50 



G. H. KNIBBS. 



Indices. 6 = stance along ^ = weig ht-coefficients of B x General _±_ 



axis, coefficients + fi) 



i 1 -A- or 0-56250000 8 or 8-0000000 0-1111111 



1 2 § „ 06666667 3 „ 3-0000000 0-2500000 



1 3 Jv2 „ 0-7071068 lw2 ,,2-4142136 0-2928933 



1 4 yf„ 0-7368063 l/(2 V t- 1) „ 2-1114303 0-3213952 



2 3 f „ 0-7500000 ' 1-A- „ 1-4545455 0-4074074 



2 4 Vf „ 07745967 1£ „ 1-2500000 0-4444444 



3 4 f „ 0-8000000 Hf „ 0-9541985 0-5117187 

 These, and the more extended results in Table IIIa., are the b 

 curves shewn on Fig. 2. The results of Table I. are also included 

 for completeness : these last correspond to p = 0. 



IIIa. — Position of second section the first being the initial section. 

 Indices q. 



Index p 12 3 4 5 6 7 



-3679 5000 5774 6300 6687 6988 7230 7430 



1 -5000 6066 6667 7071 7368 7598 7784 7937 



2 -5774 6667 7165 7500 7746 7937 8091 8219 



3 -6300 7071 7500 7788 8000 8165 8298 8409 



Indices q. 



Index p 8 9 10 11 12 13 14 15 



-7598 7743 7868 7978 8076 8163 8241 8312 



1 -8067 8178 8274 8360 8435 8503 8564 8620 



2 -8327 8420 8501 8572 8636 8693 8745 8792 



3 -8503 8584 8654 8717 8773 8823 8868 8909 



The above results are of course decimal throughout. 



If on the other hand we make 6 = 1 and determine a, the relations 

 are less simple. As before the weight-coefficient of the latter, 

 viz. a, may conveniently be taken as unity. This gives then, 

 instead of (26) 



av + p^lll, and a* + /?=I±i* (31); 



1 + p 1 + q 



consequently a can be found only by solving the equation 



qp-P(l+g) oq _ g-P. =0 (32) 



and then ft from 



/J- I { 1 -(1 ± P )a? J -.1 {. 1 -(1 + ?)<.« } (33) 



