The natural index and the divisia index on the straight line as well as the divisia index on the exponential line

In earlier papers the Divisia index on the straight line was called natural index. Representing the index problem in the 2n-dimensional quantity-price-space, it is now proposed to call natural index the limit of stepwise products of Laspeyres' , Paasche's or Edgeworth-Marshall s indices, if the steps approximate the straight line between the base point and the observed point. The numerical results of successive finer approximations of the natural index are illustrated by some examples. As expected these approximations converge to the value of the Divisia index on the straight line. The same approximation procedure is applied to the Divisia index on the exponential line.