124 
MR. J. R. CHRISTIE ON THE USE OF THE BAROMETRIC 
to be added to the error of the first observation, which becomes then —'091 ; and 
the mean error derived from the two observations is —*099. 
The instrumental error thus diminishing appears to indicate that there is a point 
on the scale where it becomes 0, and beyond which, as a correction, it must be ap- 
plied in a negative form ; and this point can readily be determined on the principle 
that the differences of the errors are proportional to the differences of the correspond- 
ing boiling-points ; for, calling B the point on the scale at which the error vanishes, 
£, £', e and e' two other points and their corresponding errors, we have the equation 
b — B _ e + 0 
b—b' ~~ e—e' ’ 
whence 
B = £ 
e.{b-b') 
e—e 1 
and, substituting in this the values above found, viz. 
£=208*967, £'=197*649, 
e= — *589, e'= — *099, 
we find B= 195*363. 
In order, by means of this result, to determine the correction to be applied as a 
multiplier to the number of degrees above or below B, it remains to determine the 
amount of error due to each degree, which, in fact, when its sign is changed, will be 
the required factor ; calling this correction C, we have 
C = 
— e _ -589 
£ — B — 13*604 
= *0433. 
It may be remarked, that the principle on which the determination of this correc- 
tion is founded remains unaffected by the supposition that the errors from which it 
is derived are partly attributable to the diameter of the bore of the thermometer in- 
creasing uniformly in descending ; this I have satisfied myself by the usual means 
to be the case, though to a comparatively trifling amount. 
The observations recorded at the Geneva Observatory and those at the Great St. 
Bernard afford an excellent means of applying my own to the determination of 
the height of my several stations, since those places present the advantage of being, 
the one my starting-point, and the other a position central to my series of stations. 
The readiest way of thus applying them appears to be, to reduce the height of the 
barometric column as given in millimetres to the form of the corresponding tempe- 
rature of boiling water, by means of De Luc’s formula above given, and then, for 
the determination of the difference of altitude between each station and Geneva, and 
the Great St. Bernard, to employ the formula 
H = {548(£ — £')+24D} { 1 -\-{t — 32) *00222}, 
where D is the difference in degrees between B(= 195*4) and the observed boiling- 
point; and the factor 24 is the product 548 X *0433; the sign -j- being used when 
my own station is lowest and vice versa , because the instrumental error is always one 
of defect. 
