(242) 
from (4) are identically the same as those which Bravats derived, 
long before Airy, from a quite different, mechanical, principle. 
(Journal de Liouville 8; 1843, p. 435). 
8. With a view to the two last breaks of STEIN’s communication, 
the wording of § 3 and the note to § 4 may seem somethat strange. 
The reason of this is that these two paragraphs failed in the M. 5. 
which the author kindly permitted me to use. 
The reply to the last part of this addition is however already 
contained in the above. The first part strikes us as very peculiar. 
The author thinks “it is superfluous to refute at large the objections 
against Arry’s method derived by Kapreyn from a few particular 
eases of proper motion,” not, as might be expected, because he has 
proved before that the treatment of these cases is erroneous *), but 
because “conclusions deduced from the consideration of only a few 
proper motions chosen quite systematically can hardly serve as criteria 
of a method...”. 
It looks as if the author is not very strongly convinced of the 
stringency of his own proof. Moreover the facts are not quite fairly 
represented. 
The special cases to which the author refers were treated, not as 
proof of any particular thesis, but only as examples to illustrate 
the different conclusions to which the conditions [7] = 0 and [zv] = 0 
can lead. As such I do not think they are badly chosen. That, in 
my opinion, especially the first example incidentally has some con- 
siderable direct power of proof, I will certainly not deny. The 
absurdity to which a treatment of this example by Arry’s method 
leads is very much of the same sort as that which would be involved ®), 
if from the indication of two clocks showing 8 minutes to and 8 
past twelve respectively it was concluded that most probably the 
time is either a quarter to or a quarter past twelve, but on no 
account twelve o'clock. 
Does Dr. Srern really mean to say that there is nothing in such 
a result that throws any doubt on the method by which it was 
obtained ? 
1) For Sretw thinks he has shown that the condition [+?]=0 for stars at one and 
the same part of the sky is equivalent, zot to [rv] =0, but to [-]=0, which both 
according to Ais and to my opinion, is the correct solution. 
2) In order that my reply might still be printed in the Proceedings of October, 
the dutch text had to be written within a few hours after I got sight of the last 
paragraphs in SreiN’s criticism. Owing to this haste the illustration contained in the 
last lines was not so well chosen as I could wish. I have taken the liberty to 
remedy to this defect in the translation. 
