386 Mr. T. R. Merton on a Method of 



given by these equations in the directions of z- 9 y, and x 

 respectively are 



3102-9568, 48*9069, and 13-4189. 



Comparing these with the results given by (fT), (£),and 

 (f ) above brings out clearly the fact that the plane which 

 satisfies one criterion for closest fit may give a very bad fit 

 if measured by another criterion. This is particularly the 

 case with (#) and (0'), though (f ') is not greatly inferior to 

 (f ) as the best fitting plane in the direction of x. 



The Sir John Cass Technical Institute, 

 London, E.G. 



December 1910. 



. 



XLIV. A Method of Calibrating Fine Capillary Tubes. 

 By Thomas Ralph Merton, B.Sc. (Oxon.)*. 



THE methods commonly used in the determination of the 

 bore of capillary tubes are direct optical measurement 

 of the bore at the orifice, or weighing a drop of mercury 

 which occupies a known length in the capillary. When very 

 fine capillaries, having an internal diameter of the order of 

 *1 mm., are to be measured, these methods present serious 

 difficulties. 



For many purposes it is necessary to obtain a value of the 

 mean bore, and as no glass capillary is uniform for any 

 considerable length, a measurement of the bore at the orifices 

 is liable to serious error. The weight of a column of mercury 

 10 cm. long contained in a capillary tube of '1 mm. bore is 

 about 0*01 grm., so that to obtain an accuracy of 1 per cent, 

 the weighing must be correct to 0*1 mgrm. 



The following experiments were performed with the object 

 of investigating the accuracy with which a measurement of 

 the electrical resistance of a fine glass capillary filled with 

 mercury can be made. From this a mean value of r 2 (where 

 r is the internal radius) can be calculated. 



The first series of experiments was conducted in a large 

 water-bath, containing about 30 litres, kept at 18° C. by an 

 electric-filament lamp which was governed by a large spiral 

 toluene regulator ; and other experiments were performed in 

 a bath kept at 25° by a small gas-flame governed by a fluted 

 toluene regulator. In both baths the temperature could be 

 kept constant to Ol 01 C. 



* Communicated bv the Author. 



