VOL. XIX.3 PHILOSOPHICAL TRANSACTIONS. 49 



radius b e (in all these figures) in the same ratio of m to a ; and their portions 

 pqt, as the versed sines of the intercepted arcs g t. But the remaining seg- 

 ments, as qtr A, qtrx, &c. will be as the sines of the complements of the 

 same arcs q t. 



Now the ratio of the velocities m to a, is compounded of the ratio of the 

 radii k e, be, and the ratio of the angles c k e, v e z, uniformly described in 

 the same time ; and therefore, that ratio of the angles being given, all the 

 aforesaid epicycloidal spaces will also be squared. 



Extract from the Journals of ttvo several Journeys of the English Merchants of 

 the Factory of Jleppo, to Tadmor, or Palmyra. N° 218, p. 129. 



July 18, at 5 in the morning, we set out from Aleppo, being l6 English ; 

 but with servants and muleteers, in all 40; and in 4 hours and ^, travelling 

 south by east, we arrived at a village called Catferabite, being at the edge of 

 the desert, where we reposed the rest of the day. July I9, we rose at ] in 

 the morning, and directed our course S. S. E. over the desert, towards a foun- 

 tain called Churraick ; but our guide losing his way, there being no path, it 

 was near noon before we found it. This well has no signs near it to discover 

 it by. Here we pitched our tents, and refreshed ourselves and horses : the 

 water is of a purgative quality. In our way we found two Arabs with two asses, 

 one carrying water and a little bread, the other they rode on by turns ; they 

 had one gun, with which they shot gazels, the bullet being a hard stone broken 

 round, and cased with lead ; they had on the palms of their hands, elbows, 

 knees, and feet, some gazel-skin tied, that they might creep the better on the 

 ground, to shoot ; one of the asses walking by as a stalking-horse, and the 

 Arab imitating the cry of the gazel till he got within shot : these Arabs are 

 called Selebee. At the well came to us some Arabs that were making ashes of 

 the ordinary sort of weeds called chuddraife, rnggot, and cuttafF; these they cut 

 and dry, and putting them into a pit, set fire to them, and the ashes cake at 

 the bottom. The ashes they carry to Eglib and Tripoli, to make soap of: but 

 the best sort of ashes are made of the weed shinon, which grows about Tadmor, 

 Soukney, Tibe, and Yarecca; it grows like broom in England, and in shape 

 resembles coral. 



July 20, we rose at 4 in the morning, and travelling two hours E. S.E. we 

 arrived at Andrene, where we found the ruins of two or three churches, and of 

 a great town lying in a large plain ; where having tarried about an hour and 

 a half, and taken some fragments of Greek inscriptions, which afforded no 

 certain sense, but yet were evidently christian, we marched again S. by E. and 

 in about 4 hours time came to a pleasant aqueduct called Sheck-alal ; this aque- 



VOL. IV. H 



