310 C. Abbe on the Repsold Portable Circle. 
An ephemeris of the azimuths and zenith distances of the 
rincipal stars, if computed for every 5° of latitude, will serve 
y interpolation for any intermediate position. The formule 
for the computation of finding ephemerides as given by Mr. 
Déllen are very simple 
Put z—(p—9)=r; the well known formula, 
; cosz—=cos (p—9) — 2cos p cosd sin? 44, 
gives . 
; ioe 4 pada 
(C.) sing7—=cos @ sin tt — ane ET 
Another well known formula may be written — 
(D.) sin A=sin t 
Or by a transformation of 
sinz cos A=—cos¢ sin 0-+-sin g cos 9 cost, = 
these results, approximately, 
(D’.) sin?4A—sin » sin? 42 
COs 
sin(p—d-+-r) 
cos 0 
sin(p—0)" 
Neglecting the 7 in the second members of these equations, they 
admit of a very simple arrangement for the computation of an 
ephemeris whose argument is the time for stars near the merid- 
ian, being sufficiently accurate within the limits 
g—5>10° and t<15°. 
For an ephemeris in the neighborhood of the prime vertical we 
may use the azimuth as argument; counting it from the west 
point northward, we have 
E. sind=sin 9 cosz--cos @ sinz sin A 
Boy 
(F.) tand SIL ¢ tan A-+-tan 9 cost. 
inA 
Put tan i an —— : 
tan sin p 
the first formula (E) becomes 
G. 
cosz'=cos(z—¢)=p sind ; 
whence _ 2-2’ +t. 
Put Bogs > and = ; 
n np 
the second formula (F) becomes ‘ 
H. eos t/=cos(t—w)=¢ tand; 
whence i=?’ -o, 
_ The arrangement of these computations can be made exceed- 
ingly convenient. Extensive ephemerides for latitude 35° to (@ 
north have been published by General Tenner; provided with 
