Good morning Eileen,
Without knowing Barton Howard's regiment, it will be very difficult to find him with the South African (Boer) War as a start point.
You could start with a posting with the information you do have on a forum specific to the period, such as the
Victorian Wars Forum. That forum has boards specific to the
Boer War 1899-1902 and another for
Researching Individual Soldiers & Sailors.
Howard Barton, as a Quartermaster in South Africa, may have also participated in other campaigns. With his South African service as a starting point, be sure to ask those who read the posts to check whatever medal rolls they may have, someone might find him (or a matching name) on another list that could help narrow your later searches. Also describe the book you know that he is in, some member of that forum may recognize it and have the volume in their personal library.
You can also try working back through the family line, looking for recorded traces of parental next of kin at each stage. Have you ordered service records from Library and Archives Canada (LAC) for each of those that served in the Canadian Army?
For the Second World War and those who served after 1918, instructions to order a service record are found
here.
For the First World War, LAC maintains the
Soldiers of the First World War - CEF. The record for each includes the necessary file reference to order the service record. Instructions for doing that are found
hereSince you are doing family research, I would also suggest that your consider a membership with
Ancestry.com. Pull together all of your other resources and then start with Ancestry's 14-day free trial. You may be able to get everything you want from their resources within that period before having to pay the monthly membership fees.