the Pendulum vibrating Seconds in the Latitude of London. 94 
promised an unexceptionable result. It is known that the cen- 
tres of suspension and oscillation are reciprocal; or, in other 
words, that if a body he suspended by its centre of oscillation, 
its former point of suspension becomes the centre of oscillation, 
and the vibrations in both positions will be performed in equal 
times. Now the distance of the centre of oscillation from the 
point of suspension, depending on the figure of the body em- 
ployed, if the arrangement of its particles be changed, the place 
of the centre of oscillation will also suffer a change. Suppose 
then a body to be furnished with a point of suspension, and an- 
other point on which it may vibrate, to be fixed as nearly as can 
be estimated in the centre of oscillation, and in a line with the 
point of suspension and centre of gravity. If the vibrations in 
each position should not be equal in equal times, they may readily 
de made so, by shifting a moveable weight, with which the body 
is to be furnished, in a line between the centres of suspension 
and oscillation ; when the distance between the two points about 
which the vibrations were performed being measured, the length 
of a simple pendulum and the time of its vibration will at 
once be known, uninfluenced by any irregularity of density or 
figure *. 
An unexceptionable principle being thus adopted for the con- 
* In the Conmissance des Temps for 1820, is an article by M. de Prony on 
a new method of regulating clocks. At the conciusion of this article is a 
‘short note, in which the author adds, “ J’ai proposé en 1790 & Academie 
des Sciences un moyen de déterminer la longueur du pendule en faisan‘ 
osciller un pendule composé sur deus ou trois axes attachés & ce corps. 
(voyez mes Legons de Mécanique, art. 1107 et suivans.) Il paroit qu’on a 
fait ou quon va faire usage de ce moyen en Angleterre.” On referring to 
the Legons de Mécanique, as directed, I can perceive no hint whatever of 
the possibility of determining the length of the seconds pendulum by means 
of a compound pendulum vibrating on two axes; but it appears that the 
method of M. de Prony consists in employing acompound pendulum having 
three fixed axes of suspension, the distances between which, and the time 
of vibration upon each, being known, the length of three simple equiva- 
lent pendulums may thence be calculated by means of formule given for 
that purpose. M. de Prony indeed proposes employing the theorem of 
Huygens, of which I have availed myself, of the reciprocity of the axis of 
suspension and that of oscillation, as one amongst other means of simplifying, 
his formule, and says, ‘‘ J’ai indiqué les moyens de concilier avec la condition 
a laquelle se rapportent ces formules, celle de rendre l'axe moyen le recipro: 
que de l'un des axes extrémes ; J’emploie pour les ajustemens qu'exigent 
ces diverses conditions wn poids curseur dont j'ai exposé les propriéiés dans 
un mémoire publié avec la Connoissance des Temps de 1817.” Now it ap- 
pears evident from this passage, that M. de Prony viewed the theorem of 
Huygens solely with reference to the simplification of his formulz ; for, had 
he perceived that he might thence have obtained at once the length of the 
pendulum without further calculation, the inevitable conclusion must in- 
stantly have followed, that his third axis and his formule were wholly unne- 
eessary. 
struction 
