XXXIII A AND B] Introduction Ivii 



Illustration (i). A cable of 132 - 5 is suspended over the gap between two 

 towers of the same height, 115 feet apart. What will be the droop of the cable? 



ft = 100 032-5 -115) = n . 52 



1 J.O 



Table XXXIII A, gives us a = 21-62 = 100 subtense/chord. 



.-. subtense = '2162 x 115 



= 24-86. 

 Thus the droop is 24'86 ft. 



Illustration (ii). A catenary arch is to have a rise of 50 ft., centre line 

 measurement, and a span of 200. What is the length of the centre line ? 



3=100x50/200=25-0, 

 but a = 25 by Table XXXII gives = 15-1. 



100 (arc chord)/chord = 15*1. 

 .-. arc = 230-2 ft. 



Illustration (iii). For some races the shape of the nasal bridge is very ap- 

 proximately a catenary. Thus if the nasal chord from dacryon to dacryon be 

 measured and also the tape measure from dacryon to dacryon, we obtain the 

 mesodacryal index y9. The tables enable us to pass to the mesodacryal index a, 

 and thus ascertain the nasal subtense, which is slightly harder of direct measure- 

 ment than the arcual or tape measure. 



In the skull of a male gorilla the mesodacryal chord was 22'6 mm., and the 

 mesoilacryal arc 30 mm. Determine the mesodacryal subtense 



- 100 - - _ 30-74 



~~ ~ 



Hence, from Table XXXII : 



a = 38-84 = 100 subtense/22'6. 

 .-. subtense = 22'6 x -3884 = 8'8 mm. 



The actual value of the mesodacryal subtense measured on the skull was 

 87 mm. 



ABAC XXXIV (p. 65) 



Diagram to find the Correlation Coefficient r from Mean Contingency on the 

 Hypothesis of a Normal Frequency Distribution. (Pearson : Drapers' Company 

 Research Memoirs, No. 1, "On the Theory of Contingency.") 



If n pg be the frequency in the cell of the ^)th column and qth row of a correlation 

 or contingency table, and m p be the total frequency in the pth column, n q the 



* Should there be any use for this table for constructional purposes, which there ought to be when the 

 value of the catenary arch is more fully recognised, I will in a later edition of this work give the value 

 of u corresponding to each /3, so that the parameter c can be at once read off and the form of the arch 

 readily plotted. It might also be desirable to give the values of o and /9 to two decimal places. We 

 have these data in our MS. copies. 



B. ft 



