This is one way to do it. I'm not saying it's the best or super optimized though, depends on your data and indexes.
@measurements = Measurement.find_by_sql(
%{select * from measurements
where date_part('year', date) = 2013
or date = (select max(date) from rounds where date_part('year', date) = 2012)
or date = (select min(date) from rounds where date_part('year', date) = 2014)
order by date})
Edit: I see you're using sqlite, this works for Postgres but should be easily portable.