of Edinburgh, Session 1879-80. 
563 
where y is the remaining ascent, x the time, and A + B the total 
ascent. After two or three intervals x, the value of B j3 x is 
usually inconsiderable ; so that the ascent may at an early period 
be represented by the simple expression — 
y = Aa x . 
The probable error of a single comparison of theory with experi- 
ment is, as a mean result of eleven curves, 0 o, 012 C. Inci- 
dentally, it is shown that the above law is obeyed whether the 
thermometer is vacuous or open to the air. In a similar manner, 
the movements of the zero with temperature can be expressed by 
the equation — 
y = AoA — B [3 X , 
where x represents equal successive intervals of temperature. In 
this case, the value of B J3 X is always appreciable. The probable 
error of a single comparison of theory tvith experiment is, as 
deduced from four curves, 0 o, 023 C. 
Under the influence of heat, the zero of a vacuous thermo- 
meter at first descends, until the heat reaches a definite degree for 
each instrument; the “mean degree’ 7 observed was 154°. After 
this, the material of the bulb becomes, I think, semi-plastic and 
gives way to atmospheric pressure, the' zero then rising. This 
phenomenon continues until the 'mercury has a sensibly strong 
vapour tension, which causes enlargement of the bulb and depres- 
sion of the zero. A thermometer open to the air and kept 
upright, should, of course, on the application of an increasing heat, 
exhibit nothing but depression in the zero ; and this is shown to 
be practically the case. 
4. The correction known as Poggendorff’s is then alluded to, 
and the importance of habitually employing it is distinctly 
pointed out. 
5. The results of compressing a thermometer’s bulb show 
that, up to 134 atmospheres, the effect is a linear function of 
the pressure. The instrument is in fact an excellent pressure- 
gauge. 
6. In the course of the memoir, an apparatus is described for 
comparing the mercurial with the air thermometer, and the results 
of the comparison are stated. Attention is drawn to a compound 
