This is an anticipation of the division by Leuckart in 1839 of the Radiata of Cuvier into Coelenterata and Echinodermata.
The "Polypes" of Lamarck included not only the forms now known as such, but also the Rotifera and Protozoa, though, as we shall see, he afterwards in his course of 1807 eliminated from this heterogeneous assemblage the Infusoria.
Comparing this classification with that of Cuvier[121] published in 1798, we find that in the most important respects, _i.e._, the foundation of the classes of Crustacea, Arachnida, and Radiata, there is a great advance over Cuvier's system.

In Cuvier's work the molluscs are separated from the worms, and they are divided into three groups, Cephalopodes, Gasteropodes, and Acephales--an arrangement which still holds, that of Lamarck into Mollusques cephales and Mollusques acephales being much less natural.

With the elimination of the Mollusca, Cuvier allowed the Vers or Vermes of Linne to remain undisturbed, except that the Zooephytes, the equivalent of Lamarck's Polypes, are separately treated.
He agrees with Cuvier in placing the molluscs at the head of the invertebrates, a course still pursued by some zooelogists at the present day.

He states in the _Philosophie Zoologique_[122] that in his course of lectures of the year 1799 he established the class of Crustacea, and adds that "although this class is essentially distinct, it was not until six or seven years after that some naturalists consented to adopt it." The year following, or in his course of 1800, he separated from the insects the class of Arachnida, as "easy and necessary to be distinguished." But in 1809 he says that this class "is not yet admitted into any other work than my own."[123] As to the class of Annelides, he remarks: "Cuvier having discovered the existence of arterial and venous vessels in different animals which have been confounded under the name of worms (_Vers_) with other animals very differently organized, I immediately employed the consideration of this new fact in rendering my classification more perfect, and in my course of the year 10 (1802) I established the class of Annelides, a class which I have placed after the molluscs and before the crustaceans, as their known organization requires." He first established this class in his _Recherches sur les corps vivans_ (1802), but it was several years before it was adopted by naturalists.
The next work in which Lamarck deals with the classification of the invertebrates is his _Discours d'ouverture du Cours des Animaux sans Vertebres_, published in 1806.
On page 70 he speaks of the animal chain or series, from the monad to man, ascending from the most simple to the most complex.

The monad is one of his _Polypes amorphs_, and he says that it is the most simple animal form, the most like the original germ (_ebauche_) from which living bodies have descended.