PHILOSOPHICAL SOCIETY OF WASHINGTON. 169 



Their solution gives — 



J A = -(- i. // io9 i o." 109 

 6 D = -f- oZ'637 zfc o. // 224 



(J w = -f- 0. // 0252 dr 0. // 0595 



Combining these values of 8 A, 8 D, and 8 w in accordance with 

 their probable errors, we have, finally, 



8 A = -|- o/'c^ ± o. // oo6 

 <JD = -f 2.^083 ± 0.^067 

 (Ju = -(- o/^s ± o. // 034 



The assumed value of w being 8."848, we have, therefore, for the 

 mean equatorial horizontal parallax of the sun, 



8. "883 i o."c>34, 

 corresponding to a distance between the centres of the sun and 

 earth, equal to 92,028,000 miles. 



(This paper appears in part in The American Journal of Science 

 for June, 1881.) 



Mr. Haekness remarked that the Americans who were engaged 

 in the last transit observations may fairly congratulate themselves 

 upon the results obtained from the photographs, as he had no doubt 

 that they were more satisfactory and consistent than the photo- 

 graphic results obtained by any other nation. There may be said 

 to be two distinct methods of obtaining photographs involving 

 instruments differing widely from the other. The English method 

 employed a telescope of four or five inches aperture producing an 

 image of the sun about three-fourths of an inch in diameter. It is 

 necessary to enlarge this image to a diameter of about four inches, 

 and therefore they used in connection with it a Dallmeyer rapid rec- 

 tilinear lens, enlarging it by that amount. It is obvious that this en- 

 largement by the use of such a lens must be accompanied by an 

 amount of distortion of the image, which, unless it can be accurately 

 determined and eliminated, must introduce a serious error in the 

 measurements of the negatives, and in the results derived from them. 

 This distortion varies in the direction of radii from the optical center 

 of the image, and is equal in circles about that center. Thus far the 

 amount of this distortion has not been determined. The other 

 method, employed by the Americans, involved the use of a lens with 

 forty feet focal distance giving directly the required size of image, 

 and involving no appreciable distortion inherently due to the con- 

 struction of the apparatus, and thus avoided the causes of error 



