DIALLING, 
wherein he lays down a method of drawing the pri mary 
dials on a very eafy foundation. The fame foundation is 
defcribed at length by Sebaftian ae in his Rudimenta 
Mathematica, publifhed in 1651. mius, in 15 oi 2, pub- 
lifhed a new edition of Walperus’s Dialling, wit e ad- 
dition a a whole fecond part, about inclining md ‘declining 
Gials, & n 1408, the fame work, with Sturmius’s addi- 
tions, was meer tage with the addition of a fourth part, 
containing Picard’s De la Hire’s method of drawing 
large oe which ee much the beft, and falled book on 
the fubjedt. Peterfon, Michac l,and Muller, have each written 
on dialling, i in the German tongue Degas in his olo- 
giographia Plana, aaa in 1689; Gauppenins, in a 
Soman Mecha im, in is Dialling, fol. ; 
e of Mathai Inftruments ; and Wells, 
of Shadow have a treatife by M. De 
par cieux, in oe. Mr. Fergufon has aifo ae on this 
fubje& in his LeQures on Mechanics: Mr. Emerfon, in 
the goth ‘nee of his works; and Mr. W. cae in his 
Inftrumental Diallin 
Diarrine Cylinder, Univerfal, is reprefented by fig. 3 
_A BCD isa glals cylindrical tube, clofed at both ia 
. with brafs plates, in the centres of which a wire or axis 
is fixe he tube is sa fixed to an horizontal 
H, fo that i its axis pe! ma 
particular latitude. 
with a diamond on the outfide of the glafs, equidiftant from 
‘each other, and parallel to the axis. "I'he XII next B flands 
for m apie t, and the XII next the board H for noon. 
axis of this inftrument is elevated ramen to the 
sae ae e board fet level with the line H N in the 
plane of the eee te an nd 
the axis EF Gw 
y 
the tube, with lines drawn from the 
centre to the feveral parallels cutting its edge, will be an 
horizontal dial for the given latitud 
cafes for the ftyle of the dial; and if a a . 
ia the diane fo as to decline, ae or recline, 
of degrees, and ace 
% 
e 
oa 
2 
a 
t up in fun- 
fhine in the (ine pole oS were in a tube, A D will 
be an equinotial dial, efan oracles dial, and g ca ver 
tical fouth dial, and the time of the d will be fhewn by 
the axis E F G. If the cylinder were aod inftead of glafs, 
upper plate with lines drawn to the feveral 
jnterfeGtions oF the parallels, which appears obliquely in fg. 
38, would be an equinotcti al dial, as in Je. 39, and the axis 
perpendicular to it be its ftyle. An horizor > dial for the 
latitude of the elevation of the axis co be made, by draw- 
ing out the axis and cutting the cylinder, as aa ef gh, pae 
rallel to the horizontal board H; the fe&tion would be “elliptic, 
asin fig. 40. Accircle might be defcribed on the centre, 
and lines drawn to the divifions of cs BAe would a the 
s pla as ae ould 
dicular to the hor. mae board H, or 
beginning at g, the plane of the ection coud be cllip- 
tic, asin fig. 41, and lines drawn to tle points of inter- 
fe&tion of the parallels on its edge would be the hour-lines 
of a vertical direét fouth dial, which tien e made of 2 
fhape, either aera or f{quare; an the axisof thec 
der would be yle. Thus alfo mchining declining oF or 
reclining dials ok be cated confrudied, for any given 
oy ubi fu 
Linc Globe, is an inftrament made of brafs, or wood, 
Dia 
bition . the principles of t 
Diatuine Lines, or Scales, are pe adusted lines, placed on 
ae or ‘the edges oe a adrants, and other initruments, to 
exped of dials. 
Tne Gee of cen lines are, 1. A cas of fix hours, 
which is only a double tangent, or tw es of tangents, 
each of 45 degrees, joined together in ee middle, and equal 
to the whole line of fines, with the declination fet againtt the 
meridian altitudes i in - latitude aire 
, fuppole, or any 
place for which it e: the ra E vag line a fines 
is equal to the dang eae of fixhours, 2. A line of lati- 
tudes, enti is fitted te the hour-fcale, me is ne by this 
canon: as aan is to the chord of 90 degrees; fo are 
the Sits oe each refpcétive degree of the line o latitudes 
to the tangents of other arches : a poh iy natural fines of 
thofe arches are the numbers, which n from a diagonal 
{cale of equal parts, will ee the cvion of the line of 
latitude to any radius. ‘Phe lin and latitudes is ge- 
wo all dials ed centres. For the 
met f conftrnGing thefe {cales, fee ScAtz. There are 
feveral other lines put upon {cales 2 ee ae dae to par- 
ticular latitudes. Such are, 1. A lin 2. A line of 
the fubftyle’s diftance from the endane : . ‘A line for the 
height of the ftyle above the ‘gr 4. A line of the angle of 
the hours of 12 and 6: line of the plane’s difference of 
longitude, or inclination of meridians ll thefe are calcu- 
lated for every degree of ey a fome particular lati- 
tude,e. g. that of London, by the follo owing problem. et 
e dial-plane, the diftance of the fubftyle from 12 
Beek, cu the plane’s difference of longitude. es 
NES SW (jig. 42.) be the horizon, C its centre, NS th 
meridian, P the pole, a Z the zenith; H Athe dean 
vertical plane ; P 1, 3, &e. ae or femi circles, 
ee the circle ti A in?, v, &e. the meridian 
2 be perpendicular to HA, then the ne of the meri- 
dns v il be perpendicular to the plane of the diai; 
and therefore the angle Z Pv is the plane’s difference of lon« 
i the me- 
ridian of the place and the meridian of the plane, called alfo 
the ‘* inclination of meridians,” and the arc P uv is the e height 
of the pole above the plane ; and the arc Zv is the diftance 
of the fubftyle from the meridian. Therefore in the right~ 
angled {pherical triangle PZ wv all the three requifites will 
be found. For we have PZ the complement of the latitude, 
and the angle PZA the oncieaae of the declination 
: whence will be fc Vv, » andt gle " 
Thus 1. As radius is to the fine of deciination, fo - 
the c 
tangent of latitude to the tangent of the fubftyle’s diftance 
rom 12 o’clock; for bya cafe of right-angled {pherical tri- 
angles, rad. : ee PZwv : tang. 
dius is to the cofine of declination as the cofine of latitude is is 
to 
