68 DISCUSSION OP THE INFLUENCE OF THE MOON 



happens about 9'', western hour angle, and its least value about three hours before, 

 giving a range of nearly one-tenth part of the principal range. The observed values 

 for the hours 8, 9, 10 (west) however, seem to indicate that the secondary wave is 

 really larger, but in the present case apparently reduced by the accidentally low 

 values at the hours 11 and 12. 



The following expression has been deduced to express the lunar-diurnal variation 

 of the vertical force : — 



Vd = —0.04 -f 0.27 sin (6 + 72°) + 0.20 sin (20 + 134°) 

 6 counts from the upper culmination, westward ; V^ is expressed in scale divisions. 

 The smooth, full curve in the diagram is computed by the formula ; the differences 

 between the observed and computed values are sufficiently well exhibited in the 

 diagram. The probable error of any single hourly value is ± 0.20 scale divisions. 



In the following expression M signifies millionth parts of the force : — 

 31 M M 



F(j; = — 1.3 + 8.9 sin {6 + 72°) + 6.6 sin {26 + 134°). 

 Maximum value of F^, 28" before the upper culmination, = + .38 scale divisions; 

 minimum value at 15'' 30"°, — 0.43 scale divisions, hence lunar-diurnal range 0.81 

 scale divisions = 0,000027 parts of the force = 0.00034 in absolute measure. This 

 range is so small that the correction for temperature due to a change of but 0°.08 

 would surpass it. 



We ha^e already seen that we cannot bring a sufficient number of observations 

 to bear upon any pa?-< of the entire series, and are therefore not in a condition to 

 pursue this subject of the lunar effect to any greater length. 



At Toronto the curve is also double-crested with maxima three and a half hours 

 after the moon's transits, but compared with Philadelphia the principal and second- 

 ary waves appear exchanged. The range at Toronto is 0.000012 parts of the force, 

 nearly one-half of the Philadelphia range ; we have already noticed a similar differ- 

 ence of range in the solar-diurnal variation, the Toronto range of which was also 

 about one-half of that at Philadelphia. In connection with this it may be well to 

 state that the dip at Toronto is 75° 15', and at Philadelphia 71° 59.' 



Lunar Effect upon Inclination and Total Force. — The combination of the hori- 

 zontal and vertical components to inclination and total force, is effected by the 

 formuUc: — 



A0 = sin 6 cos 6 (^— ^) 



Ad) 2a ^^ • 2fl A F 



_-X =z cos ^6 -_- -I- sin ^6 

 ^ Jl 1 



in Avhich expressions X= horizontal force, F= vertical force, ^ = total force, and 



Q = inclination. The discussion of the observations for dip, in Part XII, gives the 



value 0^ 71° 59', answering to the year 1843. Column 2 of the following table 



is derived from the preceding Table IX, after changing the scale divisions into their 



equivalents of parts of the force, one division being equal to 0.000033 ; column 3 



is formed similarly from Table VIII, of Part VI, one division being equal to 



0.0000365. Columns 4 and 5 contain the corresponding values of the lunar-diurnal 



