be obtained, but by separating the experiments that are con- 

 sistent and belong to the mean figure of the earth, from those 

 that are anomalous. 



In 32 independent experiments with the pendulum, made 

 by different observers with the most improved apparatus and 

 after the methods of experimenting have been fully perfected, 

 I showed, in the last Number of this Journal, that 26 are con- 

 sistent among themselves, and concur in giving the same figure 

 to the earth. The resulting ellipticity is about ^^ which 

 agrees with what is deduced from the inequalities of the lunar 

 motions. If we apply a proper mathematical method to any 

 sufficient combination of the experiments in my Table, the 

 same results will always be obtained, or, at least, the small 

 differences will be of the same order as the unavoidable errors 

 cf observation. But the remaining six experiments do not 

 belong to the same elliptical figure with the others, at least, 



without 



