Ellen Wood’s East Lynne was serialized in X parts in The New Monthly Magazine between January, 1860 and September, 1861. Wood’s novel first appears in Series 2, Volume 118.
Full volume issues of The New Monthly Magazine are available on Hathi Trust and, in part, on Archive.org.
Links to Full Text of The New Monthly Magazine:
The New Monthly Magazine, Series 2, Volume 118, 1860 (East Lynne) @ Hathi Trust
The New Monthly Magazine, Series 2, Volume 119, 1860 (East Lynne) @ Hathi Trust
The New Monthly Magazine, Series 2, Volume 119, 1860 (East Lynne) @ Archive.org
The New Monthly Magazine, Series 2, Volume 120, 1860 (East Lynne) @ Hathi Trust
The New Monthly Magazine, Series 2, Volumes 119-120, 1860 (East Lynne) @ Archive.org
The New Monthly Magazine, Series 2, Volume 121, 1861 (East Lynne) @ Hathi Trust
The New Monthly Magazine, Series 2, Volume 122, 1861 (East Lynne) @ Hathi Trust
The New Monthly Magazine, Series 2, Volume 123, 1861 (East Lynne) @ Hathi Trust