354 Dr. Schunck on Rubian and its Products of Decomposition. 

 depend upon the determinants 



n, 2,..2 2p - l i 



ll, 2 } ..2 2p - 1 J 



r2 2 "- 1 + l, 2 2p - l + 2,..2- 2p - 1 + 2 2p ~ 1 '\ 

 La^^ + l, 2- p - l + 2,..2- p - x +2- p - 2 S 



r2 2p -2, 2 2/, -n 



l2 2p -2, 2 2p -il"' 



and taking the sum of the half of the orders of the alternate de- 

 terminants of this series, as in the case of 15 persons, the sum is 



2 2p -l 



for the number of combinations for each day, as found above. 



In conclusion, the following are the general results of the 

 above considerations : — 



Number of persons 3, 15, 63, 225, 1023, 4095, . . 2 2p -l, 



Number of days . 1, 7, 31, 127, 511, 2047, . . 2 2p_1 -l, 



No. of combina-"! ni __ _ (1 ..„_ 2 2p — 1 



tionsforeachday/ 1 ' 5 ' 21 > 8o > 341, 1365, .. ^-J. 



LI. On Rubian and its Products of Decomposition. 

 By Edward Schunck, F.R.S. 



[Concluded from p. 226.] 



ACTION of Sulphuric and Muriatic Acid on Rubian. — The ac- 

 tion of these two acids is precisely the same ; but for the 

 purpose of studying it, it is better to employ sulphuric acid, as 

 it is more easily removed again afterwards. On adding sul- 

 phuric acid in considerable quantity to a watery solution of 

 rubian and boiling the liquid, no perceptible change takes place 

 at first, except that the solution loses a little of its transparency 

 and becomes slightly opalescent. If the solution was not very 

 dilute, there begin to appear very soon a number of orange- 

 coloured flocks. After boiling for some time and allowing to cool, 

 these flocks are deposited in large quantities, and the liquid is now 

 found to be much lighter in colour than before. After allowing 

 to cool and filtering, the liquid, on being mixed with fresh acid 

 and boiled again, often deposits on cooling a fresh quantity of 

 these flocks. When after repeated boilings no more flocks 

 separate on cooling, the process is completed. The last portions 



