* 
” 
318 J. H. Alecander on the Tension of Vapor of Water. 
here, once for all, in justification of such application, that there 
need be no “apprehension of its affecting the results ; for it is easy 
to see, by inspecting a few instances taken at random from the 
table, that the rational deviation of the formula (i. e., the differ- 
ence between calculated and observed pressures ) is, for small dif- 
ferences of temperature, either null, or so remote a fraction as to 
be inappreciable in the calculation 
In applying this formula, I shall take up the principal series of 
experiments separately, beginning with the most recent ; and sha 
then make assemblage of the mean results. 
1. Experiments of Mr. Regnault—To deduce the absolute 
mean error of the erous quantities of this observer, it would 
be obviously ead to take up each experiment ;—a labor of 
which I am me no means ambitious, and which would be dispro- 
ionate at once to what is admissible i in the other series pres- 
ently to be noticed, and to the present aim. I shall, therefore, in 
all, only make use of short general methods which, "without lay- 
ing claim to the accuracy of geometrical refinements, will yet be 
recognized as having foundation in the theory of mathematical - 
probabilities ; and will, by their popular form, recommend them- 
selves the more readily to the convictions of those who are chiefly 
conversant with steam in practice, and for whose benefit the 
whole of the present discussion is mainly intended. 
It is obvious, then, in the first place, that the idea of freedom 
from error is associated with symmetry in the results. Such sym- 
metry will always be observable in quantities that progress (as 
natural quantities may be assumed to do) according to some con- 
stant law; and as, in our ignorance of what the true law is in 
this case, all that we can deal with is relative symmetry, it is of 
no importance what law or formula we take as the other term 
omparison, provided there be no material difference between the 
rig fend termination of the two. I shall therefore compare a 
ew of Mr. Regnault’s observations at the lower temperatures 
— the Soe ois ape pesent formula ; as under: | 
" “Pres hedel Mears? 
a “oncner ire in in in ae of Sete — Diffsrehers: " 
Dan v1063 ~ Oin-00664 | 4-0-00399t 
0 02047 0 -01799 +0-00248 
0 .02835 ; 0 -03055 ce —- 0 we 
0 -04567 0 -04375 -+4-0-00192 
0 -06378 0 '-06643 — 000265 
0 09410 0 -O9111 +0-00299 
0 +12559 0 13451 0-:00892 |. 
0 -15000 0 +16106 —0-01106 
0 ‘18111 0 19561 —0-01450 
He is apparent then, that so far, these observations do not follow 
uniform or symmetrical progression ; and without pretending 
to eriticize. the experiments themselves, which doubtless have as 
