June 16, 1899.1 



SCIENCE. 



843 



purpose one may properly enough select the 

 conventional material and methods found in 

 such authoritative treatises as those of Chau- 

 venet and Bruennow, and for the most part this 

 has been done in the present work with great 

 fidelity, although the author has found room for 

 some few ameliorations of astronomical practice. 

 The material selected for presentation is that 

 leading up to the determination of time, lati- 

 tude and azimuth with portable instruments, 

 together with a brief treatment of the meridian 

 circle and equatorial telescope and a welcome 

 chapter, not usually found in such works, upon 

 the surveyor's transit. This really efficient in- 

 strument has been strangely neglected by 

 astronomers, and its astronomical capabilities 

 find scant appreciation even in the present work, 

 whose author, doubtless through a slip of the 

 pen, appears to consider the accuracy attain- 

 able with it to depend upon the least count of 

 the verniers. A further most welcome innova- 

 tion, which the author has not seen fit to make 

 here, but which we bespeak for a future edition, 

 would have been the introduction of an ele- 

 mentary treatment of the spectroscope consid- 

 ered as an adjunct to the equatorial telescope. 



As a whole the work may be cordially com- 

 mended, but its general excellence is marred 

 here and there by sins both of omission and 

 commission. Opinions may differ as to the 

 author's wisdom in appending to the test a bald 

 exhibit of the principal formula; of the 

 method of least squares, with no pretense at 

 their derivation and with but little explanation 

 of their use, but surely ' the best modern prac- 

 tice of observing' does not justify the giving 

 up of four per cent, of the entire treatise to 

 such antiquated matter as lunar distances and 

 the ring micrometer, nor does the scope of a 

 beginner's book seem to call for giving up 

 another four per cent, to diurnal parallax as 

 affected by the earth's compression, although 

 precedent for such treatment may be found in 

 the standard works. 



The author's methods of observation and 

 computation are for the most part those of 

 Chauvenet, an excellent model for half a cen- 

 tury ago, but one which now admits of improve- 

 ment in respect of formulse to be employed for 

 the reduction of observations. The general in- 



troduction of addition and subtraction loga- 

 rithms into all the better logarithmic tables in 

 common use has removed that supposed neces- 

 sity for ' adapting formulas to logarithmic com- 

 putation ' under which the older writers labored, 

 and in many cases permits their formulas, and 

 those of Professor Campbell, to be considerably 

 simplified. An instance in point may be found 

 at p. 107, where the author derives the hour 

 angle of a star from its measured altitude 

 through the formula for tan J t and is obliged 

 to write down seventeen numbers for this pur- 

 pose. The same result may be derived through 

 cos t and the addition and subtraction loga- 

 rithms with thirteen numbers, and the latter re- 

 sult is in no wise inferior to the former in re- 

 spect of the unavoidable errors in logarithmic 

 computation. In this particular case the two 

 methods, when applied with five-figure loga- 

 rithms, give results which diiTer by only one sec- 

 ond of arc, after correction of two errors in the 

 the author's computation which make his 

 printed hour angle 74'' wrong. 



A similar case occurs at page 199, where the 

 author introduces the parallactic angle into the 

 formulae for determining the azimuth of a cir- 

 cumpolar star when its declination, hour angle 

 and the latitude are given. In the example 

 given to illustrate these formulae and solved at 

 p. 201 with six-figure logarithms the author 

 writes down nineteen numbers in order to pass 

 from tto A, where the ordinary formula which 

 furnishes tan A directly in terms of the data 

 permits the transformation to be made with 

 eleven numbers. In respect of precision the 

 short method has an even greater advantage, 

 and when applied with five place tables will 

 in general give results as precise as can be ob- 

 tained with six place tables by the method of 

 the text. 



Throughout his entire work the author ap- 

 pears to have ignored the advantage offered by 

 addition and subtraction logarithms, with re- 

 sults distinctly unfavorable to his formulae. 

 Another example of correct and conventional 

 but cumbrous methods of reduction may be 

 found in connection with the readings of a 

 spirit level, p. 80. By the use of diagonal 

 differences the result may here be found and 

 checked without writing down a single figure. 



