( 383 ) 
will begin with zero; then this expression will obtain a positive 
value, which rises to a maximum; after which it will diminish 
again and after having passed through zero, it may even become 
negative. 
It appears from this vemark, that at a given value of 7, we 
may give to vj, and so also to p, such a value that the cooling 
has its maximum value; or in other words there is a most advanta- 
geous value for pj in LINDE's apparatus. The existence of such a 
most advantageous value follows of course by no means from the 
approximated empiric formula of Lord KerLviN and Joure, which 
is generally used to explain the LiNDeE-process. Yet the existence of 
a most advantageous way of working has been observed, but it is 
ascribed to a quite different cause. So we read in „La liquéfaction 
des gaz. J. CAURO, pag. 33” about this what follows: „Comme 
„la production frigorifique de lappareil dépend de la différence de 
„pression p;— pz avant et après |’écoulement et que, d'un autre 
„côté, le travail de compression est fonction du quotient de ces 
A . Pi 5 ; . 
,»mémes pressions 2 , il est clair, que l'avantage est d'avoir une 
P2 
„grande différence de pression, mais en même temps un rapport 
,aussi faible que possible entre ces mémes pressions.” 
In this phrase very great importance is attached to the quantity 
of heat, which is developed when the gas, returning under the 
pressure pz, is again compressed to its original pressure p, — and 
this heat is in fact, considerable, and the more considerable the 
smaller pz is at given pj. It is even greater than the heat which 
is annihilated when the pressure is lowered to ps. But in the appa- 
ratus of LiNpe the arrangement is such, that the developed heat is 
given out in quite a different part of the apparatus, from that where 
the cold is produced; and the gas heated by compression loses this 
heat before it reaches the cooling-spiral, so for instance by passing 
through the cooling mixture, which serves to dry the gas. And 
if this were not sufficient for taking away the heat which is pro- 
duced by compression, it would not be difficult to find more effica- 
cious means. 
But in the quoted phrase the usual mistake has been made, 
against which I will warn here, viz. to put the cooling proportional 
to (pi—p2) — or to expect at any rate that the cooling will always 
increase with the increase of pj — pz. 
In order to find the condition which must be fulfilled that the 
cooling be maximum, we may consider 7; as function of 7} and Pp: 
and 72 as function of 75 and ps. The value of 7) we think as 
