NO. 6.| INTRODUCTION. CHRONOMETERS. LI 
This material was examined on the supposition that the rate could be 
represented in the form 
Daily rate = a + ty 
where ¢ is the temperature. For Hw after the return an attempt was also 
made to introduce a term proportional to the time, but it was found quite 
insensible. The results are contained in the following synopsis, where 7 is 
the number of equations employed. 
Dv? 
Hohwit .-<.. { 1893 16 + 9591 + 08165 | — 0.8172 + 0.80127 0.053 
1896, 97 79 + 2,00 + 0. 048 | — O. 192 + 0. 0056 0.073 
Kutter ces { 1893 15 — 0. 88 + 0. 194 | + 0. 056 + 0. 0325 0.100 
1896, 97 79 — 1.93 + 0. 054 | + O. 022 + 0. 0062 0.091 
Iversen .....f 1893 99, — 0. 45 + 0. 245 + 0 236 + 0. 022 0.400 
{ 1896 14 — 0. 76 + 0. 45 + 0. 270 + 0. 040 0.157 
It will be seen that K¢ has the smallest temperature-coefficient, but that 
its constant term has changed considerably more from 1893 to 1896 than the 
constant term for the other two. From Table d it is also apparent that a 
similar change in the opposite direction has taken place in the interval. The 
relatively large probable errors of the constant terms depend chiefly on the 
choice of 0° as the standard temperature, the mean temperature during the 
comparisons being of course considerably higher. The last column gives 
the mean of the squares of residuals (v) as a good means for comparing the 
qualities of the three chronometers. 
Hohwii is evidently the best of the three and it was deemed safest to 
rely solely upon it for the intervals without observations. A formula deduced 
from comparisons ashore is of course not immediately applicable on board, 
because the exterior conditions, especially the humidity, in a narrow ship’s 
cabin are very different from those of an observatory room. ‘That these 
different conditions affect not only the constant term but also the temperature 
' For Kt in 1893 it was found more convenient to count the temperatures from 10°, 
and the constant term was found as —0.832 + 0.8194 for this temperature, so that 
the probable error for 0° should have been considerably higher than that given 
above; but as the mean temperature during the comparisons in Hamburg had been 
higher than in Christiania, the value for 10° was retained in order not to prejudice 
the chronometer as compared with the other two. 
