data <- scan(what = list(period=0,subj=0,treat="",area=0), multi.line=F)
              1      1    soln           1799
              2      1 capsule           1846
              3      1  tablet           2147
              1      2 capsule           2075
              2      2  tablet           1156
              3      2    soln           1777
              1      3  tablet           1396
              2      3    soln            868
              3      3 capsule           2291
              1      4  tablet           3100
              2      4    soln           3065
              3      4 capsule           4077
              1      5 capsule           1451
              2      5  tablet           1217
              3      5    soln           1288
              1      6    soln           3174
              2      6 capsule           1714
              3      6  tablet           2919
              1      7 capsule           1430
              2      7    soln            836
              3      7  tablet           1063
              1      8    soln           1186
              2      8  tablet            642
              3      8 capsule           1183
              1      9  tablet           1135
              2      9 capsule           1305
              3      9    soln            984
              1     10 capsule            873
              2     10    soln           1426
              3     10  tablet           1540
              1     11    soln           2061
              2     11  tablet           2433
              3     11 capsule           1337
              1     12  tablet           1053
              2     12 capsule           1534
              3     12    soln           1583

data

oex13.10 <- data.frame(data)
rm(data)

oex13.10$period  <- as.factor(oex13.10$period)
oex13.10$treat   <- as.factor(oex13.10$treat)

oex13.10  <-  within(oex13.10, 
                {
                   square                        <- NA
                   square[subj < 4]              <- 1
                   square[subj > 3 & subj < 7]   <- 2
                   square[subj > 6 & subj < 10]  <- 3
                   square[subj > 9]              <- 4
                })

oex13.10$subj    <- as.factor(oex13.10$subj)

oex13.10$square    <- as.factor(oex13.10$square)

oex13.10.lm1 <- lm(area ~ square +square:subj +period +treat, data = oex13.10)

anova(oex13.10.lm1)

 # check model assumptions

par(mfrow=c(2,2))  
plot(oex13.10.lm1)
par(mfrow=c(1,1))