74 G. H. KNIBBS. 



through the point defined by the terminal at noon, the point E 

 in figure. At any other time, i.e., between the equinoxes and 

 the solstices, the shadow-terminals on any day lie on an hyperbolic 

 curve, whose vertex is defined by the position at noon, and whose 

 asymptotes intersect at the equinoctial point E. 1 



In the frigid calottes, or zones as they are called, the curves may 

 become ellipses. Turning to the diagram, suppose a vertical line 

 or pole to stand at O, Fig. 7, of the length, equal to OX, (i.e. y 

 1 foot or metre, or 100 feet or metres, or any other unit length): 

 this vertical will be perpendicular to the plane of the page. In 

 latitude 35° S., let the line OP be placed true north and south: 

 then the shadow of the south celestial pole will be the point P; 

 and the noon-shadow of the summit of the vertical, say of the 

 length of 1000 units, will reach the following points on the days 

 indicated : — 



III. — Length of shadows at noon of a vertical of 1000. 

 Summer solstice. Dec. 22 



Jan. 19, Nov. 24 



Feb. 19, Oct. 24 



Mar. 21, Sep. 23 



Apl. 21, Aug. 23 



May 22, July 23 

 Winter solstice. June 22 



At the hours afternoon denoted by the lines radiating from 

 the point P, the shadow will terminate at the intersection with 

 the curves SS, J J, etc. ; that is to say, on the 22nd December 

 the shadow of the top of the vertical line will move along the 

 curve SS ; on 19th January and 24th November along the curve 

 JJ, and so on, the shadow reaching the intersection with the 

 curve of the line radiating from P at the hour marked on the 

 latter. If now a straight line be drawn from the point O to this 

 intersection, it will shew the length and direction of the shadow 

 at any particular hour after noon. 2 The morning shadow for the 



1 The declination change being disregarded, at least for each day. 



2 Measured of course by the uuit height OX. 



0- 



-S 



204 



O- 



-J 



262 



O- 



-F 



433 



0- 



-E 



700 



O- 



-A 



1057 



0- 



-M 



1446 



0- 



-W 



1629 



