800 



Mr. A. Ferguson on the Construction and 



c + f x. It appears, therefore, that, warping apart, any slight 

 deviation from trueness in a side of the square can be readily 

 computed and allowed for. 



§ 14. We now proceed to consider the effect of the finite 

 bending of the wire or strip at the corners of the square. 



Fio-. 



Fig-. 9. 



The above figures — which are drawn out of all true pro- 

 portion — require no explanation. We assume the wire or 

 strip at the corner of a square of side 2c to be bent into an 

 arc of a circle of radius a, a being small compared with c. 

 In figs. 8 and 9 above corresponding letters refer to the same 

 points. Suppose the origin to be taken at 0; then with the 

 notation shown above, the relations 



d?<= 



ds sin 



ds' — ds sin 0, and — = d<j>, 



give at once 



Also, since 



and 



we have 



dcj>_ 



r. 



x+p=^r cos <£, 



r =p cos <f) + \/ a 2 —}) 1 sin 2 <£, 



