THE CLASSES OF FKEQUEXCiT POLYGONS. 39 



Type IV: log = log ft + log (&+ 3) -log w-0.301030. 



Type V: log a = log 2 + Hog (p- 3) -log p. 



Type VI : log a = log (& + g 2 ) + i log (^ - ? 2 - 3) - log (q, - q 2 ) 



TYPE IV. 



This is the most difficult of all the types to be fitted. The 

 work of fitting is carried out by the use of logarithms, as 

 follows : 



log y 



log a=log/-log ( + 2) -0.301030. 



log Z=i log / 2 4- J log{#[log (8-1)4-1.204120] 



-N[\og ft 4-2 log(s-2)J! -0.602060. 



s + 2 



log mD = log k - 0.602060. 



log T= log k 4- log s - 0.602060 - log I 



log tan <=log T log s. 



g cos log 3s) 

 -.(8.920319 -log s)-JV(log r + log ^)] + 9.637784} 

 -0.399090-log Z- (s4- 1) log cos <. 

 log y = log 2/ + A^ [log (s + 2) + log log cos 0] 



T AT7.S796612 + log 0* + log T]. 



MULTIMODAL CURVES. 



Multimodal curves are given when the frequency in the 

 different classes exhibits more than one mode. False mul- 

 timodal curves result from too few observations, or when the 

 classes are too numerous for the variates. By increasing the 

 number of variates or by making the classes more inclusive 

 some of the modes disappear. 



* Tn degrees and fractions of a degree; see Table VII. 



