Anibll +an2b12+ï¿½ ï¿½ï¿½ +annbin a11b21+a12b22+ï¿½ï¿½ï¿½ +alnb2n, a21b21+a22b22+ï¿½ï¿½ï¿½ +a2nb2n, ï¿½ ï¿½ ï¿½ ani b21 + a n2 b 22 + ï¿½ ï¿½ ï¿½ +annb2n alib31+a12b32+ï¿½ï¿½ï¿½+ainb3n, a21b31+a22b32+ï¿½ï¿½ï¿½+a2nb3n, .ï¿½.a n lb 31 + a n2 b 32+ ï¿½ï¿½ï¿½ +annb2n a ll b **nl** + a 12 b n2+ ï¿½ï¿½ï¿½ + a ln b nn, a21bn1+a22bn2+ï¿½-ï¿½+a2nbnn, ï¿½ ï¿½ ï¿½ ani b **nl** + a n2 b n2 +ï¿½ ï¿½ ï¿½ +annbnn and all the elements of D become zero.

Taking any number n to be represented by a point on a line at distance **nL** from a fixed point 0, where L is a unit of length, we start with a series of points representing the integers I, 2, 3,.

Keeping the same tension, it may be shown that **nl** is constant by finding n for various lengths.

If we measure the time from an instant at which the two are in the same phase the resultant disturbance is y=a sin i t+a sin 27rn2t =2a cos ir(n i - n 2)t sin ir(**nl-t-**n2)t, which may be regarded as a harmonic disturbance of frequency (ni+n2)/2 but with amplitude 2a cos 7r(n i - n 2)t slowly varying with the time.

- :2 a2A cos e-2 cos (4nnit+e) b2µ b2µ cos f - cos (41rn 2 t +f) 2 2 + a 2 A cos {2a(n l - n 2)t+e} - a 2 A cos {2a(**nl-F** n2)t+e} a 2 µ cos {21r(n i - n 2)t - f} - a 2 µ cos { 2 ?

Divide the span L into any convenient number n of equal parts of length 1, so that **nl** = L; compute the radii of curvature R 1, R2, R3 for the several sections.

?_?**nl** - the Royal Palace is the Storkyrka (great church), dedicated to St Nicholas, the oldest church of Stockholm, though greatly altered from its original state.

Then the following relations hold: 0 = 4)1+4)2= ('**nl** - I)(I /r' 1 - I /r "1) + (n21)(I/r' 2 - I/r" 2) = (**nl**- 1) kl+(n2 - i)k 2; and (3) (14) = k l dn l k 2 dn 2.

' eiskfll **nl**; ?ut Isoline ii etl r F E H S r o Dindridg ' o.

In mentioning any single tooth, such a sign as mi will mean the first upper molar,, **nl** the first lower molar, and so on.