172 Mr. Ivory on the Ellipticity of the Earth 



This table shows the errors of the formula. The greatest 

 error is at Drontheim, and it is nearly as much with the ellip- 

 ticity ? ^ F . The next greatest error is at San Bias ; but this 

 would be considerably diminished by adopting the length 

 found by Captain Foster, viz. 39*03881, instead of the mean 

 of the lengths found by that gentleman and Captain Hall, 

 which stands in the table. The excess at Galapagos is little 

 greater than the defect at Drontheim ; and as we know that 

 the former pendulum was determined in unfavourable cir- 

 cumstances, the experiment seems to be sufficiently well re- 

 presented by the formula. We may therefore affirm that, if 

 we adopt Captain Foster's pendulum at San Bias, the formula 

 represents 35 experiments out of 40, within the limits of the 

 probable errors : for the difference between the observed and 

 the calculated lengths is less than what would arise from an 

 error of 2 vibrations in a mean solar day, except at Sierra 

 Leone, Jamaica, San Bias, Bourdeaux, and Spitzbergen, where 

 the error is 2| vibrations ; and at Drontheim and Galapagos, 

 where it amounts to 3 \ and 4 vibrations. But at the five ano- 

 malous stations, the errors are between 6 and 10 vibrations in 

 a day. 



Without laying any stress on the mode of investigation we 

 have here followed, it cannot, I think, be denied that the el- 

 lipticity Q-gjj represents the observations much better than 

 2^; it ought therefore to be adopted until another shall be 

 found, if it be possible, that will represent the same observa- 

 tions still better, or until future experimental researches shall 

 have corrected and enlarged our present knowledge on this 

 subject. What other reason can be alleged for preferring one 

 ellipticity to another ? 



But if the experiments can be represented within the limits 

 of the probable errors, what becomes of the splendid specula- 

 tion about local attraction, which connects the apparent in- 

 equality of gravity with the variation of the soil. It is evident 

 that we can have no measure of the excess or defect of gravity 

 caused by the attraction of the adjacent matter, if the errors 

 of observation be sufficient to account for the irregularity in 

 the length of the pendulum. This theory too is quite uncer- 

 tain, so long as there remains any doubt about the exact quan- 

 tity of the ellipticity. At Maranham and Trinidad, Captain 

 Sabine makes the observed pendulums gain upon the calcu- 

 lated ones upwards of 4 vibrations in a mean solar day; in 

 my table the acceleration is only 1^, which may be attributed 

 to the inaccuracy of experiment. According to the same gen- 

 tleman, 



