306 Royal Astronomical Society, 



of two cusps, were observed, the instrument was clamped in R.A., 

 and one of the micrometer wires (this instrument has two), the posi- 

 tion of which was previously read off, was brought upon the cusp 

 by the tangent screw of the declination circle, as the cusp passed 

 the centre wire ; and the time was noted. The second cusp was 

 bisected by the second micrometer wire when it passed the centre 

 wire, the time being also noted and the micrometer read off after 

 the observation was made. The subjects registered in this observa- 

 tion are the clock times of the passages of the cusps, and the read- 

 ings of the two micrometers when the wires were placed upon each. 

 The differences of R.A. were obtained by observing the transits of 

 each cusp over all five wires when the interval allowed, and in other 

 cases over the three middle wires. These observations were care- 

 fully made on the same part of the wires, the declination circle 

 being undamped and moved by hand. 



"By observing differences of either N.P.D. or R.A. of the cusps 

 near the beginning and near the end of the eclipse, the effects of 

 errors in R.A. and N.P.D. would have been obtained, largely multi- 

 plied and combined in opposite ways; and by observing differences of 

 N.P.D. of the cusps near the middle of the eclipse, the effects of 

 errors of R.A. would have been obtained with large multipliers. The 

 only defect in these determinations would be, that, as far as errors 

 in the semidiameters of the sun and moon enter, they always enter 

 with the same signs. There seems to be no good method of finding 

 the effects of errors in the semidiameters combined with different 

 signs, except by measuring the difference of declination of the N. 

 or S. limbs when those of both bodies are visible. It would, per- 

 haps, therefore, have been best to divide the duration of the eclipse 

 into five nearly equal parts, and to observe difference of N.P.D. of 

 cusps during the first, third, and fifth parts, and difference of N.P.D. 

 of limbs during the second and fourth. I am here supposing the ob- 

 ject to be (as mine was) to correct all the elements ; if the object were 

 only to ascertain differences of longitude (supposing the elements 

 corrected), it would be best to observe differences of R.A. of the 

 cusps during the second and fourth parts, as the whole of the mea- 

 sures thus obtained would vary rapidly with the time. Different 

 considerations will be necessary in every different eclipse ; and in 

 none can measures be made to the utmost advantage without more 

 of previous examination than I was able in the present instance to 

 give." 



The observations made are, 



1. Excess of N.P.D. of 1st cusp over that of 2nd cusp. 6 observations. 



2. Excess of N.P.D. of sun's lower limb over 1st cusp. 4 observations. 



3. Excess of N.P.D. of sun's lower limb over moon's lower limb. 5 obs. 



4. Excess of N.P. D. of 2nd cusp over that of 1 st cusp. 10 observations. 



5. Excess of R.A. of 2nd cusp over that of 1st cusp. 10 observations. 



After pointing out the mode in which the corrections for refrac- 

 tion, parallax, &c.,are obtained, Professor Airy proceeds to calculate 

 the small variations depending on the errors of the tables, and to 

 obtain equations of condition involving the corrections of the R.A., 



