venture to interpret this wave as follows:-If an interior thermometer were disturbed by sources of heat of constant temperature alone, such as the observer's body and the gas flames, its excess over the standard thermometer would probably be simply a function of the external temperature. Consider, for

instance, the observer's body alone. When the external temperature was that of the body, both thermometers should agree; but the colder the weather the larger would be the influence of the body in raising the reading of the interior thermometer.

But the disturbance arising from the walls of the room is different. Their sub-permanent temperature is higher in summer than in winter, and hence, on a day in summer, when the external temperature was (say) 45°, they would raise the interior thermometer more than on a day in winter when the external temperature was also 45°. Thus an expression for the reading of an interior thermometer as a function of external temperature alone is not sufficient. We must add a term following the temperature of the walls of the room. And it seems to me that the " squashing" of the above curve affords evidence that the influence of the walls is a vera causa. ascribe this break of continuity to the fact that fires are lit in the adjoining buildings during the winter months, but not used from about May to October. If they were retained the subpermanent temperature of the walls would make a simple sweep of annual period, but the rise is checked by losing the fires, as is the fall by recovering them. This is, however, at present, mere conjecture.

I

The fact remains that the readings of the interior thermometers are functions of the external temperature and of the time of year combined. This is exhibited more directly in the following tables of double entry :

The effect of the seasons is best seen in the column 45° to 50° common to all the months. The gradual diminution with rise of temperature is seen in any horizontal row.

This paper was already in type when Mr. Ellis suggested to me a concise method of dealing with these tables. He remarked that the reading of any thermometer appeared to be approximately a function of the difference of the external temperature from the average. The excess of any thermometer is, for instance, about the same in January for temperatures of 28°, 38°, and 48° as in July for temperatures of 50°, 60°, and 70°; the average temperature in January for the period under consideration being 383, and in July 59°5. I therefore analysed the tables afresh from this point of view. I was at first in doubt whether to select the average temperature for the approximate hour of observation (say, 9 P.M.) or the general average throughout the day as the basis; but a few figures show at once that

this point is not important. The two systems of averages for the period in question are shown in the following table:

The greatest difference between the two systems is 207 in May, corresponding to a difference of about 0°3 in the excess I—F. It is, therefore, almost immaterial which system we select; but as the influence of the walls (whose temperature would be more nearly related to the general average than to the average at a particular hour) has been suggested, it seems preferable to take the general average as our basis.

Assuming, then, that the excess of any thermometer over F may be represented by the expression

a b (excess of F above average),

I find the following approximate values for a and b :

There is obviously a very fair accordance between these numbers. If we divide the year into two periods of six months, November-April and May-October, the mean values of the above quantities are-

Now, according to the views already expressed in this paper, we may regard the constant (a) in each case as resulting from disturbance by the gas-flames and the observer's body. When the temperature is just the average the walls will be nearly at the temperature of the external air, and but for the gas-f -flames and the observer's body the interior of the room should be so too; but these disturbing causes raise the temperature of any given point in the room by a nearly constant quantity throughout the year. The quantity is a little greater in winter than in summer, as we should naturally expect; close to the instrument (thermometer I) it is about o°1 greater in winter out of 2o5; at the boundary of the shutter opening (thermometers N, M, S) it is about o°9 in winter and o°6 in summer. The difference between winter and summer is o°3 also for thermometer E; but it is not easy to explain the negative value for E, which is, however, possibly accidental.

The term with coefficient (b) is to be considered as due to the walls, which tend to lower the internal temperature when the external is above the average, and to raise it when the external is below. Close to the instrument (thermometer I) the influence of the walls annuls that of the gas-flames when the external temperature is about 16° above the average, and doubles it when about 16° below. In the shutter opening (thermometers N, M, S) the annulling is effected at 11° above, and the doubling at 11° below. We are thus led to the following important conclusion::

A phenomenon which depends purely upon the distribution of temperature inside the transit-circle room should disappear when the external temperature is about 13° above the average, and be doubled when the temperature is about 13° below the average.

Two minor points have been investigated-(A) the change in reading as the shutters have been left open for a longer time; and (B) the influence of the direction of the wind.

(A) As stated above, it was directed that the thermometers should be read only when the shutters had been thrown open at least fifteen minutes; and the time since opening was to be recorded. The results were arranged according to these recorded times, and means taken, as in the following table: