14 DISCUSSION OF THE HORIZONTAL COMPONENT 



At Philadelphia the progressive change is so large as to require a systematic' correc- 

 tion throughout the series. In the manuscript tables used for the preparation of 

 the monthly normals and containing the observations reduced to 63° Fahr., the 

 readings corrected for progressive change 1 were written in blue ink underneath each 

 observation. If the monthly differences are taken from Table No. III., it is appa- 

 rent that the change is irregular, and in three cases at least it is certain that other 

 causes were in operation, which produced larger monthly differences than could lie 

 attributed to the gradual loss of magnetism. These cases are the following (alreadj 

 noticed in the preceding temperature discussion): between June and July. 1S40, a 

 difference of 170 divisions; between December and January, 1S40-41, a difference 

 of 77; and between May and June, 1841, a difference of 103 divisions. They 

 require separate treatment, as will be presently explained. For the correction of 

 the progressive change the mean reading from one month's series was made out for 

 the first, middle, and last of each month. By this process of taking the mean from 

 14 days preceding and 14 days following each of the epochs the lunar effect on the 

 solar variation is practically eliminated from the resulting mean value. 1 These 

 means corresponding in time to the beginning, the middle, and the end of each 

 month, furnish the rate of change for the first and second half of the month, and 

 by simple interpolation give the correction for progressive change for each day. 

 If the rates for the first and second half of the month are different, the monthly 

 means of each hour (from the blue figures) will differ by a small but constant quan- 

 tity from the former monthly means. Thus, for instance, for the month of June, 

 1842, the monthly mean is 651 divisions, corresponding in time to the middle 

 of the month, the mean of the readings (at 63°) for (he second half of May 

 and the first half of June is 641, corresponding in time to the first of June, and 

 the mean of the readings (at 63°) of the second half of June and the first half 

 of July is 673, corresponding in time to the last of June; the correction applied to 

 the bi-hourly readings (at 63°) on June 1st was + 10, and to the readings on June 

 30th was — 22 divisions. At the middle of the month the correction is zero, and 

 for the intermediate days it is in proportion to their respective distances from the 

 middle. The- algebraic sum of the daily corrections divided by the number of days 

 of observation is — 3, which gives the new monthly mean 648, as corrected for 

 irregularity in the progressive change. In the exceptional case of a break, or 

 beginning and termination, the required rate (4' change for half the month was 

 found by a similar process, using half monthly and quarterlj means. 



The following table, No. IV., contains the monthly means of the bi-hourlv and 

 hourly readings of the bifilar magnetometer referred to a uniform temperature (63° 

 Fahr.), and corrected for irregularity in the progressive change. It is here inserted 

 for the purpose of comparing it with the monthlj normals, showing the change pro- 

 duced by tin 1 exclusion of the disturbances. The means in the month of June, 1840, 

 are suppressed, and the readings between June 1 and June 5, 1841, were not used. 



1 In connection with this subject, the first part of an interesting paper by Mr. Broun maybe 

 consulted, viz. : " On the lunar diurnal variation of the magnetic declination at the magnetic equator " 



— Proceedings Royal Society vol X. N,, :;'.!, lSGO 



