Look what I found. Googling for the phrase, from the Winchester Profession, "holiness and true happiness are inseparably connected" -- or rather I searched for "holiness and happiness are inseparably connected" and I found references predating 1803. It's not the kind of language you see too often.
Now I have three possible inspirations for the phrase, assuming of course that it wasn't a product of Walter Ferris, the profession's chief author.
The necessity of holiness is evident from the purpose or decree of God; "He hath chosen us, that we should be holy and without blame before him in love." Ephes. i. 4. The principal design of God in ordaining any to eternal life, is, that, by holiness, being made meet for an inheritance with the saints in light, they may be for ever happy, to the praise of the glory of his grace. Holiness and happiness are inseparably connected. As then, without holiness no man shall see the Lord, so likewise without holiness no man can be happy.
That this change is essential to salvation. For our Lord himself declares, Except a man be born again, be cannot seethe Kingdom of God. He has no native meetness for it, nor any capability of enjoying it; his carnal propensities must be stain, and a spiritual capability to enjoy God and glorify him, must be imparted to him. Without this, no man can enjoy true happiness, cither in the present life, or the life to come; for holiness and happiness are inseperably connected, nor can they be parted ; for a God of unspotted purity and holiness can have no communion with impurity and sin, nor impure sinners with a God of spotless purity. Therefore, in order that his own children may be brought to that happiness to which they are appointed, it is essentially necessary that they be born from from above; for it is this which constitutes their meetness for glory. Consequently, all who go to heaven are prepared for it by this heavenly birth, in the present life; none can go there without it.
Q. When is our conversation suited to the principles of our profession?
A. When we distinctly know them, firmly believe them, openly prosess them, stedfastly adhere to them, and have our practice corresponding to our profession, particularly, when we live and walk as those who fixedly believe.