a 
TRANSACTIONS OF SECTION A. 463 
(iii) Generally 72,1 = 9 (mod 1), v, == 0 (mod v), 4 : 
7. U, at Yu =O (mod m™ U,, X,, Y, respectively) } Soi te ustiahy SOmmpeRte, 
Tny Un are factors of vy, and recur iN T,42mny Ve+ann Tespectively, and both recur 
in Vamn, [m=1, 2, 8, &e.}. 
(T,,, U,), or (Xn, Y,) are factors of von, and recur in (Tryp) Unsy), (Xniuy Yn+u), 
respectively, and also paired together in v,, where «=(2x—1)m: and the same 
rules apply to the prime factors (p) of Tn) Un» Tn, Un, Xn, Yn. 
(iv) As to division by a prime (p) :— 
1°. If D=p, or =0 (mod p), then v, = 0 (mod p). 
Tn — +1 (mod p), T2n41 = 71, and r, = + 1 (mod p). 
2°. If D £ 0(mod p), then v; = 0(mod p) requires that } {p — (°) } = 0(mod r) 
as a preliminary condition. 
If g be prime, and p=2ga+1, and i{p - (°) \=0 (mod q), then v? 
= 0 (mod p). 
In both 1°, 2°; if vs, =:0 mod p, then one of r,, v, =O (mod p) ; and, if vap_1 
= 0 (mod p), then one of T,,, U,, or one of X,,, Y, = O0(mod p). The 2'* forms given 
above often sutlice (especially when D = 2) to show which of Ty, vp, Try Un; Xny Yny 
can = 02 (mod p). 
8. Report on Bessel Functions.—See Reports, p. 94. 
9. Report on the Teaching of Elementary Mechanics.—See Reports, p. 97. 
DEPARTMENT OF ASTRONOMY AND CosmicAL Puysics. 
The following Papers and Reports were read :— 
1. Lhe Variation of Latitude. By Dr. O. BackLunp. 
2. On some recent Developments of the Method of Forecasting by means 
of Synoptic Charts. By W.N. Suaw, LL.D., Sc.D., PRS, 
The method of forecasting based upon the movements of cyclonic depressions 
and anticyclonic areas has now been in use for some thirty years, and may be 
called the classical method. It deals with the relations of pressure, wind, and 
other meteorological elements to centres of low pressure and high pressure 
respectively, and may be described briefly as consisting in detecting the existence 
of a cyclonic depression, locating its centre, and anticipating its path. 
The reference of all the phenomena to a centre tends towards the smoothing 
of the isobars, as far as possible, into curves, with the minima as centres, and to 
dealing with the characteristics of an average or typical depression as generally 
applicable to the individual cases. Observations of pressure and wind which 
show marked deviation from the conventional type are apt to be regarded as due 
to errors of observation, or in transmission, or to local conditions of no general 
importance, 
That this method gives a fairly satisfactory ‘first approximation’ to the 
solution of the question of forecasting is evident from the fact that of the evening 
forecasts of the Meteorological Oflice based upon it 61 per cent. were classed as 
completely successful for the year 1906 and 656 per cent. for the past ten years, 
while 30 per cent. and 29 per cent. respectively were partially successful. 
At the same time, the margin of failures and incomplete successes is sufficiently 
