306 



KNOWLEDGE. 



August, 1911. 



In order to appreciate the action of the dial, 

 consider the position of the earth with regard to the 

 sun at different periods of the year. In the height of 

 summer, when the sun is high over-head, if a stick of 

 known length lie held (_)Ut parallel with the earth's 

 surface — i.e.. horizontalh' — a shadow will be cast 

 verticallx' down the bod\- of the person holding the 

 stick, which will be ver\- long at mid-day, decreasing 

 to zero at sunrise or sunset. Also at any particular 

 period of the year the length of the 

 shadow, measured vertically, cast hv 

 a horizontal stick, will \ar\' with the 

 declination of the sun and with the 



month m 



a [)iece of thread is 

 lurpose, and spin the 



time of da\- — being, in general, shorter 



^ 



opposite the \-ertical for the da\- of th 

 question. 



Hold the c\iin<ler \-ertica 

 attached to tiie cap for the 



dial round until the shadow cast b\' the gnomon 

 down the cNJintler is \ertical. The end of the 

 shadow will show the time of day, the reading 

 being taken from that vertical most nearl\- coinciding 

 with the shadow, while the curves allow an accurate 

 interpolation to be made. 



corres- 

 above 



;i\en length 

 ength of the 



in winter than in summer. 



The gnomon of the sundial 

 ponds to the stick in the 

 illustration, and for a gnomon ol 

 it is a sim[)le matter to calculate tlu' 

 shadow which ought to be thrown on any particular 

 da\' of the year, at any time of the day. As it 

 is not possible to construct a dial with three hun- 

 dred and sixty-five sides, a side for each dav of 

 the year, a certain interval oiiK on 

 the cylindrical surface of the dial can 

 be allotted to each month. 



These intervals are shown Iw the 

 vertical divisions and suii-di\isions on 

 the de\'eloped plan. 



The numbers 1, 2, ,5, 4, and so on, 

 refer to the hours of the da)' — 1 for 

 one o'clock, and so on. 



At 12 o'clock the sun is high oxer- 

 head, so that one curve represents this 

 hour, but as the sun's angle at 1 1 is 

 the same as it is at 1 o'clock, each 

 of the other curves can represent the 

 hours in pairs before and after noon. 



The vertical for December indicates 

 that the sun rises about seven, because 

 onlv the curves for 7. X. 0, 10, 11 and 12 o'clock 

 pass through it. On the other hand the June 

 vertical starts with a point almost at four o'clock, 

 all the curves subsequent to this number being 

 marked upon the vertical. 



Although the above description is, of necessity, 

 somewhat lengthy, yet the manner of reading the 

 dial is simplicity itself. 



Take the conical top out of the cylinder and after 

 j)Utting the gnomon in a horizontal position replace 

 the cap, jamming it firmly into the top of the 

 cylinder so as to hold the gnomon in that posi- 

 tion (Figure .^), but before jamming turn the top 

 round so that the sharp edge of the gnomon rests 



Figure 5. 

 riie gnomon. 



FiGUR?: 6. 



Angle between the two planes 

 HOADC and K()ALC=sun's 

 doclinatiiin on any day of 

 the year. At Midsnmnier 

 these two planes will coincide. 



No \ery great accuracy can be ex- 

 pected from such a simple and cheap 

 instrument, but an accurac\' ecjual to 

 that of a small sundial might be 

 anticipated. 



Like all sundials, this curious instru- 

 ment can only be used in the latitude 

 for which it is designed, though in such a small dial 

 considerable margin in this connection might be 

 allowed. 



This particular dial is (juite modern in appear- 

 ance, though there is no indication of the place 

 of manufacture upon it. The writer was given to 

 understand that it was found in use 

 amongst the shepherds in the North of 

 I'rance, though the princijial dimen- 

 sions of the dial, including the gnomon, 

 are in inches, and denote in consequence 

 an English or American origin. It is 

 almost certainh' a copv of some older 

 f( inn. 



The elementary mathematical theor\- 

 (■\ol\L'd is as follows (see Figure 6) : — 



(1) AOI5CD is the plane of the sun 

 at meridian. 



(2) KOAFC is the equatorial (ilane 

 at right angles to this plane. 



t J) KOALC is any plane within 23A" 

 N. or S. of the meridian plane. 



Then if the sun is supposed to rise at A and set at 

 C on an\' particular da\' of the \'ear, it will pursue 

 such a path as ALCKO. 



Suppose P be an\' point on the same jiaths on this 

 day. Join PO, PB. BK and KO. 



Then PKBO is a right-angled spherical triangle of 

 which the angles POK, KOB are known, KOB 

 being the sun's declination from the vertical and 

 POK being 90 — hour angle. 



The soluticju of this triangle will lie found in any 

 good work on surveying, and is of the form 



cos (( = cos j8 cos y, 

 where a ("i and y are the angles of the spherical 

 triangle. 



DISCS FOR SOLAR PROJ I-XTION. 



By JOHN McHARG, M.A. 



Ox the following pages are given four more of the Maps for Solar Projection wlm h com[)lete the set. Number 

 V. was printed on page 199 of this volume, while Numbers I., II. and III. appeared in the June issue for 

 this \-ear on pages 207 to 209. It is intended to rejirint the series and issLie them as a separate publication. 



