A barge is hauled along a straight-line section of canal by two horses harnessed to tow ropes and walking along the tow paths on either side of the canal. Each horse pulls with a force of $859 \mathrm{~N}$ at an angle of $15^{\circ}$ with the centerline of the canal. Find the sum of these two forces on the barge.

Step 1 ：Given force exerted by each horse: \(F = 859 N\) and angle with the centerline of the canal: \(\theta = 15^\circ\)

Step 2 ：Convert angle to radians: \(\theta_{rad} = \frac{15 \times \pi}{180} = 0.2618\)

Step 3 ：Find the horizontal component of the force exerted by each horse: \(F_{horizontal} = F \times \cos(\theta_{rad}) = 859 \times \cos(0.2618) = 829.73 N\)

Step 4 ：Find the sum of the horizontal forces exerted by both horses: \(F_{total} = 2 \times F_{horizontal} = 2 \times 829.73 = 1659.46 N\)

Step 5 ：\(\boxed{1659.46}\) is the sum of the two forces on the barge.