SOMK MI.KCI KV ST\NI>Al;l>S <F KKSISTANCK, KTC. S 



and calculated resist. -mecs ,nv in tin- pn>| Million it'll /*- 4 s )/4 sin 2 . To obtain 

 an iilea nC tin- iiMiriiitnde of this, let a = 1, ft = 0'05 centim., and a = 40 centime., 

 under which conditions AB=0'7 centim. approximately; then the value of the 



me expression is 1 '000036. Thus, supposing the axis of the tuhe to be of :m 

 undulating character, such that the curvature is everywhere equal to 0'025 

 ( 4 \j centim.), and that points of inflexion occur on the assumed axis of the tube at 

 equal distances of 0'7 centim., then the resistance of the mercury column will be 

 greater than that calculated on the assumption of a straight axis by '00:50 per 

 <vnt. Under these conditions, the maximum angle made by the real and hypothetical 

 axes is 0'5 only, and the maximum displacement of the real from tin* hypothetical 

 axis 0'015 millim. The true axis, if drawn on paper, could not be distinguished by 

 tin- unaided eye from a straight line, and when the refractive effects of the walls 

 of a tube be taken into consideration, the problem of determining the condition of 

 the axis by experimental methods seems impossible. Indeed, such irregularity cannot 

 be allowed for, and since it must hold good for every tube in some small measure, the 

 calculated resistance must always be too small. The extent to which the axis 

 undulates in this way will probably lie largely dependent on the uniformity of the 

 cross-section ; this is an additional reason therefore for a careful choice being made. 

 ( 'nnsider the section of a tube by a vertical plane containing its axis. Let the upper 

 Ixmnding line be straight, so that all variations in the diameter of cross-section are 

 shown by undulations in the lower bounding line. Then, for a tube of average 

 radius 0'5 millim., with a maximum variation in cross-section of 4 per cent., the 

 extreme displacement of the lower bounding line is 0'02 millim. The maximum 

 displacement of the axis is therefore O'Ol millim. only. 



Some criterion of the irregularity is afforded by the final results of the resistance 

 measurements. If the probable error of all the determinations is not greater than 

 O'OOl per cent., then the calculated and observed resistances should not differ by 

 more than this. The greatest difference actually observed is 0'0036 per cent. 

 (TaMe IX., Method I., Tubes V and Y). The axes, therefore, appear either to 

 approximate very closely to straight lines, or to vary very much to the same extent. 



It is evident from the foregoing that, when lengths are measured, every precaution 

 must be taken to avoid bending the tubes. A slight curvature when observing the 

 resistance is, however, of no consequence, as illustrated by the term 1 &*/4a* being 

 so nearly equal to unity. 



l>''tails of Operations. 



The tul>es employed were eleven in number. Eight of these were of Jena 16"'glass, 

 obtained from Messrs. SCHOTT and Co., while the remaining three were of " Verre dur," 

 and procured from M. BAUDIN. 



These eleven tubes were selected from a large number sixty to eighty in all the 

 results of a rough calibration with a 5 -centim. thread determining the choice, 



VOL. mv. A, K 



