834 Description of an Astronomical Instrument. [Oct. 



tainly have used them in the present case, as their object would thereby 



have been less indirectly attained ; since ^-g = jj^ = tan. zen. dist. 



These observations being premised, let us again return to the 

 examination of the plate. It will be observed that its surface 

 within the circles is crossed by equidistant straight lines, inter- 

 secting each other at right angles, and that at the twelfth division 

 counting from the angle where the axis of the index-rod is placed along 

 on the one side, the perpendicular has the points of intersection of the 

 other lines numbered 1, 2, 3, 4, &c. If then the outer line thus inter- 

 cepted by the line last mentioned be taken to represent the axis of 

 the gnomon, the lines 1, 2, 3, 4, will represent the section of its shadow, 

 and if the edge of the rod, adjusted as before, be brought over the 

 number signifying the length of the shadow, that edge will also in- 

 tercept a segment of the quadrant of latitude equal to the zenith dis- 

 tance. This will readily appear on inspection of the diagram just given. 

 Thus the length of the shadow at any place being known, our in- 

 strument at once reveals the latitude. 



The only use of this side of the instrument, so far as I can make 

 out, which remains to be explained, is in the determination of heights 

 and distances. To show its 

 usefulness in this respect, little 

 more will be necessary than to 

 adduce an example of its appli 

 cation ; let A B be an inacces- 

 sible object standing on the 

 horizontal plane B D, whose 

 height is required. 



Observe through the tube the summit A, and mark what division 

 of the line 1, 2, 3, the index allowed to revolve freely on its axis 

 intersects, and let that be, for example, at the number 12 ; then 

 go backwards in a direct line from the object to any new station 

 D and observe the summit of the object as before ; let us suppose that 

 now the edge of the rod is found to intersect at the number 16, 

 then we have 16-12 : 16 : DC : D B=4CD 



and 16 : 4CD : 12 : BA=3CD, the height required. 



It is unnecessary to multiply examples, as from the one now given the 

 readiness with which trigonometrical measurements of a simple kind 

 may be effected without the introduction of angular functions, is suffici- 

 ently evident. As to the accuracy with which they can be performed, 

 it maybe perhaps sufficient to state that, after a little practice, I found 



