OK ... I have made some test with your data and your code.
At least some changes where necessary. I think with my method-sample it would be easy for you to modify your code that it works.
Private Sub Button1_Click(sender As System.Object, e As System.EventArgs) Handles Button1.Click
Dim col3 As New List(Of Double)
Dim col4 As New List(Of Double)
Dim Easting As Double
Dim Northing As Double
Dim s(17) As String
Dim item As String()
s(0) = "194787.5 2667200.0"
s(1) = "194812.5 2667200.0"
s(2) = "195662.5 2667200.0"
s(3) = "195687.5 2667200.0"
s(4) = "201937.5 2667350.0"
s(5) = "195737.5 2667200.0"
s(6) = "195762.5 2667200.0"
s(7) = "195787.5 2667200.0"
s(8) = "196512.5 2667200.0"
s(9) = "201837.5 2667350.0"
s(10) = "198562.5 2667650.0"
s(11) = "201887.5 2667350.0"
s(12) = "201912.5 2667350.0"
s(13) = "198187.5 2667500.0"
s(14) = "201962.5 2667350.0"
s(15) = "201987.5 2667350.0"
s(16) = "202012.5 2667350.0"
s(17) = "198412.5 2667650.0"
For i As Integer = 0 To 17
item = Split(s(i), " ")
Easting = CDbl(item(0))
Northing = CDbl(item(1))
col3.Add(Easting)
col4.Add(Northing)
Chart1.Series(0).Points.AddXY(Easting, Northing)
Next
col3.Sort()
col4.Sort()
Chart1.ChartAreas(0).AxisX.Minimum = col3.Item(0)
Chart1.ChartAreas(0).AxisX.Maximum = col3.Item(col3.Count - 1)
Chart1.ChartAreas(0).AxisY.Minimum = col4.Item(0)
Chart1.ChartAreas(0).AxisY.Maximum = col4.Item(col4.Count - 1)
End Sub
In my opinion your basic mistake was that you all the time added strings as Chart-Limits and also as Chart-Points.