"Of the age of eighteen years, and under the age of forty-five years" was part of the law by which all* able-bodied white male citizens were required to enroll in their state militias. The President called forth this militia on the 4th of August, 1862, ordering the members in each community to gather and draft enough men needed to fill the quota required of them. In lieu of this, volunteers were allowed to enlist, to avoid any draft from being needed.  

One of those volunteers, enlisting for the quota of Lebanon, Maine, was Millett Blaisdell, who signed off as being 18 years of age. His father said otherwise.

Thomas Blaisdell, with attorney William Emery, Esq. of Lebanon, petitioned the court for the discharge of his son Millett from the 27th Maine, as he was underage at the time of his enlistment. The case won on the 20th of Oct, Millett was sent home, while the regiment marched out of camp to board the trains for the south. 
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He turned 18 six days later.  

Private Blaisdell was not the only underage volunteer in the 27th Maine, just the only one that was caught and discharged. Among the others:
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William Bail [Co. C], born 1846 [on grave]
Richard W (aka Whitney R) Carpenter [Co. B], born Oct 1847 (age 15 in Sept '62)
William H Carpenter [Co. B], born July 1845 (age 17)
John W Center [Co. K], b. ca Dec 1846 [Soldiers Home file; 1900 census]
John W Earl [Co. B], died 18 Oct 1862, aged 16 yrs, 9 mos, 21 das [grave]
Walter A Gowen [Co. F], b. 17 Apr 1846 (aged 16 1/2 when enlisted)
​Charles Guilford [Co. C], b. 4 Oct 1845
Anthony Jackson [Co. I], b. 18 Jan 1845 (17 1/2 in Sept '62)
Roscoe Jewell [Co. H], b. ca 4 Dec 1846 [calc from age at death; census recs]
Frank Mildram [Co. D], b. 18 Nov 1845 [grave; Nov '46 on 1900 census]
Robert Philbrick [Co. E], b. ca 30 Dec 1846, based on age at death (15 in '62)
Charles T Smith [Co. F], b. 7 Apr 1846 (age 16 at enlistment)
Horace Taylor [Co. I], b. 1846 [grave] or Mar 1848 [1900 census, prob error]
Frederick L Willey [Co. G], b. ca Jan 1846 (died Mar 1867, aged 21 yrs, 3 mos)

[There are likely others that I have yet to record, so this list may need to be amended in the future]

Note:
*There were exemptions to the militia enrollment, including those in positions within the government and the courts, religious preachers and followers (shakers and quakers), and men who held key occupations that ran the communities (such as postal workers and ferryman). See the book Militia Laws of the State of Maine (Google Books)

This 1862 bible was presented to Horatio W Trefethen of Kittery, Maine, who was a private in Company G (of the 27th Maine Infantry), by Isaac D Phillips. As can be seen in the photograph of the inscription on the inside cover, both the company letter and regiment number had yet to be assigned when this book was distributed. Horatio probably was the one who added his own middle initial, as well as the "G" for his company, though he wrote the "27" in the wrong spot.

Isaac Deering Phillips, a Kittery resident, was town clerk in the 1850's, employed as a cooper and retail grocer, and was a Justice of the Peace. His gravestone lies in the First Baptist Church Cemetery in Kittery Point, and is engraved with "Dea" for deacon, presumably a position he held at the church in 1862, when this bible was given out. It is not known (at this time) how many bibles were given out, or if they were handed out (by Phillips) to only those parishioners of this particular church, or if Mr. Trefethen was even a member.

Inside the bible was found a newspaper clipping, a poem titled "Heaven", by Martha Remick. She was a Kittery resident, the daughter of Rufus and Sally (Cram) Remick, who was a poet and author. Many poems of hers were printed in various newspapers in Maine and New Hampshire (usually the religious ones), but I did not find the exact issue this writing was clipped from.

​Also:
Individual page on this site for Horatio W Trefethen