813 
of Edinburgh, Session 1881-82. 
fall off. That is to say, the maximum density point for water 
under 1 ton pressure is - 1° cent. 
This temperature is only given, of course, as an approximate one. 
The causes of error enumerated by Professor Tait in his note attached 
to this paper all affect it, and if the lowering of the maximum den- 
sity point is not directly proportional to the pressure, it can only be 
regarded as a very rough approximation. 
4. Note on the Preceding Paper. By Professor Tait. 
If we assume the lowering of the temperature of maximum 
density to he proportional to the pressure, which is the simplest 
and most natural hypothesis, we may write 
to =t 0 ~ Bj? , 
where p is in tons-weight per square inch. 
Now Thomson’s thermodynamic result is of the form 
Bt = A(t — t 0 ')Bp . 
This becomes, with our assumption, 
Bt — A (t -t 0 + B p)Bp . 
As the left-hand member is always very small, no sensible error 
will result from integrating on the assumption that t is constant on 
the right (except when the quantity in brackets is very small, and 
then the error is of no consequence). Integrating, therefore, on the 
approximate hypothesis that A and B may be treated as constants, 
we have for the whole change of temperature produced by a finite 
pressure p, 
At = A(£ - t 0 )p + JABp 2 . 
I have found that all the four lines in the diagram given in the 
paper above can be represented, with a fair approach to accuracy, 
by the formula 
y = 0 -0095(£ - % + 0-01 7 p 2 , 
where p has the values 1, 2, 3, 4, respectively. Hence, comparing 
with the theoretical formula, we have the values 
A = 0-0095, B = 3°-6C. 
B expresses the lowering of the maximum density point for each 
ton-weight of pressure per square inch. 
4 R 
VOL. XI. 
