1836.] Note on the Nautical Instruments of the Arabs. 787 



has the advantage in point of portability. The rules for dividing the 

 wooden bar are the same as for the string, but the marks must be laid 

 off invertedly, beginning at the eye end, which is in this the fixed 

 point. 



Fig. 3 is an instrument still used by the Arabs for taking the sun's 

 altitude. It is exactly the same in principle as the above, but to 

 obviate the inconvenience of looking at the sun, the eye is directed to 

 the opposite point of the horizon, from the lower end of the cross bar, 

 while it brings the solar shadow of the upper end of the same to meet 

 the horizon by adjusting the slider d to or fro on the divided arm. 

 The mode of dividing this arm, as performed in my presence by the 

 muallim, or pilot, is represented in the plate ; but it is obviously incor- 

 rect. A space c e is laid off equal to radius a c ; from e a perpendi- 

 cular e f is raised, and with the same radius a quadrant e g is drawn, 

 which is divided into eighteen equal portions (of five degrees each) ; 

 through these points are drawn radii to meet the tangential line ; 

 and the subdivision into simple degrees, and sixths, is either done 

 by the eye, or by a continuation of the same rule. It will be seen 

 on inspection of the figure, that as the angle g f d is equal to the sum 

 of the angles/ d b and b d e, while b d e is equal to half the angle of 

 observation, angle g f d can only be equal to angle of observation when 

 f d b and b d c are equal, and that the 90° point is therefore the only 

 true one on the scale of divisions. The true mode of division is, as in the 

 case of the string, to describe a quadrant from centre b, and to draw radii 

 through each semi- degree of the arc from 45° downward, because the 

 angle of observation a d b is, as before, equal to twice the angle/ b d, 

 of which c d(c0, c 10, c 20, c 30, &c.) are respectively cotangents. 



To ascertain whether the fault lay with my Arab informant, or 

 with the instrument, I compared the actual divisions on the latter 

 with a scale of cotangents, and found the following results, calling 



True angle Error of Error if false mode 

 deduced. division. had been used. 



90° ' 



84 46 



79 48 



74 46 



69 44 



65 26 



60 22 



55 14 



50 04 



45 



39 50 



It is evident from this comparison, that the instrument was divided on 

 correct principles, and that the muallim had ventured upon an explana- 

 5 k 2 



the radius a c = 



1.00. 



Angle of Angle 



Length c d or 



altitude, marked. 



cot. i angle. 



90" 0° 



1.000 



85 5 



1.096 



80 10 



1.196 



75 15 



1.308 



70 20 



1.435 



65 25 



1.557 



60 30 



1.719 



55 35 



1.911 



50 40 



2.142 



45 45 



2.418 



40 50 



2.759 



0° 



0° ' 



— 14 



—0 30 



— 12 





— 14 





— 16 



—3 30 



+0 26 





+0 22 





+0 14 



—7 27 



+0 4 











— 10 



—10 23 



