The phrase "a barometer of race" is correct and usable in written English.
It can be used to describe a measure or indicator of racial dynamics or issues within a specific context.
Example: "The study serves as a barometer of race relations in the community, highlighting the disparities that still exist."
Alternatives: "a measure of racial dynamics" or "an indicator of race issues".
If Uttar Pradesh lacks an overriding issue this time, analysts regard the race as a barometer of many key issues shaping Indian politics: the changing roles of caste and religion, the impact of public disgust over corruption and the rising public desire to share the fruits of economic growth.
Congo's elections, particularly the presidential race, may be a barometer of how well drastic geopolitical changes in Africa's Great Lakes region have been received in Congo, especially concerning Congo's relationship with its neighbor Rwanda.
Thirty years after Loving v. Virginia struck down the last laws barring interracial marriage, the new change in the census and the ensuing controversy have become a barometer of the complexity of American attitudes toward race, and their contradictions.
Those off-year races are not always a barometer of the political climate in the next year, but they can give the winning party an important psychological lift that helps fund-raising and stirs the activists.
And, as FiveThirtyEight recently noted, Virginia's off-year results "haven't been so predictive" as a barometer of each party's strength in the following midterm House races.
The race is one of several likely to be viewed as a barometer of the president's popularity.
About the campaign to defeat Lieberman, the New York Times wrote, "The Connecticut race drew national and even international attention this summer as a barometer of the mood of American Democrats over the Iraq war".
The campaign for governor here in St .Petersburg, Russia's second city, has been widely cast as a barometer of President Vladimir V. Putin's political strength heading into parliamentary elections in December and his own re-election race next March.
