THE GREAT STAR MAP 435 



the work has taken twenty years. Of course with a larger staff 

 the time might have been shortened ; and at Greenwich, where the 

 available resources are greater, a more elaborate programme 

 has been completed in a time shorter by a year or so : but 

 nowhere else is the work yet finished, the prospects of com- 

 pletion being in many cases very remote ; seeing that at the 

 outset five or ten years was mentioned as the proper time for 

 the work, the present situation gives some cause for anxiety. 

 The fact is that the necessity for strenuous economy in detail 

 has not been sufficiently realised : some of the larger obser- 

 vatories strained at an accuracy scarcely possible even for 

 them ; and their weaker brethren, in attempting to copy their 

 example, hav^e been left far behind. Moderation and self-denial 

 are just as necessary in astronomical work as in other walks 

 of life. 



Let us consider in detail the nature of the work to be 

 undertaken. The process of measurement of the positions of 

 the star-images on the photographic plates has been much 

 facilitated, as already mentioned, by the impression of a 

 j'cseau on the plates. Two series of equally spaced lines are 

 ruled, one set at right angles to the other, so that the plate 

 is divided up into a number of small squares of exactly the 

 same size. It is necessary to specify what is meant by 

 "exactly" in this connection. Nothing, of course, is really 

 perfect or exact, but for practical purposes we may regard a 

 ruling as exact if the errors are so small as to be negligible 

 in comparison with the accidental errors of measurement. In 

 this sense and for the purposes of the Map we may regard 

 the little rescan squares as accurate and exactly equal. If we 

 number them from left to right (.v) and also from below to 

 above (jv), then two appropriate numbers {x and y) will specify 

 the square in which any star-image lies ; and if in addition 

 we measure the distances of the image from the sides of the 

 square, we shall complete the specification of its exact posi- 

 tion. The distances are expressed (in the decimal notation) as 

 fractions of the side of a square and written down immediately 

 after the whole numbers specifying the square. There is no 

 difficulty about the whole numbers : the doubtful points all arise 

 in connection with the fractions. It would take too long to 

 consider them all ; we take two important ones as illustrations. 

 Firstly, how often should we recur to the image of a single 



