584 POPULAR LECTURES AND ADDRESSES. 



It has also a determinate finite solution even 

 though the land be nowhere valueless, if the wall 

 is sufficiently more and more expensive at greater 

 and greater distances from some place where there 

 arc quarries, or habitations for the builders. 



The simplified case of this problem, in which 

 all equal areas of the land are equally valuable, 

 is identical with the old well-known Cambridge 

 dynamical plane problem of finding the motion 

 of a particle relatively to a line of reference 

 revolving uniformly in a plane : to which belongs 

 that considerable part of the " Lunar Theory " 

 in which any possible motion of the moon is 

 calculated on the supposition that the centre of 

 gravity of the earth and moon moves uniformly 

 in a circle round the sun, and that the motions 

 of the earth and moon arc exactly in this plane. 

 The rule for curvature which I have given you 

 expresses in words the essence of the calculation, 

 and suggests a graphic method for finding solu- 

 tions by which not uninteresting approximations ] 



1 Kelvin, " On graphic solution of dynamical problems." /'////. 

 half-year). 



