A couple of general points. First, the Mormon web site is an absolutely wonderful finding aid. However it is not infallible, and it does contain some trees and some 'community contributed' information that is unreliable. The 'community indexed' information is generally more reliable. However it is an index, not a primary source, so you need to check the original source for each bit of information to make sure.
Second, the concept of 'correct spelling' didn't really arise until the late 19th/early 20th century. The spelling was how the person writing down the name thought it should be spelled. So it is meaningless to ask if 'Thirlow' is a misspelling of 'Thurlow' or vice versa.
The International Genealogical Index lists the birth of Thirlow Fraser, mother Margaret Fraser, in the parish of Tyrie on 20 May 1859.
Interestingly, it lists three more. The son of George Fraser and Jean Ranken, born in the parish of Gamrie on 30 June 1841; son of William Fraser and Isobel Mitchell, born on 22 July 1858 in the parish of New Deer, and the son of Thurlow Fraser and Jane Cowie, born on 23 December 1863.
The census transcriptions at FreeCEN
http://www.freecen.org.uk/cgi/search.pl list Thirlow Fraser, aged 15, as a male servant in the household of George Fraser, innkeeper, and his wife Jean and five children in the parish of Gamrie in Banffshire. So just three weeks after the census, Jean gave birth to a son who was named Thurlow.
In 1851 George Fraser, aged 37, innkeeper, born Fraserburgh, is listed in New Pitsligo, parish of Tyrie, with wife Jane and eight children including Thirlow, 9, born Mcduff (the town of Macduff is in the parish of Gamrie).
The 1851 lists a 25-year-old Thurlew Fraser, born Fraserburgh, working as a farm servant in the parish of New Deer.
According to the IGI William Fraser and Isobel Mitchell had seven of a family, all born in New Deer, and the 1851 census transcription at
http://www.freecen.org.uk/cgi/search.pl lists at Land of Old What, parish of New Deer, William Fraser, aged 32, farm servant, born Fraserburgh, with wife Isobel and four children (of whom the eldest is not listed in the IGI).
Thurlow Fraser and Jane Cowie were married on 22 September 1860 in New Pitsligo.
So we have, so far, Th*rl*w Frasers linked to:
George Fraser, born 1813/14 in Fraserburgh
William Fraser, born 1818/9 in Fraserburgh
Thurlow Fraser, born 1825/6 in Fraserburgh
So far, everything points to Fraserburgh. The 1851 census lists seven Margaret Frasers born in Fraserburgh. Two can be discounted as too old to have a child in 1859. Three of them, aged 9, 10 and 12, are in the parish of Fraserburgh, and two, aged 19 and 28, are in the parish of Tyrie.
I
speculate that the 19-year-old is the most likely candidate to be the mother of your Thurlow. However she is a domestic servant in 1851 and I have yet to find her in 1841.
Unfortunately the 1861 and 1871 censuses for Aberdeenshire are not yet available at FreeCEN, because the obvious thing to do is to look for your Thurlow and see if he is living with either his mother or possibly his grandparents. It is available on Scotland's People, which is a pay-per-view site. I have, however, looked at the index at SP, and I note with interest that there is a Thurlow Dunlop, aged 11, in Pitsligo in 1871. Could this be your Thurlow using his father's surname?
So, where do you go from here?
First, you should go to
www.scotlandspeople.gov.uk and invest in a few credits at modest cost. Use these to view and download image of the original birth certificate of Charles Fraser. I note that there is no listing of a marriage of Th*rl* to a Miss Skene, so it may be that Charles, like his father, was illegitimate and registered under his mother's surname.
You should also view Th*rl*w's own birth certificate. This will tell you where his mother lived at the time of his birth, and if you are
very lucky the birth might have been registered by a grandparent, uncle or aunt.
If you think there is merit in my ramblings above, you could also view the originals of the various censues, birth/baptisms and marriages referred to above.
One source you should also investigate is whether the Tyrie Kirk Session had anything to say about the birth of an illegitimate child to Margaret Fraser. If so, they would almost certainly have obliged her to name the father. Unfortunately the KS minutes are not available online, so you would need to hire a professional searcher, or find a kind volunteer who is going to the National
Archives Records of Scotland or one of the other archives that has these available, to take a look on your behalf.
Happy hunting!
Edit: My reply crossed with Gadget's above. However I will leave mine to stand, as I have come to a slightly different conclusion from hers. Given that there is a birth certificate of a Th*rl*w Fraser to Margaret Fraser in 1859, which matches the original information you provided, I think you would need more evidence to deduce that the son of William F and Isobel Mitchell is your one.Tyrie and New Deer are neighbouring parishes. See
Oldwhat
http://www.geograph.org.uk/gridref/NJ8651New Pitsligo
http://www.geograph.org.uk/gridref/NJ8855which are less than 5 kilometres from one another.