If you're new to vintage machines you may not be familiar with a Boye dispenser, an "aftermarket" supplier of needles, shuttles, and bobbins. Here's what one looks like
Quite a surprise arrived today
My Boye needle/shuttle dispenser shows a #9 shuttle and #10 needle for both an Alliance and a Davis-New, which would match what Janey is telling you about it being the same as a Davis. The Boye numbers can be helpful when searching for needles, etc on ebay or etsy or similar.
But, as Janey said, hopefully Jon will come along and confirm.