which we call Heat. 123 
gas; hence representing the same by v, we have 
mnu2 
Sprite Seanad soo AB) 
The same formula would have been obtained if, with Krénig, 
we had, for the sake of simplification, assumed that one third of 
the whole molecules move perpendicularly to the side under 
consideration, and the two remaining thirds in two other direc- 
tions parallel to the side. Nevertheless I preferred deducing 
the formula for the pressure without using this simplifying hy- 
pothesis. 
If we write the last equation in the form 
2 
3 nmu 
ge= “39” ° . . By 0 . . (6a) 
the right-hand side then denotes the vis viva of the translatory 
motion of the molecules*. But, according to Mariotte’s and Gay- 
Lussac’s laws, 
pv=T . const., 
where T is the absolute temperature ; hence 
nmu> 
2 
and, as before stated, the vis viva of the translatory motion is 
proportional to the absolute temperature. 
18. We may now make an interesting application of the above 
equations by determining the velocity « with which the several 
molecules of gas move. 
The product nm represents the mass of the whole given quan- 
tity of gas, whose weight we will call gy. Then g being the force 
of gravity, 
=='P .const.y 
am= f, 
and from equation (6) we deduce 
a stim pile 3h © “gobi 
Adopting the metre as unit of length, and the kilogramme as 
unit of weight, let us suppose a kilogramme of gas under the 
pressure of 1 atmosphere—10333 kilogrammes on the square 
* In accordance with a practice lately become general, and with what I 
have myself done in former memoirs, I call the semi-product of the mass 
into the square of the velocity the vis viva, because it is only with this de- 
finition of the notion that we can, without the addition of a coefficient, 
equate the expressions representing a quantity of work and the increase or 
decrease of vis viva which corresponds to the same. 
