XXXIII A and B] Introduction lvii 



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 ? 



g-100< 18 ^* 18) -ll-52. 



llo 



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 ? 



a =100 x 50/200 = 25-0, 

 but a = 25 by Table XXXII gives /3 = 151. 



100 (arc — chord)/chord = lo'l. 

 .-. arc = 2302 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 @. 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 

 mesodacryal arc 30 mm. Determine the mesodacryal subtense 



S - 100 3 °- 22 ' 6 - 1Q0 * 7 " 4 - 32-74 

 / *" 100 22-6 _ 226 - d27 *- 



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 ou the skull was 



8'7 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 plJ be the frequency in the cell of the pth 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 f>, 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 a and /3 to two decimal places. We 

 have these data in our MS. copies. 



B. ft 



