"example of the manner" is correct and can be used in written English.
It is typically used to give an example of how something is done or the way in which something is carried out. Example: "Let me give you an example of the manner in which the project was completed."
We have in this immediate context another example of the manner in which Jewish zeal and energy are ready to outrun economic caution of the ordinary Western pattern.
In breathtaking example of the manner in which oil has corrupted the Bush administration we have prima facie evidence of the perverted priorities of the last eight years.
Yolanda's conflict with her father regarding the potentially controversial speech she has prepared for the Teacher's Day Address provides a classic example of the manner in which the García girls are pressured to conform to the norm.
Our goal was to provide a transparent example of the manner in which a genomics-based cancer predictor might be developed from training data and evaluated on independent test data with sufficient detail and documentation to allow the full process to be replicated by other researchers.
These are but a few examples of the manner in which the former system sucked the life out of the school day.
But few of his works offer as many and as memorable examples of the manner in which love can go awry.
Table 1 provides two examples of the manner in which the scenarios were altered to either preserve or remove emotional ambiguity.> To assess changes in biased interpretation, ten emotionally ambiguous test scenarios were dispersed within the latter half of the imagery task.
Abdullah Gul, the president, had already declared that, in a democracy, every citizen's view deserved respect.Mr Erdogan's response was a perfect example of the polarising manner in which he has governed in recent years.
Thompson provides a vivid example of the way in which a decadent manner could, paradoxically, be combined with fierce religious enthusiasm.
An example of the step-like manner of a reaction are SN1 reactions with intermediates.
The Vatican's communications operations are a striking example of the complex and wasteful manner in which the Church's institutions have evolved.
