28 Professor En eke ofi the SolarEclipses 



dividing the value of B (8), and withdrawing x from under 

 the symbol, (9) 



/{AYZT ... («)} + ^/{XYZT ... («)} = 



which establishes the theorem to be true for n, if true for n — \ 

 equations. The simple equation Ai + XjJt = evidently con- 

 forms to the rule, which is therefore true when n = 1 ; it is 

 therefore generally true. 



(12.) The rapidity of this method is best estimated by 

 examples. Take three equations, in which by the rule 



/(AYZ) 



/(XYZ) + ^ - '^ 



The series of indices is +123—132 + 231-213 + 312—321; 

 therefore 



A^( Y,Z3- Y.,Z,) + A,( Y,Z, - Y,Z.3) + A3( Y,Z, - Y.ZQ 

 XiCY,Z3-Y3Z,)+X,(Y3Z,-YiZ3) + X3(YjZ,-Y,Zi)'^ 



For four equations the series of indices, deriving each from 

 the one preceding it, is + 1234-124.3+ 134-2 -1324 + 1423 

 — 1432 +2143 — 2134 + 2314-2341+2431—2413 + 3124 — 

 3142 + 3241 —3214 +- 3412 — 3421 + 4132-4123 + 4213 — 

 4231+4321—4312 



, . /(AYZT) 



and smce x + vf/^YZT) ~ 



A,{Y2(Z3T,-Z,T3)+Y3(Z,T„-Z,T4) + Y4(Z2Ts-Z3T2)} + 



A,{Yi(Z4T3-Z3T,)+Y3(Z,T4-Z4Ti) + Y4(Z3Ti-Z,T0}+ &C. - 

 "" X,{Y2(Z3T4-Z4T3)+Y3(Z4To-Z,T4)+Y4(Z„T3-Z3Tn)} + 



X2{Y,(Z4T3-Z3T4) + Y3(Z,T4-Z4T,)+Y4(Z3T,-Z,T3)}+&C. 



III. On tJie Sola?- Eclipses and Transit of Mercury over the 

 Sim's Disc, in 1832. By Professor Encke*. 



TN 1832 there will be two solar eclipses, and a transit of 

 -*■ Mercury. The latter phaenomenon only will be visible at 

 Berlin. No lunar eclipse will happen. 



Solar Eclipse 183% February 1. App. time of 



Berlin. 



Beginning on the earth in general S** G' 



in 176° 52' east longitude from Ferro. 

 8 49 south latitude. 



* From the Berlin Astronomical Ephcmeris for 1S32, page 200— 205. 



Beginning 



