296 Mr Glaisher, On Legendre's formula for [Dec. 8, 



is derived from secondary dorsal posterior tubules of the Wolffian 

 body, 



1. because it lies dorsal to the Wolffian body. 



2. because according to Braun the kidney of Lizards is de- 

 veloped from cells which are derived as irregular solid ingrowths 

 of the peritoneal epithelium after the primary Wolffian tubules 

 have completel}^ developed, and at a time corresponding to the 

 development of the secondary dorsal tubules. My observations 

 show that the kidney blastema of the chick does not arise as 

 Braun has described in Lizards. 



In the chick the blastema of the kidney arises contempora- 

 neously with the primary tubules of the Wolffian body, and for 

 the chick, at any rate, disproves one of the facts on which Fiir- 

 bringer rests his suggestion. With regard to the dorsal position of 

 the kidney, I may mention that this is easily explained as being 

 due to its great development, which has caused it to overlap the 

 less developed Wolffian body. 



December 8, 1879. 

 Professor Newton, President, in the Chair. 



The following communications were made to the Society; — 



(1) Mr J. W. L. Glaisher, M.A., On the value of the constant 

 in Legendre's formula for the number of j^rinies inferior to a given 

 nuynber. 



§ 1. Legendre's formula for the number of primes inferior 

 to a given number x was given by him in the second* edition 

 (1808) of his Essai sur la Theorie des Nombres (Part IV. § viii. 

 pp. 394 — 398). The Chapter is entitled "D'une loi tres-remar- 

 quable observde dans lenumeration des nombres premiers," and 

 commences " Quoique la suite des nombres premiers soit extrSme- 

 ment irreguliere, on pent cependant trouver avec une precision 

 tres-satisfaisante, combien il y a de ces nombres depuis 1 jusqu'a 

 une limite donnee x. La formule qui resout cette question est 



X 



^" log ^-1-08366' 

 log X dtant un logarithme hyperbolique." 



* The first edition was published in 1798. I have never seen a copy and do not 

 know wliether the subject of the distribution of primes is referred to in it. 



