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I read this book as a kid, and it always stood out in my memory, partly because the main character's name was also Danny (as I was called as a kid) and he was into science like I was (and am, I guess). But mostly it was because the plot of this story, unlike a lot of similar children's books, was pretty engaging.
The basic background to the series of books is that Danny Dunn lives with a Professor Bullfinch, a kindly inventor who keeps coming up with revolutionary products that Danny and his friends get to play with. There was a mini-supercomputer, anti-gravity paint, some contraption trying to get messages from aliens in outerspace, and, best of all, the invisibility machine. The thing that was especially neat about how they pulled off the invisibility effect was that the authors didn't even try to come up with some hokey nonsense science to try o explain how someone could become transparent. They bypassed it completely and came up with an ingenious workaround: if you have a small robot that looks like something natural (in this case, a dragonfly) which you can control with a machine and see and hear what it senses, it's like you were there invisible even though you aren't really. And, as a bonus, they put a little speaker into the dragonfly so it could talk.
This may not sound all that special at first, but it really was a quite amazing thing to have in a children's book at the time it came out. The control mechanism for the robot in the book was quite a lot like the virtual reality helmets and gear computer scientists now use. What's even more remarkable about the story is that it is copyright 1974 (so probably thought up before that), and we now know that the CIA was actually working on a dragonfly robot in the '70s to try to spy on people. In the book, Professor Bullfinch doesn't want the military to have the invention because he thinks they aren't ready to use it ethically. I wonder if this was some concept that both the author and the CIA techs read about somewhere else, or if perhaps someone in the agency had read the Danny Dunn series looking for ideas, heh.
An excerpt of the book is reproduced below:

The Danny Dunn was ahead ahead of its time in many ways. There
was the science, of course (although it was considerably less
realistic in most of the other book), but also the concern about
the morals involved in using the inventions. Plus the Irene character
proved to be just as smart and athletic as any boy. I recommend
the series and especially this book to anyone looking for good
stories for children insterested in science.
Danny Dunn, Invisible
Boy
by Jay Williams and Raymond Abrashkin, Illustrations by Paul Sagsoorian
Publisher: McGraw Hill Consumer Products
April 1974
154 pages