^tACH!W£ ^OR TAKING LAkGE STONES otJT OF TiiE GkOT '. 



would be aa integer"^ and having also demonstrated, thiis \io 



oae of these quantities can be an integer, it foliovvs that the 



': .latida whence they were derived is impossible; that is 



::e equatioa *"— ~j/"r::s" is impossible, vphen w is a prim^ 



niiiber. 



But we have also shown, that the impossibility of the eiqnti- 

 tlon r" — }/^~:f, when w is a prime, involves with it the 

 impossibility of every eqv.ation of the form 

 of' + f ~ z'\ 



hi which n is iany number whatever except 2, or sonn6 power 

 of 2; and we have likewise shown, that the impossibility of 

 the equation,! when n is any power of 2, is involved in that 

 of X* — i/'^zzz\ which particular case has been proved to bti 

 impossible by Euler; and consequently the equation 



X-" -f r - *" 



is always impossible, when « is any integer number what- 

 ever greater than 2. And since the equation a-" -V if — c"i 



x^ w" 2" 

 is impossible, so also is —+—=:—, for this is the same 

 ^ m' — p q 



as :t" + y" — ~— : and therefore the equation is likewise 



impossible in fractionSi 



V. 



Method of raising large Stoves out of the Earth ; hy BIr. Ro- 

 KERT RicHARDsoi>s of Keswick, iii Cumberland*. 



Gentlemen, 



Jl , Robert Richardson, bf lCeswic1<, in the |jarish of Cros- New irtfth^d 

 thwaite, and counry of Cutnberlahd^ beg leave fo inform ^(j,aVh"if ^'^' 

 you, that I have found out a method of taking large self- stones out o! 

 stones out of the ground in a very expeditious manner; and ^''^C^'^"' • 

 that by this means two men will take as many stones out 

 yf the ground in one day, as would require twelve men in 



* Trans, of the Soc. of Arts, vol. xxvi, p. 190. The silver niedal rtaS 

 ^•)t^ to Mr, Richardsoa for tni» itnentieas 



