AND GEOLOGICAL RELATIONS OF CERTAIN HOT SPRINGS. 
579 
If we assume that the small space by which it exceeds or falls short of 212° is cor- 
rect, (and the error must necessarily be extremely trifling-, and by a little pains in 
adjusting the length of the column may be reduced as low as we please,) since we 
also know by experiment the true thermometric interval between the points 32° and 
212°, we know the true thermometric interval between the point marked 32° and the 
point which the summit of the moveable column last marked. But this thermometric 
interval was divided into a certain number of spaces of equal capacity and therefore 
corresponding to the same number of true thermometric degrees. Whence, by divi- 
sion, the true length of the moveable column employed is known, and therefore as 
many points of a true scale are fixed as the column was caused to step to between 
32° and 212°. 
Or the method may be more concisely stated thus : The errors of the points marked 
32° and 212° being directly determined, let the number of true thermometric degrees 
between them be 180° + a ( a being -J- or — ). Let the moveable column (starting 
from 32° on the scale), after measuring n intervals of equal capacity (whose coinci- 
dences with the scale are noted), have its summit but little differing in position (at 
the wth step) from 212° on the scale ; let its indication be 212° -j- b (b being + or — 
as before). Then, admitting that the small space of the scale b does not sensibly differ 
from a true scale, the true interval which it has measured will be 1 80° + a -j- b ; the 
1 80 ° \ g \ b 
true interval, corresponding to the length of the column itself, will be = I ; 
and the true temperatures, corresponding to the divisions noted on the scale at the 
successive steps, will be 1, 2 1, 3 I, &c. degrees above the true temperature, correspond- 
ing to 32° upon the scale. This mode of operating may be applied as often as desired; 
and it is better to reiterate it with columns of different lengths than to employ too 
short columns. An example will best illustrate the method ; 
its accuracy depends on two essentials in practice : 1st, that, 
the column may be brought with considerable accuracy to 
the desired length (how this is done has been mentioned in 
a preceding note) ; and 2ndly, that the lower extremity of 
the column can be brought with great accuracy to the spot 
marked before by its upper extremity. This may be accom- 
plished with extreme accuracy by tapping one end or other 
of the tube or scale. By the same process of tapping, any 
sensible error which might arise from the unequal convexity 
of the extremities of the mercurial column under different 
circumstances may be overcome. To secure accuracy, and 
to avoid parallax in the readings, I have found a telescopic 
apparatus particularly adapted. A B is a telescope having- 
cross wires in its focus, and having a lens, C, attached in front of the object-glass, so 
that an object placed at D, in the focus of the lens C, can be distinctly seen by the 
4 e 2 
but I will premise that 
B 
C 
D 
rfi-L 1 1 1 
-J — 1 — ! — ! — '-a 
Mj , n-rp'T 
M M 1 ' 1 “ 
