1836.] Note on the Nautical Instruments of the Arabs. 785 



Fig. 1. is the .JL^ kamdl, an instrument for taking the altitude of 

 the polar and circumpolar stars*, in its most elementary shape. 



It consists of a small parallelogram of horn (about two inches by 

 one) with a string (or a couple of strings, in some instances), inserted 

 in the centre. On the string are nine knots. To use the instrument 

 for taking the height of polar is, the string is held between the teeth, 

 with the horn at such a distance from the eye, that while the lower 

 edge seems to touch the oceanic horizon, the upper edge just meets 

 the star : the division or knot is then read off as the required latitude. 



The mode of marking off these knots is curious. Five times the 

 length of the horn is first taken, as unity, and divided into twelve 

 parts : then at the distance of six of these parts from the horn, 

 the first knot is made which is called " 12." Again the unit 

 is divided into eleven parts, and six of these being measured on the 

 string from the horn as before, the second knot is tied and denominat- 

 ed " 11." The unit is thus successively divided into 10, 9, 8, 7, and 

 6 parts, when the knot tied will of course exactly meet the original 

 point of five diameters : this point is numbered " 6." Beyond it one 

 diameter of the horn is laid off for the "5" division, and one and a 

 half again beyond that for the " 4" division, which usually terminates 

 the scale. 



It is easy to determine by calculation the value of these several 

 divisions, measured from the centre of the horn or diameter b d, and 

 at right angles to it. They represent the tangents of the angle c b a, 

 to radius b c, or cotangents to the complementary angle e b a : but e b a 

 is equal to b a c, which is half of dab, therefore the divisions represent 

 cotangents of half the angle of observation. To judge then of their 

 actual value, expressed in altitude, we have but to convert their nu- 

 merical ratio to radius, by a table of natural cotangents, into degrees 

 and minutes ; and to take the double as the latitude in each case : thus, 

 the horn being equal to double radius b c, we have 



The first dmsion, No. 



12 = 



2X5r 



12 X 6 



= 5.00 





Lat. 

 22°38" 



11 



10 4- 



11X6 



5.45 



C8 



20 46 



10 



10 -f- 



10 X 6 



6.00 



<*-. 



18 54 



9 



10 — 



9 * 6 



6.66 



"(3 



17 4 



8 



10 -u 



8X 6 



7.50 



q 



15 12 



7 



10 -L 



'/ X 6 



8.57 



bO 



13 18 



6 



10 1. 



6X6 



10.00 



S3 



o 



11 24 



5 



10 



+ 2 



12.00 



O 



9 32 



4 



10 



+ 5 



15.00 



II 



7 36 



Diff. 

 1»52' 



1 



52 



1 



50 



1 



53 



1 



53 



1 



54 



1 



52 



1 



56 



It will be seen by the last column that the harmonic progression 

 of the divisions obtained by this simple rule, agrees A^ery closely with 



* The man assured me it was for taking the longitude, and promised to come 

 one night and use it in my presence, but failed. 

 5 K 



