All 4 Uses

solemn
in
The Narrative of the Life of Frederick Douglass
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such was his disposition, and success at deceiving, I do verily believe that he sometimes deceived himself into the solemn belief, that he was a sincere worshipper of the most high God; and this, too, at a time when he may be said to have been guilty of compelling his woman slave to commit the sin of adultery.†
Chpt 10

solemn = very serious--possibly dignified
Every man stood firm; and at our last meeting, we pledged ourselves afresh, in the most solemn manner, that, at the time appointed, we would certainly start in pursuit of freedom.†
Chpt 10
The clanking of fetters and the rattling of chains in the prison, and the pious psalm and solemn prayer in the church, may be heard at the same time.†
Chpt Appe *
Sincerely and earnestly hoping that this little book may do something toward throwing light on the American slave system, and hastening the glad day of deliverance to the millions of my brethren in bonds—faithfully relying upon the power of truth, love, and justice, for success in my humble efforts—and solemnly pledging my self anew to the sacred cause,—I subscribe myself, FREDERICK DOUGLASS LYNN, Mass.†
Chpt Appe

solemnly = with seriousness and dignity

Definitions:

(1) (solemn)
in a very serious (and often dignified) manner
(2) (meaning too rare to warrant focus)
Less commonly, solemn can mean that something was done with great or appropriate ceremony. It can also be used to describe something as dark or undecorated.