You can find out at Proofhouse.com
The list I have shows a Colt new service with that serial number as being made in 1915.
made about 1911
about 1918
1918
1923
About 1903.
Check the butt.
1916.
if it's a New Service model it was made about 1920
Around 1917.
To determine the age of a 32 caliber Secret Service Special revolver with serial number 178866, you would need to consult production records specific to that firearm model and manufacturer. The Secret Service Special revolver was produced primarily in the early to mid-20th century, so the serial number can help establish a rough manufacture date. Generally, collectors and firearms experts can provide more precise dating based on the serial number and other features of the revolver.
Your colt was made in 1916.