74 
ASTRONOMY: H. N. RUSSELL 
It resembles in its component parts the desert of Arizona. (4) The 
semi-arid region of eastern central Brazil, including most of Bahia and 
Pernambuco. It is very similar to the desert region of Santo Domingo 
and the t3^ical genera are nearly all West Indian. (5) The desert of 
southern Brazil. This region we have not yet studied. (6) The 
states of Rio de Janeiro and Sao Paulo and the southern part of Minas 
Geraes, Brazil. 
The last region is one of abundant rainfall and where all ordinary cacti 
would be killed. Here, however, the cacti not only grow on rocky 
knobs and along the beaches, but especially on the trunks of trees. 
Under the last named condition these plants find the same zerophytic 
conditions that their relatives find which grow in New Mexico and 
western Texas. They attach their roots to the bark of trees, their 
stems are reduced to long, shoe-string-like bodies, while the spines are 
reduced to hairs or they disappear altogether. About 40 of these 
epiphytic species, mostly belonging to the genus Rhipsalis, have de- 
veloped in this region and they represent a most interesting group. 
We have made large collections in South America in the fields visited; 
and we have ascertained that many species of cacti had never before 
been collected, and that many of those which had been collected had 
been poorly described and often wrongly classified. 
ON THE ALBEDO OF THE PLANETS AND THEIR SATELLITES 
By Henry Norris Russell 
PRINCETON UNIVERSITY OBSERVATORY 
Read before the Academy, November 17, 1915. Received January 10, 1916 
L The most suitable definition of albedo for astronomical purposes 
appears to be that proposed by Bond^ in 1861, namely, the ratio of the 
whole amount of Hght reflected in all directions from a sphere illumi- 
nated by parallel rays to the amount of light incident on the sphere. 
2. The albedo A of any planet, according to this definition, is the 
product of two factors, one of which depends only on the size of the 
planet, its distances from the earth and sun, and its brightness at the 
full phase, while the other depends upon the way in which the brightness 
varies at different phases. The first factor, which may be called p, 
can be calculated from known data for all the planets. Its value de- 
pends mainly upon the material of the surface, being high if this is nearly 
white, and low if it is dark colored. The second factor, q, can be com- 
puted only when the planet is observable over a considerable range of 
phase, so that the law of variation of its brightness with phase can be 
determined, and its values are known only for the moon and the planets 
