286 



SCIENCE. 



[N. S. Vol. III. No. 60. 



independent witnesses, all testifying to the same 

 fact, may be ' vitiated ' by one of them being 

 very much mistaken. It is to be regretted that 

 the writer of the note does not tell us just how 

 far the one erroneous star must have been 

 wrong in order to vitiate the result. The cor- 

 responding testimony of the ten Pulkowa ob- 

 servations upon another group of ten stars 

 may be left out of consideration, because 

 this conclusion might be vitiated in the same 

 way. S. Newcomb. 



THE PERTUEBATIONS OF 70 OPHIUCHI. 



Peof. Jacoby's review in a recent number of 

 this journal (p. 197) is eminently fair in spirit ; it 

 is incomplete, and therefore I fear it will be 

 misleading. It is a mistake to say that my 

 work on the perturbations of 70 Ophiuchi is 

 supported by the American observations, but 

 contradicted by those made at the same time in 

 Europe. On the contrary, the deviation from 

 Schur's orbit and the work of the American ob- 

 servers is confirmed by the measures of all the 

 best observers abroad. Thus the deviation ap- 

 pears unmistakably in the observations of 

 Bigourdan, Callandreau, Schiaparelli, Glase- 

 napp and Knorre. Since publishing the paper 

 in American Journal 363, measures have been 

 received from several of the above observers, 

 and there is absolutely no doubt of the substan- 

 tial accuracy of the American observations. 

 Among the European observers Schur and 

 Ebell (a student at Berlin) alone find no devia- 

 tion, but Schur's measures are very discordant, 

 and he admits (A. N. 3324) that they are of 

 little value ; while Ebell's measures show dis- 

 crepancies on the several nights amounting to 

 over ten degrees in angle. 



Hence it is evident that all the best observa- 

 tions, both American and European, confirm the 

 deviation from Schur's orbit and point to the 

 existence of the dark body as the cause of this 

 unexpected phenomenon. My researches on 

 the orbits of 40 binary stars, which are now 

 practically complete, will probably remove all 

 doubt as to the propriety of using the distances 

 in such investigations. Indeed the discovery 

 of the perturbations in 70 Ophiuchi by using 

 both angles and distances, after Schur had con- 



sciously rejected the distances which would have 

 given him the discovery, is a striking illustra- 

 tion of the evil of orthodoxy in scientific pro- 

 cedure. T. J. J. See. 

 The UNiVEESiTy of Chicago, February 11, 1896. 



PSYCHOLOGY OF NUMBER. 



To THE Editor of Science — Sir: As Prof. 

 Fine in his review of McLellan's and Dewey's 

 Psychology of Number (January 24, 1896) raised 

 a question of considerable importance to- 

 educators and to psychologists, permit me to 

 add a few words to the discussion, first thank- 

 ing the reviewer for the generally appreciative 

 tone of his article. 



1. The question of principle raised is whether 

 or no counting is measuring, whether or no 

 integral number has a metric origin or purpose, 

 and involves the idea of ratio. Now measure- 

 ment is a word both of a more general and a 

 more technical sense. That, in the most tech- 

 nical mathematical sense, counting is not 

 measurement, is clearly recognized in the book 

 referred to. But as it is held that in the larger 

 sense of the term it is a process of measuring, 

 and that the technical mode of measurement is 

 an outgrowth, psychologically, of the bi-oader 

 and looser sense, this disclaimer amounts, per- 

 haps, to little. 



Starting from the larger sense, it is held 

 that number has its psychological genesis in the 

 felt need for valuation, and that its function 

 (psychologically once more) is to serve the pur- 

 poses of valuation. Now counting seems 

 to me indubitably one mode of defining the 

 value of a previously unvalued mental whole, 

 and in that sense to be a mode of measure- 

 ment. Any process of defining value is, I 

 should say, a form of measurement in the 

 broad sense of that term. Counting implies 

 first a mental whole ; secondly, the breaking up 

 of that whole into distinct parts ; third, the use 

 of one (any one, not some one) of these parts as 

 a unit ; fourth, the measurement of the amount 

 or value of the original whole, through equal- 

 izing it to a certain definite number of the 

 selected unit. 



But Prof. Fine says: "In however loose a 

 sense the word may be used, ' measuring ' at- 

 least involves the conscious use of a unit of ref- 



