Rolling up a value for Records in a set date range

I have an Hours Log sheet, and each record in it has a ‘project’, ‘date’ and ‘hours spent’ field.
I have another sheet with our Project Milestones on it, each record with a ‘project’, ‘date start’ and ‘date end’ field.
The ‘project’ field for both sheets is itself a link to a record in a separate Project sheet.
I would like to find a way to add a field to the Project Milestone records that displays the sum of all of the ‘hours spent’ in the task list on a ‘project’ within the date range of ‘date start’ and ‘date end’.

I would also be grateful for any advice on whether or not there is a better way of accomplishing this. Essentially, we use the Hours Log to log the hours we spend on each project each week. Each person creates a new record each week for each project that they worked on that week. And I would like a way to automatically see how many hours we have spent during each milestone for each project based on the milestone dates. I would prefer that people not have to manually link the milestones because there is a lot of room for error there.

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