in the Velocity of Propagation of Light in Water, 275 

 tion, then 



£ = <£+ i/r, 



and 



, OPsin<£ 



tan < \Zr=_= — - . 



r OS-OP cos cf> 



In order to determine ty, it is not only necessary to know <£ 

 (which is measured directly on the universal circle), but also the 

 distance of the slit from the centre of that circle and its distance 

 from the prism. 



III. The Instruments employed in the Investigation. 



(1) The theodolite served both as carrier for the prism and 

 as reflexion goniometer. It is divided into sixths of a degree, 

 and by help of the vernier allows a reading of 10". As two 

 verniers were consulted, which stood at an angle of 180° from 

 one another, any possible error of excentricity was thereby eli- 

 minated. That no serious errors occur in the graduation of the 

 instrument is guaranteed partly by the name of the maker, and 

 partly by the testing and use which the instrument underwent 

 in the hands of Professor Hankel. 



(2) The universal circle is provided with a bent telescope and 

 a very exact level for adjusting its axis of rotation vertically. 

 The graduation of the horizontal circle is by Repsold. The 

 reading off degrees and sixths of a degree is made with an index 

 and lens ; the reading of minutes and seconds by means of two 

 microscopes. Divisions of 10" are read off directly, quantities 

 of one second are estimated. 



(3) The straight measurements were made by means of two 

 mahogany rods divided into millimetres and provided with brass 

 ends. Since we are here only concerned with relative lengths 

 and the accuracy of the divisions was established, the rods could 

 be used without correction. 



The measurement of the lengths was effected thus : — the slit 

 and the centre of the universal circle were plumbed down upon 

 the stone basement, a thread was stretched between the two 

 points so obtained in order to establish their rectilineal relation, 

 and upon this line the measuring-rod was placed. It was more 

 difficult to determine the distance of the prism from the axis of 

 rotation of the universal circle. Since the prism is of consider- 

 able size, it might be doubtful from what point the distance 

 should be measured. That point was chosen which was formed 

 by the intersection of the axis of the telescope with the plane 

 bisecting the angle of the prism. As my prism was provided 

 with a little circular opening exactly in the middle for the intro- 

 duction of a thermometer, I generally read off the measure at 



