why were more elements discovered in 1795-1815 and 1875-1895 than any other time in 1700-1940?

Answer 1

Interesting observation ! The answer may be Scientific zeal and technological innovations.

Answer 2

Because back then, there were still plenty of undiscovered elements to discover. There were plenty of holes and gaps in what we now understand to be the "complete" Periodic Table" to be "filled in" as the appropriate elements were discovered and isolated from nature or (later on) synthesized in the laboratory.

Before 1795, there wasn't sufficient equipment or techniques to isolate, describe, and prove that a compound was actually an element. So progress, specifically the stage of PROOF that something was indeed elemental, was slow going.

Nowadays, we can only ADD elements with larger molecular weights...which get less and less stable due to the distance electrons have to be from the nucleus. (Electrons, once they are far enough from the nucleus, will not stay associated with the nucleus, will fly off, and result in decay of the compound ultimately). This is why the NATURAL elements pretty much STOP at around 103-ish or so. The latter elements beyond that are completely synthetic, and have very small lifetimes.

Between those two factors, the probability of finding "new" undiscovered elements drops quite a bit.

Answer 3

Individual scientists worked on multiple discoveries. Inbetween times there were bunches of wars. (1848 the year of revolution etc. ) Once they hit the radioactives, they needed instrumentation to progress and didn't have it until the 20' to the 30's.