October 18, 1895.] 



SCIENCE. 



503 



of time which can be assigned it in the cur- 

 riculum, and as a compromise between con- 

 flicting interests we suggest a required 

 course of sixty exercises, to be followed bj^ 

 an elective course, luhich the student should 

 have an opportunity to elect, and for which he 

 should receive credit. 



The Required Course. It is presup- 

 posed that the student is familiar, as a 

 matter of common information, with the 

 diurnal and annual motions of the earth 

 and the rising and setting of stars. His 

 technical instruction maj^ begin with a for- 

 mal definition of the zenith, poles, horizon, 

 equator, meridian and an explanation of 

 the coordinates, altitude, azimuth, declina- 

 tion, hour angle and right ascension, to- 

 gether with the geographical latitude and 

 sidereal time, which should be introduced as 

 concepts strictly analogous to the coordi- 

 nates. An armillary sphere or some equiv- 

 alent apparatus is almost essential to the 

 ready acquisition of a working knowledge 

 of the coordinates, and it will usually aid 

 the student if emphasis is placed upon the 

 fact that while any two coordinates suffice 

 to fix the position of a star they naturally 

 fall into pairs, altitude and azimuth, decli- 

 nation and right ascension, etc., the com- 

 mon element between the coordinates con- 

 stituting a pair being that they refer to the 

 same fundamental plane. It should be 

 further noted that the latitude and sidereal 

 time constitute the relationship between 

 the different systems of coordinates, and it 

 will be advantageous to point out the rea- 

 sons for employing several different systems. 



The astronomical triangle, Pole-Zenith- 

 Star, should next be introduced as a device 

 for transforming coordinates from one sys- 

 tem to another, and the student's interest 

 will be stimulated if it is pointed out to him 

 that the practical problems with which he 

 is soon to deal, such as the determination 

 of time, latitude and the direction of the 

 meridian, are in so far as their theory is 



concerned nothing other than cases of the 

 transformation of coordinates. 



The convenient use of the astronomical 

 triangle for the purposes here indicated re- 

 quires a knowledge of the ' general spheri- 

 cal triangle,' and it will frequently be found 

 that the student's mathematical attainments 

 are in this respect insufficient. In such 

 cases it is often an economy of time to de- 

 vote an hour to the derivation of the gen- 

 eral formulse of spherical trigonometry by 

 the transformation of rectangular coordi- 

 nates, accompanying the demonstration with 

 the requisite precepts for the application of 

 these formulse to numerical calculation. 

 The student should apply the astronomical 

 triangle to the derivation of formuhe for 

 passing from each sj'stem of coordinates to 

 each of the others, and should preserve 

 these formulas for use in the reduction of 

 his observations rather than to resort anew 

 in each case to the triangle. 



At this stage of progress the student 

 should devote some little time to the nu- 

 merical transformation of coordinates, both 

 for the purpose of familiarizing himself with 

 the several sj'stems and mode of passing 

 from one to another, and for instruction in 

 the technique of computing, the arrange- 

 ment of his work, the checks against the 

 commission of error, the mechanical devices 

 for economy of time and labor, and the use 

 of addition and subtraction logarithms, 

 which are usually neglected in the depart- 

 ment of mathematics. 



It is a common saying among experienced 

 computers that the only waj'' to avoid mis- 

 takes in numerical work is to have acquired 

 experience through the commission of every 

 possible kind of blunder, and there is per- 

 haps no part of his course in astronomy 

 from which the future engineer will derive 

 more practical advantage than this training 

 under the guidance and criticism of an ac- 

 complished computer such as every profes- 

 sor of practical astronomy should be. 



