352 
towardsthe north. Two others were, at 
the same time, exposed to the direct rays 
of the sun. 
Other two were placed in the interior 
of Ins cabinet. 
Ail these thermometers were construct- 
ed with the greatest care, and under the 
immediate inspection of different mem- 
bers of the Academy of Sciences. 
Before endeavouring to ascertain the 
effect produced by these different expo- 
sures, M. Cotte determined, by a great 
number of observations, the comparative 
range of these thermometers in the same 
position. 
From these experiments it follows, that 
the differences between the mercurial and 
spirit of wine thermometers are much 
greater when they are exposed to the 
direct rays of the sun, which the author 
chiefly attributes to the red colour of 
the spirit of wine; and this difference is 
greater in proportion to the intensity of 
the heat. 
The greatest horary variation occurs at 
from six to seven o’clock, and especially 
between seven and eight in the morn- 
Ing; it continues to diminish until eleven, 
afterwards augments till two, and di- 
minishes a little between two and 
three. 
The difference between the mercurial 
and the spirit of wine thermometers, ex- 
posed to the sun is nearly the same from 
ten o'clock in the morning till four in the 
evening. 
' The maximum of the thermometer 
within doors did not happen on the same 
days as that of the thermometers ex- 
posed in the open air. 
A cloud passing rapidly before the sun, 
caused the spirit of wine thermometer to 
fall suddenly trom two to three degrees, 
and the mercuria! one #rom one to three 
seconds 6f a degree. As soon as the 
cloud had passed by, they instantly as- 
eended to the former point. 
The range of the mercury is more uni- 
form. 
The maximum of the thermometers ex- 
posed in the shade, occurred between 
two and three o’clock. 
In those exposed to the sun, between 
three and four o’clock. 
And in those within doors between 
six and seven in the evening. 
When the heat is most intense, there 
is perceived, in the mercury, but more 
especially in the spirit of wine, a kind 
of fiuctuation and agitation, which causes 
them to ascend and descend continually. 
~ ‘The reporter next notices a work pub- 
a 
Proceedings of Learned Societtes. 
£4 . 
[March }?, 
lished by M. Carnot, enutled Mémoire 
sur la relation qui existe éittre les distances 
de cing points quelconques pris dans l’es- 
pace, to which is subjoined an Essai sur 
la Theorie des Transversales. 
This memoir forms, we are told by M. 
Delambre, an interesting continuation to 
the Geometrie de Position of thesame au- 
thor. it contains a vast number_of use- 
ful, or at least of very curious theorems,va- 
rious analytical formule for solving 
all the problems relative to the quadran- 
guiar pyramid, without pre-sapposing any 
other knowledge than that of angles. All 
these formule are symmetrical, and pos- 
sess a neatness which renders them €x~ 
tremely agreeable to geometricians. It 
is certain that some of them may justly 
inspire with terror the boldest caiculator, 
and that by means of trigonometry we 
might often arrive at a much shorter and 
easier solution of the questions; but re- 
specting each problem new considera- 
tions would occur, which did not at first 
present themselves to the mind, whereas 
according to Carnot’s method, the whole 
flows with the greatest clearness from a 
small number of known principles. But 
the greatest advantage, which it pos- 
sesses over trigonometrical solutions, is- 
that from the combination of these for- 
muiz originate a great number of new 
propositions, which without this means 
would probably have remained a long 
time undiscovered. This work may be 
considered as a repertory, where ge- 
ometricians, in case of need, may find 
expressions, which will facilitate the so- 
lution of the most complicated problems. 
In. order to convey some idea of the 
mode in which these calculations are ex- 
ecuted, M. Delambre quotes the last pro- 
blem, which may be considered as a sum- 
mary of all the preceding: Of ten 
straight lines which join two and two any 
five points taken im space, nine being 
given, to find the tenth. ; 
The Essay on Transversals is not less 
curious. ‘Lhe fundamental principle had 
been assumed in the Geometrie de Posi- 
tion, and is one of the two principles, on 
which Ptolemy founded his spherical tri- 
gonometry. By the word transversal 
must be here understood any right lime 
whatever, which bisects the three sides 
of a rectilinear triangle, or their prolon- 
gations. iA 
A very simple equation expresses the 
relation between the segments and the 
sides. The author likewise deduces three 
other formule of the same nature, which 
afterwards being transferred to sphepieal 
