OF ARTS AND SCIENCES. 801 



inches from it. The graduated circle, carrying tlie lens, was now 

 brought to zero, so that the rays from the cross should fall normally 

 on the centre of the lens. Lastly, the telescope was focussed on the 

 cross-hairs. The zero point of the graduated circle was obtained with 

 great accuracy, by lighting the gas, then, placing the eye at some dis- 

 tance behind the gas flame, the graduated circle was moved till the 

 reflections from the anterior and posterior surfaces of the lens exactly 

 coincided with the flame ; in this way the true vertical as well as hori- 

 zontal position was obtained. The instrument being thus adjusted, the 

 graduated circle and lens were turned five degrees. The screen having 

 the cross slits was now moved, by means of a rod attached to it, until 

 the rays from the vertical slit were properly focussed by the observing 

 telescojje, the distance of the screen from the lens was read from 

 the scale, the reading repeated three times, and the mean recorded. 

 The same was afterward done for the rays from the horizontal slit. 

 The graduated circle was then moved on, and the same readings re- 

 peated every five degrees. It was impossible to take readings from the 

 vertical slit beyond Qo^ ; for, after that, the screen could not be brought 

 near enough to the lens to focus the rays properly, and the image be- 

 came quite indistinct; but with the horizontal slit the readings were 

 continued to 85^. After com[)leting this set of readings, the screen 

 was placed at one and a half times its focal length from the lens, the 

 graduated circle brought to zero, and the telescope focussed as before ; 

 then the same readings were repeated every five degrees, also when 

 the screen was at one half and at twice the focal distance. 



Having obtained these readings, curves were constructed by the 

 Graphical Method, the vertical distances being equal to the distance 

 from screen to lens, and the horizontal to the angle through which the 

 graduated circle was moved. As a test for the accuracy of the readings 

 when the telescope was focussed for ditferent points, all the readings 

 were reduced, so as to be compared with those taken when the distance 

 from lens to screen was equal to the focal length of the lens. This 



was done by means of tiie formula — | — = —, in which u and v are 

 the conjugate foci, and / the principal focus of the lens. In these exper- 

 iments, — is a constant, for, when the telescope has been once focussed, 

 u 



it remains fixed through that set of readings, and the reciprocal is 



easily found by — = -t ; that is, subtracting the reciprocal of the 



distance from screen to lens, when the angle is equal to zero, from the 

 reciprocal of the principal focus of the lens. This reciprocal is to be 



