Vienna is not in a position to enter into the question. The Academy of Turin offers the most _distinct_ thanks. The Academy della Crusca attends only to literature, but gives thanks. The Queen of Spain has received the work with the highest appreciation. The University of Salamanca gives infinite thanks, and feels true satisfaction in having the book. Lord Palmerston gives thanks, by the hand of "William San." The Viceroy of Egypt, not being yet up in Italian, will spend his first moments of leisure in studying the book, when it shall have been translated into French: in the mean time he congratulates the author upon his victory over a problem so long held insoluble. All this is seriously published as a rate in aid of demonstration. If these royal compliments cannot make the circumference of a circle about 2 per cent. larger than geometry will have it --which is all that is wanted--no wonder that thrones are shaky. I am informed that the legend of St. Vitus is given by Ribadeneira[132] in his lives of Saints, and that Baronius,[133] in {63} his _Martyrologium Romanum_, refers to several authors who have written concerning him. There is an account in Mrs. Jameson's[134] _History of Sacred and Legendary Art_ (ed. of 1863, p. 544). But it seems that St. Vitus is the patron saint of _all_ dances; so that I was not so far wrong in making him the protector of the cyclometers. Why he is represented with a cock is a disputed point, which is now made clear: next after _gallus gallinaceus_[135] himself, there is no crower like the circle-squarer. CELEBRATED APPROXIMATIONS OF [pi]. The following is an extract from the _English Cyclopaedia_, Art. TABLES: