242 REPORTS ON THE STATE OF SCIENCE, ETC. 
The harmonic constants (H, «) are as follows :— 
S, R, | T, K, | Tis a, | M, | 2sM |» 
H 1:868 020 ‘110 “503 "386 O47 5:621 “100 "189 
K 189-42 | 191:4° 186°8° | 188°8° | 156°9° 93°B° | 145°S° | 49°62 | 119°8° 
N, Me 2N 8, P, K, 0, Q, 
H 1:091 182 130 ‘010 ‘O71 -200 180 “060 
K 122:4° | 176:9° | 123°7° | 340°5° | 113-72 iste 345°3° 292:4° 
These are obtained from (R,e) by multiplying R by a certain factor depending 
upon the longitude of the moon’s node, and by adding to e¢ the ‘astronomical 
argument.’ 
PART III. 
Tests on the Accuracy of Tide-predicting Machines. 
In collaboration with the Hydrographic Department of the Admiralty and with 
the National Physical Laboratory, it has been possible to use the Newlyn calcula- 
tions for a direct test on two tide-predicting machines. The Report for 1920 gives 
certain indirect tests where predictions from two machines are compared, and the 
absolute errors of each are unknown. The harmonic numbers used to represent the © 
five chief semi-diurnal constituents for Newlyn were supplied to the Hydrographer 
and to Mr. Selby, of the N.P.L., for use with Mr. Roberts’ machine (R) and the India — 
Office machine (N) respectively. The curves for six months were forwarded to the 
Tidal Institute, where they were read and compared with the calculations. 
Measurements of heights at intervals of four hours, and of heights and times of Ha 
and L.W. were made on nineteen days at intervals of ten days, and every effort was — 
q 
i 
made to ensure the greatest possible degree of accuracy in measurement. The machine 
scales were, in height, one inch to a foot, and, in time, one inch to four hours; con- — 
sequently the gradients were sometimes very steep and measurements were difficult | 
to make. The errors of measurement are essentially random, and not systematic, | 
errors. The calculations are correct to within 0-01 foot in height and one minute in | 
time. ‘The errors are taken as machine value minus calculated value. 
High and Low Water Heights (feet). 
Average Zero ‘Throw’ 
Range of error error error error 
R-machine ... H.W.errors —‘l0 to —‘24 = SST eae eee 
Ti Wer teqgr OT tor 2 
N-machine ... H.W. ,, 00 to —'13 bee 03 —-07 
a ts, “09 to —-05 -00 
By the ‘ throw’ of the machine is meant the distance from maximum to minimum in 
the tide. In these cases H.W. are systematically 1oo low and L.W. systematically 
too high by about ‘035 foot when the zero error is corrected. 
High and Low Water Times (minutes). 
Range of Average Greatest range f 
error error in one day 
R-machine ... H.W. errors salto 10 5'8 \ 0 tod 
L.W. 5 0 to 10 4:8 
N-machine ... H.W. ,, 0 to 12 52 } 9 
Ew. 8 0 to 13 72 1 toda 
