ApriL 28, 1904] 
NATURE 
607 
137, by about 90. The spectrum evidence confirms then the 
determination 225 made by Madame Curie. 
As quite a number of investigators are working at 
relations between spectrum data and atomic weight, it 
seems important to make generally known the fact that 
mathematical series, like that of Balmer’s law or that given 
above, are the main feature in the laws of spectra. The 
approximate law of Rydberg arises from the fact that the 
atomic weights of the elements form a series. Certain re- 
lations between this series and the series belonging to the 
spectra of the natural families are probably the cause of 
Rydberg’s approximate law, which is not suitable for the 
extrapolation attempted by Runge and Precht with their 
modified form of it, unless other better means of estimating 
the atomic weight are lacking. All that we are warranted 
in saying at present is that the atomic weights of some of 
the elements in a family are nearly proportional to some 
power of A+B(1—3n/2+7n7/2), where n has positive 
integral values, and A and B are parameters characteristic 
of the family. WILLIAM SUTHERLAND. 
Melbourne, March. 
Graphic Methods in an Educational Course in 
Mechanics. 
I snoutp be glad if I could, through the columns of 
Nature, elicit opinions from those who have taught 
mechanics from the beginning as to the advisability of either 
omitting graphical methods altogether from an educational 
course in mechanics or of introducing them at a very late 
stage. 
By graphical methods I mean those methods which depend 
entirely on the use of mathematical instruments of pre- 
cision, and from which calculation is absent. I do not 
refer to the plotting of curves from results obtained 
analytically, or to such simple graphical considerations as 
enable one to draw (freehand) a useful working figure. 
I myself, after many years of teaching, have come to the 
conclusion that until the principles of statics and dynamics 
have been thoroughly grasped, it is better to keep graphical 
methods out of sight altogether. 
My contentions are as follows :— 
(1) Analytical methods give a grasp of the principles of 
statics, while graphical methods disguise them. When a 
body is at rest and in equilibrium, the obvious facts are 
that it does not move in this direction or in that, and does 
not rotate. Now the idea of a resolute as the effective 
component of a force in any direction is one readily grasped, 
and the analytical statement that “‘ the resolutes in any 
direction balance one another’ brings vividly before the 
mind the equilibrium as regards translation. Any experi- 
ment made suggests this balancing of resolutes. But the 
closing of a polygon of forces, on the contrary, does not 
suggest, with anything like the same degree of vividness, 
that there is no translation. In fact, the closed polygon of 
forces, representing as it does a couple, rather suggests 
that there is rotation. An experiment with a body on an 
inclined plane, for example, suggests a balance of resolutes 
and does not suggest a triangle of forces. 
Again, as regards rotation. The analytical method of the 
“balancing of moments”’ brings clearly before the mind 
the fact that the body does not rotate. I am sure that most 
people will agree with me when I say that the correspond- 
ing graphical proposition, that ‘‘ the funicular polygon 
closes,’’ will not suggest non-rotation to any ordinary 
learner. 
(2) Analytical methods must be mastered in any case. In 
any educational course, it is important that the learner 
shall have to rely on as few principles as possible. Now 
when he has mastered the principles of ‘‘ resolution ’’ and 
i attack any useful 
“taking moments,” he can be led to 
problem in statics without further theory. 
But he may master the ‘‘ polygon of forces’’ and the 
“funicular polygon,’’ and yet find himself totally unable to 
deal with machines and with other constantly occurring 
cases of equilibrium. He will find that, while he can 
obtain by graphical methods the resultant of a system of 
NO. 1800, VOL. 69] 
forces if these be parallel, he will probably fail if the forces 
be not parallel (and non-concurrent), owing to the difficulty 
of getting his diagram on to a given sheet of paper. In 
fact, analytical methods must be mastered, while graphical 
methods, however convenient in certain cases, need not be 
mastered save for special professional purposes. If, then, 
there be not time for both, it is the latter that should be 
sacrificed. A student well trained in analytical methods can 
always pick up graphical methods rapidly when he needs 
them for special work. ; 
(3) Analytical methods connect statics with dynamics. I 
do not think that this contention will be disputed. Re- 
garded analytically, statics are a part of dynamics; the 
equations are the same and the ideas are the same, only 
the acceleration, in statics, is zero. 
(4) Graphical methods confuse learners of statics. Here 
I rely on experience, and report what I have observed. 
I have noticed, over and over again, that, while a learner 
of analytical statics may fail to solve a problem, he yet 
knows what he is trying to do, and he does not, as a 
rule, lose sight of principles. 
But I find that beginners, who have learned something 
of graphic statics, appear to lose sight of principles 
altogether, and are content to make the wildest ‘‘ shots.” 
They make triangles out of ladders, walls, and ground, 
and continually take the lengths of bars or strings to re- 
present the stresses in them in their attempts to “‘ get a 
triangle of forces.”’ 
I find no beginner so difficult to teach as one who has 
learned some graphic statics at a preparatory school, and 
I much prefer those who have learned no statics at all. 
There seems to be something in graphical methods that 
paralyses the learner’s powers of thought and reasoning, or 
at least allows them to slumber. 
To sum up. I have come to the conclusion that graphical 
methods (as defined above) should be reserved for a re- 
latively late stage in any educational course in mechanics, 
or even be omitted altogether until required for special 
work. In addition to the reasons given above, I may add 
that graphical work consumes an amount of time that seems 
out of proportion to the mental training and knowledge of 
principles gained. W. LarbDEN. 
Devonport, April. 
Sunspots and Temperature. 
Tue following view of this subject (related to that given 
by Dr. Lockyer a short time ago) may be of interest. 
“Consider the last five sun-spot waves, as measured from 
the first year after a minimum to the next minimum, thus :— 
(1) 1844-56 (13 years) Maximum 1848 
(2) 1857-67 (11 years) 360 on a 1860 
(3) 1868-78 (11 years) <— Sas es 1870 
(4) 1879-89 (11 years) oer oes no 1883 
(5) 1890-1901 (12 years) .. wae $5 1893 
Using Wolf and Wolfer’s sun-spot numbers, ‘and finding 
the annual average for each of these waves, we get the 
curve marked A (dotted line) in Fig. 1 (p. 608). 
Ascertaining next the averages of several meteorological 
items at Greenwich for those periods, we obtain curves 
By GD, E, BR] Dheatems! aret:— 
(B) Mean temperature of winter (December—February). 
(C) Frost days in winter (an inverted curve). 
(D) Days with maximum temperature 7o° or more (in 
year). 
(E) Mean temperature of summer (June-August). 
(F) Mean temperature of year. 
The amount of agreement between these weather curves 
and the sun-spot curve seems remarkable. The sun-spot 
wave with highest average number (that for 1868-78) corre- 
sponds with the time of greatest warmth in each case, and 
