The thorny way of truth - Free Energy Community

- 81 -We will insert this into the expression for D, getting^+'-^)(5-%))'To the extent that this function is dependent on x,y,z. it does not satisfyLaplace's equation, but the complicated differential equation(4) A,AjD = 0.In order to prove this, we have+(-'.)(S--^-)l=«-('-.'(5-^)+(s'-v.)(f-^)The single summands in D, then, regardless of constant factors, are of theform G*H. But,"^I '^ Z)x Sx- ^y ^y "^ D2 ^z) 'and it can easily be proven through differentiation that A2G=0, A2H=0.Consequently, we will obtain the simpler equation"*^^ ^\^x Dx ^ c^y Dy ^ ^z Dz /Factors^ 3^^will be independent of x,y,z. So,^ ' ^ ^ y^x Dx- ~ Dt/ ^y ^2 ^2 ^and this is equal to zero because A2G=0. This also proves equation (4).