544 



SCIENCE 



[N. S. Vol. XLIV. No. 1137 



merits is to increase the concentrations of the 

 salts in the cells of the tissue. 



On Certain Asymptotic Expressions in the 

 Theory of Linear Differential Equations: 

 W. E. Milne, Department of Mathematics, 

 Bowdoin College. Formulas more precise 

 than those previously obtained by Birkhofi are 

 given. 



On Newton's Method of Approximation: 

 Henry B. Fine, Department of Mathematics, 

 Princeton University. A condition is given 

 under which Newton's method of approxima- 

 tion for computing a real root of an equation, 

 and the extension of this method used in com- 

 puting a root of a system of equations, will 

 with certainty lead to such a root or solution. 

 Edwin Bidwell Wilson 



Massachusetts Institute of Technology, 

 Cambridge, Mass. 



SPECIAL ARTICLES 

 THE FUNCTION OF THE APYRENE SPERMA- 

 TOZOA 



Since the discovery of the dimorphism of 

 spermatozoa in Paludina by von Siebold, 1836, 

 numerous biologists have worked with this 

 strange phenomenon without being able to 

 find a conclusive explanation. On the one 

 side investigators were found, like v. Brunn, 

 who regarded the abnormal type of spermia 

 as abortive elements without any function, 

 whereas others, like Brock and Auerbach, 

 thought it impossible that such typical ele- 

 ments could be produced regularly without 

 being functional. It is well known how a new 

 basis was given to these discussions, when 

 Meves (1903) 1 worked out' the details of the 

 spermatogenesis of these two types of sperma- 

 tozoa. He first proved that the atypical 

 spermia in Prosobranchs contain only a small 

 part of the chromatin of the cell and called 

 them oligopyrene spermatozoa. He further 

 discovered a similar dimorphism in some 

 moths, but here the atypical spermia contain 

 no chromatin at all, they are apyrene. Meves 



i Meves, F., ' ' TJeber oligopyrene und apyrene 

 Spermien und ueber ihre Entstekung naeh Beo- 

 bachtungen an Paludina und Pygaera, " Arch. 

 Mikr. Anat., 61, 1903. See there the quotations 

 of the previous literature. 



could get no evidence regarding the possible 

 function of these elements, but he felt sure 

 that they must have some function and 

 pointed to the possibility of a fertilization by 

 these elements, which would be interpreted as 

 an " Entwicklungserregung." Since then 

 much morphological work upon the structure 

 and development of the atypical elements has 

 been done, especially by Retzius, Kuschake- 

 witsch, Reinke, 2 which, however, does not in- 

 terest us here. 



The interest in the possible function of these 

 elements was awakened again, when the facts 

 about the sex-chromosomes became known and 

 their relation to the other kind of dimorphism 

 of spermatozoa in insects and the mechanism 

 of sex inheritance. The idea was promoted 

 by B. Hertwig 3 that this dimorphism might 

 also be connected with sex-determination and 

 he tried to fit these possibilities into his gen- 

 eral ideas of sex-determination, considering 

 the possibility of fertilization by apyrene 

 spermatozoa as a kind of male-producing 

 parthenogenesis. These ideas were the start- 

 ing point of some work which Popoff 4 did 

 with Paludina. But he was unable to prove 

 that the oligopyrene spermatozoa of that snail 

 take any part in fertilization, although they 

 are found in sufficient numbers in the ovi- 

 duct. The only positive result was that in im- 

 pregnated snails the oligopyrene spermia de- 

 generate and die much earlier than the normal 

 ones. Lamas, 5 who later studied the fertiliza- 

 tion of Murex, was also unable to find any 

 such spermatozoon inside the egg. On this 

 point we have only a single positive observa- 



2 Betzius, G., Biol. Vnters., N. P., Vol. 12, 13, 

 14, 1905-1909. Kuschakewitsch, S., "Studien 

 iiber den Polymorphisms der mannlichen Ge- 

 sehleehtselemente bei den Prosobranchia, " Arch. 

 Zellforschg., 10, 1913 (complete literature). 

 Eeinke, E. E., "The Development of the Apyrene 

 Spermatozoa of Strombus tuberculatus," Publ. 

 183, Carnegie Inst., Washington, 1914. 



3 Hertwig, E., ' ' Ueber Correlation von Zell- 

 und Kerngroesse, etc.," Biol. Central., 23, 1903. 



* Popoff, M., ' ' Eibildung bei Paludina vivipara, 

 etc.," Arch. mikr. Anat., 70, 1902. 



D Lams, H., ' ' Beeherches concernant le di- 

 morphisme des elements sexuels ehez le Murex," 

 Ann. Soc. Med. Gand., 89, 1910. 



