This section is from the book "The Manual of Phonography", by Benn Pitman And Jerome B. Howard. Also available from Amazon: The Manual of Phonography.
A diphthong is not a simple speech-element, but is the result of continuous voice-production during a change made in the shape of the oral cavity. A diphthong may therefore be described as a glide from the position of one vowel to that of another. There are but three diphthongs in our language, and they may be heard at the beginning of the words isle, oil, owl, respectively.
As the diphthongs are compound sounds, so they are represented by compound signs: I is a glide from the position of
to the position of
and is written
See lines 1 to 6. Oi is a glide from the position of
to the position of
and is written
See lines 7 to 9. Ow is a glide from the position of J to the position of
and is written
See lines 10 to 12. In writing these characters, both strokes should be formed before lifting the pen from the paper.
The place of a diphthong-sign is properly determined by that of the final vowel of the glide. I and oi are therefore written in the first place and ow in the third. However, as v is represented by an absolute sign, that is, one which does not depend upon its place for its legibility, it may, for greater convenience, be written in any place. The rules given in par. 41 apply to diphthongs as well as to vowels. Oi is written after the first and ow before the second of two consonants between which they occur. I may be written either after the first, or before the second consonant.
The diphthong-signs should always point exactly up and down. They never change their direction to correspond with that of the stroke to which they may happen to be written. In this respect they are unlike the dash vowel-signs. Compare par. 32.
When i or oi begins a word, and when i or ow ends a word, the diphthong-sign may be joined to the adjacent stroke without lifting the pen whenever it forms a distinct angle with it. See lines 13 to 15.
On account of its great frequency the word now may be imperfectly but conveniently vocalized by attaching only the second half of the diphthong-sign without lifting the pen; thus
now.
Exercise on the Diphthongs.

 
Continue to: