MEASUREMENT OF ANGLES. 



a star in the sky, for instance the image produced at the focus 

 of the telescope is not a point. Owing to diffraction, this image 

 consists of central circular spot surrounded by a dark circle, and 

 then by a series of concentric circles alternately light and dark. 



In order to distinguish two stars which are very close, the 

 central images which correspond to each of them must be sepa- 

 rated, or at any rate must not trench too much on each other. 

 According to the laws of diffraction, the apparent angle of the 

 central spot seen from the optical centre of the object-glass (or 

 from the mirror in the case of the reflecting telescope) is inversely 

 as the diameter of the object-glass. We cannot a priori define 

 the extent to which the central spots overlap that is to say, the 

 smallest angle of two stars, beyond which the eye could not affirm 

 the existence as distinct objects of two adjacent stars ; but it is 

 certain that this limiting angle is inversely as the diameter of the 

 object-glass; it is the angle of penetration ; the inverse of the angle 

 of penetration is called the optical power. The optical power is 

 accordingly proportional to the diameter of the object-glass. 



To determine the optical power by experiment, Foucault* recom- 

 mends the use of a grating, consisting of equidistant parallel white 

 lines, separated by dark lines of the same thickness. The greatest 

 distance is measured at which the grating must be placed so that the 

 lines are still distinctly seen by means of the object-glass, provided 

 with a suitable eye-piece ; the apparent angle of two consecutive 

 lines measures the penetration of the instrument. Foucault found 

 that a telescope of 14 centimetres aperture will show lines whose 

 distance does not exceed i", whatever be its focal distance. It 

 follows from this, that the constant ratio of the optical power of an 

 object-glass to the diameter of this object-glass, expressed in centi- 

 metres, is equal to the inverse of the product of 14 by the arc of a 

 second that is, about 15,000. The result would not be quite the 

 same if we estimated the optical power of a telescope by the sepa- 

 ration of two adjacent stars of the same magnitude. We can under- 

 stand that it is quite possible, in measuring angles, to direct the line 

 of the cross wire on the image of an object with a less error than the 

 angle of penetration of the telescope, especially when we can 

 multiply the sightings. This is particularly the case in transit obser- 

 vations and in geodetic triangulations ; the error of the sighting is 

 then not more than one-tenth of the angle of penetration of the 

 telescope. 



* Annales de I' Observatoire de Paris, Vol. v. 1858. (Euvres, p. 259. 



