AA42 
of Analytical Contemporary History of 
the happiest Efforts of the Human Mind. 
The theory of Mathematics has long 
enjoyed one primary advantage, that of 
different Elementary Treatises, com- 
posed by the greatest geometricians. 
We are indebted to Newton for the 
Principles of Universal Arithmetic ; to 
Euler, for the Elements of Algebra; to 
M. Le Gendre, for a System of Geo- 
metry. The twelfth edition of this 
work has just been published. M. La 
Croix has republished his Elements of 
the Analysis of Probabilities, an impor- 
tant science, and hitherto but little un- 
derstood, originating from a speculation 
of Pascal, and subsequently reared in 
England, to ascertain the degree of emi- 
nence from which immediate practical 
advantages are derived. It has re- 
ecived a further augmentation from M. 
Ya Croix, whose publicatious on this 
subject, considered collectively, appear 
to comprise the whole extent of mathe- 
matical analysis. He has annexed to 
his present work some valuable Remarks 
on Saving Bank Societies, Modes of 
Insurance, Life Annuities, Tontines, 
&¢. His intention is to distinguish be- 
tween such establishments as are useful 
and respectable, and such as are noxious 
and reprehensible. 
The Treatise on Statics of M. Poinsot 
has been reprinted. ‘The author bas 
therein discovered new principles, in ad- 
dition to a theory that was originally in- 
vented by Archimedes, and which re- 
ecived great improvements from Galileo, 
Messrs. Poisson and Canchy have 
heen directing their labours to the study 
of natural phenomena, and have brought 
this part of science to a high degree of 
perfection. 
The first theorems of Optics were dis- 
covered by Descartes, Huygens, and 
Newton. This science acquired a fresh 
impetus about the beginning of this 
century, and has had recent accessions 
rom the investigations of Messrs, 
Malus, Arago, Biot, and Fresnel ; and 
also, in England, from those of Wollas- 
ton, Young, and Brewster. 
~ Light is transmitted, with an im- 
-mense velocity, through all parts of thie 
universe. Tt traverses, with a uniform 
motion, about 210,000 miles in a second, 
becomes ‘yeflected on the surface of 
bodiés, and some parts of its rays penc- 
irate transparent bodies. In decompo- 
sition, it falls into coloured homogeneous 
rays, refraneible, but unequally. When 
a tay of light passes through certain 
Proceedings of Public Societies. 
[Dec, 1, 
crystals, it divides into two distinct 
parts ; it is this which constitutes double 
refraction, The law of this phenome- 
non has been deduced from the observa- 
tions of Haygens; and M. La Place has 
reduced it to the general principles of 
rational mechanics. Each of the two 
refracted rays acquires, in the interior of 
the crystallized median, a peculiar dis- 
position, which has been designated by 
the name of polarization, and which 
keeps up a singular but constant rela- 
tion with the situation of the elements 
of crystals. ‘l'his property becomes ma- 
nifest, when a polarized ray falls; ob- 
liquely, on the surface of a transparent 
body, which reflects a part of it; for the 
cflects of reflection and transmission are 
very different, and in some measure 
opposite, according as the surface’ pre- 
sents itself to the ray on different sides. 
M. Malas has employed himself in 
the study of this kind of phenomena ; 
his numcrots and ingenious discoveries, 
combined with the experiments of 
Messrs. Wollaston and’ Young, have 
thrown new light on opti¢s, ‘and “ascer- 
tained the boundaries’ of its’ recent 
progress. FING 
We owe to M. Arago the discovery of 
coloured polarization. His researches, 
which have brouglit to some degree of 
perfection all the other parts of optics, 
are remarkable for adding to the science 
new instruments, which reproduce and 
perpetuate the utility of preceding expe- 
riments. By observations on the pheno- 
mena of coloured polarization, he has 
been enabled to compare the rays which 
proceed from the edges of the sun’s ap- 
parent disc, with those that are emitted 
from his centre. M. Arago has con- 
structed a new process for illustrating 
the effects of diffraction, by measuring, 
with precision, the slightest differences of 
Fefrangible jorce, in aériform bodies or 
substances. This forms a valuable ac- 
quisition to optics. 
Messrs. Biot and Brewster have con- 
tributed, not a little, to enrich ‘this sci- 
ence with correct calculations, new 
facts, and -a great number of) obser- 
vations. 
M. Fresnel has been applying bim- 
self, of late years, to all the parts of op- 
tics with singular success. He bas de- 
termined the mathematical laws of the 
most. complicated phenomena, and all 
the resulls of his analysis are-exactly 
conformable,to the obscrvations.:'Those 
fringes, alternately brilliant ‘and’ ob- 
scure, that attend the shadows of ates, 
the 
