2« CAEPMAEL AND McLEOJJ ON THE 



the other over the tAvo outside groups. Slight uueertuiuty in the position of the stars 

 had therefore uo influence on the result as they would affect both observers alike. In 

 the ease of the determination between Prof. MeLeod and myself, however, alter we 

 had waited several nights at Montreal Avithout a chance of observing, the time at our 

 disposal being limited, Ave had to abandon the attempt to get a comparison at Montreal, 

 Prof. McLeod left for Toronto, wher." I joined him after the observations for longitude 

 were completed, and aa^c then, on September 15th, obserAnxl together for jiersonal 

 equation. The Toronto transit instrument had a set of &ve spider lines only, so stars of 

 various declinations were selected iu pairs of as nearly as possible the same declination, 

 one of each pair being observed by Prof. McLeod, the other by myself. The error of the 

 clock was determined from Prof. McLeod's observations and from my oavu separately, 

 each set being Avorked up in the same way as that observer employed in the longitude 

 work, and the difference between the clock errors as obtained by the two observers gave 

 a determination of the personal equation. This result Avould be affected by any errors iu 

 the adopted star places, as well as by change in the instrumental errors ; the personal 

 equation AA'as not therefore taken as a known quantity iu discussing the timi- exchanges 

 for the final determination of the difference of longitude, but AA^as alloAved to enter as an 

 unknoAvn quantity in the equations of condition, the result of the determination on 

 September 15th furnishing one of the equations. We had then seven equations, three 

 furnished by the time exchanges Avhen each observer was at his oavu station, A'iz., on 

 August 25th, 30th, 31st; three after exchanging obserA'ers, viz., on Sejitember 5th, 0th, 

 11th ; and one Avith both obserA^ers at Toronto. The approximate solution of these seA^^n 

 equations for the determination of the diflerence of longitude, and for personal equation, 

 was effected by the method of least squares. 



Instruments. 



The transit instrument at Toronto is by Troughtou and Simms, London, Eno-land, 

 1882. It is of 3 inches aperture and 34v5 inches focal length, mounted on a solid stone 

 pier. The equatorial intervals from mean wire of the different wires as determined hv 

 numerous obserA'ations, both of polar and other stars, was for circle west 



+ 28-907 + 14-421 — 0-042 — 14-442 — 28-841 

 but in only a xl'Tj tew cases Avere stars employed in the Avork xA^hich were not observed 

 ovi-r all fiA^e Avires. 



The level, also by Troughton and Simms, was supposed to haA^e a scale A^alue of 1", 

 but Prof. McLeod determined the value of the scale of another level by comparison Avith 

 it, and afterwards independently, Avhich comparisons would give 1".0!»5 for the A'alue of 

 one division of the Toronto level. The Toronto instrument had, prior to this second 

 determination, been broken whilst preparations Avere going on for accurate uK^asiirement 

 of its scale value, so that no such determination could be affectinl. The value adopted in 

 redutino- the obserA^ations was 1".05. 



The observations were recorded on a chronograph by Cook & Sons, York, England, 

 andAvere measured off to the hundredth of a second Avith the aid of a glass scale divided 

 to tenths of a second. The time piece was sid(>real clock No. 8T9 by Ghas. Frodsham, 

 London. 



