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it is manifest that t may then be takenysec.$

?»log.sec.<f>

But, by the nature of logarithms, a num-ber indefinitely great is infinitely greaterthan its logarithms; consequently t must,in that case also, be indefinitely great.Since, therefore, t is indefinitely great when<p is taken either = 0, or indefinitely nearto 90°; and that between these limits t isof a finite magnitude, it follows that, bymaking y constant, some value of may befound at which t is a minimum. From this,article naturally arises the following :

15. Problem. Given two points A, B,in the same horizontal line, and a flexiblechain of an unlimited length fixed at oneof them, but moving through the other soas to form successively the different figuresACB, AC'B , AC'B , &c.,to find the angleABC when the tension at B is a minimum .