Thanks all. Umm Brucy it was an arithmetic question not bees in general. After 30+ years I have sort of a handle on that. It was just the metric to imperial that has caused confusion elsewhere and I wanted to double check my figures. Thanks all.
PH
yebbut...
a) if you have been keeping bees for thirty years (something that you wouldn't necessarily guess from the nature of your question) then you will presumably have been doing something that worked already, why not just carry on doing that? [If you are in doubt you can always weigh the amount of water you are using and compare with a 'known good' recipe ratio.] Also
b) it only actually matters if the exact strength of the syrup matters (beyond basic things like how runny it is or how likely it is to start fermenting). This is to my mind at least as interesting a question. I've always made up syrup to some 'by rote' type recipe and have not (not intentionally) varied it. Nor have other beekeepers I know, either, but if folk get confused about it they may have done so without realising..?.
if the bees quite happily feed on syrup that varies in moisture content then that is one thing, but if the bees need to work to change the moisture content of the syrup (in either direction) before it is useful to them as food, that is quite another.
I'm wracking my brains here but I do remember someone describing experiments with dry sugar as a winter feed, and there was a problem of some kind, either the bees wouldn't always take it or it caused them another problem in some way. If they would take it dry (or in 'cakes' perhaps), it would make life easier in some respects. The bees need to control humidity within the hive, and more humidity = a greater ventilation requirement and that presumably stresses the bees more, because they lose heat when they ventilate to control humidity. Dry (or dryer) sugar would act as a desiccant to some extent, as well as alter the amount of moisture (net) within the hive.
cheers