Notices respecting New Boohs. 171 



and is constant for all rays that go from P to P'. Similarly 



the optical path from Q to Q' is 



p.QS + (SS')-/a'.Q'S\ 



and is constant. Subtracting-, and denoting the difference of 

 the two constants by c, we have 



/i (PS-QS)-/ t '(P'S'-Q'S')=c, 



or (calling the obliquities Q. Q') } 



fju . PQ sin — /LiT'Q' sin 0' = c. 

 But and vanish together, therefore c is zero : and we 

 have 



fM,TQ>md = fM' .V'Q'>in6'. . . . (3) 

 The ratio of ft sin to /// sin & has therefore the constant value 

 P'Q'/PQ for all the rays by which the image is formed. 



The present paper has been framed with a view to sup- 

 plementing two papers by Lord Rayleigh. one of them (in 

 two parts) in the Phil. Mag. for the second half of 1879, 

 and the other (which has been already quoted) in Phil. 

 Mag. vol. xlii. 1896. They contain a much fuller treatment 

 of the theory of resolution than 1 have met with elsewhere. 



11 Leopold Road, Ealing, W. 



XVI. Notices respecting New Books. 

 Histoire de VOhservatoire de Paris cle sa fondation a 1793. Par 

 C. AVolf, Memhre de VTnstitut. Astronome Honoraire de 

 VOhservatoire. Paris : Gauthier-Yillars, Imprimeur-Libraire. 

 npHIS is the first part of a work in which it is proposed to give a 

 -"- history, not of the astronomical observations and results 

 which have been accomplished at the famous Observatory of Paris, 

 which was founded about eight years earlier than that at Greenwich, 

 but of its buildings, instruments, and the personnel composing its 

 staff, with the successive modifications and additions in these. It 

 is well known that the Paris Observatory, for more than the first 

 century and a quarter of its existence, was directed by four 

 generations of the family of Cassini, the first of whom was invited 

 from Italy by Colbert, and eventually appointed to take charge of 

 the new establishment. The fourth, also J. D. Cassini, was in 

 charge at the time when the great Revolution transformed not only 

 the rule of the Observatory, but that of all Prance. Before leaving 

 his post. Cassini formed the project of writing a complete history 

 of the establishment, and requested of the Director of the royal 

 buildings that a search should be made in the public archives for 

 the documents relating to the foundation of the Observatory and its 

 early annals. Though the answer gave him very little encourage- 

 ment in his scheme, he took the trouble to gather together all the 

 accessible papers which were left by his ancestors, particularly his 

 great-grandfather: these he presented in 1811 to the Bureau des 

 Longitudes, and they form one of the principal sources of information 



