366 <A. D. Bache on a Magnetic Survey of Pennsylvania 
Mean total change in 21 years = 8’°8. 
The increase in the dip is, therefore, very slight, and if we con- 
sider that, according to Mr. Schott’s investigation (Appendia, 
iVo. 32, Coast Survey for 1856), the dip near the Atlantic coast 
about the years 1841-1844 was at its minimum value and hence 
could not have changed sensibly for several years—we can 
without sacrificing anything in the accuracy of our reduction, 
use our results as if all belonging to the mean epoch 1842°0. No 
reduction to epoch has therefore been applied. It is probable 
that the present annual increase amounts to about 1’. At 10 
ronto, between 1844 and 1855 (see Zoronto Observations, vol. i), 
the annual increase was 0'8. In the formula of interpolation, 
I retain the factor cos L, thus making it comparable with sim- 
lar expressions for other localities where the introduction of 
cos L may be more important. ages 
The value of the magnetic survey of Pennsylvania is increased 
from the fact that the isoclinal lines are presented for an € 
at which the dip was probably near its minimum value. 
The conditional equations are of the form 
O=I, —I-+i-fedL+-ydM cos L-p2dLdM cos L-}-pdL?+-qdM? cos? be 
Next, nine groups of five or six observations in each, ig 
formed, arranged in regard to the geographical position 
area with as much regularity as the nature of the case admits 0 
Recapitulation of mean values of groups. 
Group. Latitude. | Longitude. — Dip. 
° 
5 40°40 7502 TVA 
IL 39°56 76:85 71°73 
Hi. 40°22 80°06 72°20 
EY. 41-56 80°32 73:20 
Vi 40°65 78-02 72°54 
Vi 42°75 78°93 74:56 
VIL 41-53 56-07 73-50 
VII. 42-96 76°95 74-74 
ix: 42°26 74°33 74st 
Mean, | 41-32 77°39 7a35 | 
The trial of an equation of the form, 
I=1,+i+-rdL+-ydM cos L-++-2dLdM eos L; 
and of the form, 
I=1, +i-++rdL-+-ydM cos L-++-qdM? cos? L, re 
showed that the extent of the survey is not sufficiently Bers — 
admit of the determination of curvature of the isoclin 
and finally the following expression was adopted: : 
—I=73°25-+0-°912 dL—0:069 dM cos L. 
This equation represents the observations as follows: 
