574 MR EDMUND J. MILLS’S 
been at that time attributed to faulty designation of the zero, or “ pointing” as 
it is technically termed. 
BELLANI* seems to have been the first to recognise clearly that an ascent 
does habitually occur, and to have proposed the view, substantially identical 
with my own, that it is owing to secular changes in the physical nature of glass. 
Conclusive evidence will be adduced below to prove that atmospheric pressure 
has no share in producing this ascent. 
If we observe at intervals the zero of a thermometer kept at rest at the 
ordinary temperature, the relation between the time and ascent can be repre- 
sented graphically by a line which, within the limits of accidental fluctuation, 
is distinctly continuous and curved. The exact nature of this curve would 
probably be very difficult to determine. It is not identical for any considerable 
length, with the ordinary parabola or hyperbola, as has been sometimes sup- 
posed. If, however, the values of the remainder of the ascent to a given point 
be taken for equal intervals of time, they will be found on the whole to diminish 
by a constant factor. A logarithmic curve with two terms is sufficient to 
represent, within the limits of experimental error, the ascent of a thermometer’s 
zero with time; the second term being such as to be materially required only 
in the earliest stages of the ascent. Thus, taking y to denote the remaining 
ascent, and w successive intervals of time, we have the relation 
y= Aa* + BB’ ; 
where (A+B) represents the total ascent, and a, 8, are constants, 6 being much 
less than a. There is thus no difficulty in establishing for any given thermo- 
meter an equation sufficiently exact for all practical purposes, and probably 
applicable to bulbs of any shape whatever. It is important to illustrate this 
equation. 
JouLE’s Results.—In the “ Memoirs of the Manchester Literary and Philo- 
sophical Society,” xxiii. 292, 293, JoULE gives particulars of nearly twenty-nine 
years’ observations of the zero of a single thermometer, the longest series 
hitherto recorded by any physicist. It is not stated whether the instrument 
was kept during this period at the ordinary temperature only. A smooth 
curve is drawn to represent the observations. One division of the scale corre- 
sponds to ‘043 C. Taking three years as the value of a unit of time, the 
equation is 
y =8'6('81)* + 4:9(-08)* in divisions, 
or ='370('81)? + °211(-08)” in degrees. 
* Cited by Kimrz, Schweigger’s Journal, xl, p, 200, where a historical resumé is given of the entire 
subject to the year 1824. A later exhaustive survey has been written by Eon, Pogg. Ann. xi. p. 276, 
et seq. 
