Modifying Powershell to display Security Event log statistics for multiple computer

People,

Can anyone here please assist me in how to configure the below script to run on multiple computers ?

Get-Content C:\Users\user\Documents\server_list.txt | ....

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When I execute the below script with the log name System it works with no issue, but when I modify it to Security, it does not work ?

$logName = "Security"

#get date
$dateCurrent = Get-Date

#For the Week
$NDays = -7
$dateNDaysAgo = $dateCurrent.AddDays($NDays)

$logLevel = @("Critical", "Warning", "Error")
$logLevelCritical = "Critical"
$logLevelWarning = "Warning"
$logLevelError = "Error"

Write-Host "Log Entries since $dateNDaysAgo"

Get-WinEvent -Logname $logName  | `
where-object {($_.timecreated -gt $date) -and ( ($_.levelDisplayName -eq $logLevelCritical) -or ($_.levelDisplayName -eq $logLevelWarning) -or ($_.levelDisplayName -eq $logLevelError) )  } | `
Group-Object ProviderName, levelDisplayName, ID | `
Sort-Object Count -descending | `
Format-Table Count, Name -auto

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Thanks in advance.