1. Spider Line Comparisons. 



In making tliese comparisons the réseau line was always comparée! at 25 

 points with a spider line stretched above it, by projecting it upon the réseau 

 itself and measuring the distance between the projected spider line and the 

 réseau line. It was therefore not necessary to consider the errors of the cy- 

 linder of the Repsold machine. Two small clips, connected by a spring pressing 

 against the under side of the plate, carried the tightly stretched spider 

 thread. The two clips, which slid on the upper surface of the plate and to 

 whose surfaces the extreraities of the web were cemented, were made of exactly 

 equal thickness so that the web was always parallel to the plane of the 

 réseau. Thus the thread could readily be moved about, so as to be set över 

 and nearly parallel to any desired line of the réseau. A special excentric cam 

 was constructed by which the microscope could be raised through a definite 

 vertical distance equal to the distance of the web from the plane of the 

 réseau. Thus, by reading first on the spider web (the microscope being raised 

 by the excentric cam) and then by lowering the microscope and reading on the 

 reseau-line, the différence of the two readiugs gave the interval between the 

 reseau-liue and the projection of the spider web on the reseau. At first the 

 comparisons with the spider line were made at the intersection points of the 

 réseau. But after a few lines had beeu done, it was found better to observe 

 at points half way between the intersection points. The corrections for sinuo- 

 sity finally adopted for any intersection point are then the means of the two 

 values obtained just above and below it. 



To avoid confusion in the réductions, we have always placed the réseau 

 in such a position that increasing numbers on the réseau corresponded to in- 

 creasing numbers on the head of the micrometer screw, and to decreasing 

 numbers on the standard scale A of the Repsold machine. This applies to 

 all observations of every kind, as well as to the spider line comparisons. 

 Moreover, in observations of every kind, we have invariably subtracted the 

 micrometer reading in the lower position from that in the upper position; and 

 wo shall call „upper reading" the one obtained when the microscope was 

 raised by its cam. 



