( 847 ) 
In 1908 (3d quarter of the year) another strong increase of 
the solar activity has taken place, which almost reached the highest 
monthly averages of 1907 (Worrer le). On the other hand accord- 
ing to Gurraume the 4 quarter of the year showed less than half 
the spotted area of the preceding three months. 
Along with the dotted curve 6—7 (fig. 2) obtained in this way 
which thus represents the (sufficiently established) true course of the 
solar activity in this century, I have given a curve (7) consisting 
of separate dashes. It represents the course which the curve would 
have shown, if, as required by a 35-year period, N°. 7 had agreed 
with Nes. 1 and 4.') 
I need not insist that there is not the slightest agreement. 
This shows sufficiently that Lockysr’s opinion, according to which 
a 35-year period should be traceable in the materials now at hand, 
is untenable. . 
Mathematics. — “A family of differential equations of the first order.” 
By Dr. Z. P. Bouman. (Communicated by Prof. JAN pr Vries). 
(Communicated in the meeting of March 27, 1909), 
_ Prof. Jan pr Vries has pointed in These Proceedings Vol. XI 
(Febr. 27, 1909 p. 756) to a family of differential equations of the 
first order which are reducible by a projective substitution to a linear 
equation 
d 
= = Pla)y + Qa). 
Such an equation has the property that the singular point is the 
vertex of a “critical” pencil of rays, which means that the tangents of 
the integral curves in the points of each ray meet in one point, the 
“pole” of that ray. j 
The general form of the equations 
dy _J(@, y) 
dex (i, y) 
belonging to the indicated family can be found in the following 
manner, in the supposition that fand g are integer algebraical functions. 
1) “As we are now approaching another maximum of sunspots, which should 
correspond with that of 1870.8, it will be interesting to observe whether all the 
solar, meteorological and magnetic phenomena of that period will be repeated” 
(LockyER, Proc. R. S. LXVIII, p. 300). 
