130 POPULAR SCIENCE MONTHLY. 



CHAPTERS ON THE STAES. 



By Professor SIMON NEWCOMB, U. S. N. 



Masses and Densities of the Stars. 



THE spectroscope shows that, although the constitution of the stars 

 offers an infinite variety of detail, we may say, in a general way, 

 that these bodies are suns. It would perhaps he more correct to say that 

 the Sun is one of the stars and does not differ essentially from them in 

 its constitution. The problem of the physical constitution of the Sun 

 and stars may, therefore, be regarded as the same. Both consist of vast 

 masses of incandescent matter at so exalted a temperature as to shine 

 by their own light. All may be regarded as bodies of the same general 

 nature. 



It has long been known that the mean density of the Sun is only 

 one-fourth that of the earth, and, therefore, less than half as much 

 again as that of water. In a few cases an approximate estimate of the 

 density of stars may be made. The method by which this may be done 

 can be rigorously set forth only by the use of algebraic formulae, but a 

 general idea of it can be obtained without the use of that mode of 

 expression. 



Let us in advance set forth an extension of Kepler's third law, 

 which applies to every case of two bodies revolving around each other 

 by their mutual gravitation. The law in question, as stated by Kepler, 

 is that the cubes of the mean distances of the planets are proportioned 

 to the squares of their times of revolution. If we suppose the mean 

 distances to be expressed in terms of the earth's mean distance from the 

 Sun as a unit of length, and if we take the year as the unit of time, 

 then the law may be expressed by saying that the cubes of the mean 

 distances will be equal to the squares of the periods. For example, the 

 mean distance of Jupiter is thus expressed as 5.2. If we take the cube 

 of this, which is about 140, and then extract the square root of it, we 

 shall have 11.8, which is the period of revolution of Jupiter around the 

 Sun expressed in the same way. If we cube 9.5, the mean distance of 

 Saturn, we shall have the square of a little more than 29, which is 

 Saturn's time of revolution. 



We may also express the law by saying that if we divide the cube 

 of the mean distance of any planet by the square of its periodic time 

 we shall always get 1 as a quotient. 



The theory of gravitation and the elementary principles of force and 

 motion show that a similar rule is true in the case of any two bodies 

 revolving around each other in virtue of their mutual gravitation. If 



