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The methods given by our late Astronomer Royal, for solving the two problems alluded to, were printed in his introduction to Taylor's Logarithmic Tables. Since their appearance before the public, they have met with the warmest approbation from those most capable of judging of their merit; but no one, so far as i know, has fully demonstrated them; nor has any one, so far as my knowledge extends, observed two mistakes with which they are accompanied, and which in certain cases would affect the accuracy of their application. These circumstances, and a consideration of the high cha­racter of the author of the formulæ, induced me to reduce the following demonstrations and remarks into the form of a short memoir. I trust I shall not be charged with any im­proper motive for thus noticing the mistakes. Candour, I hope, will view them only as accidental oversights, and the most sincere regard for his memory will allow the propriety of correcting them.

philosophical transactions of the royal society of london

VIII. Demonstrations of the late Dr. Maskelyne's formulæ for finding the longitude and latitude of a celestial object from its right ascension and declination; and for finding its right ascension and declination from its longitude and latitude, the obliquity of the ecliptic being given in both cases