Roof repair _ leak in slate roof.

Tar on slate. Temporary at best, likely to cause more problems at worst.
In this case the original roof was installed with tin sheet metal used as flashing along the roof dormers. The thin metal flashing probably lasted 60 yrs before it rusted away and the roof began to leak.
The right way to repair the roof would be to remove the slate shingles and replace the rusted tin flashing with new flashing. Preferably copper.
Here, the roof repair was made by spreading tar along the roof slate and dormer slate intersection. Covering over the rusted tin flashing.
This may slow down the worst of the water leak, but will not eliminate the water intrusion.
Wind driven rain can still enter the house at the dormer wall above the tar from between the slate joints. Also it will not take long for the tar to dry out and crack, allowing in more water. This may just be a little, and not enough to show up in the house on the ceiling. But, it will be enough to soak the roof boards and rafters and cause much more damage in rotted wood.