VOL. LXXXI.3 PHILOSOPHICAL TRANSACTIONS. 43 



The light caravans were, 



Irwin, 1 r21 days 



Capper, > from 80 to 100 camels. J 33 



Hunter, J 134 .. .. 



Messrs. Irwin, "i f 21 days, 9''12" 



8 38 



8 45 



Mean of the three 8 52 



Here then the mean of the heavy caravan day is under 74- hours ; and that of 

 the light caravan between 8-J-, and 9 hours. Thus the mean daily rate of the 

 heavy caravan, appears to be J 8.64 British miles, reckoning 24- miles for each 

 hour; and 10. 06 if taken at 2.56: and the mean rate of the light caravan 

 22.17 miles, at 24-; 22.7 at 2.56. 



In order to apply this scale with effect, to the African geography, it is neces- 

 sary to state the number of days that the caravans usually halt on the road. 

 Now it is evident, that if the length of the journey in the gross, is given, the 

 requisite information will not be obtained, without a previous knowledge of the 

 time lost by necessary or unavoidable halts on the road. Inquiries have fur- 

 nished an account of 13 halts, to 149 days of travelling; or, which is the same 

 thing, 13 halts out of 162 days, reckoned from the time of departure, to the 

 time of the arrival of the caravans at the place of destination : that is, 1 halt to 

 12-1- travelling days. This, of course, must be deducted from the aggregate of 

 the distance ; or, should it be averaged on each day, the heavy caravan day must 

 be reckoned at 17-14 miles instead of 18.64; and that of the light caravan 

 20.4, instead of 22.17 ; when the hourly rate is taken at 24- miles. 



It also remains to be stated, from the proportion that the road distance bore 

 to the direct distance, by the trace of Mr. Carmichael's route ; what length in 

 direct distance, and in geographic miles, may be allowed for each day, for the 

 heavy caravan, on similar lengths of journey, and over similar tracts of country. 

 It appears then, that on the 28 days between Aleppo and Rackama, opposite 

 Mesjid Ali, the mean length of the day's journey, in direct distance, is about 

 154- geographic miles : and on the whole 45 days between Aleppo and Bussorah, 

 13.8 such miles. But this is without any allowance for halts ; which, as has 

 been observed before, require a deduction of 8 parts in 100, to be made from 

 the gross amount of the whole journey, when applied to the purposes of 

 geography. 



IX. On Infinite Series. By Edivard Waring, M. D., F. R. S., &c. p. 146. 



Mercator first published the continuation of the common method of division 

 to an infinite series of terms proceeding according to the dimensions of a variable 

 quantity ; Newton did the same for the common method of extraction of roots. 

 Dr. Barrow before applied the same principles in some easy examples to find the 

 asymptotes of curves. The methods of division and extraction of roots were long 



G 1 



