VOL. LXXXIV.] PHILOSOPHICAL TRAKSACTIONS. 353 



enough to me to estimate it pretty exactly. At lO'' IS™, I looked out with the 

 natural eye for the planet Venus, and soon perceived her. In the telescope, with 

 287, she appeared very sharp and well defined, and was a little gibbous. 



It may seem perhaps extraordinary that, in the trial above-mentioned, the eye 

 should be able to ascertain the proportion of a quantity so little as the 1500th 

 or 2000th part of the diameter of the moon ; but the experiment may be easily 

 repeated in the following manner : On a line, 6 or 8 inches long, drawn on a 

 sheet of paper, make several small marks, representing mountains on the pro- 

 jected circumference of a large globe. The paper being then placed in a proper 

 light and situation, withdraw the eye to the distance of 7, 8, or Q feet, and take 

 notice which of the marks appear of the same size, and distinctness, with the 

 mountains they represent. Then, from the known angular magnitude of the 

 moon, calculate its diameter at the distance of your situation ; this, multiplied 

 by the power of the telescope, gives the diameter of a circle, to the circum- 

 ference of which belongs the line, on which are placed the marks above de- 

 scribed. Now measure the elevation of these marks, above that line, and you 

 will obtain the proportion they bear to the diameter of the circle. 



In my experiment, I found that I could plainly see some small protuberances 

 at 9 feet distance, which were no higher than the 50th part of an inch. Then 

 putting the diameter of the moon at 30', we have the sum of the logarithms of 

 the tangent of 30' ; of the power 287 ; and of the 50ths of an inch contained 

 in 9 feet ; which, taken from the logarithm of the diameter of the moon in 

 miles, gives the logarithm of .16. By which we find, that so small a mountain 

 as the -jVo-j or not much more than the 6th part of a mile, may be perceived and 

 estimated, by the telescope and power that was used on this occasion ; and that 

 consequently the estimation of mountains near a mile and a half high must 

 become a very easy task. 



f^II. The Latitudes and Longitudes of several Places in Denmark ; Calculated 

 from the Trigonometrical Operations. By Thojnas Bugge, F, R. S. Regius 

 Professor of Astronomy at Copenhagen, p. 43. 



The geographical surveying of Denmark was begun in the year 1762. The 

 foundations of geographical maps are the trigonometrical operations, or great 

 triangles, whose bases were measured with deal rods. The angles of the tri- 

 angles were observed with a circular instrument of 1 foot radius ; the divisions 

 of this instrument are double, in 90 and 96 degrees. With this instrument 

 the angles may be observed to a less error than 8", and the sum of ail the angles 



tains beyond the enlightened part of the disc ; the length of their shadow on the surface of the 

 moon ; and their perpendicular projection on the fiiU edge of the moon's limb. Some of these 

 observations are contained in a former paper (see Phil. Trans, vol. 70) j but most of them remain 

 uncalculated in my journal, till some proper opportunity. — Orig. 

 VOL. XVII. Z /. 



