( 105 ) 



plane, and ??,.o is the refraclivo index for air- water. Tlie angle ^ was 

 measnred by means of a combination level. For this pnrposc was 

 used a level from a cathetomcter bv the Société Gcnevoise (1 scale 

 division =r 0/()(i) j)la('0(l upon an auxiliary apparatns (PI. II fig. 1). 

 This arrangement consisted of an arm R tnrned accurately cylindrical 

 and attached perpendicularly to a heavy copper |)late P. By means 

 of the three adjusting screws a, h and c this plate li can so be 

 placed against a glass comparison surface, which has been made 

 accurately vertical that the level |)lacod on the arm 11 indicates a 

 perfectly horizontal position. The s(piare end of the level is then 

 pressed against the windows of the \olumenometer jacket and the 

 level is again brought to the horizontal. From the number of turns 

 of the divided screw head of the screw c necessary- to accomjilish 

 this, from the pitch of the screw c which has been determined 

 beforehand, and from the known distance of the point of the screw 

 c to the line ah the angle 6 may be calculated. From this the error 

 in the reading follows at once when the angle of refraction of the 

 window is allowed for. (The application of the combination level 

 assumes that the curvature is negligible, which will probably always 

 be the case with plate glass for degrees of accuracy up to 0,05 mm.). 



The results are given in Table III, column II (p. 111). 



In our present experiments the auxiliary apparatus employed for 

 the spirit level has not yet allowed us to attain with sufficient cer- 

 tainty an accuracy greater than that corresponding to an error of 

 about 0',3 (that is to say a correction of 0,01 mm.j 



The 2"'^ method of determining the eri'ors in the readings consists 

 of ol)taining readings of the heights of the middle mark on the 

 screens when no water is in the jacket and also when the jacket is 

 full. For simplicity this measurement is reduced to a determination 

 of the change in height of one of the marks and the change in distance 

 of the other mark from this one. For during the measurement of the 

 differences in height for one mark a layer of water 8 cm. thick is 

 alternately interposed and removed, and therefore the cathetometer 

 must be moved as a whole so as to allow its being focussed upon 

 the standard metre with which every care is taken to ensure its 

 fixed position and to protect it against any temperature change. 

 Absolute height measurements were rendered very tedious on account 

 of this repeated moving of the cathetometer, while the determination 

 of the alteration in the distances betweeji two central lines was 

 comparatively simple. The determinations of the changes in the 

 distances of each line from (he fundamental one were, in order to 

 ensure the invariability ot the lengths measured, reduced in every 



