QUARTZ FIBRES AXD ITS TEMPERATURE COEFFICIENT. 415 



scale comes under the cross- wire. The position of the cross- wire in this last '1 millim. 

 is then found by measuring the amounts through which the rocking plate has to be 

 tilted, in order to bring the bounding lines, in turn, on to the cross-wire. In this way 

 the number of revolutions made by the fibre while the upper glass tube travels a 

 known distance over the lower one is obtained. The fibre itself evidently travels 

 through half this distance, and BO, dividing the measured distance by twice the 

 number of rotations counted, the circumference of the fibre is obtained, and hence 

 its radius. 



Each piece of the fibre was measured in three places, and there were usually 10 or 

 12 pieces. The mean of all the measurements was taken as the radius of the 

 fibre. The agreement tatween repeated measurements of the radius at the same 

 part of a fibre was always very close. A single reading could be trusted to '01 per 

 cent. The diameter of most of the fibres was found to vary along their length, 

 generally in such a manner as to indicate that they were slightly conical in shape, 

 but sometimes in an irregular way. The difference between the largest and smallest 

 diameters was generally less than 1 per cent, of the whole, but it was sometimes 

 more. The greatest difference found during these experiments was 4 per cent, in the 

 case of a fibre 14 centims. long and of mean diameter -0010256 centim., as found by 

 measurements at 40 places approximately equally spaced along its length. In order 

 to illustrate the accuracy of this method of measuring small diameters, I give below 

 the results of four consecutive observations on one of the first fibres measured. 

 These are repeated measurements of the same part of a fibre, the mean diameter of 

 which was 0012483 centim. 



In 127 revolutions of fibre the scale travelled (a) "99609 centim. ; (h) '99609 centim. ; 

 (c) '99608 centim. ; (<l) '99609 centim. 



When differences between two successive readings were obtained, it is probable that 

 they were due to a slightly different part of the fibre being traversed on each occasion. 

 This easily happens unless great care is taken in drawing back the sliding table after 

 an observation has been taken. 



As an example of the manner in which the diameter of a fibre varies at different 

 points, I give below the values of the diameter of the first fibre experimented on, as 

 measured at 20 places approximately equally spaced along its length. 



DIAMETER of Fibre in Centimetres. 



0021090, '0021184, '0021160, '0021145, 



0021071, '0021172, '0021175, '0021150, 



0021103, -0021191, -0021200, '0021228, 



0021080, -0021132, '0021219, '0021182, 



0021130, -0021149, '0021256, '0021181, 



Mean diameter = '0021160 centim. 



