So there's good news and disappointing news with your bowl.
The disappointing news is that this is not sterling, unfortunately, it's silverplate, that is, coated with a thin layer of silver by electrolysis, so the total silver content is less than 2%. The "Quadruple" refers to the number of times (four) that the piece was turned in the electroplating bath to ensure the most even coating of silver.
"Hard White Metal" in this case, means that under the silver there's a base metal that's an alloy of tin, copper and zinc made white by the addition of nickel. It used to be called "Britannia metal" or "EPNS" (Electro-Plated Nickel Silver) or "German silver" and so on and had the advantage, if the silver plating wore thin, of not showing wear in the same way that traditional silver-on-copper showed the unsightly copper coming through when exposed by excess polishing or wear.
The good news is that it's quite old. The Manhattan Silver Plate Co. was in operation under that name from 1877-1898 after which it became a subsidiary of International Silver (who continued to use the Manhatten brand name, but also added "International" to the mark as well) so we know your bowl is around a hundred and twenty years old, or more, and therefore officially an antique. Strictly speaking, an item must be 100 years old or more to qualify as being "antique".
Originally this piece with its elegant rococo handles and scalloped and beaded rim would have been used as vegetable server or perhaps a soup tureen, and would have had a matching lid that would have looked something like this one and when all polished up and on display on the sideboard would have looked the height of opulent chic! Manhattan specialized in making silverware for upmarket hotels as well as for the restaurant cars of many of the railroad companies of the day.
I notice the condition of yours is not the greatest, with the rim bent in a couple of places (though this could be carefully straightened by someone with strong fingers as the "Hard White Metal" is relatively pliable).
As for value, these Victorian era silverplate pieces are enjoying a modest resurgence in interest, probably as a result of the Downton Abbey TV show, who knows! But more likely it's because the collecting world is beginning to discover how well-made and functional these pieces are as well as looking good. Having said that, they are never going to be anything approaching the value of those made in solid sterling silver.
If you saw your bowl for sale in an antique store (as is) it would have a retail price tag of around $80. This is also the replacement value for insurance purposes.
Expect to net in the range of 30% - 40% of this if you were to sell at a good antique auction house or on line (eBay etc).
I do hope this helps and isn't too disappointing and you won't shoot the messenger! But you'd be doubly disappointed if I gave you false hope (if you ever came to sell it) that it was worth more than it is.
Meanwhile, please let me know if you'd like me to explain or expand on any of the above, I would be glad to.