set, two or more taken at nearly the same temperature. Reject those that differ too greatly from the average temperature of their set, remembering that the change of rate is as the square, and not directly as the difference of the temperature. Reject also any rate that is phenomenal, for the best chronometers will sometimes run wildly for a term or two without apparent cause and then come back again to their usual rates.

Take the mean rate and mean temperature of each set and substitute them in (2), (3), and (4). A convenient way to form the sets is to plot the rates on the card as before described, then to combine in groups those of nearest temperatures and rates.

Chronometer No. 1262 Negus, Plate VIII, was worked up and plotted in this way. It was running at the Observatory from January 6, 1880, to August 18, 1881, when it was issued. It was again returned to the Observatory, March 1, 1883, having been in service afloat. Its record is as follows:

Temp.

Rate.

Mean date, April 11, 1880.

Temp.

Rate.

Jan. 16, 59.0°-1.448s. Mar. 6, 66.7°-0.936s. July 4, 82.5°-2.18os.

Feb.15, 56.0 1.670

Temp. Rate.

Apl. 5, 63.7 -1.145

Apl. 15, 64.5 -0.979 July 14, 84.3 -2.341

Feb.25, 59.5-1.394

Mean, 58.2°-1.5045.

0=68.07°.

Jan. 20, 56.5°-1.694s. Apr. 10, 71.3°—0.762s. July 19, 83.2°-1.910s. Jan. 30, 56.6 -1.733

Aug. 8, 82.2 -1.936

Apr. 10, 56.01.297 May 10, 68.9 -0.709 Aug. 18, 81.1-1.802

Mar. 11, 53.8°-0.768s. Apr. 21, 73.0°+0.707s. Apr. 29, 85.2°+0.011s.

May 19, 72.9 +0.866

June 5,73.6 +0.696 May 8, 85.0 -0.149

Temp.

Rate.

Mar. 31, 55.0 0.562

Apr. 6, 55.0 -0.550

Mean, 54.6°-0.6275. 0=71.79°.

curve, determined by observations from Jan. 6 to July 14, 1880.

»urve, determined by observations from Jan. 1 to July 19, 1881.

curve, determined by observations from March 1 to Oct. 23, 1883.

The above data were taken from the records of the chronometer, without application of the effect of time, running in natural temperatures; the highest temperature for 1883, however, was obtained in the temperature room. The sets were selected by grouping the rates near the same temperature, the dotted lines showing the groups used, and the dots OX A, the mean rates and temperatures, each for ten days, during the time under comparison. The values of and z remain practically constant for 1880 and 1881, and change but little for 1883. A portion of this change may be attributed to the coefficient of time, which has not been considered.

☛ changes more or less with time in all chronometers, generally increasing if its sign is +, and decreasing if it is. That is, from the time of cleaning, chronometers, as a rule, run faster as their age increases. This is especially so with new chronometers, which sometimes take two or three years to settle down to a steady rate. Not unfrequently do they gain, in the course of a three years' cruise, three or four seconds on the rates given them when issued. This change is gradual, and the daily acceleration or retardation is the coefficient of time.

Let T be the date at which the rate at a given temperature is r; T1 any other date at which the rate at the same temperature is r1; T1-T=t, the elapsed time, and g the coefficient of time.

And (1), the general equation of the chronometer, becomes

r'=r+z(0—0′)2+gt

(9)

(10)

With No. 1262 Negus, from April 11, 1880, to April 21, 1881, g+.00067; and from April 21, 1881, to April 17, 1883, g= +.00204. Owing to the change of 0 and z the latter value of g was a little larger for temperatures above 70°, and a little smaller for temperatures below 70°.

In the ordinary uses of the chronometer for navigation purposes, the last term, gt, of equation (10), may be, and should be, omitted, as the value of g may change with time, and its use would indicate a greater degree of accuracy than would actually be obtained. Again, its value is always small, and the accumulated error from its rejection would come within the probable error of observation when ratings are frequent. It should, however, always be used in the establishment of longitude by meridian distances, and in other work where back calculations are made.

The temperature corrections should be used at all times, more especially when changes of temperature are frequent and extreme, and in making long voyages. A change of a few degrees in the higher or lower temperatures will change the daily rate one or more seconds, soon making the accumulated error amount to several miles in longitude. It is well to keep the chronometer record up for temperature even while lying in port, as it gives the navigator a knowledge of how it is running, and shows him what reliance he can place upon it at sea. By reference to Plate VIII, it will readily be seen what the effect would be on the rate of No. 1262 Negus were it rated in about 68°, and then taken into a temperature of either 55° or 80°, as often occurs.

Having determined the curve, on obtaining a rate at any subsequent time, if the rate does not plot on the curve, the difference will be a constant to be applied to all rates taken from the curve at different temperatures.

Great care should be taken when chronometers are suspended in their gimbals that they swing perfectly free, but without play enough to give them a jar; and the gimbals should be so adjusted that the chronometers will always hang with their faces level.

Nos. 725 and 1262 Negus, both running very regularly and adhering closely to their curves, were canted 9°, first with the XII down, then with the VI, IX and III down successively, leaving them two terms of seven days in each position, and placing them level again for two terms between the successive changes. They both lost on their level rates, varying from five-tenths to three seconds, and were more or less irregular; but when placed level again they each time came back to their regular rates, running a little irregularly at first.

Their mean rates reduced to a temperature of 70°, were as follows:

No. 725 Negus.

Face level, +0.72s; XII down, — 2.18s; level, +0.77s; VI down, —1.275; level, +0.78s; IX down, +0.175; level, +1.01s; III down,

Face level, +0.74s; XII down, ―0.20s; level, +0.82s; VI down,

-1.70s; level, +0.75s; IX down, — 2.36s; level, +0.84s; III down, 2.65s.