This article discusses the propagation of waves in wireless telegraphy, focusing on whether these waves are space waves or surface waves. The author, A. Sommerfeld, examines the behavior of electromagnetic waves between a transmitter and receiver, considering the role of the Earth. Two main theories are presented: one based on Hertzian waves in free space and another on surface waves, which are more relevant for wireless telegraphy due to their interaction with the Earth. Hertzian waves, derived from the potential function Π, describe waves in free space, while surface waves, such as those studied by Uller and Zenneck, are influenced by the Earth's properties. The propagation of these waves is analyzed using partial differential equations and boundary conditions. The article introduces the concept of "numerical distance," a parameter that depends on the wave's frequency and the material properties of the surrounding medium. This parameter helps determine whether the wave is a space wave or a surface wave. The study concludes that the propagation of wireless telegraphy waves is a combination of both space and surface waves, with surface waves playing a significant role due to their interaction with the Earth. The article also discusses the practical implications of these findings, including the effects of ground conditions, wave frequency, and antenna design on signal propagation. It highlights the importance of understanding the difference between space and surface waves for optimizing wireless communication systems. The analysis is supported by mathematical formulations and examples, demonstrating the complex nature of wave propagation in wireless telegraphy.This article discusses the propagation of waves in wireless telegraphy, focusing on whether these waves are space waves or surface waves. The author, A. Sommerfeld, examines the behavior of electromagnetic waves between a transmitter and receiver, considering the role of the Earth. Two main theories are presented: one based on Hertzian waves in free space and another on surface waves, which are more relevant for wireless telegraphy due to their interaction with the Earth. Hertzian waves, derived from the potential function Π, describe waves in free space, while surface waves, such as those studied by Uller and Zenneck, are influenced by the Earth's properties. The propagation of these waves is analyzed using partial differential equations and boundary conditions. The article introduces the concept of "numerical distance," a parameter that depends on the wave's frequency and the material properties of the surrounding medium. This parameter helps determine whether the wave is a space wave or a surface wave. The study concludes that the propagation of wireless telegraphy waves is a combination of both space and surface waves, with surface waves playing a significant role due to their interaction with the Earth. The article also discusses the practical implications of these findings, including the effects of ground conditions, wave frequency, and antenna design on signal propagation. It highlights the importance of understanding the difference between space and surface waves for optimizing wireless communication systems. The analysis is supported by mathematical formulations and examples, demonstrating the complex nature of wave propagation in wireless telegraphy.