Dr. William Budd: J.B. Berkart, in his 1878 book "On Asthma" wrote extensively about Budd, and how he aimed to disprove the convulsive theory of asthma. Berkart explains that Budd repeated experiments previous authors wrote would produce bronchospasm and he didn't produce the same results. In fact, as Berkart explains, Budd flat out "rejected the theory of a bronchial spasm, and even doubted whether the circular fibres were muscular, as alleged." (1, page 25)
Dr. Charles J.B. Williams: He is the same brilliant physician who came up with the term lub dub to describe the sounds emitted by the beating of the two chambers of the heart. He also studied asthma, and for that we are fortunate, as he's the person who ultimately proved the spasmotic theory
Berkart explains that Williams performed experiments that proved without a doubt "that mechanical and electrical stimuli do produce contraction of the air-tubes. Thus the theory of a bronchial spasm obtained the support of experimental physiology. And even those who until then wavered in their opinions as to the possibility of such a spasm saw now no reason for doubting, but readily accepted that doctrine." (1, page 26)
John Charles Thorowgood, in his 1878 book "Notes on Asthma," explains:
"The larger bronchial tubes have their cartilaginous rings as elastic spring-openers; the smaller tubes, lying nearest to the vesicular parts of the lung, have no cartilaginous rings, but are entirely muscular; and (Rene) Laennec and (Daniel) Reisseissen, and more recently Gratiolet, have detected muscular fibres in air-tubes less than one line in transverse diameter. The contractility of these fibres under the influence of electrical, chemical, and mechanical stimuli was proved in a series of ingenious and conclusive experiments by Dr. Williams many years ago."Williams became the first to break asthma into two types: spasmodic and paralytic. Berkart wrote that as of the writing of his (Berhart's) book in 1878, the two terms described by Williams were the ones accepted by most experts. However, other doctors would continue to reclassify asthma to their own content and amusement.
The ideas of these two men would be debated the rest of the century, although, in the end, Williams came out the winner.