60 



REPORTS ON THE STATE OF SCIENCE. — 1915. 



We may now form tlie first liarmonics for these sets of twelve readings, 

 which are as follows : — 



Table III. 



The coefficient for the M.-S. machine is given with reversed sign, to 

 make it directly comparable with M.-B. It will be seen that the mag- 

 nitude of the displacement is much less for the M.-B. machine, though 

 the ratios are not very consistent. A slight correction may be required 

 for error in estimating the hourly travel. This error cannot be large, 

 but there may be 



(a) Error in estimating the pitch of the screw, which gives a spiral 

 character to the trace. Thus for the M.-B. machine the screw was seen 

 to have 17 turns in 4 inches. This estimate could not be so much as 

 half-a-turn in error, and since a day uses 12 turns only, we may put the 

 limit of error as less than 12 in our units of hundredths of an inch. Now 

 if we form the first harmonic for the numbers 



0123456789 10 11 



we find — 4 sin 6—1 cos 0. Applying this correction with the sign appro- 

 priate to making the ratios of M.-S. to M.-B. more accordant, and apply- 

 ing an equal correction to M.-S., guided by the same consideration, we get 



It will be seen that there is no great improvement in accordance of 

 the ratios, while the phases are conspicuously more discordant. 



(6) Errors may also arise from the diaim not revolving in an exact 

 hour or two hours. These again are not likely to be large, and their 

 general efiect would be as for case («). 



(c) Or there may be a real travel of the index during the day, owing 

 to gradual change of temperature, for instance. If we treat this as a 

 uniform change, its general form is still the same as case (a). 



Coming to the phases, we see that there is a difference of about 90°, 

 or 6 hours. The inference appears to be that the effect is not due to 

 tilt of the ground, which should aft'ect both instruments at about the 

 same time, but an effect of temperature which acts promptly on the 

 M.-S. instrument but much more slowly on the M.-B. The fact that 



