in the Solar Si/stem. 27 



Now tliis annua! diminution of Laplace's, and which De- 

 lambre uses in his Tables of the Sun, is considerably too great, 

 and will not at all agree with modern observations. 1 have 

 in the following table compared the observed obliquity with 

 that deduced from it, and also with that from an annual di- 

 minution of -42667, the number which I think answers better 

 than any other I have tried, 



Ulubeg 1437 23 30 27 23 31 'frO + SiVo 23 30 3i-9-f-4'9 



Tyehd 1587 23 29 30 23 29 47-9+ 17-9 23 29 27-9— 2-1 



Cassini 1672 23 28 54 23 29 3-6+ 9-6 23 28 51-6-2-4 



Richers 1672 23 28 51-5 23 29 3-6+12-6 23 28 51-a+O-l 



Condamine ... 1736 23 28 24 23 28 30-34- 6-3 23 28 24-4+ 0-4 



Bradley^Miyer \ ^^^^ ~^ ^^ ^'^'^ ^^ ~^ -^■^+ ^'^ ^'^ -^ 18-3+0-0 



Brinklev ...... 1755 23 28 15-5 23 28 204+ 49 23 28 16-2+0-7 



Maskelyne 1709 23 28 100 23 28 13-1+ 3-1 23 28 10-2+0-2 



Philoso. Trans* 1772 23 28 8-7 23 28 11-6+ 2-9 23 28 8-9+0-2 



Lalande 1786 23 28 00 23 28 43+ 43 23 28 3-0+3-0 



Cassini 1788 23 27 58-6 23 28 3-2+ 46 23 28 21 + 3-5 



Delambre, &c. 1800 23 27 57-0 23 27 570+ GO 23 27 57-0—0-0 



Sievjigo^^^^ -^ ^^ ^^'^ "^ ^^ ^^-- ^^ ^'3 27 51-4+0-9 

 Thus we see that 230 years ago Laplace's formula errs 39", 

 while the greatest error arising from the assumption of "'42667 

 is only 4"*9 ; we may therefore consider it nearly correct. The 

 progression of the perihelion of the Earth's orbit came out, as 

 we have seen above, 10"*723; butDelambre from the compari- 

 son of a great number of observations makes it 1 1""808 : I 

 have therefore assumed 42"'667 and ll"'808 to be the exact 

 values for the changes in the obliquity and in the longitude 

 of the perihelion, and afterwards calculated the multipliers of 

 Venus's and Mars's masses upon two suppositions ; the one 

 that Mercury's mass is what Laplace supposes it, and the 

 other that it is equal to nothing ; and then examined which 

 result agreed with observation. 



If we take Mercury's mass what Laplace supposes it, we 

 have the two following equations, to determine the multipliers 

 for Venus's and Mars's mass (that is the true mass of Venus 

 yjBV?2-^» and Mars g^^^^-j/: then) 



3022^+1121 v/ = 5228 

 3336 jr + 75-68 j/ = 2473 

 whence x = -676905 and j/ = 2-8389. But if we suppose Mer- 

 cury's mass =0, then the expressions become 

 30220-+ 1121 y = 4813 

 3336 x + 75-68. y = 2559 

 whence x=-71331 and j/ = 2-371. (>n these two suj)positions 

 the following tables have been constructed. 



* Sec Philobopliiciil TransactitMis, 177'5, |*i»§« 93. 



I) 2 Motion 



