140 STONE, Graphic Representation of Bird Migration. [April 
I have always desired to collect sufficient data to form some 
definite idea of this rate of increase and decrease during the 
different seasons of the year; and for some years past have con- 
ducted observations chiefly with this end in view. ‘To estimate 
the number of individual birds in a given locality at any time, 
especially during the migrations, is wellnigh impossible, and 
therefore the only investigations that could be carried on were 
with regard to the number of species. Living in a locality fav- 
orable for ornithological investigations I have noted for several 
years the species of birds seen on each day from January to June 
inclusive, and, with the assistance of several others interested in 
the subject, have accumulated a considerable amount of data. 
On some days in winter no birds were observed at all,—the En- 
glish Sparrow of course excepted—on other days perhaps only a 
Snowbird or a Crow was recorded. In spring, too, on rainy days 
the number of species noted was very small, while on clear days 
when the migration was at its height upwards of fifty species 
were sometimes recorded on a single morning. Similar observa- 
tions were carried on in the fall, but owing to the difficulty in 
recognizing many species at that season on account of the thick 
foliage of the trees, the results were much less accurate and there- 
fore less interesting. 
While I said above that an estimate of the number of individ- 
uals was hardly possible, this is perhaps not strictly the case. 
For, as the number of individuals of a given species increases, 
the probability of seeing that species every day increases, and 
hence by taking an average of the number of species seen per 
day for each consecutive week, the results obtained must show an 
increase in regard to individuals as well as species. Moreover, 
the comparison of the total number of species seen in each con- 
secutive week would show the increase in regard to species alone. 
After noting the dates of arrival and departure of each species 
seen during the year, the result may be represented as in Fig. 1 
(a small portion of the spring migration, 1888, at Germantown, 
Pennsylvania), the horizontal lines representing the time of the 
birds’ stay, and the vertical columns the consecutive weeks. The 
horizontal lines represent, of course, only the probable continu- 
ous presence of a species, for very few birds are actually seen 
every day from their arrival to their departure. Now by count- 
ing the number of lines crossing a given column it is easy to see 
