Analyses of Books. 
147 
Mass of the Moon= g A,j xthat of the Earth; and the limits of 
DeLambre s tables, roughly estimated, would be as follows ; 
Error in epoch for 1830. 
Grearest error, from error in place of perigee, ... ± 
Greatest error, from error in greatest equation of centre, ... ± 
Greatest error, from the combination of these, 
Greatest error, from error in mass of Venus, ... 
Greatest error, from error in mass of Mars, 
Greatest error, from error in mass of the Moon, 
the errors of 
... ± 5", 6 
1,5 
0,8 
... -fc 1,7 
... + 1,5 
... ± 1,9 
... - 4 — 1,0 
Greatest possible negative error. 
— 11", 7 
Greatest possible positive error, . . . -f- 0", 5 
These conclusions agree, upon the whole, with the results of a similar comparison 
made by M. Burkhardt, founded on Maslcelyne’s observations from 1771 to 1810. 
The principal difference, is in the diminution due to the mass of Mars, which by 
M. Burkhardt is 5 ‘ 5 ; but Mr. Airy thinks that his conclusion is sufficiently well 
established, to be entitled to confidence. In the motion of the perigee too, there is 
some difference : and upon the whole it appears, that this latter is of such an irre- 
gular character, as to require the introduction of some yet undiscovered inequali- 
ty of the form a. sin ( 5 0 -f c), where 0 is the sun's mean longitude, and b a 
coefficient differing very little from unity. In a Postscript to the paper, he finds that 
in consequence of the action of Venus, the Earth's motion in longitude is affected 
t 'th an inequality for which the expression, taking the mass of Venus as determined 
la this paper, is 
2",G X Sin (8 X mean Long, of Venus — 13 X mean Long, of Earth-f- 39°. 57 ) 
The period of this inequality is about 240 years. “ This term,” he says, “ com- 
pletely accounts for the difference in the secular motions, given by the com- 
?»mottofthe epochs of 1783 and 1821, and by that of the epochs of 1801 and 
loti ’’ \y e must j*efcr to the paper for further details, 
TV. Experiments to determine the difference in the length of the seconds Pendu- 
‘ : lh London and in Paris. By Captain Edward Sabine, R. A. and Sec . R. S. com* 
'"Wncatedby Thomas Young, M. D. For. Sec.li.S. and Sec. Bd. Long.pp. 35 to 77- 
The length of the pendulum vibrating seconds, having been measured in 
j by the method and apparatus of Kater, and in Paris by those of Borda 
I “tot ; and the standards of linear measure of the two countries, having 
!“ n referred respectively to those measurements for future verification ; an en- 
reavour was made by M. Arago, in 1817 and 1818, at the instance of the “ Bn- 
U “ es Longitudes," to bring the lengths so measured into direct comparison with 
j other, by ascertaining, by means of invariable pendulums conveyed interme- 
l "tely between Paris and London, the difference of length that actually exists be- 
l ' retn the pendulums at those places ; which difference ought also to be that be- 
the absolute measurements.” 
Hus**?. 11 made use of an invariable pendulum, which had been prepared 
■tk j < T' rect ions for M. Schumacher, and which that gentleman had placed 
1 “is disposal for the purpose. The Board of Longitude added a second, which 
' ien made for them, at the same time as M. Schumacher’s, and has been 
e supplied at the request of the Russian Government to Captain Liitke of the 
bv M* 01 "ployed on a voyage to the Pacific ocean. He was assisted in Pans, 
Lins' , iTheu, M. Nicollet, M. Savary, and Captains Freycinet and Duperry; in 
k on by M, Quetelet and Captain Chapman, R. A. 
laji* 1 ) 1 of all the experiments is, that one of these pendulums performed 
oth,. ;lr: bra ti<ms in a mean solar day in Paris, and 85945,80 in London. The 
sea irs ,22 and 85933,30 in the temperature of 60° and at the level of the 
12 q- R eacceleration is in one case 12.03, in the other 12.08 vibrations ; mean 
Nm 7 ^ selection the acceleration may be reduced to 11.93 vibrations. 
Katf the Tength of the seconds pendulum in Mr. Browne’s house, London, by 
ObJ, * “'easurement is 39. 1 3908 inches ; and in the Salle de la Meridienne in the 
w»esnn °i y 0f Paris ’ b 7 Biot ’ s measurement 39.12843 inches. The difference 
The .Off t0 an acceleration of 11.76 seconds. . 
12 se merence in length of the pendulums corresponding with an acceleration of 
««„, j S a PPl> e d to Captain Rater’s measurement, would give for the length of 
The (lift T )en . llulu m in Paris 39,12820 instead of 39,12843, as found by Biot, 
erence is ,00023= ? J 5S of an inch, a proof of the extreme accuracy with 
