On a Four-valued Function of three sets of three-letters each. 515- 
76°54 years. This would seem to favour the idea of a perma- 
nent diminution of the orbit ; and I understand that: De Vico 
regards the movements of his own comet as indicative of a similar 
‘result from the widely diffused ether. But the information on 
this subject hitherto deemed worthy of the most confidence, has 
been derived from the successive returns of Encke’s comet. The 
advantages which this body affords for such inquiries depend. 
chiefly on the moderate eccentricity of its orbit and the position 
of the transverse axis, which is. nearly perpendicular to the line- 
of the. sun’s progressive motion. This arrangement must give 
a more decided preponderance to the perihelion resistance, which 
has the greatest. influence in diminishing the size of the orbit. 
As shooting stars are now regarded as small bodies describing 
very elongated ellipses around the sun, they seem calculated to 
furnish perhaps the most satisfactory means of testing the per- 
fection of the celestial vacuum. Supposing these bodies to be 
more sensitive to the resistance of the medium than to planetary 
disturbances, the transverse axes of their orbits will have a ten- 
dency to assume a uniform direction in consequence of the sun’s 
progressive motion. From the same cause the planes in which 
they move will have their intersections confined for the most 
part to a very limited range, and will also exhibit, though im a 
less degree, a tendency to coincidence. This peculiar arrange- 
ment of their orbits must cause vast swarms of these minute 
cosmical bodies to congregate from the most distant parts of the 
solar domain to a comparatively narrow region at their perihelion 
passage. For the appearance of the zodiacal light and the perio- 
dical fall of meteors, I have endeavoured to account in this man- 
- ner in a paper sent to the meeting of the British Association 
and. published in the Sections (1854, p. 26). My late researches 
on the subject exhibit a closer accordance with observed facts 
than I could then obtain, and they give much support to the 
ideas very prevalent in scientific circles, with regard to the agency 
of meteors in reflecting the zodiacal light. 
Cincinnati, May 11th, 1861. 
LXXVI. Ona Problem in Tactic which serves to disclose the ex- 
istence of a Four-valued Function of three sets of three letters 
each. By J.J. Syuvester, M.A., F.R.S., Professor of Mathe- 
matics at the Royal Mihtary Academy, Woolwich*. 
x page 375 of the May Number of the Magazine (in that 
paragraph commencing at the middle of the page) I gave 
a Table of Synthemes, correct as far as it went, but left in a very 
* Communicated by the Author. 
212 
