"The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom."
(Extra nerdery follows that; for those who are curious at what *temperature* that's measured:
"The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second."
although
"The original international prototype of the metre, which was sanctioned by the 1st CGPM in 1889, is still kept at the BIPM under conditions specified in 1889."
presumably for the lulz.
The kilogram isn't quite so exotic:
"The international prototype of the kilogram, an artefact made of platinum-iridium, is kept at the BIPM under the conditions specified by the 1st CGPM in 1889 when it sanctioned the prototype and declared:
This prototype shall henceforth be considered to be the unit of mass.
The 3rd CGPM (1901), in a declaration intended to end the ambiguity in popular usage concerning the use of the word "weight", confirmed that:
The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.
The complete declaration appears here.
It follows that the mass of the international prototype of the kilogram is always 1 kilogram exactly, m(
) = 1 kg. However, due to the inevitable accumulation of contaminants on surfaces, the international prototype is subject to reversible surface contamination that approaches 1 µg per year in mass. For this reason, the CIPM declared that, pending further research, the reference mass of the international prototype is that immediately after cleaning and washing by a specified method (PV, 1989, 57, 104-105 and PV, 1990, 58, 95-97). The reference mass thus defined is used to calibrate national standards of platinum-iridium alloy (Metrologia, 1994, 31, 317-336)."
FTW.