xi 



Supplement to a Paper on certain Properties of Square Numbers and 

 other Quadratic Forms, with a Table, &c. By Sir Frederick Pollock, 

 F.R.S., &c page 388 



On the Geometrical Representation of the Expansive Action of Heat, 

 and the Theory of Thermo-dynamic Engines. By William John 

 Macquorn Rankine, Civil Engineer, F.R.S.S, Lond. and Edinb., &c. 388 



On the Vibrations and Tones produced by the contact of bodies having 

 different Temperatures. By J. Tyndall, Esq., F.R.S 392 



Letter from Prof . Hansteento Col. Sabine on variations of the magne- 



tical inclination 393 



Sur la Theorie de Forientation du Plan oscillatoire du Pendule simple, 

 et son application a la recherche de I'aplatissement du spheroide 

 terrestre. By M. Oliveira 396 



On the Extension of the value of the Base of Napier's Logarithms ; of 

 the Napierian Logarithms of 2, 3, 5, and 10 ; and of the Modulus of 

 Briggs's, or the Common System of Logarithms ; all to 205 places 

 of decimals. By WilUam Shanks, Esq 397 



Further researches into the properties of the Sulphate of lodo- Quinine 

 or Herapathite, more especially in regard to its Crystallography, with 

 additional facts concerning its optical relations. Bv William Bu-d 

 Herapath, M.D . / 398 



