They all three worked over the problems yet to be solved, Morse going backwards and forwards between New York and Morristown.

That both Gale and Vail suggested improvements which were adopted by Morse, can be taken for granted, but, as I have said before, to modify or elaborate something originated by another is a comparatively easy matter, and the basic idea, first conceived by Morse on the Sully, was retained throughout.
All the details of these experiments have not been recorded, but I believe that at first an attempt was made to put into a more finished form the principle of the machine made by Morse, with its swinging pendulum tracing a waving line, but this was soon abandoned in favor of an instrument using the up-and-down motion of a lever, as drawn in the 1832 sketch-book.

In other words, it was a return to first principles as thought out by Morse, and not, as some would have us believe, something entirely new suggested and invented independently by Vail.
It was rather unfortunate and curious, in view of Morse's love of simplicity, that he at first insisted on using the dots and dashes to indicate numbers only, the numbers to correspond to words in a specially prepared dictionary.

His arguments in favor of this plan were specious, but the event has proved that his reasoning was faulty.

His first idea was that the telegraph should belong to the Government; that intelligence sent should be secret by means of a kind of cipher; that it would take less time to send a number than each letter of each word, especially in the case of the longer words; and, finally, that although the labor in preparing a dictionary of all the most important words in the language and giving to each its number would be great, once done it would be done for all time.
I say that this was unfortunate because the fact that the telegraphic alphabet of dots and dashes was not used until after his association with Vail has lent strength to the claims on the part of Vail's family and friends that he was the inventor of it and not Morse.