The Theory of the Double Gamma Function. 



265 



explained l)y the fact that when the monkeys received a banana or an 

 apple every day, they would be less likely to eat as much of the meat 

 as they "Would otherwise do, and would thus daily receive a smaller 

 dose of ptomaine. 



In spite of this fact, in no less than four cases out of the five did we 

 get bloody motions, and in two of the cases spongy gums. In these 

 cases tainted meat alone seems to have produced scorbutic symptoms, 

 although the animals in this group took longer to develop the 

 symptoms, and seemed not to suffer in such a severe form. 



Looking at the results of our experiments on monkeys, as a whole, 

 we venture to think that they afford important confirmation of the 

 conclusion derived from Arctic experience, as referred to in the early 

 part of this paper, that the absence or presence of fresh vegetables or 

 lime juice is not alone sufficient for the prevention or the cure of 

 scurvy, and that we must regard the condition of the food in general, 

 and especially the state of preservation of the meat, as the essential 

 factor in the etiology of the disease. 



We have to express our thanks to Dr. Francis Goodbody for his 

 untiring assistance in the numerous observations that had to be made 

 during the eighteen months the research was continued. 



" The Theory of the Double Gamma runction." By E. W. 

 Barnes, B.A., Fellow of Trinity College, Cambridge. Com- 

 municated by Professor A. E. Forsyth, Sc.D., F.E.S. Ee- 

 ceived February 26,— Bead March 15, 1900. 



(Abstract.) 



The memoir deals with a function which is substantially one-quarter 

 of the o- function of Weierstrass, just as the ordinary (simple) gamma 

 function is substantially one-half of the infinite sine product. The 

 analogy between the two functions determines the nomenclature. 



In any development of the simple gamma function from the function- 

 theory point of view, it is necessary to use Euler's theorem 



to obtain the product Ti {zjoi) given by 



as a solution of the difference equation + w) = 2/(3). 



Similarly for the elementary theory of the double gamma function 



