266 



Mr. S. M. Drach on the Polyhedric Fan. 



searches on the heat generated by voltaic electricity, the heat 

 of electrolysis and of chemical combination, vital dynamics, the 

 calorific effects of rarefaction and condensation on the tempera- 

 ture of air, the ignition of meteors by friction in our atmosphere 

 and the thermo-dynamic actions of elastic solids. 

 Believe me, my dear Sir David Brewster, 



Yours most truly, 

 6 Greenhill Gardens, Edinburgh, P. Guthrie Tait. 



March 17,1863. 



XXXVIII. The Polyhedric Fan : giving by common Geometry the 

 Arc = Radius to within a four -millionth part of its true value. 

 By S. M. Drach, F.R.A.S. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 



LET AP = 32 = AB, BAP = 90°, join BP = 32\/2, Draw 

 BC = 16_L_BP, CP = 48. Draw CD = 12v/2 = |BP and 

 i_CP, DP = 36v/2. DrawDEJ_DP=iDP = 18^/2; then 



'£ 



EP= 1V10. Draw EFjLEP = 45v/2=f of PD, and 

 PF=27*/10. Lastly, let angle FPX= half BPF. The 

 dotted lines Y P, Z P will be noticed afterwards. Then by 

 Vlacq-Vega's ten fig. logs, we get 



BPC = CPD= 19 28 16-394297 Octahedron 



DPE= 26 33 54-184238 Dodecahedron 

 EPF = 48 11 22-866613 Icosahedron 



