888 INDEX, 
Spectroscopical Exumination of Colour in Practical Astro- 
nomy, 779-843. By Piazzi SmytH, Astronomer-Royal 
for Scotland. 
Sulphate of Dimethyl-Thetine, 597. See Lurts (Dr EH. A.). 
T 
Tabulation of all Fractions having their Values between Two 
Prescribed Limits. By EDWARD SANG, 287. 
Tair (Professor P. G.). On Knots, 145-190. Forms of 
Knots suggested by Sir W. Thomson’s Theory of Vortex 
Atoms, 145. “What has become of all the Simpler 
Vortex Forms?” or, “ Why have we not a much greater 
Number of Elements?” 145. Previous writers on 
Knots or Links—Listing, Gauss, and Clerk-Maxwell— 
referred to, 146. The Scheme of a Knot, and the 
Number of Distinct Schemes for each Degree of Knotti- 
ness, 146. Two Alternatives for the Initial Crossings— 
the crossing of the branch begun with may be under 
instead of over, 147. _ Listing’s terms—Inversion and 
Perversion, Dexiotrop, and Leotrop Crossings, 147. 
Necessarily nugatory Intersections defined and illus- 
trated, 148, 160, 161, 166. The Scheme of a Knot, 
defined and illustrated, 149. Given the number of tts 
double points, to find all the essentially different forms 
which a closed curve can asswme, 150. The different 
possible numbers of intersections, 149. With one inter- 
section, or two only, a Knot is impossible, 153. Scheme 
of the only Knot, with three intersections, 158 ; the only 
Knot with four intersections, 153; those with five 
intersections, 153. There are but two schemes for 
five intersections, 154. The Pentacle or Solomon’s 
Seal, a form of this case, 155. Case of six intersections, 
155. There are only four forms of 6-fold Knottiness, 
155. Case of seven intersections, 156. Only 87 possible 
forms can be obtained from seven combinations, and of 
these only 22 correspond to real Knots, 157. Certain 
forms of 7-fold Knots convertible into one another, 159. 
Problems of arrangement bearing on Knottiness, 159. 
There are a greater number of distinct forms of Knots 
than there are of their plane projections, 160. Amphi- 
cheiral Knots defined, 160,164. At least one Knot of 
every even order is amyphicheiral, but no Knot of an odd 
order can be so, 160. The number of Forms for each 
Scheme, 161. Effects of Deformations or Distortions— 
and a particular species of Deformation, 161. Con- 
tinuations of Sign, 162. Practical processes for produc- 
ing graphically all such Deformations as are represented 
by the same scheme, 162. Deformations of the 

additional compartment, 166, A tentative method of 
drawing all closed curves with a given number of 
double points, 168. Distinction between a Knot and 
Linkage, 168. An Amphicheiral Link, 168. The 
Spherical Projection will in general allow any Knot to 
be regarded as a more or less complex plait, 168. If 
the number of windings is even, the number of cross- 
ings is odd, and vice versa, 169. The solenoidal 
arrangement has only nugatory intersections, 169. 
Illustrations of irreducible clear coils, 169. Ilustra- 
tions of certain relations obtainable from Platean’s 
Glycerine Soap Solution, 170. All clear coils may be 
regarded as specimens of more or less perfect plaiting, 
170. The number of ways in which clear coils can 
be exhibited in plaits essentially distinct is n—1 n-2 
21 (n being the number of laps.) Another 
notation for clear coils i A . . 171. Methods of 
reduction, 172. Case of a Theorem that any portion of 
a coil which may be treated as a separate coil, and 
which, if alone, could be reduced, may be reduced i 
situ, 174. A more general theorem which includes the 
preceding, 174. Beknottedness defined as the smallest 
number of changes of sign which will render all the 
crossings in a given scheme nugatory, 177. Knotfulness 
used to indicate the number of Knots of lower orders 
of which a given Knot is built up. Lemmas for examin- 
ing the plane projection of a Knot, 177. Illustration of 
Beknottedness from the work required to carry a mag- 
netic pole round any closed curve once linked with a 
current, 178. Determination of value of m in Gauss’s 
formula 4m, from the number of Linkings, 180, 
186. A simple method of determining the amount 
of Beknottedness for any given Knot not yet discovered, 
181. The simple 7wists (or clear coils with two turns) 
are the forms which, with a given amount of Knottiness, 
can have the greatest Beknottedness, 182. Cases of 
clear plaits where the number of crossings is a multiple 
of six. These are formed by three unknotted closed 
curves, no two of which are linked together, yet the 
whole is irreducible, having alternate signs. Hence a 
third term required, and so we have Knotting, Linking, 
Locking, 182. The Gaussian integral does not, except 
in certain cases, express the measure of what may be 
called Belinkedness. Amphicheiral Forms, 187, Some 
tentative Modes of getting Amphicheirals, 187, 188. 
Proof that there is at least one Amphicheiral form of 
every even order, 189. 
“trefoil” Knot, 163 ; of the 4-fold Knot, 164. Every | Tarr (Professor P. G.). On Thermal and Electric Conducti- 
Knot which can be deformed into its own perversion 
is called amphicheiral, 164. On symbolising the pro- 
jections of a Knot, 165. The proposition that any closed 
plane curve, or set of closed plane curves, divides the 
plane into spaces which may be coloured black and white 
alternately—may be employed to symbolise the pro- 
jections of a Knot, 165. In a Symmetrical Symbol the 
number of joining lines is the same as the number of 
crossings, 166. Every additional crossing involves one 

vity, 717. Professor Forbes’s investigations on this sub- 
ject, 717. Angstrom’s Method of conducting Experi- 
ments on the Conductivity of Iron, 719. Aneasily applied 
Interpolation Method for Determining Thermal Con- 
ductivity, 721. Dr Balfour Stewart’s Thermometers 
described, 723. Dr Crum Brown’s Method for Securing 
Uniform Source of Heat, 724. New Method of Heat- 
ing the Short Iron Bar, 725, Method of estimating 
the true Temperature of the Thermometers employed 

