230 
SECOND REPORT -1 832 
of Duperrey and Freycinet; and where reduction on account of 
the hours employed has been necessary, he has introduced a 
formula similar to that for temperature depending upon the 
sine of the arc corresponding to the time from noon. Such a 
formula has also been employed by Carlini* and Hallstrom. 
The general result to which M. Bouvard’s interesting inquiry 
led him was, that at the equator the amount of the oscillation 
is proportional simply to the temperature, on the centigrade 
scale, of the period during which the oscillation is observed at 
the given spot, the oscillation and temperature at the level of 
the sea being unity ;—that in any other latitude the same law is 
to be modified by introducing the additional proportionality to 
the square of the cosine of the latitude. Or representing by m 
and t the oscillation and mean temperature at any place and 
for any period in latitude Q, and by m! and t f those quantities 
at the equator, we have, according to M. Bouvard, 
m 
in 
t' 
t COS-0 
or, the latitude and temperature being given, to find the oscilla¬ 
tion 
t COS 2 0 / 
m = —j— m 
V 
When the temperature (on the centigrade scale) becomes nega¬ 
tive, whether by change of latitude or from height, the oscilla¬ 
tion will become negative also and take place in an opposite di¬ 
rection; this inference M. Bouvard confirms by the fact, that 
the mean oscillation at the convent of the Grand St. Bernard is 
actually negative. 
The observations by Mr. Goldingham at Madras, printed 
(not published) by the East India Company, confirm the re¬ 
sults of former observers. As an attached thermometer seems 
to have been neglected, the amount of oscillation cannot be de¬ 
pended on, but the critical hours are extremely well fixed. 
Dr. Russell at Berhampour (lat. 24<° N.). and Mr. Prinsep at 
Benares (: 25%°) have also added to our list of recent observa¬ 
tions f. In more northern climates we are also lately indebted 
for valuable observations to the Royal Society of London,—an 
abstract of the results of which has recently been published by 
Mr. LubbockJ, giving an oscillation equal to 0*57 millimetre §;— 
* Memorie della Societa Italiana, tom. xx. 
f Philosophical Transactions , 1828. % Ibid. 1 S31, p. 223. 
§ Since the publication of Humboldt’s Essay on this subject, millimetres 
have become the more usual reference for the measure of the oscillations. 
