I assume that due to the lack of any further mention in the census, plus his getting up in years, that he probably passed away sometime between the 1860 and the 1870 census.

So, from the slash marks on the census records, and the fact that Gurdon and Hannah were married on March 18, 1813,  we can conclude that Orson L, was most likely the first born.  Orson L, born June 20, 1814 (based on findagrave, see stone below). Orson married Martha C. Eddy. According to the 1900 census they had five children (3 living into 1900). Those children all appear on the 1860 census and are as follows.
1.  Climina (female) born 1844/45 and died Dec. 11, 1866. Based on the fact that her gravestone has her surname as Miller, I am assuming she never married.
2. Cordelia (female), based on the census records I get her birth as 1846 to date, I have no known husband for her.
3.  Celestia Jane (often referred to as Ettie J on the census) born May 14, 1848 in Braceville, Trumbull County, Ohio. She married Edwin D. Harmon. Ettie died on April 22, 1942 in Euclid, Cuyahoga County, Ohio. She was 93 years, 11 months, and 8 days at the time of death. Buried at Braceville Center.
4.  Ransom Gurdon born 1852 and died  Dec. 12, 1936 in Painesville, Lake County, Ohio.
5.  Dennis Eddy [Eddy on most census records, but Dennis E] on the 1880 census. On his Ohio death certificate it gives his date of birth as August 2, 1855 Braceville, Ohio, he was married to Lilly J. Norton on March 25, 1880 in Trumbull County, Ohio. He died on June 16, 1924 in Warren, Trumbull, Ohio. He was buried on June 18,  1924 in Oakwood Cemetery. Orson has a daughter-in-law Lillian [Mrs. Eddy] J living with them in 1880.

The second born child of Gurdon and Hannah Lane Miller was also a boy, Isaac Lane Miller. Much of his information comes from two of his great granddaughter's unpublished books on births, marriages, deaths, and obituaries. Isaac was born September 13, 1818 in/near Braceville, Trumbull County, Ohio. On February 15, 1844 he married Miss Lucy Ann Doane of Cleveland. She was the daughter of Job D. Doane and Harriet Woodruff. While it is purely speculative at this time, I believe Isaac Lane was named after his grandfather  (Hannah Lane's father) who may have been Isaac Lane.  Buried in the same cemetery as his parents is an Isaac Lane, Sr. (old enough to be Hannah's father), and an Isaac Lane Jr..  A careful glance over the internet seems to show Isaac Lane Miller would have been the 5th consecutive generation to be given the name "Isaac Lane."

Isaac Lane Miller 1818
nephew of
Isaac Lane, Jr.
son of
Isaac Lane, Sr 1754
nephew of
Isaac Lane
son of
Isaac Lane 1683

It may have gone beyond that, but I quit looking until I can prove the first part.  Isaac and Lucy's children come from Romelia Rowe Finney's book of Births, Marriages, Deaths, and Obituaries, those with places after their name appeared in the application for probate of will which lists heirs and place of residence in 1902 when the will was probated.

1.  Romelia Hanks Stevens of Dayton, Ohio born October 16, 1845, Dayton, Ohio. She married James Hadley Stevens on July 4, 1867 in Appanoose County, Iowa.
2.  Halsey Doan Miller, of E Cleved [his abbreviation for Cleveland] born July 22, 1847
3.  George Gurdon Miller of Cambridge, Nebraska born October 4, 1849
4. Hannah Elizabeth born May 17, 1852 died December 20, 1855
5. Harriet Isabelle born October 24, 1854 died December 30, 1855
6.  Arthur Edwin Miller, of Hastings, Nebraska born June 4, 1857
7.  Martha Belle Waltmire of Washington, Illinois born May 14, 1860
8.  Anna Lizzie Miller of 34 Wilbur St. City [Cleveland] born September 21, 1863
9.  Mary Jane Miller born December 14, 1865

Isaac Lane Miller died  November 18, 1879.  Lucy Ann Doane died January 6, 1902 "at 9:30 o'clock p.m."

I've seen it suggested on ancestry.com's family trees that the daughter listed in the 1830 census as being 10-15 years old is Jane Ann.  Jane Ann married John Rood on September 8, 1836. I have nothing on their children, yet.

1  Trumbull County, Ohio Early Marriages, 1800-1865.  Pg 45 lists the marriage of: Miller, Gurdon, 3-18-1813 to Lane, Hannah

Gurdon is buried at the Braceville Center Cemetery in Trumbull County, Ohio.  The following information is taken from findagrave.com, though there are no pictures of the graves so I'm not sure if the information is from the stones or some other source.  Gurdon Miller died April 26, 1870, and it is said (somewhere, may be the stone) that he was 80 years and 4 months of age at the time of death, that would make his birthday December 26, 1789 (according to the census he was born in MA).  Gurdon Miller and Hannah Lane were married in Trumbull County, Ohio on March 18, 1813.1  Hannah is also buried at Braceville Center Cemetery, and most of the following is from findagrave.com Hannah died September 25, 1846 apprarently in her 58th year. That would put her birthday about 1788.

Their son Isaac Lane Miller, has a very interesting name, for buried at the Braceville cemetery is an Issac Lane, Sr (the right age to be Hannah's father, and an Isaac Lane, Jr. the right age to be her brother. Isaac Lane, Sr.'s father may have been Ashbell Lane (who had an older brother Isaac), and Ashbell's father was Isaac, so the name "Isaac Lane" is quite heavy in the lines. (Currently, proving Hannah to be Isaac's daughter has not been accomplished, this is mere speculation.)

Gurden Miller
Shows up in the 1820 US Census in Braceville, Trumbull County, Ohio

2 free white males under 10 years  [Orson L. Miller and  Isaac Lane Miller
1 free white male between 16 and under 26 [Gurdon] (would have been 31, but I've seen stranger on census records)
1 free white male 45 and upwards
1 free white female 16 and under 26 [Hannah] (if she was 16 when married would be no younger than 23)
1 free white female 45 and upwards

Mere speculation here, but the older lady and gentleman could have been one set of parents?

Shows up in the 1830 US Census in Braceville, Trumbull County, Ohio
Gurdon Miller

1 m 10-15 probably Isaac
1 m 15-20 probably Orson L
1 m 40-50  Gurdon 41
1 f 10-15 possibly Jane Ann (I've yet to see any evidence beyond family trees on her)
1 f 40-50 Hannah 42

1840 census, my Gurdon is missing.

1850 census.
Braceville, Trumbull County, Ohio.

It's amazing for me to think that there could be two men named Gurdon Miller, the same age, living in Trumbull County; but apparently there were, at least by 1850.  I've yet to find my Gurdon in the 1840 census, his wife Hannah should still be alive for another 6 years. It is possible that they were living with one of their own children, but since the 1840 census is still slash marks it's difficult to tell.

There is a Gurdon B. Miller who shows up in the 1840 census living in Wayne, Ashtabula County, Ohio he's 50 years old (right age for my guy), and living with a bunch of children. But after careful study, I've concluded that this is not my Gurdon! By following Gurdon B through the census, he moved to Trumbull County in 1850, but he and my Gurdon both show up at the same time in the same 1850 and 1860 census,  one in Kinsman, and the other (mine) in Braceville. I discovered a book Descendants of Captain Joseph Miller of West Springfield, Massachusetts, and Gordon B. Miller shows up on page 17.  It states that he married February 28, 1822, Lydia Burr... and they lived in Kinsman, Ohio. It also lists their children including the three that show up living with Gordon in the 1850-70 census "Ann S. b. July 8, 1832... Sabra L., b. April 8, 1836... and Charles G. born May 25, 1838." All those dates match the children from the said census records. Thus, there really ARE two Gurdon Millers of Trumbull County.

1860 census Braceville, Trumbull County, Ohio
Gurden Miller

O.L. Miller50  M W    Farmer  No Real Estate  No property b. Ohio
Martha C. Miller         37   F  W        b. Ohio
Climena Miller  15  F  W         b. Ohio
Cordelia Miller  14  F  W         b. Ohio
Celestia Miller  12   F W b. Ohio
Ransom Miller            08  M     b. Ohio
Eddy Miller       04  M             b. Ohio
Gurden Miller   71  MFarmer$2340 Real estate – Personal   b. MA
Gurdon and Hannah Lane Miller.
Image courtesy of Ancestry.com
Image courtesy of Ancestry.com