Geological Society, 561 



tary muscle is not a sustained act of the whole congeries of contrac- 

 tile elements composing it, but a rapid series of partial acts, in which 

 all duljr share, becoming by turns contracted and relaxed. 



The paper is accompanied by drawings cf the microscopic appear- 

 ances therein described. 



May 6. — The following papers were read, viz. — 



1. "Investigation of a New and Simple Series, by which the 

 Ratio of the Diameter of a Circle to its Circumference may easily 

 be computed to any required degree of accuracy." By William 

 Rutherford, Esq., of the Royal Military Academy, Woolwich. 

 Communicated by Samuel Hunter Christie, Esq., M.A., Sec. R.S. 



Among various formulee for the rectification of the circle discovered 

 by the author, he has found the one given in this paper to be that 

 best fitted for computation ; and he has been enabled by means of it 

 with comparatively little labour, to extend the number, expressino- the 

 ratio of the diameter to the circumference, to 208 places of decimals, 

 a degree of accuracy hitherto unattainable, without a great amount of 

 labour, by means of any of the series which have yet been employed 



The celebrated series of Mr. John Machin, for the rectification of 

 the circle, is derived from the formula 



— = 4tan ^— tan ■ -, 

 4 5 239 



which converges with considerable rapidity, but gives rise to tedious 

 computations, in consequence of the divisor 239 being a prime num- 

 ber. But by converting the above formula into the followino- 

 T .^ -1 1 -11 -11 °' 



— = 4tan __tan htan — 



4 5 70 99 



a series is obtained by which the extended computation above men- 

 tioned was readily effected. 



The methods of computation are then stated in detail, and the 

 resulting value of tt is given to 208 i)laces of decimals, which is pre- 

 sumed to be accurate to the last figure, the computations havino- 

 been actually carried as far as 210 figures. ^ 



2. " On the Phrenomena of thin plates of Solid and Fluid Sub- 

 stances exposed to polarised light." By Sir David Brewster K H 

 D.C.L., F.R.S.,&V.P.R.S.Ed. 



From a theoretical investigation of the phrenomena described in 

 this pajjcr, tlie author deduces the important law, that when two 

 polarized pencils, reflected from the surface of a thin plate, lyio"- on 

 a reflecting surface of a difterent refractive power, interfere, hall" an 

 undulation is not lost, and white-centred rings are produced! When 

 the inclination is exactly 90°, the pencils do not interfere, and no 



rings are produced. ■ 



GEOLOGICAL SOCIETY. 



[Continued from p. 527.] 



June 10, 1840 {Continued). —On the mineral veins of the Sierra 



Almagrera, in tlie province of Almeria, in the South of Siiain bv 



J. Lambert, Esq., F.G.S. ' ^ 



The Sierra Almagrera extends from the mouth of the Almanzora 

 Phil. M(uj. S. 3. Vol. 18. No. 120. Hnppl. July 1841. 20 



