From the Official Brief History, 89th Division, U. S. A.: 

     "The sleeve insignia consists of a black 'W' in a black circle. It was selected after careful consideration and has a meaning which is as follows: 
     The division comes from the Middle West, and its insignia indicates its Western origin and all-around efficiency; inverted it indicates the Middle part of the name; on its side it indicates 'sigma,' the symbol of summation, that is, cooridination or single effort. Moreover the circle is that geometrical figure which can come to stability in any position, yet move rapidly in answer to a change of forces. In the lower part of the 'W' is placed the color of the branch of service, such as blue for Infantry, etc. Ultimately, a darker blue was indicated for the 177th Infantry Brigade, and a lighter blue for the 178th Infantry Brigade. Certain regiments, as 353d Infantry, with its Kansas sunflower, and the 341th Field Artillery with its 'C' for Colorado, still further have a distinct identification. Later when the rating system upon the comparative results obtained in the monthly inspections was adopted the best company or battery had the privilege of inlaying in white in the lower left hand segment of the circle, the best battalion the next segment and so on for the next two segments for the best regiment or brigade. Thus a perfect score for an organization would give each segment surrounding the designation of the branch of service, a white inlay."