Apeil 12, 1907] 



SCIENCE 



569 



from any trace of diffraction caused by the 

 edges of the disc-opening and were other- 

 wise indistinguishable from images of 

 fainter stars taken without the occulter. 

 In parallax work the opening of the disc 

 should be so adjusted that the apparent 

 magnitude of the star under examination is 

 about equal to the mean of the magnitudes 

 of the comparison stars. The effect of 

 guiding error will, therefore, almost en- 

 tirely disappear. Actual measures upon 

 plates taken with this device fully confirm 

 this last statement. 



PJiotographic Observations of Giacoiini's 



Comet: E. E. Barnard. 



These photographs show the almost sud- 

 den development of the tail between De- 

 cember 25 and 29, 1905, from a scant trace 

 to a splendidly developed tail. A com- 

 parison with a photogi'aph, made by Mr. 

 Duncan at the Lowell Observatory on De- 

 cember 26, limited the time of development 

 to less than three days. The tail under- 

 went remarkable changes from day to day, 

 but through interference from cloudy 

 weather it was not possible with the one 

 set of photographs to distinguish identical 

 features on different dates, even though 

 they existed, to determine the velocity of 

 the tail-producing particles. 



On the Distortions of Photographic Films: 



Frank Schlesinger. 



The question as to the amount of dis- 

 tortion that a photographic film suffers dur- 

 ing development is not yet settled. The 

 method employed in the present paper is 

 free from some assumptions that have hith- 

 erto been made and gives the average 

 amount of the distortions independent of 

 other sources of error. A plate was ex- 

 posed to the sky and developed and dried 

 in the usual -way. It was then measured 

 independently by two observers. Let us 

 call these measurements A' and B'. The 



plate was soaked in water and then dried. 

 It was now inserted in the measuring 

 engine in, as nearly as possible (within 

 0.01 mm.), the same position it had occu- 

 pied and measured a second time by each 

 observer. Instrumental errors were thus 

 eliminated. Call these second measures 

 A" and B". Then if e represents the mean 

 value of the distortion (in a sense anal- 

 ogous to mean error) and if e^ and e^ 

 are the mean errors of bisection for the 

 two observers, then by appropriate sub- 

 tractions we obtain 



[(A' — il")=J = [e^]— 2[e]], 

 [{B' — B"y} = [e']—2[el]. 



If we subtract each of the differences 

 (-B' — B") from the corresponding {A' — 

 A") the result is free from the effect of 

 distortion and we have 

 [I U' — A") — (B' — B") p] = 2[e^]— 2[e^]. 



These three equations enable us to evaluate 

 e as well as e^ and e^. Three plates, each 

 with about 60 star images, were treated 

 in this way and gave ± .0008 mm., 

 ± .0006 mm. and ± .0003 mm., respect- 

 ively, for the mean value of the distortion 

 of the film. The experiment was varied 

 and improved by spattering an undevel- 

 oped film with ink and measuring the small 

 and perfectly round dots that were thus 

 obtained, before and after the plate had 

 been cleared in hypo, and thoroughly 

 washed and dried. Five plates treated in 

 this way gave, respectively, ± .0006 mm., 

 i .0006 mm., i .0014 mm., ± .0015 mm. 

 and ± .0015 mm. These experiments in- 

 dicate that the distortions of the film are 

 considerably less than inevitable errors like 

 those of bisection, guiding error, etc. If 

 this conclusion should be confirmed by 

 other observers it must have an important 

 bearing on methods for measuring and 

 reducing plates, since it would follow that 

 elaborate precautions, such as have some- 



