26 MECHANICS. 



or e ; and the angle H G O or H G O 'is equal to X. Hence W G B' is equal to 

 W GH - H G O', or (e - X) ; and W G B is equal to W GH + H G O, or e+X. 

 Also, GWB is equal to GWH -BWH, orGWH - x. But 

 GWH = 90-WGH= 90-e. 



Hence, G W B = 90 - (e + x). 



GB'B = GWB' + WGB' 



= 90 - (e + x) + e - X 

 = 9Q-(x+X). 



Also GBW = GB'W-B'GB; 

 butB'GB = 2X. 



Hence, GB W = 90 + (x + X) - 2 X, 



or G B W = 90 - (x - X). 



By trigonometry we have 

 WB : WG 

 or F : W 

 WB': WG 

 orP": W 



sin. WGB : sin. WBG 



sin. (e + X) : cos. (x - X) 



sin. WGB': sin. W B' G = sin. G B' B 



sin. (e - X) : cos. (x + X) 



Hence we find, p( _ -yy sin. (e+X) 



' cos. (x X) 



which are the formulae already determined analytically, and by reversing this 

 process, the construction may be deduced from the formulae. 



If the power be parallel to the plane x = o, and the formulae become 



(36.) It is evident that all the preceding reasoning will be applicable, whether 

 the body slide or roll, or be moved on wheels. The only difference will be that 

 the proportion of the friction to the pressure, or the value of / or WA will be 

 different in each case. 



CHAPTER VII. Tables of the Results from experiment, we shall lay before the 



of Experiments on Friction and Hi- student some tables containing the re- 



gidity of Cordage. suits of experiments instituted by Cou- 



lomb, and by comparing these results 



(37.) SINCE no theory of friction and with the principles which have been 



the rigidity of cordage has been yet deduced from them, the degree of yali- 



established on perfectly satisfactory dity to be allowed to these principles 



principles, and all our knowledge re- will be apparent. 

 specting it must be derived immediately 



The following tables are extracted from Dr. Gregory's Treatise on Mechanics. 



TABLE I. Friction of Woods, the Directions of the Fibres being the same, and 

 the pressure being Unity. 



Value of/. 



Oak against oak ........... 0.43 



Oak against fir ...... ..... 0.65 



Fir against fir ........... 0.56 



Elm against elm .......... 0.47 



Friction of Woods, the Directions of the Fibres being at Right Angles. 

 Oak against fir ........ ... 0.158 



Fir against fir , .......... 0.167 



Elm against elm .......... 0.100 



