French National Institute. 499 



liardt fairly discussed it. Several objections were started : — 

 the result was, however, that the idea deserved a trial. M. 

 Caroche undertook to make the plain mirror proposed by 

 M. Burckhanlt, and to adapt it to a telescope the great 

 mirror of' which was two metres in focal length, and the 

 aperture about a sixth of its length. 



The invention of Borda's circle, from its exactitude, light- 

 ness, and moderate price, forms an interesting period in 

 the progress of modern astronomy. The utility and con- 

 venience of this instrument for geodesic operations is uni- 

 versally acknowledged: it is admitted to be superior to-every 

 thing for fundamental and delicate researches, in which the 

 necessity is felt of multiplying angles in order to attain the 

 utmost precision. Thus, in order to determine the altitude 

 of the pole, the obliquity of the ecliptic, the equinoctial and 

 solstitial points, the declinations of the most brilliant stars 

 which are not too close io v the zenith, and finally for refrac- 

 tions, Borda's circle seems preferable to the largest mural, 

 or entire circles which are not repeating. It is therefore 

 doing a real service to extend to new objects the utility of 

 so precise an instrument : we may also employ it in the de- 

 termination of the hour by absolute altitudes either of the 

 sun or stars. The astronomers Avho have recently measured 

 the meridian of Dunkirk and Barcelona, have already de- 

 rived the advantage of thereby regulating their pendu- 

 lums; they have supposed that in the interval of four or six 

 minutes, during which four or six observations may be 

 made, the altitude increases uniformly in proportion to the 

 interval of time ; and thus we may without any risk take a 

 medium between four or six consecutive observations, and 

 treat them, by taking a simple arithmetical method, as we" 

 would treat a single observation. M. Delambre, in fact, as- 

 certained that there was no sensible error when the obser- 

 vations regularly succeeded each other; which is most com- 

 monly the case. As the contrary, however, may sometimes 

 happen also, he had sought for a method of correcting the 

 small error of supposition and of these various methods ; 

 he has only published one, which, however, he had never 

 occasion to make use of. These methods may also be applied 



1 i 2 to 



