733 
of Edinburgh, Session 1883-84. 
holding in it the points and Bg, Now, in general, on the accom- 
plishment of this, we shall have the three points B^ , B2 , and B3 ,'^not 
in one straight line, though all in the plane of B^ , Bg , and C. That 
is to say, the line B^Bg will cut the interminate line CB3 , but gene- 
rally not in its point B3. But now, rotate templet 1 round CA^ or 
templet 2 round CA2 till B3 kept in the plane BjCB2 comes into the 
interminate straight line BjB2 , or, what is the same, into the line 
BB. So now we have attained to the following state of things, 
videlicet : — 
Firstly. Line AA is kept at an unchangeable distance from the 
point C. 
Secondly. Three templet points Aj , A2 , A3 , are kept in the 
straight line AA ; and three other templet points B^ , Bg , Bg , are 
all situated in one straight line BB. 
Under these conditions, without departing from them, and while 
considering the point C and the line AA, and consequently CA^ , 
CAg , CA3, as being all at rest, we can mdve any one of the three 
templets by rotation round its line CA ; and the other two will be 
bound to move with that one, and to assume fixed places when that 
one is fixed ; — or, in other words, motion or rest of all the three is 
exactly decided by motion or rest of any one templet 
Two Varied Methods for Continuation. 
Having arrived at this stage, we may go forward to accomplish a 
solution by either of two branch methods which will be stated now 
successively. 
Method I. — The state of things already arrived at being main- 
tained, if now further we introduce one more templet A^CB^, 
placing its point C to coincide with the C of the previous templets, 
and bringing its point A^ into the line AA ; and if we rotate this 
new templet round the fixed side CA^ as an axis, and move also, if 
we please, or if necessary, the line BB in the freedom it has, and 
carry on either or both of such motions till we get the interminate 
line CB^ to meet the interminate line BB (that is, in other words, 
till we get CB^ into the plane of C and BB) the point B^ will not 
in general find itself in the line BB (but BB will meet some point 
of CB4 other than B^). Let us, however, while maintaining the 
arrangements or conditions already arrived at, shift the line BB in 
