178 Proceedings of Royal Society of Edinburgh. [sess. 
the month of September is connected with the depth by the 
formula 
t = a + bx. 
Combining the first four temperature differences down to a depth 
of 10 metres by the method of least squares we find 
t = 0*44 - 0*025x. 
If we include the difference for the 20-metre depth we find 
t = 0-42 - 0-018x. 
Another result obtained by using twenty-seven selected pairs of 
stations instead of nineteen is 
t = 0-47 - 0*02a. 
For this last case the mean differences at the four smaller depths 
were 0-49, 0‘42, 0’33, 0*28. 
If we compare the values of the mean differences of temperature 
here calculated with the values given in the former paper, we see 
that the present values derived from a carefully-selected number 
of stations are distinctly smaller, and that no confidence can be 
placed upon the means for depths greater than 10 metres. 
We may now complete the investigation by calculating how 
much heat accumulation and loss of heat day by day this fluctua- 
tion of temperature in the Mediterranean means. This is at once 
done by integrating the expression tdx from x = 0 to x equal to 
the value for which t vanishes. These values are for the three 
formulae given above — 17'6, 23*3, and 2 3 '5 respectively. Integrat- 
ing for these cases and using the corresponding superior limit 
for x we find 
0'Ux - 0-0125x 2 = 3-9 
0-42* - 0-009 x? = 4-9 
0-47^ - 0*01 a: 2 = 5*5 
Changing the unit from the metre to the centimetre we find 390, 
490, 550 calories as estimated values for the amount of solar 
radiation which heats the Mediterranean waters daily during the 
month of September. The probable errors in each of these 
determinations are large, so that only the first significant figure is 
of any real value. Let us consider 450 ± 50 as a fair average, and 
compare this with the amount of solar energy available as cal- 
