ON A GAUGE FOR SMALL SCREWS. 313 



It is to be observed tliat tlie numbers by which the screws are desig- 

 nated, given in the first column, are not arbitrary. Each pitch of the 

 series is yrrths of that which succeeds rt in the table. 



Thus the several pitches are : — 



9 9\- 9n3 . . 



mm. ; — mm. ; -:^ ] mm. ; :;— | mm. ',..-• ^tt: ] mm. 



9\- 9n3 9\° 



: — I mm. : — mm. : ....—-) 



' lo; ' loJ ' loy 



This series may be expressed in the form : — 



0-9"; 0-91; 0-92; 0-93; .... 0-9°;. . . (1) 



whence it is at once evident that the designating number of a screw is the 

 index of the power to which 0'9 must be raised in order to ascertain its 

 exact pitch in millimetres. 



The method by which the relation between pitch and diameter is 

 arrived at will be gathered from the following explanation : — 



Let D represent the diameter and P the pitch. Then, generally, 



Evidently there can be no constant term, for when D ^ 0, P must 

 also := 0. Moreover, D, practically cannot be a simple multiple of P, for 

 experience has shown that small screws must have a less number of threads 

 per diameter than large screws. 



Hence the formula will be of the form 



D = m Pk . . . (2) 



where m and h are constants to be determined. 



Since 1'^ is 1 whatever be the value of J:, it follows that the coefficient 

 m represents the value of D when P is 1. The Swiss Committee agreed 

 that the unit pitch (1 millimetre) should be adopted for the screw having 

 a diameter of 6 millimetres ; in other words they make m = 6. 



The value of k must be ascertained by trial. 



h = l would give a constant ratio, which we know is inadmissible. 



h = 2 will be found on trial to give a far too rapid decrease in the 

 ratio of diameter to pitch. 



The several simple fractions between these limiting values were tried 

 in succession, and the results obtained when using f were found to give 

 results that best accord with practice and experience. 



Substituting the values thus arrived at in (2), the formula becomes 



D = 6P^ . . . (3) 



The Swiss system is thus very complete, but there are reasons which 

 prevent this Committee from recommending its adoption in its entirety. 



4. No one has done more to establish gauges of all kinds in England 

 than Sir Joseph Whitworth. His classical paper on ' An uniform system 

 of screw threads ' was communicated as far back as 1841 to the Institution 

 of Civil Engineers. He had made an extensive collection of screw-bolts 

 from the principal workshops throughout England, and the average thread 

 was cai'efully measured for different diameters. The ^, -j, 1, and li inches 

 were selected and taken as the fixed points of a scale by which the inter- 

 mediate sizes were regulated. The result is an admirable thread for the 

 large iron bolts and screws used in fitting up steam-engines and other 

 machinery. The angle made by the sides of this thread is 55°. One- 

 sixth of the depth of the thread is rounded oS" from the top, and one- 

 sixth from the bottom. The actual depth is rather more than three-fifths, 

 and less than two-thirds, of the pitch. 



