RootsChat.Com

To be considered "of this parish" you only had to live there for 3 weeks -- which just happens to coincide with the number of Sundays the Banns had to be read.

But "living in the parish" could have a very wide definition. There are stories of people just leaving a suitcase in a friend's house or a lodging house for the requisite 3 weeks but otherwise continuing to live at their normal place of abode

Basically, I am wondering if I can look through all the Bradford birth certs for a specific birth date of Sept 24th, as that is the only thing I am sure of.

Birth Registrations are not in order of birthdate, but in order of registration date.

Registration was anything upto 6 weeks after the birth, so that would be a huge number of certificates to look through, comprising the end of the third quarter and half of the 4th quarter -- for each year you want to search
The public are not usually granted access to the Registers and I very much doubt the Registrar's staff would have time to do such a vague search.

What you can do is use a site such as freeBMD to search the for registration in Bradford in these time periods

Searching "William Richardson" born Bradford 1860 - 1870 brings up just 2 entries, both 1861

The same search for "William Whitehead" brings up 8 entries throughout the decade.

You would have to do further research on each of these people to see if one of them is your William

Possibly more property / money was found that had belonged to him that had not been distributed by the first will.

My 2xGreat grandfather's will was proved soon after his death in 1870.
In the mid 1890s one of his sons was legally declared to have died in Manilla in about 1867 -- and so there was a further probate of his will to distribute money originally left to that son.

One of my husband's ancestors had 14 children in the early/mid 1800s --the first when she was 20, then at fairly regular intervals but the last 5 (including a set of triplets) were born when she was between the ages of 41 and 45