CONTENTS. Vll 



NOTICES AND ABSTRACTS 



OF 



MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. 



matiie:\iatics and physics. 



Pfige 

 Adtliess by Warrex De La Eue, Esq., D.C.L., Ph.D., F.R.S., V.P.C.S., 

 V.r.U.A.S., President of the Section 1 



Mathematics. 



Professor Clifford on the Contact of Surfaces of the Second Order ^-ith 

 other Surfaces 13 



Mr. Matthew Collins on new Improvements in Approximating more rapidly 

 than usual to Square, Cube, and other Koots of a given Number X 13 



Mr. J. W. L. Glaisher on. the Evaluation in Series of certain Definite Integrals 15 



.. on the Function that stands in the same Relation to 



Bernoulli's Numbers that the Gamma-function does to Factorials 17 



on the Law of Distribution of Prime Numbers 10 



Mr. J. E. IIilgard on a ^'erification of the Probability Function 21 



Mr. F. W. Ne-wt-ian on Tridiametral Quartan Curves 22 



on Quartan Curves with 3 or 4 Diameters 23 



on ]\ronodiametral Quartan Curves 23 



Professor II. J. Stepiif.n Smith on the Circular Transformation of Mubius . . 24 



Gekeral Physics. 



Sir. P. G. Tait on Sympathy of Pendulums 24 



I'rofessor James Thomson- on Relations between the Gascou.s, the Liquid, 

 and the Solid States of Matter -1 



ASTROKOMT. 



Mr. Howard GnLnss on some new Points in the ^Mounting of Astronomical 

 Telescopes '^" 



Dr. Janssen sur le Resultat de ses Observations dans I'lnde sur TEclipse du 12 

 Dec. 1871 ^^ 



