292 



SCIENCE. 



[N. S. Vol. XV. Ko. 373 



there is a subtler and perhaps more im- 

 portant use of the method; when it is em- 

 ployed to decide which of two hypothetical 

 theories has the greater probability of 

 really being a law of nature; or to decide 

 between two methods of reducing observa- 

 tions. Cases abound in astronomy where 

 the method of least squares is used for this 

 purpose. It has been so employed, for in- 

 stance, to decide whether stellar parallax 

 observations should be reduced with equa- 

 tions involving terms depending on atmos- 

 pheric dispersion, and terms depending on 

 the hour-angle, to ascertain whether port- 

 able transit observations should be re- 

 duced on the supposition of a change of 

 azimuth on reversal of the instrument (an 

 application of the corollary), etc. 



In such cases, astronomers not infre- 

 quently give preference to the solution 

 which brings out the smallest value of [vv], 

 the sum of the squared residuals. But in 

 the light of the above theorem, it becomes 

 clear that the mere diminution of [vv], 

 alone is insufficient to decide between two 

 solutions, when one involves more un- 

 knowns than the other. To give preference 

 to the second solution it is necessary that 

 the diminution of [vv] be quite large, and 

 that the additional unknowns possess a de- 

 cided a priori probability of having a real 

 existence. 



The Neiula about Nova Persei, 1901: 



Prank "W. Very. 



The rapidly shifting and fast fading 

 nebulosity around the new star is regarded 

 as an evanescent phenomenon comparable 

 to the tail of a comet. Velocities of propa- 

 gation of different orders are surmised, but 

 as there is no known motion of material 

 particles, even when of the dimensions of 

 negative ions, swifter than that of light, 

 the latter may be taken as a limiting value 

 of velocity, from which it is deduced that 

 the distance of the nova can not exceed 



750,000,000,000,000 miles, an estimate 

 which gives us a first approximation to the 

 distance of the Milky Way, since the novae 

 all belong to the galactic stream. An ex- 

 planation of the meaning of the complex 

 structure of the hydrogen bands in the 

 spectrum of the nova is given, and a fur- 

 ther cometary analogy is sho-wn through 

 the existence of concentric spherical en- 

 velopes near the star, resembling comae, 

 which are inferred from the structure of 

 the spectral bands. From the spectral 

 variations attending the formation and 

 motion of these envelopes, the mass of the 

 star is concluded to be about 1,150 times 

 that of the sun; and as this mass does not 

 appear to have been appreciably changed 

 in the first month, in spite of the enormous 

 outpourings of hot gases, it follows that 

 the luminosity of the star is not con- 

 ditioned by the mass or by the state of the 

 star's internal activity; and it is suggested 

 that the brightness of the star's continuous 

 spectrum depends upon the formation or 

 dissolution of clouds of cosmic dust in the 

 spaces immediately surrounding the nova. 



A Short and General Method of Determin- 

 ing Orbits from Three Observations: A. 

 0. Leuschner. 



The method is principally intended to 

 aid in the rapid determination of an orbit 

 from three observations, made at short in- 

 tervals. It is essentially an improvement 

 on Harzer's modification of Laplace's 

 method contained in Mec. eel. T. I., pre- 

 miere partie, livre II., Chap. IV. The first 

 part of the paper deals with the discussion 

 or Harzer's method. The modifications in- 

 troduced by the author consist in : (1) The 

 restriction of the number of observations 

 to three, the minimum number necessary 

 for the solution of the problem. (2) The 

 reduction of the number of fundamental 

 data to be approximated. In Harzer's 

 method the fundamental data to be ap- 



