Repeating this in case you missed it:
Originally Posted by thepolyparrot
There's a pretty comprehensive needle chart at ISMACS:
http://www.ismacs.net/needle_and_sha...edle-list.html
According to this chart, the Singer 40 takes ordinary 15x1 needles. Has your model 40 been modified to take the 24x1? Or maybe it came with a manual for the model 24? That one does take the 24x1 needle.
Is your machine a model 40?
If so, you might want to at least try a standard home sewing machine needle, since two sources tell us that the model 40 takes that needle.