26 Account of the Climate, Natural Products, Arts and 



tisfied almost every one of the truth of this conclusion : yet there 

 is one point connected uitli it which does not appear to be so 

 well understood; and which is, — that the same carriage will al- 

 ways do least injury to the roads when it moves with a consider- 

 able degree of velocity- For it has been shown that the depth 

 of the impression is inversely as the scpiare of the velocity (Prop. 

 E). Consequently, tiie velocities being represented by the num- 

 bers .. ., 1,2, 3, 4, 5,G,&c.; 

 the corresponding de-"l . J. J_ J_ _L }- R- 



pression will be J" ' *'T' lo'^'Jc' '^' 

 But the injury done to the road must be as the depth to which 

 the wheel sinks into it ; therefore the advantage gained in this 

 respect by increasing the velocity is evident. 



VIII. If the road were perfectly level, and of an uniform ma- 

 terial ; the resistance at the circumference of the wheel would be 

 inversely as the cube root of its breadth, while the resistance at 

 the axis would not be altered. That is, respresenting the breadths 

 by .. .. 1,2, 3, 4, 5, 6, 7, S,&c.j 



the correspond- '^ 



ing resistances > 1 , — , — , — , — , — ■ , — , — , &c. 



V, , i ' l-i6' 1-44 ' l-i9' I'-il ' 1-S2' 1-91 ' a' 



vvnl be . . J 

 Hence, on such a plane to increase the breadth eight times would 

 reduce the friction one-half. But this will not apply to common 

 wheel-carriages, because the roads are not uniform ; and it does 

 not appear that any advantage can be gained by increasing the 

 breadth of the wheel beyond a certain (juantity, which depends 

 on the size of the stones employed for making the road. 



Such are the conclusions to which a theoretical view of the 

 subject has led. It is easy to extend the same reasoning to in- 

 clined roads, and to cases where the line of traction is not parallel 

 to the road ; — the resulting equations of course become more 

 complicated, but they are not less important. 



July 1, 1819. Thomas Tredgold. 



IV. Account of the Climate, Natural Products, Arts, and Ma- 

 mifactures of the Kingdom of Ashanlee and some of the Ter- 

 ritories adjacent. Btj T, Edward Bowdich, Esq.'* 



Climate. 

 URiNG the firf..t two months of our residence (May and June) it 

 rained about one-third of the time; throughout July and August 

 it rained nearly half, and abrupt tornadoes were frequent in the 

 evening just after sunset, usliered in by a strong wind from the 

 south-west. The heaviest rains were from the latter end of Sep- 

 tember to the beginning of November ; they fell even in more 



* Abstracted from Account of Mission from Cape Coast Castle to Ashantee 

 Jn 1817- impetuous 



D 



