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Then if j, J be the original and transformed forms of an invariant J= (a1)wj, w being the weight of the invariant.

Operation upon J results as follows D AA J = wJ; D A J=0; D ï¿½A J =0;D ï¿½ï¿½ J = wJ.

Now D A xA k = (n - k) A k; Aï¿½ A k = k A?1; D ï¿½A A k = (n - k) A k+1;D mï¿½ A k = kA k; (n - k)A ka - w Ak - 1 aA k = O; a _ J (n - k) A k +l A k = O; kA k Ak = wJ; equations which are valid when X 1, X 2, ï¿½ 1, ï¿½2 have arbitrary values, and therefore when the values are such that J =j, A k =akï¿½ Hence °a-do +(n -1)71 (a2aa-+...

= wj, aa 1 aa 2 a a 3 the complete system of equations satisfied by an invariant.

Then if j, J be the original and transformed forms of an invariant J= (a1)wj, w being the weight of the invariant.

Operation upon J results as follows D AA J = wJ; D A J=0; D Ã¯¿½A J =0;D Ã¯¿½Ã¯¿½ J = wJ.

Now D A xA k = (n - k) A k; AÃ¯¿½ A k = k A?1; D Ã¯¿½A A k = (n - k) A k+1;D mÃ¯¿½ A k = kA k; (n - k)A ka - w Ak - 1 aA k = O; a _ J (n - k) A k +l A k = O; kA k Ak = wJ; equations which are valid when X 1, X 2, Ã¯¿½ 1, Ã¯¿½2 have arbitrary values, and therefore when the values are such that J =j, A k =akÃ¯¿½ Hence Ã‚°a-do +(n -1)71 (a2aa-+...

= wj, aa 1 aa 2 a a 3 the complete system of equations satisfied by an invariant.

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