Yet there may have been some bias here. He had done experiments on his own, and even made "Remarks on Emhysema of the Lungs" in 1839.
As Dr. J. B. Berkart notes in his book, "On Asthma: It's Pathology and Treatment," Budd repeated Williams experiments and failed to repeat the results. Budd "therefore, rejected the theory of a bronchial spasm, and even doubted whether the circular fibres were muscular, as alleged."
The thing about reading about this in their original works and by the original authors, is that when I was reading about the description of emphysema I was confused. After a while I realized that my problem was because I was going by today's definition of emphysema and not the 19th century definition.
Today we define emphysema as loss of lung tissue that causes air to be trapped in the lungs, and this results in a barrel chest appearance. In the 19th century emphysema was simply air trapping.
Berkhart (page 26) describes how one doctor (Dr. Longet?):
"not only confirmed in the main the results obtained by Williams, but added that in his experiments irritation of teh pneumogastric nerve always produced spasmodic contraction of the brnchi, whereas section of the nerve led to emphysema... since section of the vagus causes emphysema, i.e., distension of the air vesicles, there must be muscular fibres which, if liable to paralysis, are liable also to spasm."
So you see, emphysema is air trapping. It's air being trapped in the lungs due to narrowing of the bronchioles (air passages in the lungs).
What both Williams and Budd may have failed to observe was that they were both onto something. Emphysema (air trapping) is secondary to bronchospasm. Yet it may have taken a few more years to juxtapose these ideas.