GANNETT.] SOLUTION OF TRIANGLES. 17 
pole (at S), the passage is called the upper culmination, in contradis- 
tinction to the lower culmination (at S'). 
In the diagram — which the surveyor may better understand by hold- 
ing it up perpendicular to the line of sight when he looks tov/ard the 
pole — Polaris is supposed to be on the meridian, where it will be 
about noon on April 10 of each year. The star appears to revolve 
around the pole, in the direction of the arrows, once in every 23^ 56"M 
of mean solar time; it consequently comes to and crosses the meridian, 
or culminates, nearly four minutes earlier each successive day. The 
apparent motion of the star being uniform, one quarter of the circle 
will (omitting fractions) be described in 5^' 59'", one half in 11'' 58'", and 
three quarters in 17^' 57™. For the positions s^, Sg, s.^, etc., the angles 
SPSj, SPSg, SPS3, etc., are called hour angles of Polaris, for the instant 
the star is at s^, Sg, or S3, etc., and they are measured b}^ the arcs Ss^, 
SSg, S83, etc., expressed (in these instructions) in mean solar (common 
clock) time, and are always counted from the upper meridian (at S), to 
the west, around the circle from C' 0'" to 23'' 56'". 1, and may have any 
value between the limits named. The hour angles, measured b}^ the 
arcs SSi, SSg, SSg, Ss^, Ss^, and SSg, are approximately 1'' 8"\ 5'' 55'", 
gh ^rn^ -,^^h 52'", 18'^ 01'", aud 22'^ 48"\ respectively; their extent is also 
indicated graphically by broken fractional circles about the pole. 
Suppose the stai* observed at the point S3; the time it was at S (the 
time of upper culmination), taken from the time of observation, will 
leave the arc SSy, or the hour angle at the instant of observation; 
similar relations will obtain when the star is observed in any other 
position; therefore, in general: 
Suhtract the time of upper culmination fro7n the correct local mean 
time of ohservation ; the remainder loill he the hour angle of Polaris 
expressed in tiine^ or the ''^ argument for TahleSy 
The observation may be made at any instant when Polaris is visible, 
the exact time being carefully noted. 
Bull. 234—04 2 
