206 Mr. Ivory's additional Discussion 



in one particular direction ; the two pass into each other by 

 a continuous series, of which the perfect circle is merely a term 

 of transition. 



Let us now attend to the changes of position in the foci, 

 corresponding to these transitions. During the gradual change 

 of the first ellipse into the circle, the foci F, f, move along 

 the diameter AB, approach nearer and nearer to the centre 

 of the figure C, until they both coalesce in the centre. In 

 the next series of changes, we find them again separating 

 from each other ; but instead of moving in the same line as 

 before, we observe them starting off, each in a new direction, 

 CP and CO, precisely at right angles to their former lines of 

 motion, AC and BC ; and this change of direction is made 

 abruptly, per solium, and by an angular motion. Are not 

 these changes direct violations of the law of continuity ? 



As the question which I have now proposed may be thought 

 deserving the attention of such of your philosophical readers 

 as are stimulated by the appearance of paradox to renewed 

 investigation; and as the attempts to solve it may give occa- 

 sion to the exercise of ingenuity, I shall abstain from suggest- 

 ing the considerations which might, perhaps, enable us to 

 explain this apparent anomaly, consistently with the univer- 

 sality of the law of continuity. 

 Bernard-street, Russell-square, P. M. RoGET. 



November 1, 1825. 



Errata in the last Number. 



Page 118 line 23, for " operations," read " operation." 



— 118 — 23, for " greatest," read " gentlest." 



1 19 — 3, for " to," read " with." 



119 — 32, for " rectilineous," read " rectilineal." 



120 — 26, for " course pending," read " corresponding." 



XXXIII. Additional Discussion respecting the Ellipticity of 

 the Earth as determined by Experiments made with the Pen- 

 dulum. By J. Ivory, Esq. M.A. F.R.S* 

 N deducing the figure of the earth from the observed 

 lengths of the pendulum, I have always thought it neces- 

 sary to leave out a few of the experiments that were incon- 

 sistent with the rest. The inconsistency is proved by com- 

 paring the pendulums on the same parallel, or nearly on the 

 same parallel; in which latter case a small correction must be 

 made for the difference of latitude. It is evident that, if the 



I 



Communicated by the Author. 



pendulums 



