Mr. T. S. Davies on Pascal's Mystic Hexagram, 37 



cury and 26*83 of sulphuric acid, the quantity of acid left in 

 the liquor is just two-thirds of the whole, as §'26*83 = 17*98. 

 The turpeth contained therefore 73*23 of Hg O and 9*16 of 

 S O a in the 82*49 parts, or in 100 parts, 



Sulphuric acid = 11*10~1 1on . 00 

 Oxide of mercury = 88*90 J 

 The formula SO s + 3 HgO, requires 

 S6 3 = 40*1 = 10*91 

 3 Hg O = 328*2 m 89*09 



368*3 100*00 

 B. 4*525 grammes of turpeth mineral prepared with boiling 

 water were dissolved in dilute muriatic acid, and the liquor was 

 precipitated by sulphuretted hydrogen. The sulphuret of mer- 

 cury weighed 4*334, being 95*76 per cent., equivalent to 89*24 

 of oxide of mercury. The liquor, boiled to remove the excess 

 of sulphuretted hydrogen, gave then with nitrate of barytes, 

 1*402 of sulphate of barytes, being 30*98 percent., containing 

 10*65 of sulphuric acid. Hence the turpeth mineral con- 

 sisted in 100 parts, of 



89*24 oxide of mercury, 

 10*65 sulphuric acid, 

 •11 loss. 

 I need not enumerate more than these two results, although 

 some others were obtained, all of which equally indicated ex- 

 actly the relation of S 3 + 3 Hg O. Of course it will be at 

 once seen that I take for the equivalent number of mercury 

 on the hydrogen scale 101*4, and consider the red oxide as 

 containing one equivalent of each element. 



VIII. On Pascal's Mystic Hexagram. By T. S. Davies, Esq., 



F.R.S., Sj-c, Royal Military Academy, Woolwich. 

 /"\NE of the two most general and prolific properties of the 

 ^-^ conic sections yet known, is that first given by Pascal 

 in his Essai pour les Coniques, or rather one of the converses 

 of that theorem, which we are told by Leibnitz he called the 

 mystic hexagram. It was made by him the foundation of an 

 entire system of conies, of which, however, all we know is the 

 titles and general subjects of the books into which it was di- 

 vided, as given by Leibnitz in his letter to Perrier in ] 679. 

 Mersennus speaks of Pascal having deduced from it four hun- 

 dred corollaries ; and Desargues (who says that in his time, 

 1642, it was called "the Pascal") tells us that it contains, either 

 as cases or immediate consequences, the whole of the propo- 

 sitions in the first four books of Apollonius. The well-known 

 properties of the quadrilateral inscribed and circumscribed 

 to the conic section, known by modern geometers as "the 



