[170] Catalogus novus stellarum duplicium, Stellarum duplicium et multiplicium mensurae micrometricae, and Stellarum fixarum imprimis duplicium et multiplicium positiones mediae pro epocha 1830.
[171] I.e. 2·512... is chosen as being the number the logarithm of which is ·4, so that (2·512...)5∕2 = 10.
[172] If L be the ratio of the light received from a star to that received from a standard first magnitude star, such as Aldebaran or Altair, then its magnitude m is given by the formula
L = (1∕2·512)m - 1 = (1∕100)(m - 1)∕5, whence m - 1 = -5∕2log L.
A star brighter than Aldebaran has a magnitude less than 1, while the magnitude of Sirius, which is about nine times as bright as Aldebaran, is a negative quantity,-1·4, according to the Harvard photometry.