September, 1910. 



KNOWLEDGE. 



341 



simple and quite 

 can be assigned their 



The various causes 

 appropriate effects because 



during 

 When 

 Moon 

 when 



-0/0 



these causes are periodic. The Sun"s heat comes 

 round with absolute regularity every twentv-four 

 hours — while the Moon crosses the sky every twenty- 

 four hours fifty minutes. The 



Moon produces some definite .° "'^ 



effect when she is due South and 

 she produces that same effect 

 twelve hours twentv-five minutes 

 later, when she is due North. 

 Half-way between these two 

 moments when she is due ^^'est 

 and again \\ hen she is due East 

 she produces exactly the opposite 

 effect. This is only a repetition 

 in somewhat different words of 

 what we just now said about the 

 experiences of a drop of water 



one rotation of the earth. 



the drop was at A the 



for it was due South. 



it was carried to D it 

 would say the Moon was due West, setting and so 

 on. Now at new Moon the Moon is South with the 

 Sun at noon and each succeeding day she is South 

 fifty minutes later and in a month she is again South 

 at noon. Thus if the records at noon of thirty 

 consecutive days be added 

 together, we have a sample 

 of thirty different lunar 

 effects, one-half of which 

 are precisely the opposite of 

 the other half, and so in the 

 average of the thirty the 

 lunar effect vanishes and 

 only the heat effect of the 

 sun remains, and we get its 

 value for noon. Precisely 

 the same method may be 

 used for one, two, three, 

 and so on, o'clock. At any 

 named hour of the day the 

 Sun is at the same place in 

 the sky, but the Moon ma\- 

 be anywhere, and thus the whole cvcle of solar effects 

 through twenty-four hours is obtained. Putting it 

 briefly we may say that we group our records accord- 

 ing to the period of the cause which we are for the 

 moment considering, and the averages over several 

 years will eliminate all other causes. When seeking 

 for the Moon's effect we must group according to the 

 lunar period of twenty-four hours fifty minutes ; one 

 group shall give us the average record at the moment 

 when the Moon was South ; another group shall be 

 taken one hour later each da\-, another two hours 

 later, and so on. Some eight-hundred davs were 

 recorded, and so each group will give an average of 



period, will be removed. The 



give summaries of the results of this grouping and 



following diagrams 



Figure 5 



o o/c 



Figure 6. 



eight-hundred 

 influences as 

 eliminated in 



effect. 



records, and obviously such yar\ing 

 the height of the barometer will be 

 that average and, a fortiori, the solar 

 which \aries according to a fixed but diffcient 



Figure 5 gives the average doings of the 



pendulums when the whole series is consulted. The 



full line shows what would be 



2 "''<= expected of the pendulum if the 



lunar forces shown in Figure 4 all 

 produced their theoretical effect ; 

 the hours at which the plummet 

 should reach each point are given. 

 The dotted line gives the average 

 found, and again the hours are 

 indicated. It will be seen that 

 the pendulum did not swing so 

 wideh" as theory- expected, but 

 otherwise it carried out most 

 punctually what the lunar attrac- 

 tion commanded. It is this per- 

 fect accord between theon,- and 

 observation which forms the 

 success of Dr. Hecker's work ; 

 the pull of the moon is directly 

 recorded bv the instrument. 



The perfection seems marred by the one fact that 

 the swings are not so ample as they should be, but 

 far from being a defect this feature is perhaps the 

 most satisfactory point in the whole work. The 



theoretical curve is worked 

 out for an absolutely rigid 

 earth, in which no tilting, 

 no deformation of an}- sort, 

 takes place, and we have 

 seen that a tilt will shift 

 the pendulum in a manner 

 quite similar to a direct pull 

 on the plummet. If then 

 the moon's drag produced 

 a regular tilting taking 

 place precisely according 

 to the period of that drag, 

 its presence would remain 

 in tbe average : it would be 

 a maximum when the drag 

 was a maximum, and its 

 effect cannot be disentangled from that of the direct 

 drag. The deficiency in the amplitude of the swing 

 suggests that some such regular periodic tilting is 

 going on w ith an eftect alw ays contrarv- to that of 

 the drag, but only great enough to diminish, not 

 entirely to obliterate, the evidence of the drag. Can 

 we then see any reason to expect such a deformation 

 of the surface of the earth — a deformation which we 

 may at once boldly call a tide since it is to be 

 regularly periodic twice in each lunar day of twenty- 

 hours fifty minutes ? If we admit any elasticity to 

 the solid earth, the answer is clearly in the affirma- 

 tive. The forces in Figure 4 are acting as much 

 on the crust and interior as on the water and the 

 pendulum on the exterior, and to whatever extent 

 the crust gives, to that extent w ill any motion of the 

 pendulum and any tide in the ocean be diminished. 



