PowerShell's Sort-Object cmdlet changing the order w.r.t. attributes not sorted on - sorting

Question

I'm sorting some XML and would like to sort elements based on a particular, non-unique attribute, which allows me to group like-elements. Within these groups, I need to keep the original ordering. The problem is that when sorting, the order inside these groups changes and when re-sorting then the order changes yet again. I need a sort that doesn't change things if the content of the XML hasn't changed (otherwise SVN diffs are ugly). Here is a simplified example:
$xml = [xml]#"
<root>
<element name="a" number="1" />
<element name="b" number="1" />
<element name="c" number="1" />
<element name="d" number="2" />
<element name="e" number="2" />
<element name="f" number="2" />
<element name="g" number="3" />
<element name="h" number="3" />
</root>
"#
Write-Host "`nFirst Sort produces this:"
$result1 = $xml.SelectNodes('//element') | Sort-Object -Property 'number'
Write-Host (($result1 | select -ExpandProperty 'number') + " <---Sorted on")
Write-Host (($result1 | select -ExpandProperty 'name') + " <---Order not maintained")
Write-Host "`nSorting the (already sorted) results of First Sort produces this:"
$result2 = $result1 | Sort-Object -Property 'number'
Write-Host (($result2 | select -ExpandProperty 'number') + " <---Sorted on")
Write-Host (($result2 | select -ExpandProperty 'name') + " <---Order changed again")
Here is the output:
First Sort produces this:
1 1 1 2 2 2 3 3 <---Sorted on
c b a f e d h g <---Order not maintained
Sorting the (already sorted) results of First Sort produces this:
1 1 1 2 2 2 3 3 <---Sorted on
a b c d e f g h <---Order changed again
In this example, I need to preserve the original "name" ordering within the "number groups".
Can anyone think of an easy way to make this maintain the original order and come out the same when sorting multiple times?
I'm trying to avoid adding dummy attributes representing the original ordering. Maybe there is a different .NET sorting function that's more deterministic? I searched but nobody seemed to be concerned with ordering within equivalent groups.
Thanks.

Answer 1

If you don't have something that already represents the natural sort order, you can just add an index property with Add-Member:
$nodes = #($xml.SelectNodes('//element'))
for ($i=0; $i -lt $nodes.Count; $i++)
{
$nodes[$i] = $nodes[$i] | Add-Member -MemberType NoteProperty "Index" $i -PassThru
}
$result1 = $nodes | Sort-Object name, Index
Then you are guaranteed to get the same ordering no matter how many times you re-sort.
Update: added syntax for PowerShell v2

Answer 2

Sort with respect to both the properties:
$xml.SelectNodes('//element') | Sort-Object -Property number, name
This produces this output:
name number
---- ------
a 1
b 1
c 1
d 2
e 2
f 2
g 3
h 3