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length oj the pendulum vibrating seconds. 
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 
construction of the pendulum, it became of considerable im- 
portance to select a mode of suspension* equally free from 
objection. Diamond points, spheres, and the knife edge, 
were each considered ; but as it was found difficult to procure 
diamond points sufficiently well executed, the knife edge was 
preferred, after many experiments had been made with 
* In the Connoissance desTemps for 1820,1s an article by M.de Prony on a new 
method of regulating clocks. At the conclusion of this article is a short note, in 
which the author adds, “ J’ai propose en 1790 a l’Academie des Sciences un moyen 
“ de determiner la longueur du pendule en faisant osciller un pendule compose sur 
“ deux ou trois axes attaches a ce corps, (voyez mes Lemons de Mecanique, art. 
“ 1107 et suivans) II paroit qu’on a fait ou qu'011 va faire usage d e ce moyen en 
<c Angleterre.” On referring to the Lepons de Mecanique, 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 a compound 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 equivalent pendulums may 
thence be calculated by means of formulae 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 formulae, and says, “ J’ai indique les moyens 
« de concilier avec la condition a laquelle se rapportent ces for mules, celle de rendre 
tc I’axe moyen le reciproque de l’un des axes extremes ; J’emploie pour les ajustemens 
cc qu’exigent ces diver ses conditions un poids curseur dont j’ai expose les proprietes 
“ dans un memoire publie avec la Connoissance desTemps de 1817.” Now it appears 
evident from this passage, that M. de Prony viewed the theorem of Huygens 
solely with reference to the simplification of his formulas ; for had he perceived that 
he might thence have obtained at once the length of the pendulum without further 
calculation, the inevitable conclusion must instantly have followed that his third axis 
and his formulae were wholly unnecessary. 
