118 MEMOIR ON ACHROMATIC GLASSES. 



EXAMPLE. 



General formula Suppofe the angle be meafured under which we perceive 

 d!ftances latnS an OD J e & °^ tne magnitude of one toife, placed vertically fo 

 as to reprefent the tangent, the radius of which is the diftance 

 from the eye ; if this angle be of 30' we (hall have the follow- 

 ing proportion : the tangent of 30' is to the radius, as one 

 toife is to the diftance. By the tables of logarithms we (hall 

 have this diftance by fubtracting from the logarithm of the co- 

 fine the logarithm of th* tangent of 30', which is 7.940853 : 

 the logarithm refulting from this fubtraction is 2.039142 ; and 

 the number anfwering to this logarithm is 114.6 nearly ; con- 

 fecpently the diftance from the eye to the object, the magni- 

 tude of which is fuppofed to be one toife, is 114 toifes fix 

 tenths ; but in the ufe of the inftrument fractions may be neg- 

 lected. 



It is proper to obferve, that in meafuring final 1 angles the 

 triangle need not be perfectly rectangular : the object may fen- 

 fibly vary from the perpendicular, without a perceptible dif- 

 ference in the angle. 



QUESTION I. 



Mode of deter- The magnitude of an object being known, to determine its 



mmingbythe diftance. 



micrometer the J 



diftance of an For this purpofe the two images of the object produced by 



m^rUtude 1 ? 10 * 11 the P r ^ ms are t0 be br ought into contact, by moving the index 

 along the axis that carries them. This rule has two divifions, 

 one (hewing the minutes and feconds, the other the propor- 

 tion between the diameter of the object and the diftance. 

 Suppofe the object 1 look at is a man : the mean height of a 

 man with his hat on may be eftimated at fix feet. Having 

 difpofed the prifms and telefcope fo that the two images are 

 in one vertical line, I move the index till the feet of the upper 

 image come into contact with the fummit of the lower : if now 

 the index point at the number 344, I conclude that the dif- 

 tance of the man from my eye is 344 times fix f^et, or 344 

 toifes. The fecond divifion will ihew, that the angle under 

 which I fee the man is 10'. By this method the meafure of a 

 diftance may unqueftionably be obtained with great precifion, 

 but there are many cafes, in which this great precifion is not 

 neceflary. 



Ships, 



