OP ARTS AND SCIENCES. 3 



Substituting in the formula for log h given above, B = 1924" 

 and S= —25.0, we obtain log b = 3.284 — 5.100 — 0.2 s — 0.5 log / 

 = 8.184 — 0.2 s — 0.5 log I. This formula is exact, and would give 

 the true diameter of any star if I was known. 



An approximate value of I might be determined by the following 

 method. Suppose that an electric current be passed through a plati- 

 num-iridium wire heating it to incandescence, and that the brightness 

 of a short portion of it be compared with an artificial star when the 

 current is varied by a known amount. As the current increases, 

 the color of the light changes, the amount of the blue light increasing 

 more rapidly than that of the red. The ratio of the two may be de- 

 termined by inserting a double-image prism in the collimator of a spec- 

 troscope and viewing the wire through it. The two images may be made 

 to overlap by any desired amount by varying the distance of the double- 

 image prism from the slit of the collimator. The blue rays may thus 

 be comhined with the red, yellow, or green, as desired. The rela- 

 tive brightness of the two images may be varied by a Nicol placed in the 

 eyepiece and turned through a known angle. We may thus combine 

 any portion of the spectrum with any other part in such a proportion 

 as to produce a tint to which the eye is especially sensitive. From 

 the readings of the Nicol when different currents are passed through 

 the wire, we may determine the varying proportion of any two rays, 

 as the ri'd and blue, when the wire is emitting a given amount of light. 

 Observing in the same way the spectra of the Sun and star, and 

 applying to them the law deduced from the observations of the wire, 

 we obtain an approximate value of the comparative light emitted by 

 equal areas of the two bodies. This will not be exact, since the 

 effect of absorption is not allowed for, a difference of temperature 

 being assumed to be the only cause of the observed difference in color. 

 Probably tbe error will not be large, except perhaps in the case of the 

 red stars. Until these measurements are made, we can do no better 

 than to assume that / = 1, or that the emissive power is the same for 

 the Sun and star. As a large portion of the stars have nearly the 

 same color as the Sun, and a similar spectrum, tliis assumption will 

 probably not be far from the truth. The term equivalent diameters 

 may be conveniently applied to the quantities thus computed. They 

 may be defined as the diameters the Sun would have if removed suc- 

 cessively to such distances that it would equal in light stars of the 

 given magnitudes. The expressions, equivalent densities and equiva- 

 lent masses, will be used in the same manner to denote the densi- 

 ties or masses of bodies in their other properties resembling the Sun. 



