I looked all over to get the various accepted value of the Planck constant since 1900. But there is never
any record about the history of this mysterious number.  

 

I think you would have to look in some journals, find papers about the measurement of the value, look up the references in those papers, and so on, to track through the historical measurements. 

This would probably be a good place to start: https://iopscience.iop.org/article/10.1088/0034-4885/76/1/016101

 

It would probably mean you and I are not up-to-mark to view those papers. 

If you don’t have access, you could try your local university library 

https://arxiv.org/abs/1409.7597

Numerous mentions of historical measurements. Lots of references for follow-up

 

Steiner’s paper on research gate (though on my iPad it renders without spaces. But the figures have info, too)

https://www.researchgate.net/publication/233948351_History_and_progress_on_accurate_measurements_of_the_Planck_constant

Yes.This Steiner paper exactly satisfy what I am looking for. It gave the first value of h to around end 1910. It also gave the method used to measure h historically, basically the photoelectric effect in the earlier years. I am not able to access any peer reviewed articles. Thanks.

I posted the same question over physics stack exchange. Because they can't give me the information, they insist that there is no reason for me to to look for such information as the "different values should not be comparable". At other time physics stackexchange do give good answers.

   

Glad you found your answers here, I don't blame you for not completely trusting physicsstack exchange.