Xo. ,)3,3] 



NOTES AND LITERATURE 



417 



consider different crops separately and take wheat first. Here 

 the studies of Boberts and his students take a leading position. 

 For some years this investigator has been engaged upon a very 

 comprehensive biometrical study of wheat. Only fragments of 

 this work have as yet been published. We may first consider 

 his paper on "A Quantitative Method for the Determination 

 of Hardness in Wheat." An apparatus was devised by 

 which the weight in grams necessary to crush a grain of wheat 

 could be directly determined. The problem was to find out how 

 large a random sample of kernels must be taken in order to 

 reach a reliable result as to mean crushing weight for a variety 

 or strain. Samples of from 100 to 500 kernels each were tested 

 and the mean for each sample determined, two varieties of wheat 

 —a hard and a soft— being used. It is shown that the mean 

 crushing weight diminishes regularly and rapidly as the size of 

 the samples increases, until a minimum at a sample of 450 kernels 

 is reached. Samples of 500 kernels show an increase in mean 

 crushing weight over the 450 kernel sample. Why the mean 

 crushing weight should regularly diminish with increasing size 

 of sample is not (dear, and is neither explained nor even discussed 

 in the paper. That the error of the mean crushing point would 

 diminish with increasing size of sample is obvious. The error 

 of the mean is found, as a matter of fact, to diminish according 

 to a hyperbolic curve. A mathematical discussion of this curve 

 of the errors of the means is given, and examination of the 

 second differential shows that the rate of diminution of the error 

 becomes negligible after a sample or group size of :?50 kernels. It 

 is then concluded that 350 kernels is a sufficiently large sample 

 to use practically in detenninimr mean crushing points. 



Roberts's paper on "Breeding for Type of Kernel in Wheat" 

 is a very thorough and extensive biometrical study of the form of 

 the wheat kernel in many different pure lines or races. Means 

 only are given in this paper, but the amount of measuring and 

 computing involved must have been literallv stupendous. Only 

 such a biometrical organization as that maintained at the Kansas 

 Station could have mammed it. Data are given on mean length, 

 width, length width index, volume, weight, and specific gravitv 

 of the individual kernel, samples of 500 kernels heing taken in 

 5 separate 100-kenml lots for each pedigree strain (pure line). 

 Also determinations were made of the weight of 100 c.c. of grain, 

 of a packed and a struck bushel of grain, and of the percentage 



