In both Morning and Evening Prayer, after the three Collects, the rubrics in our liturgy states:
The Officiant may invite the People to offer intercessions and thanksgivings.
In older Prayer Books, a handful of suggested prayers and collects were printed in this place, indicating those certain prayers for the crown, state, society, and so on, were appropriate for that point in the Daily Office. In the 1979 and 2019 Prayer Books, no such collection is provided immediately, but a larger collection of “additional” or “occasional” Prayers and Thanksgivings is provided in an appendix of sorts near the back of the book. This is, basically, the modern equivalent of the earlier, traditional, collection.
UPDATE — This order has been revised: https://wordpress.com/post/saint-aelfric-customary.org/1898
On the ACNA page for Texts for Common Prayer, and thus what will probably show up in the 2019 Prayer Book, is a list of 123 prayers and collects. A few of them are occasion-specific (like for a birthday, or for someone’s healing) but most of them are perfectly appropriate for general use. To this end, it is the recommendation of this Customary to work through all (well, most) of these prayers on a regular basis towards the end of Morning and Evening Prayer. This is a two-week rotation of prayers, averaging about 4 or 5 prayers per Office.
Week I Office Week II
95-96, 107-108 Sunday Morning 97, 99-102
98, 103, 106, 109-110 Sunday Evening 104-105, 111-113
1-5 Monday Morning 6-10
11-15 Monday Evening 16-19
26-31 Tuesday Morning 25, 32-37
70-73 Tuesday Evening 38-41
48-53 Wednesday Evening 42-47
78-82 Thursday Morning 90-94
114, 120-123 Thursday Evening 115-119
54-58 Friday Evening 59-63
20-24 Saturday Morning 64-69
85-89 Saturday Evening 74-77, 84
Let’s look at why this scheme is recommended the way it is.
Sunday, being the principle day of worship for the church gathered, has the section of prayers labeled At Times of Prayer and Worship as well as the prayers on Death, the Departed, and the Communion of Saints, as that is when most of the saints on earth are gathered. The assigned prayers skip around, numerically, in order to avoid prayers that are too similar from being read at the same Office.
On Monday the prayers start at the beginning of the list, covering the section For the Church. In general, the prayers for the morning are more specific and the prayers for the evening are more general or topical.
Tuesday morning covers the next section, For the Nation, again arranging the prayers so that too-similar collects aren’t prayed on the same day. Depending upon which country you hail from, certain prayers along the way will be appropriate to omit (mainly in the USA versus Canada distinction). In the evening, one day dips into the Personal Devotions list and the other starts the For Society section.
Wednesday morning is omitted, because that’s a traditional time for saying the Great Litany. The evening finishes the For Society section and begins the next section, Intercessions For Those in Need.
Thursday morning skips ahead to more of the Personal Life and Personal Devotions sections, while Thursday evening (in light of the day’s traditional Eucharistic theme) covers most of the Thanksgivings.
Friday morning (like Wednesday morning) is omitted so you focus on the Great Litany. The evening covers the rest of the prayers For Those in Need where Wednesday left off.
Saturday covers the prayers about Creation and Family Life, as well as Personal Life and Devotion. The creation theme matches the Morning Prayer Collect recommended for Saturdays (Collect for Sabbath Rest), and the family section is chosen to match the fact that Saturday is often a “day off with the family” for much of the working world. The remaining personal devotions also serve as a sort of introspective preparation for corporate worship on the following morning.
For sake of simplicity, “Week I” should line up with odd-numbered weeks in the liturgical calendar, and “Week II” with even-numbered weeks. For example, yesterday was (in modern reckoning) the 7th Sunday after the Epiphany, so this week could be considered an odd-numbered week.