174 
lun and Perpignan, could not be simply 
considered as arcs which were entirely in 
the same plane, but as curves with a dou- 
ble curvature. The same remark had 
been made by Clairant more than fifty 
years age, but it was always believed, 
that the effect of the double curve could 
only become sensible, when the intervals 
were much greater than those given by 
direct measurement, and it was hence 
coneluded, that the consideration of the 
spheroid would onlyrender more intricate, 
calculations already too complicated, 
without being of the smallest utility. In 
fact, the spheroid is not much less differ- 
ent frem the sphere, than the sphere it- 
self is froma plane. Now the sphericity 
f triangles only introduces into the cal- 
culation terms of the second order for the 
angles, and of the third order for the sides. 
It was therefore natural to suppose that 
the terms dependant on the spheroid, 
fhould be of a higher order, and {till move 
insensible by their extreme minuteness. 
But though no person had yet written on 
this subject, we ought not to conclude 
that they have remained contented with 
vague considerations, and a simple pro- 
bability. This point is discussed in the 
article Calcul de Triangles, in the second 
volume of the’ Meridienne, now in the 
press; we trust it will be there found de- 
monstrated, by simpleand elementary con- 
siderations, that*the difference between 
spherical and sphero‘dical angles is not 
gis of a second in the largest of our trian- 
gles, and that the double curve scarcely 
changes one centimetre in the length of 
the greatest of our sides. These results, 
we are informed by the reporter, were 
previously confirmed by M. Legendre in 
his learned analysis. To these geometri- 
cal considerations respecting the figure of 
the earth, we should next proceed, says 
M. Delambre, to give some account of 
the geographical researches, that have 
been recently made, respecting the im- 
mense plain in the interior of Africa, by 
M. Lacepede; and those on Persia, and 
the communication of the Black sea, by 
M. Olivier; but as these works, which 
more particularly belong to the physical 
class, have already been analyzed by M. 
Cuvier,* we shall proceed to consider the 
Memoir of M.Raymond on the Measure- 
ment of Mountains by Means of the Ba- 
rometer. ik s 
-In our report of 1805, we observed, 
that there was scarcely =4, of difference 
between the co-efficientof M, Laplace in 
* See Monthly Magazine, vol. xiii. p. 592. 
Proceedings of Learned Societies. 
[Sept. 1 
his calculation of the height of mountains 
by the barometer, and that’ which M, 
Raymond deduced from numereus ob= 
servations of this kind, which he made m 
the Pyrennces. Some recent experiments 
have entirely done away a difference, 
which could only pruceed from the uncer- 
tainty either of the barometrical observa- ~ 
tions, or of thé former experiments on the 
weight of the air and mercury, which M. 
Laplace had assumed im his calculation, 
M. Biot has jateiy repeated these expe- 
riments with such minute attention to all 
tle particulars, that he finds the co-efii- 
cient ought to be diminished, nearly ~4,, 
so that the agreement between the two 
methods is complete.’ On the one hand, 
we behold, continues the reporter, the 
geometrician relying on facts observed in 
the cabinet, and deducing from them a 
formula for measuring the height of 
mountams; and on the other, an obser- 
ver taking for a basis the kaown height 
of a mountain, and the effect it produces 
on the elevation of the mercury in the 
barometer, and inferring from it the rela- 
tive weight of the mercury and the air, 
and findigg the same quantity which had 
served for the foundation of the caleuia- 
tions of the geometrician. These com- 
parisons which are daily multiplied, 1 the 
application of the analysis; these ideiti- 
cal results, obtained from such contrary 
processes, and drawn from such ditferent 
phenomena, atford preofs to which the 
most obstinate and sceptical must yield 
their assent. - 
This important result is not, however, 
the only merit of this memoir of M. Ray- 
mond. In it, we are imformed, will be 
found, the means of distinguishing the 
circumstances, which are favoarable, or 
unfavourable, to these kind of obServa- 
tions. The author arranges them under 
three diiterent heads. The influence of 
time, of sfations, and of meteors. With 
respect to the first of these, the heights 
taken in the morning and evening are al- 
ways too small; from whence it follows, 
that they should be made towards the 
middle of the day, a condition which is 
easily fulfilled. The influence of stations, 
is equally real, but not so easily remedied. 
Tn all cases, however, the portable ba- 
rometer, and the harometer of compari- 
son ought to be observed im stations, 
where the local circumstances are the 
same. Great distance does not: always 
prove an obstacle; for example, M. Ray-— 
mond has remarked, that his observations - 
in the Pyrennees, compared with those 
made by M. Bouvard in the Imperial Ob- 
servatory 
