On the Errors Involved in the Determination of Cooling Powers and Air Velocities with a Kata-Thermometer.

DURING the experimental comparison of difEerent types of hot-water heating systems in a school at Easter 1934 about a thousand kata readings were taken. These were taken mostly in pairs, one immediately after the other, and a third reading was taken only when the first two differed by more than about 10 per cent. The standard deviation of the difference between the first and second kata cooling times can easily be calculated, and from this it is possible to deduce the errors involved in the measurement of cooling powers and air velocities. The statistical method used involves two assumptions: (i) That the errors of the first and second cooling times have a chance distribution, when they are taken consecutively with the same instrument. This may be checked by plotting the distribution of the differences between the first and second cooling times and seeing whether they form a normal curve. (ii) That the standard error of the first reading is equal to that of the second and that the two errors are uncorrelated. If xx, x2 are two cooling times and d = x1 — x2, a being the standard error of a single reading, then <jd 2 = 2cr (1 — r), where r is the correlation in error between the readings.