1D «ie ie 
TRANSACTIONS OF SECTION A. 387 
5. On the Molion of some of the Small Stars in Messier 92 (Herculis). 
By Professor E. E. Barnarp. 
The visual and photographic measures of the great globular star clusters 
show that very little measurable motion exists in any of the small stars 
composing them. 
In two cases in the cluster Messier 92 (Herculis) motion is certain. 
Following are the positions of these stars :— 
Star 1 (No. 11 of Schultz’s list) : 
19020 a 175 14™ 3°75 8=+443° 12’ 12’-9. Mag. 13:2, 
Visual measures (seven years’ interval) : 
Centennial motion 8’"3 in the direction 225°-3. 
Photographic measures (eight years’ interval) : 
Centennial motion 8/5 in the direction 2227-0, 
The second star is much fainter :— 
1902°0 4 17" 14™ 9°58 8+438° 14’ 50''4. Mag. 14}, 
Centennial motion from the photographs (eight years’ interval) : 
6’5 in the direction 181°4. 
The first star is moving away from the centre of the cluster ; the second 
one is moving towards the centre. 
There are several other faint stars of this cluster that seem to have a 
slight motion. 
These results show us that many of the stars in this cluster will 
doubtless develop motion in fifty years’ time, and that in a few hundred 
years we shall be able to investigate the motions that control these great 
and dense masses of stars. 
FRIDAY, AUGUST 27. 
DEPARTMENT oF MATHEMATICS. 
The following Papers and Report were read :— 
1. Theorems in General Analysis. By Professor E. H. Moorn, 
PD LOD, 6c.) 
Especially during the last decade the study of Integral Equations has brought 
to light numerous fundamental analogies between the n-fold algebra of real 
n-dimensional space and the theory of continuous functions of an argument 
varying over a finite interval of the real number system and the theory of certain 
types of functions of infinitely many variables. 
We lay down a fundamental principle of generalisation by abstraction: 
The existence of analogies between central features of various theories implies 
the existence of a general theory which underlies the particular theories and unifies 
them with respect to those central features. The form of General Analysis in 
question, designed to furnish such a general theory of Integral Equations, is apt 
to play a central réle in the comparative or organic development of various 
analytic doctrines. 
We consider analytic systems 5 of the type (M; PD; 4). Here A denotes 
the real number system, and [P denotes a class {»] of elements p, while /§ denotes 
a class [yj of real-valued single-valued functions p» of the variable element p ot 
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