OF ARTS AND SCIENCES. lo9 



and that of the upper end u^. Move the thread leps than 1 mm. and 

 read again, finding thus /^ and ic.,. Move the thread about 1 cm. and 

 read l^ and Wg. Move less than 1 mm. and read l^ and u^. So con- 

 tinue throughout the wliole length of the graduation, increasing the 

 number of settings and repeating the whole series in reverse order, if 

 the highest attainable precision is desired. Avoid, as far as conve- 

 nient, taking readings with an end of the thread apparently just at a 

 line of the scale, as the width of the line, even in the best scales, is a 

 source of considerable error.* If the zero point of the graduation 

 has for any reason been selected as the first of which the error should 

 be assumed zero, the settings may to advantage, though not neces- 

 sarily, be made to extend each way from this. 



Then u^ — l^ , u^ — I.2 , &c. will give a series of lengths of the cali- 

 brating thread in all parts of the tube. Before reuniting this thread 

 to the rest of the mercury, plot points with abscissas l^, l, , &c., and 

 ordinates ?<j — ^j , ^<2 — 4 > '^^•' ^^^ corresponding lengths of thread, 

 and draw a smooth curve through the points thus obtained. This line 

 will p;ive a general idea of the form of the capillary bore ; and, should 

 any parts of it show considerable irregularities, the corresponding 

 portions of the tube shoj-ild be at once re-explored with the thread. 



If not already done, the point, A, upon the scale, to be used as the 

 starting or reference point of the computation, should now be selected. 

 In general the extreme ends of tlie tube are to be avoided, as more 

 likely to have been rendered irregular or rapidly tapering in the pro- 

 cess of making or joining on the bulbs. If the zero of the numbering 

 is placed two or three centimetres from the bottom of the tube, it 

 forms a desirable starting-point. 



Find upon the curve the ordinate u' corresponding to the abscissa A ; 

 then with abscissa A -\- u' find the corresponding ordinate u" ; with 

 abscissa A -\- u' -\- u" find the corresponding ordinate u'", thus con- 

 tinuing to the upper limit of the graduation. If ^ is at a sufficient 

 distance from the lower end of the graduation, find for the point with 

 abscissa A — w' the corresponding ordinate w' ; as may be readily 

 done, when necessary, by inspection of the curve, finding the ordinate, 

 which, added to its corresponding abscissa, will give A ; then with 

 the abscissa A — w' — w" find the ordinate iv", &c. These points 

 A — w' — w", A — w', A, A -\- u', A -\- u' -\- u", &c., upon the 

 graduation are the points separated by equal volumes of the capillary. 

 When the calibration extends both ways from the zero of graduation, 



* Some of the advantages of Neumann's method are offset by this error. 



