189o.] of rotating liquid spheroids. 53 



method to that employed by Mr Basset on pp. 24, 25 of his paper. 

 That a mass of gravitating liquid is in stable equilibrium when its 

 form is spherical and that its potential energy is therefore then a 

 minimum, is more obvious than that the latter fact follows as a 

 consequence from the "result" stated in Equation 1. If TT^ had 

 been defined as the work done in separating the elements of 

 liquid in a mass of any form (say cubical for example) there is 

 nothing either stated or shown in this argument as it stands in 

 the paper which would preclude its being employed to show that 

 the potential energy of the cubical form would be zero. 



Again, the distinction between " energy" and " capacity to do 

 work " is at variance with the custom of defining energy as 

 " capacity to do work " in many text-books, and the statement 

 that "the presence of the term ^K^jl" diminishes the "capacity 

 to do work upon itself" of the liquid is not easily reconcileable 

 with the remark (following equation (5)) that " the capacity to do 

 work will be least when ^h^/I— Tf is a minimum." The simple 

 expedient of placing the minus sign fiirst outside and then inside 

 the bracket is not a very convincing argument on this point. 



The object of these remarks is to show that the "obscurities" 

 which exist in the statements in Natuixd Philosophy relating to 

 the stability of rotating ellipsoids have only been partially cleared 

 up, and that there is still room for a fresh investigation in the 

 same direction. 



{Remarhs on the above by Mr A. B. Basset. 



In the first place the surface of a cube is not an equipotential 

 surface for a mass of gravitating liquid, and consequently my 

 argument would not apply if the word cubical were substituted 

 for spherical. 



Secondly, the distinction between energy and capacity to do 

 luork must be obvious to everyone who considers how the state of 

 relative equilibrium of a Maclaurin's spheroid may be generated. 

 The term ^h^ll increases the total energy of the system, but 

 diminishes its capacity to do work upon itself. When ^h^jl — W 

 is a minimum the system is incapable of doing any work upon 

 itself; when it is not, the figure if free will begin to assume some 

 other form.] 



