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THE possibility that some of the factors governing the inheritance of milk might be inherited in a sex-linked manner has been suggested by one of the writers (l). The need was felt for further investigation. There are two main avenues by which this question may be explored: by planned experiment with cattle or by a study of the existing milk records. The former method is slow and very costly, but would probably give conclusive results. The latter does not require experiment to provide the necessary facts, but the data may be somewhat vitiated by lack of control over conditions of nutrition and husbandry which undoubtedly affect, to a great extent, the amount of milk which a cow may yield in a lactation.The statistical method uses the existing herd books and milk records, and approaches the question by studying the effect of various animals in the ancestry upon the yields of their female descendants. A sex-Linked character cannot be transmitted from a paternal grandsire to his granddaughter. The sex-linked qualities of a bull are all transferred to his daughters while, if a cow is heterozygous for them, only half her offspring will possess them.Attention must be drawn to the fact that it is not reasonable to expect that all the factors influencing milk yield may be inherited in a sex-linked manner. Milk yield must be dependent on many factors, not merely on those directly connected with secretion of milk, but also on those which govern constitution, size, weight, etc. The purpose of the present paper is to explore the subject further from the statistical aspect in order to find out whether any of the factors governing milk yield are inherited in a sex-linked manner and, if so, how they compare with the factors inherited in the ordinary autosomal manner.The material was taken from the annual records of the Scottish Milk Records Association and from the Ayrshire Cattle Herd Book. Thirty leading herds of pedigree Ayrshire cattle, all located in the south-west of Scotland and which have been continuously recorded from 1922 to 1928, were selected from their alphabetical order. One other herd, out of alphabetical order, was included', as it had a great effect on many of the other herds.In all, some 5000 records were obtained, and these eventually represented 1518 cows. The records were corrected for age on the figures of Kay and M'Candlish (2) for Ayrshire cows in the south-west of Scotland. No correction

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1. The post-weaning growth of 135 litters has been analysed with a view to determining the relationship of certain arbitrary subdivisions with each other. For this purpose, the weight increases during three periods of 28 days have been denned in two ways—first, by age, the periods being 10–14, 14–18, and 18–22 weeks, and secondly, by weight, the periods beginning at 40, 80 and 120 lb. and continuing as before for 4 weeks.2. When the periods are defined by age, the mean increase per pig per litter is affected by weaning weight, but not by litter size (Table III). The variability of the individual increases becomes greater as the pigs become older and heavier (that is, passing from one period to a later one), but less within a period as the rate of growth increases (Table IV). It was not affected by litter size.3. The distribution of individual weights became increasingly skew with age. This is regarded as a graphical illustration of the fact that while absolute rate of growth is increasing, initially small animals must fall farther and farther behind (Graph 3).4. The correlations between the average litter increases in different periods were calculated for litter sizes 6–11. In general, the coefficient for periods 1 and 2 was about 0·4, and for periods 2 and 3 about 0·6 (Table VI). This is interpreted to mean that, when judged by results over the whole time under observation, litters with a high correlation between the increases in weight during short periods are not properly comparable with those with a low correlation. By this method, differences in rate of growth having an important influence on carcass quality may be obscured.