ASTRONOMY: A. VAN MAANEN 
387 
will therefore fail to reveal the proper motion with anything hke the 
precision attainable in a star cluster, for instance. The difficulty of 
bisection may, however, be largely overcome by measuring correspond- 
ing points on different plates in immediate succession. 
For such measures the monocular arrangement of the stereocom- 
parator is an admirable instrument, and that it is capable of yielding 
very acc:urate results has already been pointed out.^ When therefore 
Mr. Ritchey placed at my disposal for measurement two excellent plates 
of the spiral nebula Messier 101, taken in 1910 and 1915, there was no 
question but that the stereocomparator was the best instrument for 
the purpose. 
Although the results showed striking evidence of internal motion, 
the necessity of additional plates was strongly felt. At my request 
Dr. Curtis kindly placed at my disposal three photographs made with 
the Crossley reflector of the Lick Observatory, one by Keeler in 1899, 
one by Perrine in 1908, and one by Curtis himself in 1914. 
The pair taken by Mr. Ritchey was completely measured twice, the 
Lick pairs 1914-1899 and 1908 -1899 once each; each pair was measured 
in four positions, with east, west, north and south, respectively, in the 
direction of increasing readings of the micrometer screw. On the 
Mount Wilson plates 87 nebulous points were measured; on the first 
Lick pair 46, and on the second 69 points, while on all the pairs the 
same 32 stars were used for comparison purposes. The measures and 
reductions, which will be published in full in the Astro physical Journal, 
were made substantially in the manner described in my recent paper on 
the determination of stellar parallaxes,' the principal difference being 
that the quadratic terms could not here be neglected and were accordingly 
included in the reductions. 
The results showed that to each pair of plates could be given the 
same weight, and the direct mean of the values found for the proper 
m^otions of each point is therefore used in the discussion. The resulting 
motions, which are those relative to the mean of the 32 comparison 
stars, are due partly to a motion of translation of the nebula as a whole, 
and partly to a possible internal motion. The annual motion of trans- 
lation, which was derived by three different methods of reduction, was 
found to be: = + O^'OOS, ^5 = -0''013. Subtracting these from 
the total motions, the results are what may be called the internal motions. 
The accompanying plate shows these mean internal motions for each 
of the 87 points of the nebula. The individual motions for the com- 
parison stars, which are surrounded by circles are also shown. The 
scale for the annual motions is given at the bottom of the plate. The 
