This great old photo shows the Arts and Industries Building on the Mall under construction in 1879.

The United States National Museum Building, now the Arts and Industries Building, designed by Architects Cluss and Schulze, is under construction, December 1879. Scaffolding is in place around the exterior of the building. The center rotunda has been partially constructed. This view is from the South Tower of the Smithsonian Building, looking east towards the United States Capitol. A very small portion of the Smithsonian Institution Building can be seen on left. The ceremonial ground breaking for the new museum was on April 17, 1879.
The United States National Museum Building, now the Arts and Industries Building, designed by Architects Cluss and Schulze, is under construction, December 1879. Scaffolding is in place around the exterior of the building. The center rotunda has been partially constructed. This view is from the South Tower of the Smithsonian Building, looking east towards the United States Capitol. A very small portion of the Smithsonian Institution Building can be seen on left. The ceremonial ground breaking for the new museum was on April 17, 1879. Source: Smithsonian

And below we found an interesting 1878 rendering of what the building should look like.

Rendering of the new United States National Museum, now the Arts & Industries, building designed by Adolph Cluss
and Rudolph Schulze, Philadelphia architects, to contain the exhibits donated to the Smithsonian from the Philadelphia Centennial Exposition. Small Card.

And finally, here’s a photo of the building after being completed.

The exterior to the north side of the newly completed United States National Museum Building, now the Arts and Industries Building (A&I) designed by architects Cluss and Schulze. Ground breaking ceremony was held on April 17, 1879. Second Secretary of the Smithsonian Spencer F. Baird assembled a distinguished Building Committee that included General Meigs and General William Tecumseh Sherman. Baird and his building committee worried over every detail of construction. The building was completed by 1881, on schedule and within budget. Per square foot, it was the cheapest permanent government building ever built. It had 80,000 square feet of exhibit space. Note grillwork of the original gates of the north entrance.
The exterior to the north side of the newly completed United States National Museum Building, now the Arts and Industries Building (A&I) designed by architects Cluss and Schulze. Ground breaking ceremony was held on April 17, 1879. Second Secretary of the Smithsonian Spencer F. Baird assembled a distinguished Building Committee that included General Meigs and General William Tecumseh Sherman. Baird and his building committee worried over every detail of construction. The building was completed by 1881, on schedule and within budget. Per square foot, it was the cheapest permanent government building ever built. It had 80,000 square feet of exhibit space. Note grillwork of the original gates of the north entrance.