The thermometers were placed in the comparator in the order indicated by the columns. Readings were taken from left to right and then right to left. Between each two sets of readings the water in the comparator was slightly stirred.

As the rise in temperature is so small, a day was considered sufficient for the return of the zero point, though our standard seems to have lowered somewhat. But the error is small, at most.

6163 is best standard. We therefore give these observations twice the weight of those of 6165.

The mean errors are then

Mean error of 21472, as compared with the absolute thermometer, is:

The above are the errors of the thermometer when in a vertical position.

JOHNS HOPKINS UNIVERSITY,
Baltimore, January 30, 1880.

DEAR SIR: Inclosed please find four independent comparisons of your Casella 21472 with our standards, in a vertical position. I have made several attempts, and in different ways, to obtain a correction for the horizontal position, but find it useless, from the fact that your thermometer, although always at exactly the same temperature, will never read twice the same when laid in a horizontal position. The difference at 90° may be as much as half a degree.

The error is probably due to an air bubble in the bulb, which in a Casella thermometer it is impossible to remove.

The thermometer is only accurate when used in a vertical position, but it is then, as you may see from the inclosed results, very accurate, indeed, when compared with the air thermometer.

Trusting that the results I send will prove satisfactory, I am,

Yours, very truly,

C. B. COMSTOCK,

But. Brig. General, U. S. A.

W. W. JACQUES, Late Fellow in Physics, J. H. U.

BALTIMORE, March 27, 1880.

DEAR SIR: I am sorry you have discovered any arithmetical error in the tables I sent you, but it arose from my having sent off the tables before any final check on them. They were in my study some time, waiting for the comparison in the horizontal position and I forgot that they had not been verified.

The systematic error you speak of comes from our using a different value for the "M" in the formula of reduction to the air thermometer. The published table was computed from the mean value of M as obtained by direct observation and by comparison with a thermometer, No. 6167, see p. 111. But on making more observations I rejected the result from No. 6167, and returned to the value M=.00015 as I had before found directly. See bottom of page 119. In Table LIII you will find the corrections by comparing the first two columns. The correction must be added, and amounts to Too° C. at 20°.*

I took your thermometer in hand myself at last, and have got some very good results in the horizontal position. I send two comparisons, the first of which was made by Mr. Koyl and myself together, and the second by Mr. Koyl alone.

I succeeded after some time in getting the air bubble safely out of the bulb, which accounts for our getting better results. It could hardly be seen by the naked eye, and could not have influenced the comparison in the verical position much.

The comparison was made in a copper vessel holding about one gallon, as in the drawing. The bulbs were close together. Thermometers were tied to the stems of each to indicate the temperature of the protruding mercury column. This varied considerably on account of the lamp used to heat the water, but the calculated correction is always very small, as our thermometer has to be vertical and the other horizontal, it is difficult without a special apparatus to make an exact comparison with the stems wholly immersed. I also compared the vertical with the horizontal readings by putting the thermometer in a small vessel of water, which was covered with a cloth to prevent cooling. The thermometer was then quickly turned from one position to the other and readings made. It was also turned completely over, so as to get twice the effect. In reducing these observations it is probably best to assume that the effect is proportional to the distance of the mercury above the bulb, as the 150-point came about at the bulb we can write approximately

A=c(t-15°).

We can then compute c from the different observations. From the observations which I sent, I have computed c roughly and without verification to be as follows:

I will tell Mr. Jacques and Mr. Koyl to send their bills, and hope that the various observations will agree when worked up, though the thermometer does not read close enough for the highest accuracy.

Yours truly,

General C. B. COMSTOCK.

H. A. ROWLAND,

See Mechanical Equivalent of Heat by Henry A. Rowland, Prof. of Physics, Johns Hopkins University. Cambridge, 1880.

NOTE.-Correct zero reading, or 320.088 is the only vertical reading; 0°.088 must therefore be subtracted from each to complete the reduction.

I.

CASELLA.

[Experiments to determine the correction for horizontal positions.]

II.

KOYL.

In this comparison (March 16) readings were made by Professor Rowland; reduction was made by Koyl.

Second comparison, March 18, 1880. Readings and reduction by Koyl.

In experiments 1 to 7, inclusive, Casella in water to 45°, and Baudin in wa'er to 100mm.
After experiment 7, Casella as before; Baudin in water to 110mm.