376 F. L. O. Wadsworth — Determining the Eccentricity, etc. 



2oo— J' a = £ sin (y + 6)—. fsin (;'4-2gj + 0) (6) 



2&3— J'j = esin (rp + O) — «sin (^ + 2a?4-0j (7) 



If the settings are taken by repetition so that y = a + 2co and 

 (p = y+2a> = a-f-4w, and the first setting is made when the 

 circle reads 0, we have 



2gd—A\ = e sin 6 — e sin (6 + 2gj) 

 2go—A'„ — s sin (Q-\-2ao) — 8 sin (6 + 4 go) 

 2go—4' s = fsin (# + 4&)) — f sin (# + 6gj) 



If many arcs are to be tested it would be convenient to 

 have a prism cut to a convenient angle of either of the forms 

 shown in fig. 3. 



In the first of these forms, 

 the faces a] b, c are polished 

 and a and b are silvered. 



In the second form, only 

 the two adjacent faces a, b 

 are polished and silvered. 



The angle 2<w may be deter- 

 mined carefully once for all, 

 and the number of sets of 

 readings necessary for the 

 determination of the eccentricity reduced to two, as only the 

 two unknown quantities s and d then remain to be determined. 

 It is obvious also that in the determination of the eccen- 

 tricity of a complete circle we may use an ordinary 60° prism 

 instead of the plane parallel glass silvered on one side — the 

 only disadvantage being that the reduction of the observations 

 is not quite so readily accomplished. 



If we know the angle of the prism (60° ±<?), two sets of 

 readings only are necessary, and we have 



A'-2go= Z/ — iesin 6—^1 fC os 6 

 i 2 



and for a second set 90° from the first, 



^ 3 e sin 



\ xa O 



whence 



and 



J 2 =|ecos 6.-4- 



^4, + 3 J, 

 34-V^A 



tan?- (j — 



V4 2 + A 



a/6 



If the angle of the prism is not known three sets are neces- 

 sary and the resulting equations are the same as those already 

 deduced — (5), (6), (7) — from which the values of the three 

 unknown quantities w, e, and may be calculated as before. 



Astro-Physical Observatory, Smithsonian Institution, 

 Washington, D. C., January, 1894. 



