571 
purpose the situation of the point designated as “Entrance Mecca” 
had first to be determined. We adopted as such point II in the plan 
of Mecca, plate Il fig. 2, and according to this its co-ordinates relative 
to the Ka'bah are 
Aa = 638 m. = 22".2 West 
Ay = 253 m.= 8".2 North 
Using these values we obtain as relative co-ordinates of points 93 
and 1 according to the astronomical determinations 
X = — 38’ 2".2 = — 65705 m 
Y=-4+ 3/38"9=—-+ 6729 m 
while the results from the observations on the journey were 
a=—78324m y=-+ 5271 m. 
As the errors in the astronomical results may be regarded as 
small compared with the accumulated errors of the observations on the 
journey, we may conclude that the latter results need corrections 
Av = + 12619m Ay=- 1458 m. We may regard these corrections 
as owing to an error in the accepted value for the length of a step 
and to a constant error in the deduced azimuths. 
We then obtain, designating the true length of a step in meters 
by 0.78 (1 ~p) and the constant error of the azimuths by d, the 
two equations 
Ar = — (pcos d + 1 — cos d) « + (1—p) y sin dD = + 12619 
Ay = — (p cos d + 1 — cos d) y — (1—p)e«snd=-+ 1458 
The solution of the two equations vields 
pcos d +1 —cosd=a=+ 0.15913 
(1—p) sin d= 6 = + 0.02932 
So the true length of a step and the constant error of the azimuths 
are found to be 
(1—p) 0” .78 = 0" .6563 d= + 2°0’ 
while the values found for @ and 4 may be used to correct the 
co-ordinates of cur 92 points. These corrected co-ordinates are found 
in the two last columns of our table. 
At the same time they have also been drawn, and with them the 
whole of the road Mececa—Jidda, ii our plate HI. No scale has been 
appended, but in the map itself lines have been drawn at distances 
of 2’ in longitude and latitude of each other. These have been drawn 
perpendicular to each other, and as length of a second of latitude 
and longitude in meters we have accepted after Busser’s dimensions 
of the earth 30.753 and 28.789, the latter value holding rigorously 
for g = 21°27’. As the absolute longitude from the meridian of 
