Jlly 5, 1907] 



SCIENCE 



21 



venienee of those who have to read their 

 descriptions. This recommendation will be of 

 great aid in identifying species and genera 

 and will help towards that end when men will 

 see there is honor in furnishing good diag- 

 noses, but no honor in simply naming species. 

 Thos. H. Montgomery, Jr. 

 The University or Texas, 

 June 4, 1907 



ANOTHER WORD ON THE VULTUR CASE 



My brief allusion to Dr. Allen's inconsis- 

 tency in his latest elimination of Vultur seems 

 to have been clear to all with whom I have 

 discussed the question except Dr. Allen, who 

 fails entirely to see my point. 



It seems necessary, therefore, to restate the 

 matter. The case is as follows : 

 Sarcorhamphus 1806. 



gryphus. 



papa = type of Gypagus 1816. 



auricularis = type of Torgos 1828. 

 Cathartes 1811. 



papa = type of Gypagus 1816. 



aura. 

 Gypagus 1816. 



papa. 



gryphus = type of Gryphus 1854. 



Dr. Allen says that while gryphus is the 

 type of Sarcorhamphus it was not the type 

 in 1806 and only became so in 1828 by the 

 removal of the other species. Therefore, he 

 claims that in eliminating Vultur we have no 

 right to remove gryphus at 1806 and can only 

 remove it at the date at which it became the 

 type of Sarcorhamphus. 



This is absolutely contradictory to his own 

 practise in all other cases, nor can I find a 

 precedent in the " current usage " of other 

 eliminators. For instance, papa is the type of 

 Gypagus 1816, but it was not the type in 1816, 

 and only became such in 1854; and yet Dr. 

 Allen in all his eliminations removes papa at 

 1816, which any one can see is the date of 

 establishment of the genus, not the date at 

 which papa became its type. To be consistent 

 gryphus must, of course, be removed at 1806, 

 as I stated previously. Dr. Allen's recent 

 note in which he repeats that papa must be 

 removed at the date at which its genus was 

 established, while gryphus must be removed 



at the date it became the type of its genus, 

 only emphasizes his inconsistency — an incon- 

 sistency which is too self-evident to require 

 the employment of any " imagination." 



Wither Stone 

 Academy of Natural Sciences 

 OF Philadelphia, 

 May 24, 1907 



SPECIAL ARTICLES 



RELATION BETWEEN BIRTH RATES AND 

 DEATH RATES 



A SHORT notice appeared on page 641 of 

 Science, 1907, of a paper read by C. E. Wood- 

 ruff before the American Association for the 

 Advancement of Science, on the relation be- 

 tween birth rates and death rates, etc. 



In this connection, it may be of interest 

 to note that a mathematical expression can 

 be obtained for the relation between the birth 

 rate per head 6 and the death rate per head d, 

 for the case where the general conditions in 

 the community are constant, and the in- 

 fluence of emigration and immigration ia 

 negligible. 



Comparison with some figures taken from 

 actual observation shows that these at times 

 apijroach very nearly the relation deduced on 

 the assumptions indicated above. 



I give here the development of the formula, 

 and some figures obtained by calculation by 

 its aid, together with the observed values, 

 for comparison. 



Let c{a) be such a coefficient that out of 

 the total number Nf of individuals in the 

 community at time t, the number whose age 

 lies between the values a and (a -j- da) is 

 given by Nic{a)da. 



Now the Ntc(a)da individuals whose age 

 at time t lies between the values a and 

 (a'-\-da), are the survivors of the individuals 

 born in time da at time (t — a). 



If we denote by B^t.ai ^^^ total birth rate 

 at time (t — a), and by p{a) the probability at 

 its birth, that any individual will reach age a, 

 then the number of the above-mentioned sur- 

 vivors is evidently S(j_a,p(a)(ia. 



Hence : 



