259] HOMOGKAPHIC SCREW SYSTEMS. 273 



are so related, that when nine are given, the tenth is immediately deter 

 mined ; for this two data are required, that being the number required to 

 specify a screw already known to belong to a given three-system. 



We may, as before, denote by 12 the condition that the screws 3, 4, 5 

 shall be co-cylindroidal. This, indeed, requires no less than four distinct 

 conditions, yet, as pointed out ( 76), functions can be found whose evanes 

 cence will supply all that is necessary. Nor need this cause any surprise, 

 when it is remembered that the evanescence of the sine of an angle between 

 two lines contains the two conditions necessary that the direction cosines are 

 identical. The function 



12.34 

 13.24 



can then be shown to be an invariant which retains its value unaltered when 

 we pass from one set of five screws in a three-system to the corresponding 

 set in the other system. 



B - 18 



