178 French National Institute. 



Peltro William Tomkins, esq. historical engraver to the 



quccii, vice-president. 



Anker Smith, esq. A. R. A. treasurer. 



Abraham Kaimbach, esq. 



Charles Warren, esq. 



James Parker, esq. 



Cosmo Armstrong, esq. 



Robert Mitchell MeadimSj esq. 



Thomas Medland, esq. 



•Tames Fitler, esq. A. R. A. naval engraver to the king. 



Thomas Milton, esq. honorary secretary. 



Wilson Lowry, esq. "| i- 



T , c 1 \ . ? auditors. 



John Samuel Agar, esq. J 



Philip Hammerslcy Leaths, of the Middle Temple, ho- 

 norary consulting member. 



FRENCH NATIONAI, INSTITUTK. 



Notice of the Labours of the Mathematical and Fhyslcal 

 Class oj' the Sciences since the last Public Sifting. 



The name of tautochrones is given to curves in which 

 the oscillations of a heavy body are always of the same 

 duration, whatever maybe their extent. Tautochrones have 

 been rendered celebrated by the labours of the greatest 

 geometricians, who have successively endeavoured to over- 

 come the difficulties exhibited by the different hypotheses 

 which may be formed in regard to the laws of gravity and 

 resistance. But though their ibrmuUe had all tb.e gene- 

 rality possible, they sought only for plane tautochrones, 

 while for each hypothesis there exist an infinite number 

 which are of a double curvature. 



An examination of these new tautochrones, and their re- 

 lation with plane tautochrones, form the object of a me- 

 moir by C. Biot. From a consideration of the formulas 

 the author has deduced some theorems remarkable for their 

 simplicity. But whatever may be their elegance or novelty, 

 xve shall not enter into any detail respecting a matter so ab- 

 stract, that Bossut in his Essay on the History of the Ma- 

 thematics thought it his duty to give an exculpation of 

 those gcomttricians who have employed their powers and 

 their genius ou these problems, which are merely theoreti- 

 cal. . Nothing can be added to the solidity of the reasons 

 which he ailduces in favour of these speculations, which on 

 the first view a])pear barren, but which in the end may be 

 applied to useful purposes. But this may be rendered more 

 sensible by a striking example. When the antient geo- 

 metricians were endeavouring witli so much care to disco- 

 . - .. ver 



