His mother is unknown.  She might have been Mary Greenwood, the mother of Joseph Priestley’s two known children, but if so, he was born a few months before the record of their almost certain marriage date.

He is known particularly from a petition he wrote and which is quoted in the “Leeds & Liverpool Canal” by Mike Clarke, and at the end of which he asserts that he was the son of Joseph the late Superintendent of the L&LC:

On the Death of Joseph Priestley, the Canal’s first Manager   letter from his son to the Canal Committee and recorded in the minutes of the Committee, held at The National Archive at Kew.

“I feel it a duty imposed upon me from the respect I must ever owe to the memory of the late Mr Priestley to submit to your consideration a few circumstances, the correctness of which from the length of time I served with him in his office I can fully confirm.

It will be unnecessary for me to dwell upon the superior attainments and enviable qualities he possessed, as they are generally known to the proprietors at large and have been frequently acknowledged by those at a distance from the ready and obliging disposition at all times shewn in affording them every information respecting the concerns of the Leeds & Liverpool Canal. By his death the company have lost a most intelligent, faithful and industrious servant, and altho’ some of the proprietors who attended the last General Meeting and who were fully sensible of his real merits, were individually anxious, as I am informed, to testify their high opinion of them by some remuneration to his family, yet from a feeling of delicacy with regard to distant proprietors they deferred proposing any resolution thereon at that time.

Mr Priestley had been employed on making plans etc when living at Halifax in the year 1769 by the direction of the late Mr Hustler, and his appointment as principal agent to the company took place in the following year at the salary of £100 to which an addition of £70 was made in the year 1771: [note: he moved to Bradford in March 1772] from that time and with that salary he performed for the space of twenty years the arduous duties of that office usually prevailing in the infancy of so important an undertaking, and most particularly at a time when canal navigation was but little known or understood in this country. It was well known to the gentlemen composing the committee of that day how many serious difficulties he had to encounter at that period, but no one, had he been living, could have given a more corroborative testimony of Mr Priestley’s indefatigable application of his time and ability than that very respectable character, the original projector of this great undertaking.

By an order of the General Committee held at Bradford on the 1st June 1792, Mr Priestley was allowed an additional clerk, but from his wish frequently expressed of not increasing the expences of the company, he by greater exertion persevered in transacting the affairs of the canal notwithstanding the greater accumulation of business since that time.

From the beginning of 1799 on the death of Mr Whitworth (late Engineer to the L&LC) the committee effected a saving of £300 per annum by Mr Priestley taking upon himself the superintendence of that department at a time too, when a most important part of the works was in execution. On various applications to Parliament, the attendance of Engineer, as well as other parties necessary on such occasions, was seldom required, because Mr Priestley’s comprehensive knowledge in that department and acquaintance with the whole concern of the L&LC fully qualified him to confirm by his evidence alone the necessary allegations stated therein. Mr Priestley’s close attachment to the interests of the proprietors was never shaken at any time by the many very lucrative and superior situations that have at various times been offered to him by persons, who knew well how to estimate his integrity and abilities. Situations, judging from those with whom he might have been connected, that would have placed him and his family in a state of affluence and independence. That zeal for the welfare and prosperity of the L&LC overcoming every feeling of self interest I do assert is almost unprecedented, and the high character and present flourishing state of this great concern may in a great measure be attributed to his superior abilities and management.

In offering to your consideration the inferior salary of £170 for twenty-one years, the saving of the expence of an additional clerk for twenty-five years, and of £300 per annum for eighteen years in the Engineer department, together with advantages derived by the proprietors on their different applications to Parliament, I earnestly hope they will evince their liberality by supporting the feeling of those proprietors who have expressed a wish in favour of a remuneration to the son for the very able and disinterested conduct of the father, whose life and services have been anxiously devoted to their interests for nearly half a century.

Jos. Priestley, Wakefield [A&CN Manager and his son]
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Additionally he wrote the voluminous text to accompany the canal maps of 1830, published by himself, J Walker (caertographer) and Nichols (publisher).
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No baptisms found for a Joseph the son of Joseph in Yorkshere in 1767 plus or minus 5 years.

But a baptism has been found for a Joseph son of Joseph Priestley of Shelf:

“Joseph son of Joseph Priestley of Shelf Baptized December 29 1761.”  No mother named nor in many of these noncomformist entries.
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Not found in the 1841 census.

At last his 1851 census had been found and they were living at Saint Johns, Wakefield, Yorkshire:

First name(s)  Last name  Relationship  Marital status  Sex  Age  Birth year  Occupation  Birth place
Joseph    Priestley  Head     Married    Male    78  1773  -                Halifax, Yorkshire
Sarah     Priestley  Wife     Married    Female  77  1774  -                Halifax, Yorkshire
Mary      Whitty     Visitor  Married    Female  52  1799  -                Bristol, Yorkshire
Ann       Robinson   Servant  Unmarried  Female  31  1820  Cook             Wakefield, Yorkshire
Mary Ann  Johnson    Servant  Unmarried  Female  26  1825  General Servant  Sandal, Yorkshire
Mary      Wilkinson  Servant  Unmarried  Female  50  1801  General Servant  Sandal, Yorkshire

Ref:
Archive reference  HO107
Piece number       2327
Folio              20
Page               32
Combined:          HO107, piece 2327, folio 20, p. 32
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In his will he refers to his dear wife Sarah and Mike Clarke says he married Sarah Whitworth in 1800 odd, Whitworth being a canal Engineer.
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This burial ties up with the will that was proved in 1853, particularly with the references in the latter to St John’s parish:

First name(s)      Joseph
Last name          Priestley
Sex                Male
Age                85
Birth year         1767
Death year         1852
Burial year        1852
Burial date        16 Nov 1852
Burial place       Wakefield
Dedication         St John
Residence          St John's
County             Yorkshire (West Riding)
Country            England
Archive reference  WDP 45/1/4/4
Collection name    Wakefield district burials
Society reference  S 29
Record set         Yorkshire Burials

Though I am not completely convinced this is the Joseph Priestly who calimed to be the son of Joseph Priestley, Superintendent of the L&LC.
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In his will dated 18 March 1850 he said he was a gentleman and living in a house with stables at St John’s parish, Wakefield, Yorks and he listed by name, though mentioned no relationship to him, save for his wife:

1. ‘My dear wife Sarah’.
2. ‘Joseph Priestley of Reedymoor House, oldest son of George Priestley of Bingley’,
3. ‘The said George Priestley’,
4. ‘Martha, James and George the children of George Priestley’,
5. ‘Each of the daughters of the late Jonathan Priestley of Sonbridge’,
6. ‘Sarah, Catherine, Jane, Joseph and James the five children of Thomas Holgate of Healey(?) House near Burnley’,
7. William Whitworth Esquire’,
8. ’Sarah the widow of Abraham Sharp’,
9. ‘Mary the widow of the late Jonathan Priestley’,
10. ‘James Priestley the son of the later Jonathan Priestley’,
11. ‘John Priestley son of George Priestley’,
12. ‘Thomas Holgate and his son Joseph Holgate upon the condition that they take upon themselves the trusts and duties of Executores of my Will’,
13. John Priestley of Liverpool, son of the said George Priestley’,
14. ‘Sarah Sharp and Mary Priestley widows’,
15. ‘Mr John Drinkrow …’,

and there was a codicl dated 28 April 1852 and in which he lists (with a relationship!):

16 ‘My nephew John Priestley of Liverpool’,
17. ‘His brother George Priestley’,
18. ‘Henry Walker of of Wakefiels aforesaid’,

and there is a second codicil of 28 October 1852 and a third codicil of 7th November 1852.

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At the end of the initial will, I was wondering what game he might be playing with his gifts to apparently unrelated Priestleys.  Then the first codicil revealed that they were, some of them, nephews.  But this raised the bar more than a tad.  All other documentation has only shown his father to have had one other son, Cap’n John.  His father’s father also had only one son that has been found so far.  So where do these nephews come from?  Only his gt-grandfather is recorded as having multiple sons.

Their marriage transcription:

First name(s)           Joseph
Last name               Priestley
Year                    1800
Marriage year           1800
Marriage date           28 Aug 1800
Place                   Burnley, St Peter
Denomination            Church Of England
Diocese                 Blackburn
Residence               Bradford, York
Spouse's first name(s)  Sarah
Spouse's last name      Whitworth
Spouse's residence      Burnley
Licence or banns        Licence
Witness 1               Jo Priestley
Witness 2               Saml Fletcher
County                  Lancashire
Country                 England
Archive                 Lancashire Record Office
Archive reference       PR 3027/1/42
Register type           Marriages
Register year range     1789-1811
Record set              Lancashire Banns & Marriages
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Frrom the image of the parish register, this information cane be added:

Licence granted by: Dean of St(?) …
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