Read-only and write-only properties in a Web Service class aren't visible to the Web Service client. The reason is that XML serialization doesn't support these sort of properties, and read-only and write-only properties aren't included in the Web Services Description Language (WSDL) documentation.
To make these properties visible to clients, create a Function that returns the value of a read-only property, or a Sub that assigns a write-only property, and decorate them with the WebMethod attribute. For example:
Dim m_Count As Integer
ReadOnly Property Count() As Integer
' This is the method visible to the Web Service's clients
<WebMethod()> Function GetCount() As Integer