156 PROCEEDINGS OF THE AMERICAN ACADEMY 



It is quite obvious, from simple inspection, that in the case of Paris, Edin- 

 burgh, Washington II., and Harvard College, the corrections depending on the 

 Declination are quite large, while in every other case they are of sufficient mag- 

 nitude to be recognizable. 



For each residual, r", of Table II., there will be an equation of the form : — 



rii = a sin (5 4-6 cos (5, 



from which a and b are to be found. 



For a first approximation it will be allowable to arrange the equations ia 

 groups, in each of which r", sin (5 and cos (5 are understood to be mean values. 

 The following are the limits of the groups : — 



Group I from —30° to — 8° 



Group II from — 1° to +10° 



Group III from -fl2° to -4-23° 



Group IV . from +27° to +46° 



a Piscis Australis and a Canis Majoris will now be included in the discussion. 



EQUATIONS. 



Green- "Washington, Mel- Brus- 



wich. I. 11. Paris, bourne, sels. Oxford. 



Group I. — .27 a +.95 6 = -f- 10 —4 —29 —21 —10 —7 —6 



Group II. +.10 a +.99 6-=+ 5 —5 —5 —1 —4 —7 —1 



Group III. +.27 a +.96 6 = — 5 —3 — 6 +1 +2 +0 +0 



Group IV. +.56 a +.83 6 = — 6 +8 +19 +12 — 5 —9 +3 



Edinburgh. Harvard College. 



Group I — .15ct +.99 6 = +13 —.28 a + 95 6 = —24 



Group n +.10 a +.99 6 = +15 +.10a + 99 6 = — 7 



Group III +.27 a +.96 6 = —16 +.27</ + 96 6 = + 1 



Group IV +.53 a +.85 b = —24 +.56 a + 83 6 = +15 



From these equations, we have by least-squares the following values of 

 a and b : — 



s s 



For Greenwich a = —.021 b = +.005 



Washington, I a = +.015 b = — .005 



Washington, II a = +.056 b = —.016 



Paris a = +.039 b = —.009 



Melbourne a = +.008 b = —.006 



■ Brussels « = -=-.005 b = —.004 



Oxford a = +.013 b = —.004 



*Edinburgh a = —.101 b = +.025 



Harvard College a = +.044 b = —.014 



Computing the values of r" with these coefficients, and subtracting from 

 the residuals of Table II., we have Table III., arranged in order of Right 

 Ascensions. 



* The di-scussion of a series of equations of the form r" = a — — - + b -I 



cos 6 ' cos 6 ' C08 5 

 gave results nearly identical with these. 



