SOLIDS ON BUW? WES. > T * » 



by which means the equations of motion are reduced to equa- 

 tions with constant coefficients, namely, 



U- h M y -^.-Mgyb''+Mgy l = o, 



V—My^+M&b'—Mgx = o. 



Where the oscillations take place upon a spherical areola of 

 support, which will include oscillations on a horizontal plane, 

 we have x, = !*,. y, = my;,, and therefore, by preceding for- 

 mulas, 



dx, = loa\a", ihj, = niadb" . 



Integrating, and denoting by % and -^ the arbitrary constants, 

 there results 



x, = laa -j-x, y, = mab a + ^i 



which being substituted in the above equations of motion give 

 two equations' of the second order in a", b" and / of the form 



(.51) g? + (43) g; + (43) a" 4- (44) = o, 



(2*)™ + (2,2)^+ (!&)&' + (2?4) = o, 



where the cncllicients maybe readily determined, as /'and F 

 have now the Bame value as before when there was no friction 

 and when the rotation round the normal was at the same 

 time small. These coefficients being constant, the equations 

 maybe completely integrated in finite term-, four arbitrary 

 constants being introduced by the integration, which together 

 with x and ^ introduced by the last integrals obtained, and 

 e and c arising as we have already seen from the integration 

 viii,. fir. — 5 i> 



