var soapDataString = "<soap:Envelope xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xmlns:xsd='http://www.w3.org/2001/XMLSchema' xmlns:soap='http://schemas.xmlsoap.org/soap/envelope/'> \
  <soap:Body> \
    <Login xmlns='http://schemas.microsoft.com/sharepoint/soap/'> \
      <username>username</username> \
      <password>password</password> \
    </Login> \
  </soap:Body> \
</soap:Envelope>"

// Call web service
$.ajax({
  url: "http://mywebsitename:2355/_vti_bin/authentication.asmx",
  type: "POST",
  dataType: "xml",
  data: soapDataString,
  success: resultsFeedback,
  contentType: "text/xml; charset=\"utf-8\""
});

function resultsFeedback(xData, status) {
   alert(xData);
   alert(status);
}