The microfilm roll you quote is the "Index to Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Arkansas.
M376, 26 rolls. The compiled service records to which this index applies are reproduced on M317.

However, the roll you note is incorrect representing surnames 'T'. The correct roll is no. 25, surnames 'Wh-Wi'

Below are all the applicable White's you seek.

You can view a complete list of '"J. White"s by reviewing the NPS Soldiers and Sailors System at: http://www.itd.nps.gov/cwss/soldiers.cfm

You could probable narrow your search by checking the unit histories and where their companies were organized.

George Martin

John R. White

Enlisted as a Private (date unknown).
"G" Co. AR 1st Cavalry

John R. White

Enlisted as a Private (date unknown).
"A" Co. AR 2nd Battn Infantry

John R. White

Enlisted as a Private (date unknown).
"F" Co. AR 3rd Infantry

J R. White

Enlisted as a 1st Lieutenant (date unknown).
"H" Co. AR 1st Cavalry

J White

Enlisted as a Private (date unknown).
"B" Co. AR 2nd Cavalry