**Explanation:**

Lothar Meyer, a German chemist, arranged the elements in order of increasing atomic mass. This arrangement is known as the periodic table of elements.

**Atomic Mass:**
- Lothar Meyer recognized that the properties of elements were periodic functions of their atomic masses.
- He plotted a graph with atomic mass on the x-axis and various properties of elements on the y-axis.
- He observed that when elements were arranged in order of increasing atomic mass, similar properties appeared at regular intervals.
- This led to the development of the periodic table, where elements with similar properties were grouped together in columns called groups or families.

**Density, Atomic Volume, and Atomic Radii:**
- While density, atomic volume, and atomic radii are all important properties of elements, Lothar Meyer did not arrange the elements in order of these properties.
- These properties are dependent on the arrangement of atoms in a solid or the size of atoms, which can vary even within a specific group or family in the periodic table.
- Therefore, arranging elements in order of increasing atomic mass was a more effective way to identify periodic trends and similarities in chemical behavior.

**Significance of Arranging Elements by Atomic Mass:**
- Arranging elements in order of increasing atomic mass allowed for the identification of periodic trends and similarities in chemical behavior.
- It provided a systematic way to organize the known elements at that time and predict the existence of new elements.
- This arrangement laid the foundation for further developments in the understanding of atomic structure, chemical bonding, and the behavior of elements.

**Conclusion:**
- Lothar Meyer arranged the elements in order of increasing atomic mass.
- This arrangement, known as the periodic table, allowed for the identification of periodic trends and similarities in chemical behavior.
- While density, atomic volume, and atomic radii are important properties, they were not the basis for the arrangement of elements by Lothar Meyer.