OF ARTS AND SCIENCES. 179 



For the stars observed at Harvard College, we have the following 

 equations, where the coetRcients are computed with the value of the 



latitude : — 



q) = + 42° 22'.8. 

 For Circle East, — 



= — 0.93 + J r + 0.G9 a + 0.00 a' -\- 1.00 c, 



= — 1.02 -f z/ r —0.10 a _|_ i.4o e, 



= — 0.68 -\-Jt — 2.61 a + 4.56 c, 



= — 0.96 + /JT + 0.06 a + 1.31 c, 



= — 0.89 + z/t 4- 0.55 a -|- 1.00 c, 



Or=— 1.00-f z/t —1.99 a + 3.74 c ; 



and for Circle West, — 



= — 0.37 -f- z/ T -f 0.00 a + 0.81 a' — 1.02 c, 



= + 2.23 -\-Jr — 4.64 a' — 7.26 c, 



= -{- 0.04 4- J r — 0.02 a' — 1.38 c, 



= +1.49 + Jt — 2.70 a' — 4.67 c, 



= + 0.23 -\-Jt — 0.71 a' — 2.13 c. 



A discussion of these equations has shown that the introduction of 

 the terra A' a' gives values of a and a' sensibly the same. 



We may therefoi-e dispense with this term, and our normal equa- 

 tions become 



= — 0.86 -f 11.00 zir— 10.66 a— 3.40 c, 

 = — 12.06 — 10.66 z/rH- 41.53 a + 40.74 c, 

 = — 34.69 — 3.40 Jr + 40.74 a -\- 122.60 c ; 



which give 



J 7 = _|_ 0.395, 



a = -{- 0.156, 

 c = -\- 0.242. 



But it is better to substitute the values of a a' and c in the equations for 

 the time stars, and thus determine a value for z/ z. We have then, for 

 Circle East, — 



for d Aquarii, the equation =: — 0.93 -\- J r -\- .107 -f- .242, 

 „ Cygni, „ = — 1.02 -[- z/ t + .01 6 + .350, 



„ 7 Cygni, „ = — 0.96 + z/ z + .009 -\- .317, 



„ £ Delphini, „ = — 0.89 -f J t + .085 + .242 ; 



