C 39 * 3 
produced beyond it to any diftance, and the hour- 
letters placed in a circle, as in fig. 4. 
A geometrical method for defcribing the whole or 
half an elliplis will be (hewn further on. 
From fig. 1. contiue out the horizontal line 
BAD to any length, as to XII in fig. 3. Then, 
.from the points *** in the perpendicular DE (fig. 1.) 
where the parallel lines 5 7, 4 8, 39, 210, and 
1 11 meet it, draw the right lines H, I, K, L, M, 
N, all parallel to the horizontal line BA DP XII. 
producing them at pleafure : and, in fig. 3. draw 
G XII parallel to DE in fig. 1. This done, take 
CF or CD (fig. 1.) in your compaffes, and fet off 
its length both ways from G ('fig. 3.) to VI and VI, 
on the right line E H VI G VI. So VI G VI in 
fig. 3. fhall be equal to FCD in fig. 1. and XII G 
in fig. 3. ill all be equal to DE in fig. 1. 
On VI G VI as a conjugate diameter, and G XII 
as a femi-tranfverfe diameter, defcribe the femi-ellipfe 
VI, VII, VIII, IX, &c. and, to thofe points of it 
where the parallel lines FI, I, K, L, M, and N cut 
it, draw the right lines G VI, G VII, G VIII, 
G IX, &c. as in the figure j and they will be the 
true hour-lines for an eredt diredt fouth dial : and 
they may be produced beyond the ellipfis, and li- 
mited either by circular or fquare lines, between 
which the hours may be placed. 
Laftly, drawPG in fig. 3. parallel to AC E in fig. 
1. and P G will be the axis or edge of the ftile P XII 
G for calling a fhadow on the time of the day. 
And thus, by means of fig. 1. conftrudted for 
any given latitude, either a horizontal or vertical dial 
may be made for that latitude. 
If 
