PAPER BY PROF. HAGEN 15 



duced to the barometric pressure of 28 Paris inches aud the tempera- 

 ture 12° Eeaumur or 15° C. Assuming that the resistance of the air 

 is proportional to its density I formed a table of the logarithms of this 

 correction whereby the separate reduction is very easy. In case the 

 temperature sensibly changes during the time of observation it must 

 be assumed that this change occurred gradually and therefore for each 

 individual observation the correction corresponding to the time is 

 adopted. When especially large variations occurred readings were also 

 made in the intervals; still, in such cases very large deviations were 

 sometimes apparent, and it was repeatedly remarked that then the 

 movement of the arms steadily increased or that the times in which the 

 index sank 10 inches became smaller the lower its position was, which 

 never occurred with uniform temperature. The reason of this is cer- 

 tainly nothing else but this, that the equilibrium of the warmer and 

 colder air in the room gave rise to special currents that were combined 

 with tbe movement of the disks. When the temperature during a se- 

 ries of observations changed by two degrees or more, the results deduced 

 became so discrepant that they had to be rejected as entirely useless. 

 For this reason the room before and during the observation could not 

 be heated warm. On the contrary, the oven used for heating the room 

 must be cooled down completely. Even when the sun shone on the 

 window whose shutters could not liinder the warming, nothing remained 

 but to stop the observations. 



Almost equally troublesome was the friction in the various j^arts of 

 the apparatus. This varied perpetually, wherefore its value lor each 

 individual observation had to be especialh* determined. Of course it 

 diminished when fresh oil was introduced between the rubbing surfaces, 

 but then the variations became of such magnitude and were often so 

 sudden that the observations were again useless. Only after many 

 days and after the arms had remained for a long time continuously in 

 motion there was established a greater regularity. When this, how- 

 ever, became evident from the measures immediately following each 

 other, then again on the next day the conditions would be remarkably 

 changed. It was therefore necessary that the whole of any series of 

 observations that were to be comj^ared among themselves should be 

 made in immediate succession. In order to render this possible it was 

 necessary to reduce the number of measures as much as was any way 

 allowable, namely, to the number of the desired constants. Such a 

 course is defensible also because the individual readings, in a long 

 series of observations, accord much more closely with the law deduced 

 therefrom than with the similar measures repeated at other times. 



These preliminary remarks are the result of the great number of ob- 

 servations that I have executed during a half year. These were, es- 

 pecially at the tirst, extremely unreliable, aud only gradually were all 

 the circumstances perceived that come into consideration. The follow- 

 ing observations, which are the only ones serving as a basis for the sub- 



