I've posted an extended reply to inquiries on D'ooge's "Elements of Latin" on a separate thread here
. But basically in a nutshell:
1. My copy has a 1921 copyright with no other impression dates so it should be Textkit-able. This has green boards like some of the copies of D'ooge's Cæsar and Cicero composition works that I've come across. My Beginners book has red boards (1909 and 1911 copyrights).
2. In the preface, D'ooge states that Elements is not a revision of the earlier Beginners book but "an entirely new book" that retains "all features of the earlier book that have been highly commended and have proved their value."
3. Text is divided into two parts: 56 lessons for the first half year, 54 for the second for a total of 110. There are also two optional lessons.
4. Vocabulary is about 500 words (Beginners claims 600ish if I recall correctly), ninety percent of these are used in Cæsar five or more times (I believe Beginners makes the same claim). Most are also supposed to be found in Cicero and Vergil.
5. Supplementary material is different than what is found in Beginners:
a. Greek myths and Roman legends "to arouse and hold the interest of the young"
b. Selections for sight translation
c. A Latin play - "Perseus and Andromeda"
d. An intro to Cæsar type story - "Baculus the Centurion"
e. A Latin songs section with piano arrangements (4 or 5 if I'm not mistaken)
f. An "Original Stories" section where 9 pictures are given with a supporting/suggested vocabulary given underneath each picture. The student is supposed to create short story based on what the viewer sees in the picture.
The lessons "seem" to be shorter on average than what I've noticed in the Beginners book (many seem to just fill a single leaf i.e. front and back). So this might be a viable option for folks with shorter attention spans, less time on a daily basis, etc. The above mentioned thread in the Learning Latin forum has more info lifted verbatim from the preface. I also have some of his composition works enroute so if anyone is interested I can go over those as well since they could be an appropriate follow up for folks just finishing the Beginners book (or Elements for that matter).
If anyone has more specific questions, just ask and I'll post what I can.
[edited for typos]