180 



PHILOSOPHICAL TRANSACTIONS. 



ad 



[anno 1/87. 

 If the fault in the southern latitude = — r/, in the northern 



node, Nn = 



latitude z=i -\- d, the same formula is still true ; but then en >► En, and the place 

 of the erroneous node will be between e and n. In both cases the errors in the 

 place of the node are directly as the errors in the latitudes. 



A Let us now suppose, that only the one latitude is 

 j(j E erroneous + d. Then Nn = + En If en = a X 

 " / , _t^^^ X —t-A— - ^^i T fK 



(5. ""case when the error in both latitudes is positive 

 = + c?, and |3 >- ^, or (3 -< Zr, the resulting error in the place of the node = 



fLl± — ri_J — _. In the case when the error in both latitudes is negative — d^ 



{b + I^Y + 2rf (6 + /3) 6 > 



and (3 >- Z?, or (3 -< Z>, then the error in the node = TTri^'Ynb + Jy "^^ ^^°^^ 

 two cases the error is less than in any of the former, and quite nothing when 

 Z) = (3. If the radius of the instrument, with which the meridian altitudes are 

 observed, be given, the quantity of d is also given. In a mural quadrant of 6 

 or 8 feet, of = 5 or 3 seconds. Take a = 34' 3^ b = 56'', (H = 27", d = 5", 

 and the error in the southern latitude -f- d, in the northern =—•«/; then Nn = 



12?— = 2' 12". Take now the error only in the southern latitude = -{-</; 



then Nn = ^3—^ = 1' 18''; in the case of - rf ; Nn = ^^~= V 28". Hence 

 it appears, that in comparing two single observations, it will hardly be possible to 

 avoid a fault of ± 2 minutes in the place of the node. 



If the instrument be of a less force than a mural quadrant of 6 feet, and the 

 possible faults in the altitudes greater, for example, 10 or 15", the resulting error 

 in the place of the node may very easily be calculated ; but the error in the node 

 will be enormous, and the observations of no use for a nice astronomer. 



Mean 



9 21 50 8.5 



