106 



SCIENCE. 



[N. S. Vol. XVII. No. 420. 



near the observer. He has accordingly- 

 attempted so to act on this nearer body 

 of air as to prevent what may be assumed 

 to be the main cause of the 'boiling.' 



To do this, it has hitherto been sought 

 by astronomers to keep the air in the tele- 

 scope tube as still as possible. What may 

 be assumed to be novel in the writer's plan 

 is to vigorously churn this air by means 

 of blowers, or in other ways. The still 

 air is known to produce a disturbed image. 

 That the air agitated under this new plan 

 paradoxically produces a still image, has 

 been shown by photographs (exhibited) 

 of the images of artificial double stars 

 whose beams were entirely confined within 

 a horizontal tube in which they traveled to 

 and fro through 140 feet of 'churned' air. 

 These photographs showed that the dis- 

 turbance within the tube itself appears to 

 be wholly eliminated by the device of vig- 

 orously stirring the air column. 



In continuation of the experiments, a 

 tube was pointed up toward the sky, and 

 so moved as to roughly follow the sun and 

 thus form an inclined addition to the tele- 

 scope tube itself. Within this tube the 

 air was similarly churned. Very consid- 

 erable improvement of the solar image re- 

 sulted from the whole combination, but 

 owing to the condition of the sun, the 

 weather and the apparatus, the work has 

 not yet reached a stage where it can be 

 shown that improvement was due to the 

 extension toward the sun, distinctly from 

 the agitation in the tube. 



The merit of churning the air within the 

 telescope tube itself is believed to be dem- 

 onstrated by these photographs, which 

 show the results of this artificial 'good 



The Foundations of Mathematics: Dr. 

 Paul Caeus, Editor Open Court Pub- 

 lishing Co., Chicago. 

 Having briefly sketched the history of 



metageometry from Euclid to the present 

 day, he declared that the problem was not 

 mathematical but philosophical. At the 

 bottom of the difficulty there lurks the old 

 problem of the a priori. Kant wrongly 

 identified the ideal with the subjective, and 

 thus he regarded the a priori as a concep- 

 tion which the mind by its intuitive con- 

 stitution transfers upon the object. The 

 a priori, however, is purely formal, and 

 the purely formal is an abstraction from 

 which everything particular, viz., the sen- 

 sory, is omitted. It can best be charac- 

 terized as 'anyness'; it is a construction 

 that would suit any condition, hence uni- 

 versality is implied and universality in- 

 volves necessity. 



There are two kinds of a priori, the a 

 priori of being, which is pure reason, and 

 the a priori of doing, a construction that 

 is the result of pure motion. Our meta- 

 geometrieians tried to derive the basic geo- 

 metrical principles from pure reason but 

 failed. The truth is that other systems 

 of geometry are possible, yet after all, 

 these other systems are not spaces, but 

 other methods of space measurements. 

 There is one space only, although we may 

 conceive of many diflferent manifolds, 

 which are contrivances or ideal constitu- 

 tions, invented for the purpose of deter- 

 mining space. 



The speaker developed space by motion 

 in all directions after the analogy of the 

 spread of light, and characterized the 

 straight line as the path of greatest inten- 

 sity corresponding to the ray. 



Clifford derives the plane by grinding 

 down three bodies until the three surfaces 

 are congruent. The main feature of the 

 plane is that it is congruent with itself. 

 It can be flopped, and in either case it 

 divides space into congruent halves. If 

 we halve the plane, which can be done by 

 folding a piece of paper, we have in the 

 crease a representation of the straight 



