You need to register as a user - it's easy and costs nothing.After you register you need to buy some credits.The system is secure - I've been using it for years without any problem.The minimum is 30 credits, which costs 6 pounds (about 11 dollars).Each page of search results then costs you 1 credit and each copy certificate costs 5 credits.
To find the particular one you're looking for: From the 'Home' page - click on 'Statutory Registers, Deaths 1855-1956' On the search page enter: Surname: mathers Forename: james sex: male year range: 1863 to 1863 birth year: 1803 + or - 1 year County: ANGUS District: MONTROSE
Press the green 'Search' button.You'll get 1 hit (I've tried those search terms). Press the blue 'View' button - you'll be charged 1 credit.You'll see a 'list' with only one entry. Select 'VIEW (5 CREDITS)' - you'll be charged 5 credits.What you'll then get is an image of the original page in the death register - this is the 'Death Certificate' - one of the entries will be for James Mathers.If the person registering the death knew the names of James's parents then they will be shown - including his mother's maiden name.You've got to bear in mind though that sometimes this information is not correct (but it usually is correct).
Once you know the system, it's better not to make your search as explicit as that.This will give you longer hit lists.You'll still be able to pick out the 'James Mathers, born about 1803' that you were looking for but you'll also see other people who are likely his relatives.For example - If you search on Deaths ONLY for: Surname: mathers Sex: BOTH Year Range: 1855 to 1900 County: ANGUS District: MONTROSE you'll get 19 hits on 1 page (still only costing 1 credit) one of which will be the same hit you gor before but some of the other 18 may take you in new directions (although if you choose to look at any of the actual certificates it will cost you 5 credits for each one you look at) - but obviously you don't have to look at them.
You can make your search still more general by using 'wildcards'. If for example you repeat the above search using the surname 'mather*' you'll find you get 43 hits instead of 19 - because you'll have the same 19 but also all the people with the name 'Mather' as well as 'Mathers' (also anybody called 'Matherson' or anything similar, although there probably aren't any).
You need to play around with it for a while and be creative in your searching - also bear in mind the many variations in spelling of names and the fact that people make mistakes - or sometimes tell lies.
Hope this answers your question.I apologise if this was too basic - you can never tell what someone's level of experience might be in using search engines.