April 1, 1920 A Teosinte-Maize Hybrid 5 



METHODS OF MEASUREMENT 



The field measurements^ of the characters, including dates of flowering 

 and size and number of the several organs, were transferred to punched 

 cards, each card representing an individual plant. Practically all the 

 calculations were made by the use of electric sorting and tabulating 

 machines. The distribution and means were obtained by sorting with 

 respect to each character, using the tabulator to count the cards in each 

 class. 



In calculating the standard deviation the departures were taken from 

 zero, as recommended by Harris.^ 



a=y^ 



The formula used was (t= -xl j^ — M^, where a = standard deviation ; 



Z) = departure — in this instance, the class; / = frequency; A^= total num- 

 ber; and M=mean. "LD^f was found by multiplying on a calculating 

 machine the summed values for each class (as found by the tabulating 

 machine) by the class and summing the products. 



The formula for calculating correlation coefficients proposed by Jen- 

 nings ^ was found to be admirably adapted to the use of tabulating 

 machines. 



The formula is 



^XY ' N-'2X • ^Y 



V(SX2 . ^_ (^xy) '(XY^ ' N- (S"K)2) 



in which X and Y= the values of the measurements and A^= the number 

 of individuals. 



In applying this formula the following procedure is recommended by 

 Jennings. Find the values: XX, SX^, SV, 7:Y\ and XXY; next find 

 the values of a, b, and c as follows: 



a^zxY- n-xx-i:y 



6 = 2X2 . Ar_(sX)2 

 c^XY^ ■ N-(LYY 

 Then ^ 



^y-b 

 and finally r= -\JRj.'Ry. 



Since the use of mechanical tabulating machines in the calculation of 

 correlations seems not to have been described, it may not be out of place 

 to explain the procedure followed. 



' It was necessary to go over the field at intervals of two or three days throughout the growing season to 

 record flowering dates and the position of first silk and to insure an accurate count of the total number of 

 leaves. This work, together with the planting and care of the experiment, was done by Mr. C. G. Marshall. 



' Harris, J. Arthur. The arithmetic of the product moment method of CALCtn,ATiNG the coeffi- 

 cient OF correlation. In Amer. Nat., v. 44, no. 527, p. 693-699. 1910. 



' Jennings, H. S. heredity, variation, and the results of selection in the uniparental re- 

 production OP difflugia corona. In Genetics, v. i, no. s. p. 407-534, 19 fig- 1916- 



