[deville] 



ABACUS OF THE POLE STAR 



11 



we measure multiples of n?j, n being the number of minutes of latitude 

 in a township, and mark the township number opposite the divisions of 

 the graduation. The scale of y, given by (15), is also a I'egular scale 

 laid out on Bv with an appropriate modulus l^ ; instead of the hour 

 angle, the sidereal time is marked opposite the divisions of the gradua- 

 tion. 



The cartesian co-ordinates of the points of the escale, defined by 

 (16), are given by (8) and (9) : 



, l — L 



X = d 



l^-hL 



= (h — 0.75) 



I, h 



h+l. 



C\ X 



Fig. 7. 



X being a constant, the bearer of the H scale is a parallel CD 

 (Fig. 7) to the axes, drawn at a distance x from the centre of AB. The 



-2" scale is a regular scale of modulus — - — + — - — , commencing at 0'.75 



below the line AB. 



The abacus has been made in two parts place! one over the other. 

 The sidereal time scale is identical in both. The divisions of the altitude 

 and township scales have been so arranged that they coincide, but they 

 bear different numbers. The numbers of the second part are printed in 

 red. 



Plate II shows a specimen of the abacus. 



