520 



SCIENCE. 



[Vol. II., No. 37. 



differential calculus Required is indeed ele- 

 mentary ; butj-}. jj^ygt i3g j^ t^gi ^i^jgij gj^jj ije 

 applied fyreaclily, for instance, as the knowl- 

 edge jf |.jjg properties of logarithms. All the 

 P^'Uciples are covered bj' the customar3- courses 

 in phj'sics and mathematics ; but additional spe- 

 cial practice in their employment is very de- 

 sirable. 



In the planning of observations, the theory 

 of maxima and minima gives important aid ; 

 but this theory has so manj' other applications, 

 that we can hardlj^ ask of the regular course 

 in differential calculus such attention to this 

 one point as would insure the required facilitj'. 

 In the absence of such a course of instruction 

 as is recommended in this paper, the matter 

 is left to slow acquisition through practical ex- 

 perience. Knowledge is often thus bought at 

 a high cost. 



A general understanding of instruments 

 of precision, so necessary to successful plan- 

 ning of observations, is also within the field 

 of instruction proi^osed. Instrumental errors 

 should be treated sj'stematicall}' : their pre- 

 liminarj' adjustment to zero, their elimination 

 from the mean of pairs of observations i^roperly 

 taken to that end, their determination in such 

 manner that corrections maj' be dalj ajjplied, 

 and the cost in time of variously managing 

 them, should come to be understood through 

 suitable practice. Here, particularly', each 

 professional course is liable to inculcate its 

 own narrow view. 



An examination of the proceedings of the 

 leading learned societies will convince one of 

 the importance of good method in the discus- 

 sion of results. It will also develop the fact 

 that there exist numerous valuable, analytical, 

 and graphical processes, which at present are 

 not likely to be brought to the attention of 

 the professional student. 



The theory of probabilities as applied to 

 observation would naturallj' be treated in the 

 course proposed. If it were pre^'iousl}' given 

 to the student as a branch of pure mathematics, 

 the attention could here be riveted upon its 

 use, which calls for the exercise of much 

 practical good judgment. It furnishes an 



important means of studjing the precision 

 attained, but just here is a great abuse. Its 

 results, demonstrated for a verj- large number, 

 are applied to ver}- limited series of measure- 

 ments. Again: its assumption of equal prob- 

 ability for equal positive and negative errors is 

 allowed, in face of the fact that a preponder- 

 ance of error in one direction is unavoidable. 

 The rising generation of experimenters in 

 every field of applied science should therefore 

 be taught the manj- limitations which surround 

 its application, and thej' should learn to avoid 

 that indiscriminate use of its principles which 

 has led to so many unfounded claims to ac- 

 cui-acj'. 



We have outlined a subject the successful 

 teaching of which requires qualifications not 

 to be found in every scientific professor, and 

 the successful studj' of which requires a con- 

 centration of the attention not likeh' to be 

 given to it as a subordinate part of some other 

 course. Alread}' the appearance of treatises 

 on probabilities, errors of observation, and 

 least squares, has enabled writers on astron- 

 omj', geodesj', phj-sics, and engineering, to 

 devote their attention to special applications, 

 and has saved the waste of space which would 

 otherwise be given to the general theory. 

 Similarlj-, we should avoid that distraction of 

 the student's attention from the main subject 

 of a professional course which results from 

 the necessity' of frequentlj- pausing to give 

 additional information about the subject of 

 this article. 



Although the first object of establishing a 

 course of instruction in anj' branch of applied 

 science is to put the students into possession 

 of the best methods alreadj* reached hj workers 

 in that field, the end attained is often some- 

 thing more. The instructor's attention is 

 speedilj' called to conspicuous omissions, and 

 his energies are consequently' bent upon sup- 

 plying the defect bj' demonstrating and testing 

 some theorem or method which meets the 

 want. Thus the schools come to the aid of 

 the professions. Are thej' jet doing their 

 whole duty in regard to the science and art of 

 observation ? 



