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OBESITY, other than that occurring in yellow mice, is relatively rare in mice. The obese yellow animals attain weights up to 75 or 80 grams but the average weight is around 60 grams and then there is a decrease in weight as age increases.j In the summer of 1949 some very plump young mice were found in the V stock.j Others occurred shortly after that among offspring of these V stock animals that had been outcrossed to the fuzzy sock.

we obtain the equation jp[a(1 -t)]d[;o(bt)I = ajp(a + b)jp(a), Jt0 (a + b) P which is the exceptional case in Hadamard's general theorem.We thus see that Hadamard's result corresponds to particular cases of equation (1) and (3), while there is nothing in his work which might correspond to equation (4).By means of a new theory of composition on functions in 2n variables (n = 1, 2, 3, . .) the author has derived integral addition theorems for hypergeometric series of a certain generalized type, which correspond to equations (1) to (4) of this paper.

Studies on the genetic and antigenic basis of tum our tran sp lantation Inoculation of mice from appropriate crosses with two strain A tumours and one dba (sub line 2) tumour showed close linkage of such a gene with the locus for 'fused'. With the A strain it was shown that the gene was identical with that for antigen II present in the erythrocytes. The gene is therefore labelled H 2. Of sixty-nine backcross mice tested, both serologically and by tumour inoculation, sixtyfive gave concordant results, four discordant results. In general, it appears that serological ' tests are preferable to tumour inoculation in the identification of genotypes. On serological grounds it is suggested that the dba gene is an allele of the above and should be called H2d. It is possible that there is a long series of alleles at this locus. The indicated genotype of the strains used is as follows: A, H 2H 2; dba, H2dH2d; GBA, G57 and P, h2h2; G A, Fu h2/fu h2. Further tests may show differences in the h2 allele in the last four strains. It is uncertain whether any cross-overs occurred in 257 backcross mice tested. I n t r o d u c t io n