484 PROFESSOR W. E. AYRTON, MR. T. MATHER AND MR. F. F, SMITH : 



The steel and marble cylinders were turned at or about the same temperature, and 

 the same portion of the leading screw of the lathe was used. For the axial measure- 

 ments of the coils a cathetometer was employed, but the observations are subject to a 

 greater probable error than the generality of high-precision cathetometer measure- 

 ments owing to the boundaries of the wires being somewhat ill-defined. The axial 

 length of the helices traced on the steel cylinder was determined by a simple 

 comparator, and the value thus obtained is associated with a very small probable 

 error. Table I. contains the results of- the measurements on the coils of suspended 

 cylinder No. 1. The first set of measurements was made on the whole number of 

 turns, viz., 184; the next observations on 163 turns chosen in various parts of the 

 coil, and the third, fourth, and fifth measurements were on 149, 135, and 121 turns 

 similarly chosen. Each of the values recorded in column 2 is the mean of at least 

 four readings; in all, about 100 observations were made. 



If equal weights are given to each set of observations, the mean of the values 

 recorded in the last column is 12 '9829 centims. The observations on the outer end 

 wires are not quite so reliable as those on intermediate ones, for a little irregularity 

 is always possible when starting and finishing a winding ; eight observations (each 

 being the mean of four) are therefore included in the first set. The mean of eight 

 measurements on the steel cylinder is 12'9830 centims., a much closer agreement 

 than was anticipated. Taking the value 12 '9 829 centims. and the values recorded in 

 Column 4 of Table I., the differences (observed mean) are +4, 4, +1, 1, and I//.,* 

 from which a probable error of O'OOl per cent, is deduced if we exclude the error of 

 the gauges employed. The observations on the helices of the other three cylinders 

 are equally satisfactory, and the means of the readings obtained with them are given 

 in Table II. 



As the tool carriage travelled over different portions of the leading screw of the 

 lathe when cutting the spiral grooves in the suspended cylinders 1 and 2, the 

 uniformity of the screw was tested and an estimate of 2/A was made as the probable 

 difference in length of the coils on the two cylinders, that of the coils on No. 1 being 

 the greater. The recorded measurements show that No. 2 is probably the longer by 

 this amount, the values being 12'9829 centims. for No. 1 and 12'9831 centims. 

 for No. 2. On the whole, the observation error of the axial lengths may be taken as 

 of the order l parts in 100,000. 



For the diametral measurements a machine, shown in fig. 11, was obtained from 

 Messrs. STANLEY. This consists of a double-webbed rectangular steel girder, two 

 micrometer heads, and various supports for gauges, &c. To each of the micrometer 

 heads an optical lever of the form shown in fig. 12 was attached. A well-fitting 

 hardened steel piston P is tapered and ground at one end so as to form a plane edge 

 ^ inch wide and -^ inch deep ; the other end tapers more slowly and terminates in a 

 rounded end -^ inch in diameter. This end of the piston fits into a rectangular 



* p. = 1 micron, or pg^ of a millimetre. 



