410 Mr. E. J. Lowe on Remarkable 



This will readily be verified by multiplication, or by substitu- 

 tion in the formulae of page 437 of the last volume of this 

 Journal. So, we might have considered the conditions requi- 

 site in order that the product 



may have the same form as its factors ; and the same of other 

 forms. These concluding remarks are not offered as conti- 

 nuations of the general development of the tessarine theory, 

 but as individual instances not perhaps altogether unworthy of 

 notice. 



2 Church Yard Court, Temple, 

 May 8, 1849. 



LX. Remarkable Solar Halos and Mock Suns seen at the 

 Observatory of Henry Lawson, Esq., F.R.S. S/'c., Lans- 

 doivti Crescent, Bath. By Edward Joseph Lowe, Esq., 

 F.R.A.S. 



[With a Plate.] 



1849. T^EBRUARY 12<i and 13^. From 12^ 22^'^ a halo, 

 -i- A, Plate L fig. 1, was formed encircling the sun, 

 S, apparently in a very thin vapour, for the sky was quite 

 blue. All the morning there had been a dense ground-fog of 

 some extent. 



23^ 30m. The horizontal diameter of the halo A 45° and 

 its vertical diameter 47°. The portion of the heavens en- 

 closed within this circle was many shades darker than that 

 without, especially so near the circle, for it gradually became 

 lighter near the sun. The sun was also sun-ounded with a 

 burr, and had his rays carried out considerably, at times 20°. 

 The inner edge of the halo was well-defined, but the outer 

 edge very confused ; the breadth about 1°. 



23h 4om, Xwo mock suns, B and C, fig. 2, faintly visible, 

 partaking of the same tint as the halo, viz. pale yellow, were 

 formed in the edge of the halo A on the sun's horizontal level, 



variety of forms. Thus, let A, B, C, D be four points in space, then the 

 equation 



D— C=B— A ........ (a.) 



may be used to indicate either that the lines DC and BA are equal and 

 parallel, as is done in the system of Sir W. R. Hamilton ; or we may use 

 (a.) to denote that those lines are equal and directed to some one point in 

 space; and, in this latter system, (when the last-mentioned point is at an 

 infinite distance,) we may be reconducted to the former one. And other 

 systems might be devised, each geometrical system having probably a corre- 

 sponding one in analysis, and vice versa. 



