‘ 
1883.] 93 {Hagen. 
Identity between a micrococcus-form and bacillws-form has already been 
noted. 
M. Miguel, who has recently studied in a most thorough manner the 
germs found in the air, gives figures of the development of an organism 
which, at one stage of its life, has all the characters of a very long daciilus, 
and afterwards by segmentation into spherules of equal size, forms chaplets 
of micrococet, liable to separate into small groups, 
The editor of the Revue Scientifique, that stronghold of the microbe con- 
tagion theory, admits, in a late issue, that the forms found in disease are 
probably varieties of habitat, and not species, yet still considers them as 
the cause of the diseases they accompany. 
After admitting the great variability of these simple organisms, in ac- 
cordance with their habitat, is it not arguing in a circle to maintain that 
varieties caused by certain conditions are themselves the primary cause 
of those conditions? 
On the Reversion of Series and its Application to the Solution of Numerical 
Equations. By J. G. Hagen, 8. J. Prof. College of the Sacred Heart, 
Prairie du Chien, Wisconsin. 
(Read before the American Philosophical Society, April 6, 1883.) 
In a treatise entitled ‘‘ Die alleemeine Umkehrung gegebener Func- 
tionen,’’ which was published in 1849, Professor Schlémilch maintains, that 
all the methods of reversing series, based upon the theory of Combinations, 
fail in the point of practical application and that even Lagrange’s formula 
presents an unfavorable form of such reversions. The author then proceeds 
to develop two new methods of reversing any given function, the one by 
means of Fourier’s series, the other by definite integrals. In a theoretical 
view, Professor Schlémilch’s methods are no doubt preferable to all the 
ancient ones on account of both their generality and their simplicity ; yet 
when there is question about computing the numerical values of the 
coefficients of a reversed series, it should not be forgotten, that in most 
cases these definite integrals, in spite of their elegant form, can not be com- 
puted except by development, thus in many cases causing even greater 
trouble than the old method of combinations in the case of algebraic func- 
tions, 
The treatise here published does not claim to furnish a new method, but 
isintended to give the recurring formula for determining the coefficients of 
the reversed series such a perspicuous form as to render its practical appli- 
cation easy, and then to apply the same to the solution of numerical 
equations. 
