Aug. 17, 1888.J 



SCIENTIFIC NEWS. 



149 



Its berries are first green, then take a bright yellow, an 

 finally become scarlet. In the blackberry and the bil- 

 berry we see the development of blue and violet colours 

 out of red, as both these fruits are red when half ripe. 



SUN-DIALS, AND HOW TO MAKE 

 THEM.— II. 



V HE next pattern to be considered is the ordinary 

 horizontal dial. This may also be considered to be a 

 thin slice of the globe dial, but in a horizontal plane. 

 The axis, as before, points to the North Pole, and it may 



T ] 



A 

 F 



"•■''-' (7 



CO, , N, ■ L /0 



■\ p r ° 



s 





Fig. 7. 



be either a thin wire or a stout gnomon ; in the latter 

 case the dial must be considered as though divided by 

 the thickness of the gnomon. 



Fig. 6 (page 129) shows the horizontal dial as a sli.e of 

 the globe. It will be seen that the divisions are no longer 

 equal, but decrease in size as they approach XII. 



There are a considerable number of methods of setting 

 out the divisions ; some of them are well worthy of atten- 

 tion, and those who care for pure geometry will find the 

 subject full of interesting problems, ranging from the 

 simple cases which are given in these chapters to the 



Fig. 8. 



intricacies of spherical trigonometry, into which 

 not enter. 



The least interesting method is to take the 

 from the following table of angles : — ■ 



Lat. a.m. p.m. a.m. p.m. a.m. p.m. a.m. p.m. 



T VI Tt V in r u. t.T 1.11. 



we shall 

 divisions 



50° o' 

 51 o' 

 5 1 3° 



5 2° 0' 



53° o' 

 54° °' 

 55' o' 

 56° o' 

 58° o' 



XI 

 n° 3 8' 

 1 1°46' 

 n°5i' 

 u°S5' 



12° 5 ' 



J2°l4' 



I2°23' 

 I2'32' 

 I2°4$' 



II X 



23°5i' 



24°10' 



24° 1 9' 



2 4 °27' 



24°45' 

 25° 2' 



25 19' 



25°35' 

 26 s 5' 



III XI 



37°27' 

 37°5'' 

 38° 4' 

 3*>°'4' 

 38°37' 

 38 58' 

 39° 19' 

 39 V 

 40° 1 8' 



IV VIII 



53° °' 



53°24' 

 53°36' 

 53°46' 

 54° 8' 

 54°29' 

 54'4'j' 

 55° 8' 

 55°45' 



a.m. p.m. a.m 



V VII VI 



70-43' 90 c 



7o°58' 90' 



71° 6' 9;' 



7i°i3' 90' 



7i°27' 90° 



7i°4o' 90' 



7i°S3' 90' 



72° 5' 9°' 



J2°2f 90' 



p.m. Tan. 

 VI Co. Lat. 

 o' 



'o' 

 'o' 

 'o' 

 'o' 

 'o' 

 o' 

 o' 

 'o' 



■839 



•809 



■795 

 •781 



•753 



•720 

 ■700 



■674 



•625 



The XII., or noon line, must be drawn first, and the 

 VI. line at right angles with it ; the other hour lines may 

 then be set out with a protractor, but in the geometrical 

 methods which will be given this instrument will not be 

 required. 



The last column in the table is the tangent of the co- 

 latitude. This may sound rather alarming to non-mathe- 

 matical readers, but it will be found useful in setting out 

 the angle of gnomons for those who do not possess a 

 good protractor. At the latitude of York, 54 degrees, to 

 construct a gnomon for a horizontal dial draw a straight 

 line 10 inches long, and at right angles to one end of it 

 draw a line 7 '20 inches long. Join the ends of these lines 

 to form a right-angled triangle ; this will be the shape 



of the required gnomon, the 10 inch side being the base 

 and the 7^20 inch side the perpendicular. This side is 

 generally cut in a fancy shape. 



The first method which we describe for setting out the 

 angles of the hour lines by simple geometry without the 

 use of a table of angles and a protractor, was held in 

 esteem by the old diallists for a curious ieason — it can 

 be produced by " only one opening cf the compasses." 

 Old books of geometry often describe figure methods of 

 drawing figures with as few different openings of the 

 compasses as possible ; this seems to suggest that in the 



Fig 10. 



early days of instrument making the joints of the com- 

 passes were either so stiff or so ricketty that the less the 

 legs were moved the better. 



Draw two lines AB, CD, Fig. 7, intersecting at right 

 angles at E. From E as a centre, with any ccnvenient 

 radius, draw the circle FKGL, cutting AB at F and 

 G, and cutting CD at K and L. Then, keeping the 

 compasses at the same opening, place one point at G and 

 mark off M. Then turn from M to the point N, then 

 make two steps to O and four steps back to P. JoinMF, 

 cutting CD at Q. The points ONLQEP, correspond to 

 the hours V., IV., III., II., XII., and XI. The points 

 found by repeating the process on the other side 



