330 Prof. A. Cayley's Eighth Memoir on Quantics, [Jan. 17, 



near the middle of the tube, the readings will go on for a considerable time 

 without altering the quantity of fluid in the chamber, and ten inches of 

 graduation are found to be ample under all circumstances. By thus taking 

 all the readings, so to speak, on the balance, a uniformity of proceeding 

 is secured, which is not without its value. The instrument, constructed 

 according to the dimensions here given, will denote the intensity of the 

 noonday sun at the summer solstice near the sea- level in England by about 

 100 divisions of the scale. 



Owing to the difficulty of shading satisfactorily, and anomalies found 

 to occur in observing among the snow-fields on the high crests of the 

 Alps, the following contrivance has been adopted : — 



A plain telescope-tube of bright metal, 18 inches long and 2 J inches in 

 diameter, open at both ends, is pierced in its central section with a circular 

 hole li to 1^ inch in diameter, from which springs a flanged shoulder 

 projecting about ^ inch to receive a perforated split bung, which clasps the 

 thermometer- stem and holds the bulb firmly in the centre of the axis of 

 the tube. Two caps, fitted at the ends with clean plate-glass, are made 

 to slide off and on at the two ends to admit of the glasses being readily 

 wiped. By protecting these with a little wadding, the tube serves as a 

 case for two actinometers. In the central section of the tube, made by a 

 plane perpendicular to its axis, and nearly 90° from the centre of the cir- 

 cular hole, is a screw to attach the tube to an altitude and azimuth motion, 

 by means of which it may be kept constantly directed towards the sun. 

 Below the joint is provided means of attachment to an alpenstock or ice- 

 axe. The shading is effected by means of a loose-fitting cap, bottomed by 

 a chamber with air-holes. The shadow of the large thermometer-bulb on 

 the lower glass, or on a plane held beneath it, is a guide to a perfect ad- 

 justment in the working of the instrument. 



IL " An Eighth Memoir on Quantics.^^ By Professor A. Ca yley^ 

 F.R.S. Received January 8, 1867. 



(Abstract.) 



The present memoir relates mainly to the binary quintic, continuing the 

 investigations in relation to this form contained in my Second, Third, and 

 Fifth Memoirs on Quantics ; the investigations which it contains in relation 

 to a quantic of any order are given with a view to their application to the 

 quintic. All the invariants of a binary quintic (viz. those of the degrees 

 4, 8, 12, and 18) are given in the memoirs above referred to, and also the 

 covariants up to the degree 5 ; it was interesting to proceed one step 

 further, viz. to the covariants of the degree 6 ; in fact, while for the degree 

 5 we obtain three covariants and a single syzygy, for the degree 6 we ob- 

 tain only two covariants, but as many as seven syzygies. One of these is, 

 however, the syzygy of the degree 5 multiplied into the quintic itself, so 

 that, excluding this derived syzygy, there remain (7—1 = ) six syzygies 



