142 ANNUAL REPORT SMITHSONIAN INSTITUTION, 19 3 5 



where a light-year is the distance which light travels in a year at 

 the rate of 186,000 miles a second. Koughly a light-year is 6,000,000 

 million miles. If we carry through the arithmetic we find that at a 

 distance of 33 light-years the sun, although still visible, would be 

 among the fainter of the stars seen with the naked eye, and only 

 about three times as bright as the faintest star that can be seen 

 with the eye under the most favorable conditions. The great ma- 

 jority of the naked-eye stars are much farther away than the 33 

 light-years which we have assumed, so that as compared with these 

 stars our sun is a relatively insignificant body. 



This result shows us at once that the stars differ greatly from one 

 another in the amount of light they give out, or, in other words, 

 in their luminosity or candlepower. If all the stars had the same 

 luminosity their brightness as we see them would depend solely 

 upon their distance, but since this is not the case both distance 

 and luminosity are involved. The inverse-square law, however, at 

 once gives us a simple relationship between apparent brightness, 

 intrinsic brightness or luminosity, and distance, and this relation- 

 ship forms the basis of all studies of the distribution of stars accord- 

 ing to their true brightness. Since this relationship is a simple 

 equation between three quantities, we can always find the third quan- 

 tity when the other two are known. But the apparent brightness 

 or magnitude of a star may be assumed to be known : it is obtained 

 from direct observation, and existing catalogs list hundreds of 

 thousands of stars with accurately measured apparent magnitudes. 

 So all we need to solve our equation is to know either the distance, 

 in which case we can determine the luminosity directly, or the 

 luminosity, in which case we can determine the distance. 



The first and for many years the only way in which the luminosity 

 of a star could be obtained was from a previous knowledge of its 

 distance. Naturally the earliest method of measuring stellar dis- 

 tances grew out of accurate measurements of position. If the posi- 

 tion of a star with reference to the faint gtars in the background 

 of the sky can be measured with great accuracy at a certain time, 

 and again 6 months later when the earth is on the opposite side of 

 its orbit around the sun, we have a base line of about 185,000,000 

 miles by which to measure its distance. As geen from the end^ of 

 this line the star should be slightly displaced with reference to the 

 fainter stars in the background which are vastly more distant. If 

 this angle can be measured, it is a simple matter, since the length of 

 the base line is known, to calculate the distance. The method is very 

 similar to that used in ordinary surveying. The difficulty arises, how- 

 ever, that the stars are so far away that even with this great base 

 line the angle to be measured i^ extremely small. In the case of 



