To answer the original question about The Logic of English: yes, learning the 70 basic phonograms will be enough to teach your child to read. The lessons should be just long enough to keep your child’s full attention.
I use a program (Spell to Write and Read) that is similar to The Logic of English in that it teaches 70 phonograms and 29 spelling rules. I look at these phonograms as building blocks to words and the rules as the blueprint or design plans. I teach my children these building blocks and show them how to place these blocks together in word patterns. When proficient with the phonograms, we then move into introducing the spelling rules a few at a time. These spelling rules may be what is referred to as intensive phonics. With so many ways to make similar sounds in English, these rules help us to get an idea for which combinations of letters work together in words.
As we are introducing these rules gradually and continuing to reinforce them, it reminds me of how one gets started in learning a craft: one project at a time, graduating in difficulty. Before I have my children build the chicken coop out back, I would like them to work on smaller projects such as birdhouses, the life size Christmas manger for our Christmas books, a small cabinet for our pantry, and the dogs’ shelter. They need some plan to contruct these things with each set of plans building on the skills of the last project. This is the same with reading and spelling.
My children begin to read independently with just phonogram awareness and word pattern practice. This doesn’t mean we stop our lessons once they can read. It means that they can handle the power tools now and eventually become the general contractor with the plans (very helpful when written narrations come into play). We get more involved with our spelling rules.
Most importantly, each child is different and must be taught at their comfort and readiness level with customized instruction. This customization of lessons keeps our learning time fresh and fun. I also don’t worry about their pace. One of my children at the age of nine went from reading only three letter words to reading the entire Chronicles of Narnia series. She just needed her own time and pace. Her favorite authors now are Charles Dickens, Jane Austen, and Tolkien (of course).
It is fun to blend both the phonogram system and Charlotte Mason’s word pattern method together. I don’t stick to word lists. We love to get a line from our poem, hymn, or Scripture memory and see how these individual words are designed. One resource that I also use is Wheeler’s Elementary Speller. We go slowly with the copywork exercises in this book as we first analyze the individual words with the Spell to Write and Read markings. I also have my older ones working through the Spelling Wisdom books (yes, marking a handful of the words from the dictation).
And just for a great library search, An Acorn in My Hand by Ethel Bouldin (copyright 1964) is the book that has such a special place in my heart. This slim book is the story of how one first grade teacher taught her students to read and spell using both phonograms and word patterns.