of the Royal Society of Edinburgh. 421 
was by the application of the same principles that Lord Howe^ 
Lord St Vincent, liord Duncan and Lord Nelson, achieved their 
splendid victories. 
Mr Playfair had proposed to draw up a biographical account 
of his friend ; but he was prevented by ill health from complet- 
ing his design. Although the present memoir, however, is only 
a fragment, yet it contains a full account of the great invention 
of Mr Clerk ; and is characterised by the usual elegance and 
ability of its distinguished author. It will be read, therefore, 
with the double interest which must ever be excited, to a sub- 
ject so deeply national, and to the last literary production of a 
philosopher so universally and deservedly esteemed, 
9. On circular Polarisation as exhibited in the Optical Structure 
of the Amethyst, ^c. By David Brewster, LL. D. F. R. S. 
Loiid. & Edin ; p. 139, — 153. With a coloured Plate, 
A short analysis ot this paper is given in vol. ii. p. 179^ 180, 
the properties of Amethyst detailed in this memoir, will be ex- 
plained in our general history of the polarisation of light. The 
author has shewn how to distinguish Amethyst from Quartz, by 
mineralogical characters, and he has discovered amethyst of a 
yellow, orange, olvve-green and lilac colour, and also perfecU 
ly colourless, like quartz. 
10. An Examination of some Qitesiions connected with Games 
of Chance. By Charles Barrage, Esq. F. R. S. Lond. & 
Edin ; p. 153,-177, 
This ingenious and profound paper relates to the methods of 
betting upon a number of successive events, (the probability of 
each of which is either equal to, or less than one-half,) by which 
a profit shall be realised after a considerable number of games 
bave been decided. The simplest plan, called the Martingal, 
is that of doubling the stake whenever a loss occurs ; and requires 
for its success, that the person who employs it, has the power of 
leaving off whenever he plea;ses 5 and has the command of an un- 
limited capital. If the chance of the events happening is one- 
third, instead of one-half, the stake must be tripled. 
Mr Babbage first examines the case of the Martingal, and 
then proceeds to other problems of a similar kind. 
