What does 'with departures from' mean?

Hello, my name is Takuya. I’m a Japanese, studying mechanical engineering at college.
I have a question related to a thesis that I’m reading. I would very appreciate it if anybody whose native language is English could answer it.

In the thesis, it is written that ‘John first noted that equation was not always correct, with departures from the simple linear relationship in some cases.’ In this case, what does ‘with departures from’ mean? Also, is it a common phrase in academic English?

Thank you in advance.

"It departs from the simple linear relationship in some cases = it does not follow (it goes away from) the simple linear relationship … ) It seems a common phrase in academic writing. Some people would also use “deviation”. Simply put the sentence could look like this:

‘John first noted that the equation was not always correct, in that it did not follow the simple linear relationship in some cases.’

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You can measure the degree.

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Ah I see. Good explanation! I understand it well! Thank you very much!

Very interesting link! I’ll be learning by it later again. thank you so much!!