844 



SCIENCE. 



[N. S. Vol. IX. No. 233. 



The rather tedious treatment of the transit 

 instrument in 45 pages contains no reference 

 to two innovations, the most important since 

 the invention of the chronograph, which have 

 been successfully introduced into modern Euro- 

 pean practice with this instrument. The in- 

 vention of the transit micrometer has furnished 

 a simple and effective means of almost per- 

 fectly eliminating the influence of personal equa- 

 tion in transit observations, and the practice 

 which has come into vogue in connection with 

 this micrometer, of reversing the instrument 

 upon every star observed, equatorial as well as 

 polar, is revolutionary in its effect upon work 

 with a portable transit. This reversal may be 

 employed equally well with any good form of 

 transit, and furnishes the very great advantage 

 of automatically eliminating from the observa- 

 tion of each star a host of errors, such as the 

 effects of collimation, flexure, ineqality of 

 pivots, etc., and the further signal advan- 

 tage that the number of unknown quantities 

 in the observation equation furnished by the 

 star is reduced from the three or four recom- 

 mended by the author to two. A work in 

 which these advances are ignored is of doubt- 

 ful service in ' illustration of the best modern 

 practice ' with the transit instrument. 



The most serious general criticism to be 

 brought against Professor Campbell's treatment 

 of his subject is illustrated above ; that he has 

 not chosen methods and formulte with sufficient 

 reference to economizing the time and labor of 

 the computer, although for the guidance of the 

 latter, in matters left to his own judgment, 

 there is furnished in Appendix A an excellent 

 series of hints on computing. 



Other points at which the author nods in 

 varying degree from obscurity of statement to 

 absolute error are the foot-note to p. 207 rela- 

 tive to projecting the sun's image upon a screen 

 by ' focusing the eye-piece so that the images of 

 the sun and wire are seen on the paper ' and 

 the statement, p. 75, that in the determination 

 of the value of a revolution of a micrometer 

 screw from transits of a star ' the effect of re- 

 fraction is inappreciable if the observations are 

 made near the meridian.' The first quotation is 

 technically correct, but few students would infer 

 from it that two distinct operations are to be 



performed, one of which in the ordinary type 

 of instrument consists in moving the objective. 

 The second quotation is c^uite wrong if more 

 than three significant figures are required in the 

 result and in the illustrative example given by 

 the author, by neglecting the refraction he has 

 vitiated the final result to an amount twice as 

 great as the probable error which he assigns 

 to it. 



An error made with all the emphasis of ital- 

 ics requires that an altitude measured from the 

 sea horizon shall be corrected for refraction be- 

 fore the dip of the horizon is taken into account, 

 and another error occurs at p. 160 (and also in 

 the first edition of the work) where the rate of 

 a chronometer is represented as a linear function 

 of the temperature, although experience and 

 theory alike indicate that the relation between 

 these quantities must be expressed by an equa- 

 tion of at least the second degree. 



It is very doubtful if a consensus of astro- 

 nomical opinion could be brought to sanction the 

 method of reduction of zenith telescope latitudes 

 recommended by the author, viz : a least-square 

 solution in which the value of a level division 

 is introduced as an unknown quantity. Under 

 all ordinary conditions the observations should 

 be so conducted that the direct determination 

 of this quantity shall far outweigh any value 

 which can be derived from the latitude observa- 

 tions. 



The mechanical execution of the work is ex- 

 cellent ; it is provided with an adequate index 

 and illustrated by cuts which are in the main 

 well chosen, although here we regret that the 

 author has selected as ' an excellent form of the 

 prismatic (broken) transit ' an instrument which 

 is a complete failure and has been consigned to 

 oblivion by the government bureau for which 

 it was constructed. 



G. C. C. 



Infinitesimal Analysis. Vol. I., Elementary : 

 Real Variables. By William Benjamin 

 Smith, Professor of Mathematics in Tulane 

 University. New York, The Macmillan 

 Company. 1898. 8vo. Pp. xvi + 352. Price, 

 S3. 25. 

 The book in hand is the initial volume of a 



treatise in course of composition which is to 



