Public Function AppointmentsAtDay(ByVal dtDate As Date, _
  Optional oResult As Outlook.Items _
) As Long
  Dim oFld As Outlook.MAPIFolder
  Dim oItems As Outlook.Items
  Dim sFind As String
  Dim obj As Object
  Dim i As Long

  Set oFld = Application.Session.GetDefaultFolder(olFolderCalendar)
  Set oItems = oFld.Items

  oItems.Sort "[Start]", False
  oItems.IncludeRecurrences = True

  sFind = Format(dtDate, "ddddd")

  sFind = "[Start] <= " & _
            Chr(34) & sFind & " 11:59 PM" & Chr(34) & _
            " AND [End] > " & _
            Chr(34) & sFind & " 12:00 AM" & Chr(34)

  Set oResult = oItems.Restrict(sFind)
  For Each obj In oResult
    i = i + 1
  Next
  AppointmentsAtDay = i
End Function