>>     This is a very important subject since bees must "perform actual
>> work", and thus spend energy removing the water from the food given to them
>> (in the sugar syrup). The recommended ratio is;   twice the amount of sugar
>> to water BY WEIGHT! You must weight the sugar and the water.  Aside:  It
>> does not hurt if you overdo the amount of sugar, but it does if you overdo
>> the amount of water.
 
It's not quite this simple.  If you're feeding to pack away stores, the
above paragraph is true.  But if you are trying to stimulate brood rearing,
a 1/1 ratio works better.  The bees have to dilute honey to feed it to
their brood, and are more inclined to store heavy syrup than to convert it
to brood.  Nectar, which has a much lower sugar content than any syrup you
are likely to feed, is a key stimulus to brood rearing.  Some people feed
2/1 syrup as needed in the Fall, and 1/1 syrup in January and February to
kick start broodrearing.
Michael