There's several meters here.
Art like good health -- this is trochaic meter:
'_ _ /'_ _
I never knew till now is iambus:
_ '_ /_ '_ /_ '_ /_
How precious till I lost thee -- trochee:
'_ _ /'_ _ /'_ _ /'_ _
In the first line the beat is irregular. Here's what we get if we break it down:
_ _ /'_ _/ _ _ /'_ _ /'_ _
You can see that it lacks stresses in the 1st and 3d pair of syllables - it's an irregular trochee.
P.S. " ' " is a stressed syllable.
Slashes are just to show that the meters are disyllable.