C "5 3 



XX. An Attempt towards a Theory of the Ref fiance experim 

 cnced by two and four-wheeled Carriages on different Kinds 

 xjJ Roads ; arid to determine the Circumjlances imder which 

 the one are preferable to the other. By NICHOLAS FlJSS, 

 Profeffor of the higher Mathematics at Peter/burgh, Mem- 

 ber of the Imperial Ac. demy of Sciences , &c\* 



T, 



II K following paper was written in a'nfwer to a queftion 

 propofed as the fuojecl of a prize for the year 1797 by the 

 Royal Academy of Sciences at Copenhagen, and obtained 

 the firft prize. To avoid eonfufibn or miftake, we have 

 adopted the author's notation, and have adhered as clofely to 

 the Original as the nature of the fubject would admit. — E. 



Section 1. 



The queftion, which t firft law in the 113th number of 

 the Gottingen Gelehrten Awzeigen for the year 1796, Was in 

 the following words : — Ex principiis mechanics exponere ra- 

 tionem potentite motricis ad onera, turn plauflris quatuor ro- 

 tarum^ turn carris, qui funt binarum rotatum, promo-venda; 

 ita quide?ti; ut ad impedimenta motus, fritfionem fcilicel, ac 

 reliqua qucc in viis occurrere Jolent, objlacula a vi motrice 

 J'uperunda jimul r-c/'piaatur. Quo in unit) erf um pateat, num 

 et quando hoc liltuhe genus vehiculi commode et prudenter 

 ridhiheri pofflt. That is : M To determine, from mechanical 

 principles, the ratio of the moving power to the burthen both 

 in four-wheeled and two-wheeled carriages, taking into ac- 

 count at the fame time the impediments to motion, that is 

 to lay, friction, and the other obltacles to be overcome by 

 the moving power which commonly occur in roads, that it 

 may in general appear on what occafions either of thefe car- 

 riages can be employed with molt advantage." 



The general utility of this queftion induced me, laft fum- 

 mer, to employ the leifure T then enjoyed in the country, in 

 confequence of two months relaxation from my ufual occu- 

 pations, in examining it, with a view of fubmitting my la- 

 bour to the iufpe&ion of the enlightened fociety who pro- 

 pofed it; and I lhall be happy if the learned and celebrated 

 men to whom the foeietv have entrufted the power of adjudg- 

 ing the prize, ihould find in the following refearches any 

 thing to indemnify them for their trouble. 



^ ,; Prom Perfume einer Tbeorie dt-s tViderJlandes x.weyund 'vierr'ddri^er 

 Fubvwerke, af Fabriue^en jttitr at 1 1 in c . You Nicolwus Fufs, &c. Co- 

 penhagen 179b. 



Vol:XII[7No75o^ I Se6lkn 



July 18025. 



