96 ON THE TAVTOCHRONE IN A RESISTING MEDIUM. 

 the equation in z would be 



d z z , dz 



This is precisely the form of the equation of motion on a 

 cycloid when R = hv. And as in that case ^ deduced from it 

 is independent of s v so in this it will be independent of z l9 and 

 consequently of 5 r Hence the curve whose equation is (1), is 

 tautochronous, not only when R = lev*, but also when 



For Laplace's abstruse solution, see the first book of the 

 Mecanique Celeste, or Mr Whewell's Dynamics. 



